Receiver Concepts for Dummies

Background on mediumwave, shortwave and FM receivers

Preface

In a hurry? Skip straight to table of contents.

This page aims to provide the radio enthusiast with background knowledge that might aid in the evaluation of receivers and receiver concepts and be useful for general understanding of how things work. For a more complete scope, a number of obscure but interesting, mostly historical concepts and fascinating details ("goodies") have also been included. (Besides, that's the fun part…)

Admittedly, some experience with radio (e.g. shortwave) and basic electrical engineering knowledge would definitely be helpful in a number of places, otherwise there'll be quite a learning curve. This page quickly turned out to outgrow its original mission, "superhets for dummies", and now probably is more suited for Advanced Dummies®. However, the author has generally tried to keep things as simple as possible.

Note: Some sections rely heavily on explanations in frequency domain, as this is a very "natural" way of looking at all things periodic and enables very intuitive understanding of what's going on. Occasional practical notes may be referring to receivers; the same concepts can generally also be applied to transmitters, if with a reversed signal flow.

For a different view of the subject, check out Lloyd Butler VK5BR's Introduction to the Superheterodyne Receiver. You may also want to have a look at the book "Modern Communications Receiver Design and Technology" by RF veteran Cornell Drentea, newly released as of early 2011, which covers a fairly similar choice of topics as the page you're reading.

And yes, I do like ASCII art :p

(Actually, I would love to include SVG graphics but that would require a major revamp of the whole site with a CMS for dynamic page generation and all that jazz.)

Contents

List of goodies

Intro: Things that aren't superhets

We'll start out with some concepts that are not superhets to illustrate why these are so popular.

TRF (Tuned Radio Frequency) receivers and their problems

(My German-speaking readers will know these as "Geradeausempfnger".)

Suppose you wanted to make a receiver for AM broadcasts, for the mediumwave or longwave band perhaps, just about as simple as possible. What would it look like?

First we'll need some frequency selectivity, to pick out only the desired station. Let's say we use a ferrite rod antenna, which makes a nice inductance in addition to picking up signals, and then add a variable capacitor and connect things to ground on one end to make up a parallel resonance LC circuit.

   +-----+---------o
   |     | 
   |     | /|
|| c     |/
|| c L  --- C
|| c    ---
|| c   / |
   |  /  |
   |     |
   +-----+---------o
   |
  ---
   -

This has a high impedance near its tuned frequency

         1
f  = ----------   (1.1-1)
 0   2 π √(L C)

and low impedance elsewhere. So if we connect something that doesn't load this thing too much to the "top" of the LC circuit, voltages are highest near the center frequency, just what we wanted.

Then we add an AM detector, a simple diode detector maybe. Then some very old crystal headset (4 kOhms typical) that performs some audio lowpass filtering due to its inherent low-fi frequency response, and we have a complete receiver. Actually this kind of set ("crystal set" due to the kind of primitive diode detector used, or "Detektorempfnger" in German) was the first DIY radio for many.

Now this still has a number of drawbacks – sensitivity will be close to "absolutely deaf" (it might help to do away with the ferrite antenna, resort to a normal coil in its place and connect a longish wire antenna at the top point), and as we're loading down the LC tank circuit, selectivity also isn't too great (due to reduced Q). So at the cost of some power consumption, let's put in an RF amplifier. High input impedance for good tank circuit Q, low output impedance for driving the detector, and maybe some voltage gain on top of that. For some luxury (further increased sensitivity, lower impedance load driving), add another amplifier after the detector.

Now we have a working radio – with one noteworthy drawback: Selectivity will depend strongly on frequency! That is because as you vary the center frequency of the resonant circuit, only the relative bandwidth will remain constant, which means that the absolute bandwidth scales with the center frequency. (This has its cause in the bandwidth depending on L/C ratio, and if you only vary either C or L, this inevitably changes.) If you still had good selectivity at the start of the longwave band at 153 kHz, bandwidth will be almost twice as wide on the other end of 279 kHz. If you want to scale the set to mediumwave, it gets much worse still. Oops.

Possible solution #1: Multi-circuit TRF

So if one tuned circuit doesn't cut it, maybe we can add some more, perhaps with some amplification stages in between? Yes, that'll work, once we've solved the problem of synchronicity that is. (In the early days of radio, multi-section tuning capacitors had yet to be invented!) Such receivers were commonly built in the 1920s or thereabouts. The problem of bandwidth scaling remains.

Possible solution #2: Regenerative receiver

(My German-speaking readers will know this as an "Audion".)

Sticking to a single resonant circuit and RF amplifier, what else can we do? Well, someone had the bright idea of applying some positive feedback, i.e. take some of the amplifier output and insert it in front of it again. This effectively means that the signal is passed through the resonant circuit multiple times, increasing overall Q and thus improving selectivity. If loop gain (what's reinserted referred to what comes in) becomes greater than 1, the whole construction will start oscillating and thus even generate a BFO to decode SSB and CW transmissions (not sideband selective, however).

So what's wrong with this? Well, regenerative sets are quite fussy to operate for multiple reasons, sometimes requiring three hands to operate the tuning, RF gain and feedback controls all at once. These generally are not fully independent, meaning that e.g. reception frequency will shift a little depending on feedback, and the point of optimum Q before oscillation sets in tends to vary with frequency (on the higher ones you may not reach it at all). In addition, if you want to tune in some weak station near some strong ones, you may have to back down the RF gain in order to keep the set from being "pulled" to one of the strong ones. The whole thing basically is an oscillator, so it'll behave like one!
Another drawback is that if the set is in oscillation, the resulting signal may be transmitted over the antenna.

Regenerative sets were commonly used for educational purposes in ham circles up to the 1950s/1960s.

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Superheterodyne receivers

The idea

As we've seen, TRF sets have a number of problems, non-constant selectivity (and sensitivity) in particular. Not exactly what you want in a decent receiver.

To the rescue comes a component called a mixer. The idea was to somehow mix the RF-level signal with another in such a way that the signal we want to receive is found on a constant frequency – the intermediate frequency (IF) – afterwards, where good filtering can be implemented easily and with high performance.

This kind of device is not so easy to build in real life. However, what can be built reasonably well is a multiplier, something that will output a signal proportional to the product of the two incoming ones.

Signal 2 (RF)

   |
   |
   v
+-----+
|     |
|  X  |<----- Signal 1 (LO)
|     |
+-----+
   |
   |
   v

Output signal (IF) ~ Signal 1 * Signal 2

How does this help us? This will require a little math, which you may skip for now if you're not interested in the gory details.

A tiny bit of mixer theory

Consider two periodic signals at frequencies f1 and f2...

a(t) = A * sin (2π f1 t) b(t) = B * sin (2π f2 t)

...along with this trigonometric relation:

sin(x) * sin(y) = 1/2 (cos(x-y) - cos(x+y)) (2.2-1)

The product will thus be:

a(t) * b(t) = 1/2 * A * B * [ cos(2π (f1-f2) t) - cos(2π (f1+f2) t) ]

This corresponds to two spectral components, one at the difference and the other at the sum of the incoming signals' frequencies.

So let's say we pick the difference term and consider f2 the input frequency. Then we only need an oscillator supplying the signal at f1 (Local Oscillator, LO), which has to be varied in parallel to the frequency to be received, and can then do filtering at f1-f2 = fIF = const to our heart's desire. Great!

But what's with that sum component? Well, this leads to a response at another frequency f2' if either:

a) f1 + f2' = f1 - f2 => f2' = -f2 (not too interesting, same signal)

or

b) f1 + f2' = -( f1 - f2 ) => f2' = -( 2 * f1 - f2 ) = -2 * ( f1 - f2 ) - f2 or -f2' = f2 + 2 * ( f1 - f2 ) -f2' = f2 + 2 * fIF ===================

Wait a minute, we are dealing with negative frequencies here? Yup. You see, any real-valued signal (these are the only ones you encounter in the good ol' analog world) has equally large spectral components at positive and negative frequencies (magnitude wise). As you can see above, the mixer will respond equally to f2 and -f2, or f2' and -f2' for that matter, with the sum and difference terms swapping their roles. That's a good thing, otherwise you wouldn't get any real-life signals out of the mixer, but at the same time it gives you an image response twice the IF up or down (depending on whether the desired f2 is smaller or larger than f1) from the desired frequency.

A number of people may think it strange to deal with negative frequencies – they are, however, absolutely harmless and a natural byproduct of the description of periodic functions with complex exponentials, of which both sine and cosine have "positive-frequency" and "negative-frequency" ones of equal power). We will find double-sided spectra to be quite handy soon.

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Superhets in practice

Frequency relations and images

In the last section, we have seen that a multiplier mixer with two input ports (one for RF signal, another for the local oscillator = LO signal) will mix two different input frequencies to the same intermediate frequency fIF at its output port (where all kinds of filtering and amplifying action can take place), these being:

f2 = fLO - fIF f2' = fLO + fIF

In the spectrum, the input frequency ranges are located in a distance of fIF left and right of the LO frequency. The mixer then shifts all this stuff in frequency so that things are centered around f = 0. This is easy to visualize in the common case of fIF < fLO:

                              f      f
input  ^                       IF     IF
signal |                   |<---->|<---->|
       |
       |                          |
       |                  |\      |     |\
       |                  |A|     |     |B|
...----+-----//------------+------+------+--------->  f
       0                  f       f      f '
           |  |            2       LO     2
          \|  |/
           \  /
            \/
      
      output ^
      signal |
             |
             |
     |\      |     |\
     |A|     |     |B|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF

As you can see, there is one slight inaccuracy in there – the contents of the IF signal at positive and negative frequencies differ, which of course can't be the case in a real-life signal (which are real-valued and thus fulfil some symmetry requirements with regard to frequency). The reason is that we left out the contribution of negative frequency contents. As-is, however, we can already see which frequency components will be contributing to the output signal, which in a number of cases will be all we want to know!
More correctly, however, the output signal would look like this:

      output ^
      signal |
             |
      /|     |      /|
     |B|     |     |A|
      +      |      +
     |\      |     |\ 
     |A|     |     |B|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF
             ||
             ||

      output ^
      signal |
             |
      _      |      _
     |B|     |     |A|
     |+|     |     |+| 
     |A|     |     |B|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF

Now obviously both signals A and B have been mixed to the IF and cannot be separated there. Only one of them is desired, of course, the other one (the image frequency, B in this case) must be filtered out in front of the mixer as well as possible. How well this works is qualified by image rejection.

      output ^
      signal |
             |
             |      /|
      _      |     |A|
             |
      +      |      +
             |
     |\      |        
     |A|     |      _
...---+------+------+--------->  f
    -f       0    +f
      IF            IF
             ||
             ||

      output ^
      signal |
             |
     |\      |      /| 
     |A|     |     |A|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF

This "filtering out in front of the mixer" isn't so easy, as it brings a problem with choice of intermediate frequency:
Normally one would want an IF to be both outside the reception range (if possible) and low enough for easy filtering and amplification. Now assume we use LC filters tracking our reception frequency to get rid of images, and remember the selectivity issue that the TRF sets had – this comes back to haunt us in the form of ever smaller image rejection as frequency increases. Increase the IF, and you'll need more filtering effort at this stage. This is why multiple-conversion superhets were invented.
There are some high-grade single conversion receivers from the olden days out there that achieve excellent image rejection in spite of a fairly low IF, but of course they had to use a whole lot of tracking filter circuitry! (Telefunken E52 "Kln": IF = 1 MHz, 5 tracking circuits with 2 RF amps, comprehensive shielding, image rejection still >90 dB at 20 MHz. This was arguably the most advanced WW2-era receiver.) A simple inexpensive shortwave set with an IF of 455 kHz and one tracking circuit (which is the kind of single conversion sets you can usually buy these days, letting aside some ham gear with IFs around 9 MHz) will certainly not work any wonders, with image rejection hardly reaching the double-digit dB range on the higher shortwave ranges.

It is worth noting that even a perfect mixer (multiplier) will always generate images. So-called image rejection mixers make use of two multiplier mixers and some phase shifting action to cancel out the images; with real-life parts tolerances a rejection of about 30..40 dB can be achieved. (Low-IF FM radio chips typically employ I/Q mixing with polyphase IF filters, with similar results.)

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Inverting and non-inverting operation

Consider both mixer input and output signal of our example again:

                              f      f
input  ^                       IF     IF
signal |                   |<---->|<---->|
       |
       |                          |      | filtered out
       |                  |\      |      v
       |                  |A|     |      _ 
...----+-----//------------+------+------+--------->  f
       0                  f      f      f '
           |  |            2      LO     2
          \|  |/
           \  /
            \/

      output ^
      signal |
             |
     |\      |      /| 
     |A|     |     |A|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF

Look at the positive frequency range. Our signal A has obviously been flipped in frequency during mixing! If it was an upper sideband (USB) signal before, it now is a lower sideband (LSB) one (which would result in only garbled output when tuned in with an SSB receiver in USB). Why is this? Well, during mixing the positive-frequency part was shifted as-is to the negative frequencies where things are "upside down", and vice versa. This mixing process is obviously inverting.

Now what would happen if we had been interested in signal B instead?

                              f      f
input  ^                       IF     IF
signal |                   |<---->|<---->|
       |
       |      filtered out |      |
       |                   v      |     |\
       |                   _      |     |B|
...----+-----//------------+------+------+--------->  f
       0                  f      f      f '
           |  |            2      LO     2
          \|  |/
           \  /
            \/

      output ^
      signal |
             |
      /|     |     |\ 
     |B|     |     |B|
...---+------+------+--------->  f
    -f       0    +f
      IF            IF

No such spectrum flipping occurs here. This mixing process is non-inverting.

The first configuration is frequently preferred, as in the second one LO harmonics may fall into the reception range if this is sufficiently large. (In a mediumwave receiver with an IF of 455 kHz for example, the 2nd harmonic would give trouble at around 910 kHz.)

So far we've been looking at the case of fIF < fLO. What about fIF > fLO? The best thing one can do in such cases is to grab a piece of paper and draw it (which I encourage you, the reader, to do if you find yourself puzzled over a problem like this!). Now with us being on the web here, I will resort to some patented ASCII ART(R) Virtual Paper[tm]:

                         ^ f         f
                  input  |  IF        IF
                    |<--------->|<--------->|
                  signal |
                         |      |
                    /|   |      |          |\
                   |A|   |      |          |B|
...-----------------+----+------+-----------+----->  f
                   f     0     f           f '
                    2           LO          2
                       |  |
                      \|  |/
                       \  /
                        \/

                         ^
                  input  | f         f
                  signal |  IF        IF
                    |<--------->|<--------->|
           f         f   |
            IF        IF |
      |<--------->|<--------->|
                         |
                  |      |      |
      /|          | /|   |   |\ |          |\
     |B|          ||A|   |   |A||          |B|
...---+-----------+-+----+----+-+-----------+----->  f
                    f    0      f          f '
      |           |  2        |  LO         2
     -f '        -f         -f 
       2           LO         2
                       |  |
                      \|  |/
                       \  /
                        \/
           output ^
           signal |
                  |
      /|          |          |\ 
     |B|          |          |A|
                  |
      +           |           +
                  |
      /|          |          |\ 
     |A|          |          |B|
...---+-----------+-----------+--------->  f
    -f            0         +f
      IF                      IF

Looks confusing? Don't worry, it's not that dramatic. The first figure should still look quite familiar, I have merely adapted the input spectrum drawing for the case of fIF > fLO. That in turn means that f2 now becomes negative, our first interesting observation. (How one would explain this easily without double-sided spectra and thus negative frequencies is beyond me.) The second figure adds the missing complementary components, something that I hadn't done so far because it was clear that the negative-frequency components only were the positive-frequency ones mirrored.

What we see here is that now neither of the signals is inverted. B behaves like it did before, but A is "on the other side of the fence" and thus inverted in frequency to begin with, meaning it gets inverted twice overall. You can also see that it would not be too smart to target f2 when this becomes half as large as the LO frequency, given that some LO will always leak to the RF input.

In this example we have carried out both downconversion (Signal B: fIF < fRF) and upconversion (Signal A: fIF > fRF).

Where, you might ask, is the inverting upconversion case? Well, we have already covered it when looking at the fIF < fLO case! Don't believe me? Here you are:

               f      f
input  ^        IF     IF
signal |    |<---->|<---->|
       |
       |           |      | filtered out
       |   |\      |      v
       |   |A|     |      _ 
...----+----+------+------+--------->  f
       0   f       f      f '
            2       LO     2

This figure should look quite familiar, it is nothing but the input spectrum for the inverting downconversion case shifted to the left. So basically there is no difference between inverting upconversion and downconversion other than the values of fIF and fRF. Only non-inverting upconversion requires some special treatment, being a case of fIF > fLO as we've seen.

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Intermod and spurs

A practical mixer will, in general, not only output fLO - fRF and fLO + fRF components, but

fm,n = m * fLO ± n * fRF ; m, n = 0, 1, 2, 3, ...

Our desired signal is m = n = 1. Typically the intensity of the other mixing products drops quickly with growing m and n. A number of them are harmless, never even coming near the desired IF and thus easily being filtered out (just think of the DC part, m = n = 0). This, however is not the case for all of them.
This leads to the generation of intermodulation (IM) products (including cross-modulation) as well as spurious responses. If you're a shortwave listener, you have certainly encountered some, or even plenty.

Leakage

First we'll have a look at the m = 1, n = 0 and m = 0, n = 1 cases. These are easy to understand, as they correspond to LO and RF leakage into the IF output. A real-life mixer will always have finite port-to-port isolation, so that was to be expected. (Of course it doesn't need to happen in the mixer itself, coupling can also be around it. Some shielding helps here.) Leakage of the IF signal back into the RF output is equally possible, of course.

LO harmonics

Another easily understood case are m ≥ 2, n = 1 spurs. An ideal mixer will treat LO harmonics (or actually, everything that comes in via the LO input) just like the main LO signal and thus also respond to 2 * fLO ± fRF, 3 * fLO ± fRF and so on. It is highly advisable to filter out RF at such frequencies in this case.

Where do these harmonics come from? Well, first of all it is not easy to build an oscillator that is perfectly clean, as that usually means a loop gain so low that reliable oscillation may not be achieved; ones with ALC may be quite good, however, but even then I wouldn't hope for a 2nd harmonic more than 40 .. 60 dB lower than the fundamental. Another case is that of a switching mixer (e.g. H-Mode mixer, or just a regular FET or diode ring mixer with a sufficiently high LO insertion level), which can be treated as a multiplier mixer fed with a clipped (rectangular instead of sinusoidal) LO signal, which of course is quite rich in (odd-order) harmonics. Last but not least, more complex oscillator types (beyond simple free-running LC, RC or crystal ones) may produce all kinds of non-harmonic spurs; DDS ones are quite notorious here, for example. And let's not forget about phase noise which "broadens up" the supposedly ideal line-in-frequency spectrum LO signal and may thus reduce effective selectivity.

It may be worth noting that increasing the IF reduces the risk of LO harmonics falling into the desired frequency range. (On the Panasonic RF-1410L which is a single conversion set with an IF of 455 kHz on shortwave, strong signals on 19 meters will generate weak ghost stations on 41 meters; the RF filtering of this model does not seem to be entirely sufficient. If the 2nd harmonic is comfortably outside the shortwave range on a set with high 1st IF, that can't happen, although one might still get problems with FM broadcast...)

"Classic" intermod: Intro

That brings us to another typical case, m = 1 and n ≥ 2. This is where most of the intermod comes from. It can be viewed as the effect of a nonlinearity through which the RF signal must pass before reaching the mixer's RF input, and in fact while the mixer tends to be a major contributor to intermod, components in front of it may also generate it. Here's the corresponding nonlinear mixer model:

  RF in

    |
    |
    v
+-------+
|  o| _ |
|   |/  |
| --/-- |
| _/| i |
|   |   |
+-------+
    |
    |
    v
 +-----+
 |     |
 |  X  |<----- LO in
 |     |
 +-----+
    |
    |
    v

  IF out

f1,n = fLO ± n * fRF ; n = 0, 1, 2, 3, ...

The obvious part is that harmonics of the RF signal are generated and received. Some filtering in front of the mixer (selected according to reception frequency) tends to be very useful in eliminating these.

The not so obvious part is that intermodulation distortion in a stricter sense (i.e. non-harmonic) is also generated. This is because the RF input signal is usually not just a single carrier, but in fact a whole chunk of the spectrum with many different signals. It might be a shortwave broadcasting band or a larger range, depending on frontend filtering (e.g. tracking with the reception frequency, an array of switched filters or just a wide bandpass covering the whole reception range).

2nd-order intermod

What happens in such a case? Let's have a look at 2nd order intermod, i.e. n = 2, with only two distinct input signals. What's the effect of a square-law relation? As we all know (hopefully so!),

(a + b) = a + 2*a*b + b

The two squared terms are less interesting, they correspond to the aforementioned harmonics and some DC. That middle term should strike you as familar – it corresponds to mixing! (And in fact, this has been used to build mixers with devices having a predominantly 2nd order characteristic. Additive mixing does not tend to give exceptional performance though.) This means that there will be signals at the sum and difference of the input frequencies.
Such mixing products can be readily observed on many shortwave receivers with wideband frontends, typically towards the lower end (look at the distances of high-power meter bands!) and on the higher ranges of the shortwave spectrum. Not even an AOR AR7030, which has a very good first mixer, is totally immune to them on a large antenna in a strong-signal area. A Redsun RP2000 is far less still...

Another issue that may still be interesting is how the mixing products behave when varying input signal strength. Since their amplitudes scale with the product of the source signal amplitudes, an attenuation of all the source signals by, say, 10 dB would drop 2nd-order mixing products by 20 dB. This makes it understandable why switching in some attenuation may make real stations audible that were previously covered up by intermod.

3rd-order intermod

It becomes a little more complex with the still-common 3rd order intermod, i.e. n = 3. Assuming only two distinct input signals again, we'll take a look at the binomial relation

(a + b) = a + 3 * a * b + 3 * a * b + b

The interesting part are the a * b and a * b terms. The first corresponds to mixing of b with the components of the squared a signal. If the frequency of a is fa, a has spectral components at

  1. 2 * fa and
  2. 0 (DC).

The mixing result with fb thus contains

  1. 2 * fa ± fb and
  2. 0 ± fb.

The first item corresponds to "classic" 3rd order intermod. Say we're in the 49 meter band, with two strong stations at fa = 6075 kHz and fb = 6085 kHz, respectively. Then we'll get components at (2*6075 + 6085) kHz = 18235 kHz and (2*6075 - 6085) kHz = 6065 kHz. Oops! The latter one is in the middle of our wanted signals! Pretty hard to get rid of that one.

The 0 ± fb term corresponds to cross-modulation. Why? Well, that "DC" component of signal a actually isn't DC, but the modulation of a (e.g. AM)! Thus there will be a component of signal b that has the modulation of a superimposed. This is quite obvious if b is an unmodulated signal, maybe some station transmitting CW (Morse code). An AM receiver subject to cross-mod in this case makes a "pulsed" AM station heard.

What happens if we increase the number of input RF signals to three?

(a + b + c) = a + 3 * a * (b + c) + 3 * a * (b + c) + (b + c) = a + 3 * a * (b + c) + 3 * a * (b + 2*b*c + c) + b + 3*b*c + 3*b*c + c

OK, let's sort this a bit:

(a + b + c) = a + b + c + 3 * {a * (b + c) + a * (b + c) + b*c + b*c} + 2 * a * b * c

There is one new type of term here, 2 * a * b * c, which corresponds to fa ± fb ± fc components. This means that all three signals are involved. Considering more than three signals does not lead to any more new term types.

Scaling with input levels is even more pronounced than in the 2nd order case, with a 10 dB reduction leading to mixing products becoming 30 dB weaker.

As you may be able to imagine, the number of signals potentially involved grows with order n – four at n = 4, five at n = 5, and so on. When all of these mixing products actually appear – which is all the more suddenly the higher the order is –, you have some nice intermod mud. However, the pronounced scaling with input levels means that comparatively little attenuation will get rid of higher-order intermod entirely.

Advanced cases

Finally, m ≥ 2, n ≥ 2 cases require the full-blown nonlinear mixer model.

  RF in

    |
    |
    v
+-------+
|  o| _ |
|   |/  |
| --/-- |
| _/| i |
|   |   |
+-------+
    |
    |
    v         +-------+
 +-----+      |  o| _ |
 |     |      |   |/  |
 |  X  |<-----| --/-- |<----- LO in
 |     |      | _/| i |
 +-----+      |   |   |
    |         +-------+
    |
    v

  IF out

fm,n = m * fLO ± n * fRF ; m, n = 0, 1, 2, 3, ...

These can be treated as combinations of the cases given above, i.e. LO harmonics with 2nd, 3rd and higher-order intermod.

The importance of these cases depends on what kind of mixer we are looking at. A nice linear multiplier mixer with a clean sine LO input will not show many of them, but when looking at a switching mixer where LO harmonics only taper of slowly, they are absolutely relevant and must be considered.

In the olden days, receiver developers used spur maps that plotted the locations of the various mixing products so they could choose IF combinations which made sure that the number of unwanted mixing products in the desired reception ranges was minimized.

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Multiple-conversion superhets

We have seen that intermediate frequency choice in a superhet is not a trivial task.

How could one combine the advantages of both high and low IFs? The answer is: Use multiple conversions and thus multiple IFs. Let's say we wanted to build a dual-conversion superhet. This would have two IFs, first a high one and then a lower one. The narrow-bandwidth filtering would be done on the lower 2nd IF where it is comparatively easily done, while filtering requirements on the 1st IF are more relaxed – you only have to make sure that you don't get any images due to the conversion to the 2nd IF, and it certainly is far easier to attenuate something, let's say, 910 kHz away by 60 dB than accomplishing the same only 10 kHz away!

In practice, one would usually try to keep IF bandwidths on the first IF(s) as narrow as possible, as this gives the mixer afterwards less choice among signals to generate intermod from, along with reducing overall sum signal levels, which equally benefits strong signal handling. There are a few concepts which violate this rule, i.e. use wideband IFs (i.e. classic Wadley Loop, Sony's "dual conversion light"), but these are generally not known for highest dynamic range in return. Several 1950s-vintage pro-grade receivers with wider IF ranges (used to provide better frequency readout accuracy) used tracking filters to tackle this problem.

Interestingly it is possible to make IF bandwidths too narrow, as some amateur radio transceiver manufacturers using high 1st IFs (70+ MHz) found out the hard way. In these cases the crystal IF filter starts limiting in-band intermodulation performance, rather than the mixer following (or in some cases, preceding) it. I assume the high circuit Qs required increase voltage levels this much that the quartz crystals become appreciably nonlinear. Therefore some recent designs have reverted to 1st IFs of around 10 MHz, at least for the classic shortwave amateur radio bands.

Over the years, there have been many different multiple conversion designs, with some 1980s communications receivers using up to quadruple conversion (!). However, at least as shortwave gear is concerned, receivers with more than two IFs generally needed the additional IFs for "meta" features like improved frequency stability and readout (big issues in the olden days), or IF shift (Icom IC-R70/71: 9 MHz – 455 kHz – 9 MHz, which together with the high 1st IF gives a quad conversion rx). As mixers tend to be the weakest link in terms of intermod, it's advisable to keep their number to a minimum (the good ol' KISS principle applies).

It be noted that high-performance single conversion sets can be and have been built (e.g. for longwave, mediumwave or – thanks to crystals for 4.52 / 8.83 / 9.03 MHz etc. – the various shortwave ham bands). Multiple-conversion sets tend to hold an advantage when wider tuning ranges are required, or in terms of filter ultimate rejection (as there always is some output-to-input coupling, this cannot be arbitrarily good, though careful layout and shielding and maybe some extra "tail filtering" thrown in are likely to help, with the question being whether this isn't more effort than going dual conversion to begin with). If in doubt, use the concept that gives better performance at the same or less effort – OK, admittedly "receiver performance" has many different aspects!

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Direct conversion and Low-IF receivers

These are some special cases of superhets.

Direct conversion receivers directly mix down the RF signal into the baseband. Since the signal would normally image onto itself, two mixers fed by LO signals with a 90 phase difference are being used, which yields two signals, I(nphase) and Q(uadrature). These can then be fed to phase-sensitive filters (e.g. polyphase filters) or digitized and fed to a DSP for further processing (the usual way of doing it these days).
A central problem with direct conversion receivers is noise, 1/f noise in particular. As the name implies, this rises as frequency decreases, and a direct conversion receiver works in the baseband right down to DC.

Low-IF receivers are similar to direct conversion receivers, but do use an intermediate frequency to avoid the noise problem. This IF is much lower than a conventional superhet would use, so again I/Q mixing and phase-sensitive filtering or DSPs are at work.

In both cases, image rejection is a matter of phase and filter precision; analog polyphase filters are typically limited to about 40 dB due to component tolerances (such problems typically beg for IC integration).

Low-IF concepts are commonly encountered in highly integrated radio receiver concepts – examples for ICs include the FM radio chips like the classic TDA7000 and offspring (typically found in FM scan radios with just a "scan" and a "reset" button) plus the more modern TEA5767 (something you might find in an MP3 player or mobile phone), the former also mentioned for its inclusion of frequency-locked-loop frequency synthesis here, the DSP-powered Silicon Labs SI47xx and the Sanyo LV2400x series. One very interesting IC that also includes AM reception is the Sony CXA1129N (a proprietary chip only used in several Sony products), a design dating to 1992. Details on this can be found in the archives of the IRCA mailing list and the UltraLight file area on dxer.ca.

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Frequency generation: Oscillators

We've seen that a radio receiver needs one or more local oscillator signals which need to be generated somewhere and which also have to fulfil certain requirements, e.g. with regard to frequency variation, frequency stability and phase noise / spurs. We'll therefore look at oscillators next.

There is a surprising variety of oscillator types out there. They can be distinguished into:

This short list corresponds to no less than half a decade (or a bit more) of radio technology. It will thus have to be approached respectfully and slowly.

Free-running oscillators

LC oscillators

LC oscillators are probably the oldest type used in receivers. They belong to the class of two-port oscillators using a (more or less) linear amplifier and a feedback network (FBN) to generate a phase shift of 180 degrees at the desired resonance frequency. Here's an abstract model for this type of oscillator:

                       +-------> output
         +-------+     |
         |       |     |
         |  |\   |     |   +--------+
         |  | \  |     |   |        |
+------->|  | /  |-----+-->|  FBN   |-----+
|    ^   |  |/   |         |        |     |
|    |   |       |         |  φ(f)  |     |
|   cut  |   G   |         +--------+     |
|        +-------+                        |
|                                         |
+-----------------------------------------+

To see when this will oscillate, we need to cut the loop at some arbitrary point, like the one given in the drawing above (which is quite practical).

       +-------+      
       |       |      
       |  |\   |         +--------+
       |  | \  |         |        |
 A --->|  | /  |-------->|  FBN   |-----+--> B
       |  |/   |         |        |     |
   V   |       |         |  φ(f)  |     _   V 
    A  |   G   |         +--------+    | |   B
       +-------+                       | | Z
                                       |_|  in,G
                                        |
                                        |
                                       ---
                                        -

Zin,G is the complex input impedance of the amplifier. For an ideal amplifier, it would be negligible (open), in practice it may generate an additional phase shift and influence gain over frequency. We'll just merge it into the feedback network for now (not possible in practice, but handy in theory):

       +-------+      
       |       |      
       |  |\   |         +--------+
       |  | \  |         |        |
 A --->|  | /  |-------->|  FBN'  |--------> B
       |  |/   |         |        |      
   V   |       |         |  φ(f)  |         V
    A  |   G   |         +--------+          B
       +-------+

For oscillation to occur at a given frequency f, the following condition must be fulfilled:

VB(f) = VA(f)

We are, however, not limited to voltages – this can be generalized by stuffing all the things between A and B into a box we might call "some network" with a certain frequency-dependent (and generally complex) transfer function H(f) that gives the relation between input A(f) and output B(f).

       +---------+
       |         |
A ---->|   H(f)  |----> B
  A(f) |         | B(f) = H(f) * A(f)
       +---------+

A(f) and B(f) must have the same physical dimension for obvious reasons (A and B are the start and beginning of a "round trip" after all), but other than that can be almost anything. Then the following must hold true for sustained oscillation:

H(f) = 1

This actually breaks down into two conditions – loop gain must be 1 (or greater if we not only want to sustain, but build up oscillation), and overall phase shift must be zero (or other multiples of 360). These may actually be satisfied for multiple frequencies, which in turn may cause very strange things to happen.

(It be mentioned that state-of-the-art oscillator design, especially at microwave level, would probably involve amplifiers and feedback networks characterized by a set of S-parameters. The simple model as given above will do for this page, it is quite powerful already.)

Now let's go back to actual oscillators. Assume we have an amplifier with a sufficiently large positive voltage gain and no inherent phase shift. If we then add some series resistance and a parallel LC circuit...

      _____
o----|_____|----+-----+---------o
        R       |     | 
                |     | /|
                c     |/
                c L  --- C
                c    ---
                c   / |
                |  /  |
                |     |
o--+------------+-----+---------o
   |
  ---
   -

... the voltage at the output will show a bandpass characteristic. At very low frequencies, the inductance dominates. It's close to a short there, and the voltage dropping over it (not much compared to the resistor) will show a phase shift of about +90 degrees. At high frequencies, the capacitance dominates, leading to a -90 degree phase shift and again a small output voltage. At resonance, the impedances of both just cancel each other out, so that basically they aren't there at all – full output voltage, no phase shift, thus oscillation should result.

I have used a variable capacitor in the drawing, which would be handy for use in a receiver that typically requires a tunable LO. Now of course this is just a very simple oscillator circuit. In practice, there will be a few more components depending on oscillator type (Colpitts, Clapp, Hartley, ...), also to provide temperature compensation. For free-running oscillators in particular, temperature compensation is highly important. Real-life Ls and Cs change their values slightly over temperature (as does the active element), and if you don't account for this, the result may be quite drifty indeed. Thankfully ceramic capacitors are made with various temperature characteristics, including ones opposite to the one of inductors (which typically have a small negative temperature coefficient).

Another use for additional components is restricting the tuning range. You may not always need a frequency variation that large. Add a parallel capacitor and another in series with the tuning cap, and tuning range will be reduced. If the tuning capacitor was not the most temperature stable and high-Q, this can also be used to provide higher frequency stability and lower phase noise.

A practical oscillator will in general also use some ALC (automatic level control), which means that amplitude limitation is not carried out by the amplifier's nonlinearity (which promptly generates harmonics) but by reducing gain once oscillation has started. Thus one can provide sufficient maximum gain for reliable startup, yet have low-level harmonics.

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Crystal oscillators

Crystal oscillators are related to LC oscillators. Quartz crystals can be used to form an extremely high-Q series resonance circuit, which means a very steep phase-over-frequency relation near resonance. That in turn means that the point of resonance is quite sharply defined and will shift very little due to external factors. Therefore crystal oscillators (XOs) make very good fixed-frequency oscillators.

XOs are obvious not well suited for tunable oscillators, but can be used to provide some fine tuning, as surrounding capacitance still has a slightly influence. A number of portable shortwave receivers with a high 1st IF of around 55.845 MHz and a 2nd IF of 450/455 kHz use a varicap diode in the 2nd LO (55.390 MHz xtal) to provide some fine tuning – this could be either analog, stepped to provide smaller tuning steps than the main PLL synthesizer can (some kind of DAC to generate the tuning voltage would be helpful in the latter case), or even both. I have some details on the Sony 7600 series page. The method itself dates back to the late '70s at least, when 2m ham gear like Icom's IC-245 (1977) and IC-260 (1979) transceivers employed such fine-tuning for the premixing oscillator in their PLL. The first shortwave receiver to use it apparently was the 1987 Lowe HF-125.

There have been some attempts at displacing crystal oscillators, integrated versions of which are not easy to manufacture. The most successful one so far seems to be Silicon Labs' Si500 "silicon XO" that manages to get by without any crystal or MEMS device, yet shows good long-term stability and even has a one-time-programmable output frequency. Essentially the integration levels possible today are used to measure temperature and digitally provide effective temperature compensation for an LC oscillator running at a frequency in the GHz range, and desired output frequency is obtained by adjusting LC oscillator frequency and the ratio of a following clock divider.
The catch? Well, short-term stability isn't so hot, giving an objectionable level of warbling. As temperature compensation cannot work arbitrarily quickly due to noise considerations alone, very short-term fluctuations will essentially go uncorrected and correspond to those of the bare LC oscillator (lowpass filtering in "feedback" gives highpass filtering in the forward path, the old story). Besides, not all the phase noise is rooted in thermal drift. Nonetheless, an interesting product that will find its applications.

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Pre-mixing type oscillators

This is our first complex oscillator type, meaning it consists of multiple sections. The motivation behind this was the following:

The higher the frequency of a conventional LC variable oscillator becomes, the worse frequency stability and phase noise properties are, as they scale accordingly. If one wanted to build a very good shortwave receiver, this was a problem, as such a thing was expected to be reasonably stable!

Now what if we built a carefully temperature compensated LC oscillator (frequently a PTO in actual designs, which is one that varies L) that tunes a relatively small frequency range and then mixed it with a range of nice, stable crystal oscillator signals (with low phase noise) to get it where we need it? That's how it was done.

There is one potential problem, of course: The image signal generated during mixing. This has to be filtered out or it may generate spurious responses. It would also be advisable to keep all the oscillator frequencies from creeping into the RF or IF path. Last but not least the mixers should also have decent input-output isolation, again because of spurs.

One drawback of such a concept is that it potentially uses a whole lot of crystals (depending on how many mixers you can afford to invest).

Practical examples of receivers using such oscillator setups include the venerable Drake R-4 series (and SPR-4) and the Panasonic RF-4800, among other 1970s-vintage sets and 2 m ham gear of the same time period. Usually there is more than one mixer involved. A number of these sets show very respectable phase noise properties (-135 dBc @ 10 kHz for an R-4C is not too shabby).

Even before pre-mixing concepts, there were designs that mixed the signals themselves up and down as needed, frequently with crystal oscillators for the 1st LO, i.e. a variable 1st IF. The 1st IF range usually was quite low (typically around 2..3 MHz) to allow tuning with a stable LO with well-known frequency. (Examples include the Collins 51J-4 and the Russian R-250, R-250M and R-250M2 receivers, so the concept goes right back to the late 1940s. By the mid-1960s, it had trickled down to amateur market sets like the Drake 2-C, and in the early 1970s you could even buy such receivers at Radio Shack, the Allied SX-190 / AX-190 twins. An implementation using fixed-frequency LC oscillators and a somewhat lower 1st IF was found in the late-1960s Sony CRF-230 (schematics).) These, being pro-grade or at least top-class amateur receivers, usually had extensive RF and even IF level tracking to provide good image rejection and strong-signal handling.
When this kind of receiver concept trickled down to travel portables in the early 1980s (think Sony ICF-7600A and a whole bunch of similar dual-conversion analogs that followed it), the 1st IF had gone upwards to around 10.7 MHz, but cost considerations meant that fixed bandpass filters for the various broadcast bands to be received and another bandpass (common ceramic filter(s)) on the 1st IF had to make do. This meant good frequency readout accuracy (and, if the 2nd LO was well implemented, stability), but only so-so strong-signal handling with the 2nd mixer limiting dynamic range.

Another concept that also belongs here, but involves the LO signals for two mixers in a triple conversion design, is the ingenious Wadley Loop. This basically combined the "variable IF" approach above with the idea of using a high 1st IF and pre-mixing. It's very neat in that oscillator drift (and phase noise) cancels out, as upmixing is followed by downmixing with a 2nd LO signal derived from the first. In addition, the use of a harmonic generator in pre-mixing enabled a wide reception frequency range while doing away with all but one of these then-expensive crystals. All this with high stability and readout accuracy (typically to 1 kHz from 0 to 30 MHz). No mean feat for the early 1950s. (The first commercial receiver to use this concept was the Racal RA17, ca. 1957. It reached the consumer market in the 1970s, with the classic Barlow-Wadley XCR-30, Yaesu FRG-7 and other sets.)
The downside? With two variable IFs, a Wadley Loop receiver is even more vulnerable to mixer overload than conventional variable-IF concepts.

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Reference-locked oscillators

Phase-locked loop oscillators

PLL synthesizers

If as a shortwave listener you want to escape the drift of many analog-tuned sets, you'll typically go for something with a PLL frequency synthesizer. For what a PLL is and how it works, check out articles like the one in Wikipedia or this tutorial, or matching textbooks for that matter.

This is a textbook-level PLL synthesizer:

+-----+     +-----+      +-----+     +-----+     +-----+
| XO  |     | M  /|      | PD  |     | LPF |     | VCO |
|     |     |   / |      |     |     | _   |     |     |
| /\/ |---->|  /  |----->| Δφ  |---->|  \  |---->| /\/ |--+--> LO
|     |     | /   | f    |     |     |   \ |     |     |  |
| f   |     |/  1 |  Ref |     |     |     |     | f   |  |
|  0  |     +-----+      +-----+     +-----+     |  v  |  |
+-----+                     ^                    +-----+  |
                            |           +-----+           |
                            |           |\  N |           |
                            |           | \   |           |
                            +-----------|  \  |<----------+
                                        |   \ |
                                        | 1  \|
                                        +-----+

In locked state, the output frequency is given by

fv = N * fRef = N * f0 / M = N / M * f0

Looking at an ordinary AM/FM radio with PLL synthesis, the PLL on AM will look pretty much exactly like this, with some pulse swallowing in action instead of the N divider on FM (fractional-N PLL, see references above). So if we have f0 = 75 kHz and would like to have 9 kHz steps, we'd set up the PLL for M = 15, i.e. 3 kHz reference. With an IF of 450 kHz, tuning in 1440 kHz would require an LO frequency of fv = 1890 kHz, which requires a divider of N = 630. It wouldn't work with a 455 kHz IF, unless one were content with an effective 456 kHz.

Not infrequently, however, the frequency steps possible at a certain fv are not small enough, either due to the N divider no longer being sufficient or the reference frequency being too big. Or maybe the PLL will not accept fv as high as required at all. What can one do in these cases?

If you're interested in PLL theory, try the book "Phase Locked Loop Circuit Design" by Dan H. Wolaver. It's nice for getting started (while still touching on more advanced subjects later on) and strikes a good balance between theory and practice, thus not being too dry. (I also stumbled across a truth table for a multiplier there, so it seems I reinvented the wheel in the discussion of FM quadrature detectors, which I wrote before having read the book.)

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"Semi-synthesized" PLL concepts

Something a little different, but still PLL, are "semi-synthesized" concepts, as they were popular around 1980 (think Sony CRF-320, Kenwood R-1000, Yaesu FRG-7700 or Panasonic RF-3100). The main difference is that, similar to pre-mixing setups, an analog-tuned VFO is involved. The point is that a 500 kHz or 1 MHz fRef is used, then divider N allows selecting the band. It all looks a bit complicated because in order to obtain this N * fRef signal, you need to subtract IF frequency and VFO frequency so that in the end the VCO runs at the desired N * fRef + fVFO + fIF. That fRef itself is gained from typically a 10 MHz signal which may also be used in pre-mixing doesn't exactly make things easier! Lloyd Butler VK5BR's page has some more on the subject.
Most "semi-synthesized" sets are not known for the lowest of phase noise, one notable exception being the Kenwood TS-830S, probably because of its relatively low 1st IF (8.83 MHz, while most of the others were sets with high 1st IF that partly had multiple synthesized LOs).

[TS-830 frequency configuration diagram]
Frequency configuration of Kenwood TS-830 HF transceiver, a very nicely executed semi-synthesized concept.

(excerpt from service manual as available online)

I particularly like that one for its relatively low complexity (dual conversion where Icom used quad), high frequency stability due to drift cancellation (more on that later) and ease of alignment.

Now low complexity doesn't mean simplicity – the concept is thoroughly tricked out in order to perform as well as it does. It wasn't done from scratch either. Here's what frequency configuration looks like for the unit's little brother, a single conversion set:

[TS-530 frequency configuration diagram]
Frequency configuration of Kenwood TS-530 HF transceiver.

(again, an excerpt from the respective service manual as available online)

This one should be a little easier to grasp. The most confusing part is related to components being bypassed or switched in depending on the desired reception range. Divider N then allows band selection within these ranges. For highest clarity, look at the 1.5, 3.5, 7, 10 configuration that bypasses BPF1 and MIX(2).

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Modulo-f PLLs

The Pioneer TX-9800 vintage FM tuner from the late 1970s (as well as its contemporary Mitsubishi DA-F20, it seems) employs an interesting concept to keep the free-running analog-tuned LO (with varicap diode fine tuning) on track. Its APC circuit (see block diagram) is what I'd call a modulo-f PLL. Pulse shaping circuitry and a sample & hold circuit are employed to create a sampling mixer which is used as a phase detector. (An approach similar to the "Huff/Puff" circuit but PLL rather than FLL.) As the reference frequency is 100 kHz (50 kHz for the DA-F20), the sampling mixer's inherent frequency periodicity allows the circuit to lock in integer multiples of 100 kHz (or half that for the DA-F20), thus creating sort of a frequency grid. (BTW, this wasn't the only interesting concept Pioneer had. The Series 20 F-28 tuner applied sort of a digital slide rule position readout to make a PLL synthesized LO track the frontend tuning which was done with a mechanical capacitor.)

Interestingly, the concept itself dates back almost 20 years further – the vintage hollow-state Siemens E311 communications receiver, completed by 1959 and introduced ca. 1960, employs a 1st local oscillator which is grid-locked to 100 kHz (late versions gained a 1 kHz grid for the 2nd LO as well). So here we have one of the very few vacuum tube based PLLs. Even the part used to provide fine-tuning is quite exotic by today's standards – this was years ahead of varicap diodes, so they made use of electrically variable inductors based on bias-dependent variation of relative permeability μr in ferrite cores, even far away from actual saturation (all you need for this is an additional variable DC current to provide some magnetic flux). With a crystal oven for the reference oscillator plus another for the analog VFO, frequency stability after warm-up was extraordinary, better than ±20 Hz after 24 hours. Copying RTTY was not a problem with this one!

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Frequency-locked loop concepts

Basically, frequency-locked loops are quite closely related to phase-locked loops. However, instead of a phase detector they have a frequency detector and integrator, which gives similar results.

They are not commonly used for main frequency synthesis, with the Philips TDA7088T all-in-one FM radio chip (the last one of the TDA7000 "family") being one of the few exceptions. Check out this page on the TDA7000 and offspring, NXP appnote 192 and US Patent 4658423, for example. Those ICs actively "track" the received signal (effectively reducing its deviation) in order to be able to squeeze it through narrow filters at a low IF without heavy distortion. It doesn't seem too far-fetched that the DYNAS system (selectivity enhancement system mainly found in car radios, with Onkyo's T-488F/T-4970 and T-9890DSR home tuners being two of very few exceptions) may have operated in a similar manner, probably with I/Q mixing.

An interesting variation on this can be found in the Sanyo LV24xxx all-in-one radio chips. Here the FLL is completed by an external microprocessor. Tuning the chip actually involves calculating an estimate for varicap tuning voltage, setting this (it has an internal DAC, or actually two for coarse and fine tuning) and measuring the resulting LO frequency by counting ticks. IF and stereo decoder VCO free-running frequency can be measured in the same manner. What fun. Here's the LV2400x application note which details frequency setup.

A far more common application of frequency-locked loops is small-scale frequency correction / stabilizing of free-running oscillators. In an analog FM receiver, you will frequently find an AFC circuit, which is supposed to eliminate LO drift provided an input signal is present. The most common implementation, a simple FLL, makes use of the DC voltage level on the output of a (or the) FM discriminator, which shows a monotonous increase or decrease with average input signal frequency and has a certain value when the input signal is tuned in correctly. This can not only be employed to build a center indicator, but also to generate a tuning voltage for a varicap diode which then in turn can pull the LO over a limited range (and would thus compensate for LO drift if things are implemented correctly). The integrator is usually replaced by heavy R-C lowpass filtering of the varicap control voltage.

A different approach to small-scale frequency correction is locking an oscillator to sort of a "frequency grid". It is possible to do this with a PLL concept (as we've seen for "modulo-f" PLLs), but FLL implementations also exist, notably the "Huff/Puff stabiliser" that is somewhat known in ham circles and has been used to tame drift in both free-running LO and the free-running VFOs you find in "semi-synthesized" PLL concepts. The original concept even made it into a commercial FM tuner, the 1979 Sansui TU-919, which employs the final digits of the frequency counter's output (counter used for display purposes anyway) as a frequency detector. (The vintage Sylvania R-1451(A) naval receiver, a mid-'60s design, also appears to employ this kind of concept, at least I'd guess so since the respective function is termed an AFC.) For a collection of implementations and articles on "Huff/Puff" circuits, visit the comprehensive pages of Hans Summers G0UPL.

There are several more applications for FLLs, like synchronization in TVs or even "supercharged" VCOs with improved phase noise and linearity (an interesting idea that hinges on the presence of a sufficiently wideband frequency discriminator suitable for the frequency range in question). These are usually aimed at application inside integrated circuits.

"Improved" Huff/Puff circuit

Since the author had a hard time understanding how "Huff/Puff" circuits work from what can be found on the web, here is an attempt at explaining it for the 1996 "improved" version. This is a block diagram of the circuit as implemented by PA0CMU:

                                       +--|>|--+---< +B
                                       |   D   |
                                       |       |
                             +-----+   +--+    |   
                       4f    | 4  /|      |    |
                         off |   / |      |    o
                      +----->|  /  |--||--+---|  S
                      |      | /   |  C        o  1
                      |      |/  1 |   diff    |
+-----+               |      +-----+           |
| VFO |     +-----+   |                        |
|     |     |  M /|   |    +-------+           +------+---> V
| /\/ |     | 2 / |   |    | D-FF _|           |      |      int
|     |---->|  /  |---+--->|>     Q|-          |      |
| f   |     | /   |        |       |           o      |
|  VFO|     |/  1 |   +--->|D     Q|--||--+---|  S    |
+-----+     +-----+   |    |       | C    |    o  2   |      
   |                  |    +-------+  diff|    |     ---     
   |               +-----+             +--+    |     --- C   
   +-||-+-|<|--+   | XO  |          |  |       |      |   int 
     C  |  D   |   |     |             |       |      |         
      C |   T  |   | /\/ |          |  +--|<|--+      |  
        ^     ---  |     |                 D   |      |  
       V       -   | f   |          |          |      | 
        int        |  Ref|                    ---    ---
                   +-----+          | Start    -      - 

We'll start out where one always does – right in the middle of the circuit. ;) Here we get square waves from the parts to the left. Differentiator capacitors Cdiff turn the rising and falling edges into more or less good positive and negative voltage impulses, respectively. The kind of impulses that would do funny things with the transistors used as switches S1, S2 are swallowed by diodes D, so that half of them remain. Those may then turn on the switching transistors, which transfer a certain amount of charge ΔQ per pulse – that's why the thing is called a charge pump. This charge is either added to (S1) or drained from (S2) integrator capacitor Cint, whose voltage either increases or decreases by ΔQ / C.
If the two pulse rates are the same, integrator voltage Vint will remain the same, while a constant difference in pulse rate will cause a linear increase or decrease in Vint over time. This behavior can be used to tune varicap diode DT which provides fine tuning for the VFO.
Basically, this part of the circuit is quite similar to a pulse count FM detector.

So far, so bad. Now let's look at the upper part of the charge pump. Here the incoming square waves have the frequency fVFO / 2M+2, so Cint gets charged just as many times per second.

How frequently charge is drained from Cint obviously depends on the output frequency of the D flipflop (latch).
The D flipflop is one of two within a 74HC74 in this case. As per the datasheet, it will sample the value of the data input D on a rising edge of the clock input CLK (usually marked >) and present it on its output Q. Otherwise the current value of Q will be kept. (This assumes the values of the set and reset inputs – not drawn – to be both high, which is the case in this circuit.)
Now this could be seen as a sampling mixer, however our signals are all-digital here, so we'll call it a "digital mixer". Let's examine what happens manually:

This gives us the following output characteristic:

   f  ^
    Q |
f     |
 CLK  |
---- -+- . - - - - - - - A - - - - - - - A - - - - - - - -            
 2    |   .             /.\             / \             .
      |    .           / . \           /   \           .
      |     \         /  .  \         /     \         .
 f   -+- - - \ - - - / - . - \ - - - / - - - \ - - - / - -
  off |       \     /    .    \     /         \     / 
      |        \   /     .     \   /           \   /  
      |         \ /      .      \ /             \ /   
   0 -+--...-----|-------|-------|-------|-------|------->
                 |       .       |               |      f
               N * f     . (N+1) * f        (N+2) * f    D
                    CLK  .          CLK              CLK
                       1 .
                  (N + -) * f
                       2     CLK

If one wants to use this as a frequency detector, an fD that is an integer multiple of fCLK/2 would obviously be the worst possible choice. The output would change in the same direction regardless of whether frequency went up or down. However, with an operating point that is offset by about fCLK/4 =: foff in steady state, it would be perfect.

Now let's recap what fD and fCLK were...

f  = f
 D    Ref

      f
       VFO
f   = ----
 CLK    M
       2

...how foff had been chosen...

      f
       CLK
f   = ----
 off   4

...and what the charge pump did:

.          ΔQ
V   (t) = ---- * (f    - f )
 int        C      off    Q

Here we can see that Vint will remain constant as long as foff = fQ. If there were a constant difference...

                   ΔQ
V   (t) = V     + ---- * (f    - f ) * (t - t )
 int       int0     C      off    Q          0
                         \____ ____/
                              V
                             Δf = const

...we would see a linear ramp of integrator voltage over time. Actually, it would be a little jumpy due to the discrete pulses, so overall we might see foff/Hz jumps upwards and fQ/Hz jumps downwards in a second. If the overall change is such that oscillator tuning aims to compensate the frequency difference, we've won – the loop would be able to maintain lock.

Overall, we obtain the following graph of integrator voltage time derivative vs. fRef:

      .
      V    ^
       int |
     f     |
  ΔQ  CLK  |
+ -- ---- -+- - - - - A - - - - - - - A - - - - - - - A - - - -
   C  4    |         /.\             / \             / \       
           |        / . \           /   \           /   \      
           |       /  .  \         /     \         /     \     
        0 -+- - - / - . - \ - - - / - - - \ - - - / - - - \ - -
           |     /    .    \     /         \     /         .    
     f     |    .     .     \   /           \   /           .    
  ΔQ  CLK  |   .      .      \ /             \ /             .    
- -- ---- -+--...-----|-------|-------|-------|-------|------->
   C  4               |       .       |               |    f
                    N * f     . (N+1) * f        (N+2) * f  Ref
                         CLK  .          CLK              CLK
                            1 .
                       (N + -) * f
                            2     CLK

What would be a stable operating point? Obviously in steady state (loop locked), the integrator voltage should remain constant, i.e. the time differential plotted above would be zero. There are a whole lot of points where fRef and fCLK ~ fVFO would allow this, but are all of them actually stable?
For this we need to know how the VFO will react to a change in Vint. In case of the straightforward tuning diode connection shown here, an increase in Vint leads to reduced tuning capacitance and thus higher frequency. This, however, affects fCLK. Since it may be a little hard to imagine what happens when treated directly, we will look at an increase in fCLK ~ fVFO as a decrease in fRef and vice versa. Now a voltage increase leads to a lower fRef.

Now let's say fRef started out somewhere between N * fCLK and (N + 1/4) * fCLK. In this region, Vint increases, thus fRef moves downwards. This only stops when Vint no longer changes, which is at (N - 1/4) * fCLK.

What's with an initial fRef between (N + 1/4) * fCLK and (N + 1/2) * fCLK? Here fRef would proceed to move upwards until Vint no longer decreases, ultimately ending up at (N + 3/4) * fCLK = (N + 1 - 1/4) * fCLK.

Quite apparently, only the "-1/4" points are stable, while the loop will try running away from "+1/4" points and, if it ended up in such a state anyway, would be knocked out of it by the slightest breeze.

In practice, drift in fCLK ~ fVFO means that there will be some change of Vint over time, i.e. the operating point is slightly shifted from the ideal.

Now let's look at VFO frequency resolution in the ideal case. Two adjacent locking points might be at

                   f
             1      VFO,1
f    = ( N - - ) * ------
 Ref         4        M
                     2
     and
                       f
                 1      VFO,2
f    = ( N + 1 - - ) * ------
 Ref             4        M
                         2

Solving for the inverses of the VFO frequencies and subtracting the results gives

   1        1         1
------ - ------ = ---------
f        f         M
 VFO,1    VFO,2   2  * f
                        Ref
    Δf
      VFO            1
-------------- = ---------
f     * f         M
 VFO,1   VFO,2   2  * f
                       Ref

With the approximation fVFO,1 * fVFO,2 ≈ fVFO,12 we can write ΔfVFO as:

               2
       (f     )
         VFO,1
Δf   ≈ ---------
  VFO   M
       2  * f
             Ref

With the values from the G3DXZ article (fVFO,1 = 5 MHz, M = 17, fRef = 20 MHz), we obtain ΔfVFO ≈ 9.5367 Hz, which is the value given. (Yeah!)

As you can see, frequency resolution is not constant, hardly surprising given that the setup basically has reference and "VCO" reversed (a conventional approach would have a divided-down fRef for fCLK, which would thus be constant). However, using the (in this case) lower fVFO enabled a much better frequency resolution – for the conventional approach, it would be a constant fRef / 2M, about 150 Hz with the same parameters as used above. The conventional approach pulls ahead, however, once fVFO becomes larger than fRef.

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"Fast" Huff/Puff circuit

The most recent iteration of the Huff/Puff stabilizer is the "fast" version, first presented by Peter Lawton G7IXH in 1997/1998. It replaces the charge pump with a special kind of delay line FM discriminator that uses a clocked shift register as a delay line. (Read his Nov 1998 QEX article.) The basic idea behind the changes is the following:

  1. Reduce division ratio 2M in order to allow for a higher comparison rate and thus ultimately frequency detector bandwidth and drift correction capability. (Those familiar with PLLs may know that loop bandwidth increases with phase detector frequency. Similar case here.)
  2. In order to make up for the resulting loss in frequency resolution, introduce extra frequency periodicity by means of the delay line FM discriminator.

It's certainly a neat idea to use a shift register in this way. Since it is clocked by fVFO / 2M in my terminology, the frequency periodicity found in the delay line discriminator fits perfectly within that of the digital mixer (latch).

Delay line discriminator output is zero if an integer number of input frequency cycles fit within its delay:

      L
τ  = ---
 0    f

This corresponds to input frequencies of

      L
f  = ---
 L    τ
       0

Now the delay of the shift register is given by its reference clock and number of elements:

                  M
       Z     Z * 2
τ  = ----- = ------
 0    f       f
       CLK     VFO

We thus obtain

     L * f           f           f
          VFO         VFO         CLK
f  = -------- = L * ------ = L * ----
 L         M             M         
      Z * 2         Z * 2         Z

Since the spacing of these frequencies ultimately determines the distance of locking points, we see that we can make up for a lower M by increasing Z, the number of shift register elements.

The formula for the distance of locking points looks much the same as before, save for Z coming in:

                2
          (f   )
            VFO
Δf   ≈ -------------
  VFO       M
       Z * 2  * f
                 Ref

The more digitally inclined might enjoy the explanation given by Andrew Holme.

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DDS oscillators

Digital Direct Synthesis or DDS oscillators generate signals in the digital domain with the help of sine tables and then output them via a D/A converter. This tends to work better the further away you stay from the maximum rated frequency of the part and the higher the D/A resolution is – I guess there isn't much in terms of dithering going on.

DDS is popular because it allows almost arbitrarily small frequency steps and good phase noise properties. This, however, comes at the cost of many low-level spurs throughout the spectrum, quantization noise I'd guess. Some designs therefore follow a DDS osc with a PLL (or use it for downmixing in the PLL feedback path, e.g. Yaesu FT-990) to make use of the good phase noise properties and get rid of the spurs by means of a suitably low loop filter bandwidth.

Historically, DDS oscillators have not always been fast enough to provide an LO signal directly. Therefore they were combined with other oscillator types. In the AOR AR7030, for example, the DDS output serves as the fRef for a PLL with a (presumably fixed) divider N to obtain the 1st LO frequency of N * fRef. (The 2nd LO, by the way, is generated from the filtered 4th harmonic of the TCXO (temperature compensated crystal oscillator) that is the base clock for everything else including the DDS, which is why the TCXO's frequency is such a strange 11.13625 MHz. That in turn, while ensuring optimum stability, probably leads to the odd tuning steps of 2.655 Hz.)

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Filters

Filters, in general, are frequency-selective devices that aim to separate desired signals from unwanted ones. Most of them are of the bandpass variety, though sometimes you also encounter bandstops (e.g. notch filters). The era of fixed-frequency filters began when superhets with their fixed intermediate frequencies superseded TRF receivers.

Bandpass filter characteristics

When choosing a filter type for a given application, there are several parameters that one would consider:

Normalized ^
filter     |                 -3dB bandwidth
response   |                |<------------->|
[dB]    0 _|            ___ .               . 
           |   passband     . A  A  A  A  A .     
       -3 _|   ripple   ___  / \/ \/ \/ \/ \   
           |                #               #
       -6 _|               |<--  -6dB BW  -->|
           |               |                 |
           ~             ~                     ~
           ~             ~                     ~ 
           |           |                         |
      -60 -+          /<--      -60dB BW      --->\
           |         /                             \
           |        /                               \
ultimate  -+  ~~~. /                                 \ .~~~
rejection  |     |/                                   \|
           |     '                                     '
           +//----------------------+----------------------->
	                            |               frequency
	                            f
                                     0
Group      ^
delay      |
time       |                 |             |
[s]       |                 |             |
           |                  \           /
           |                   ._________.
        0 -+-//---------------------+----------------------->
	                            |               frequency
	                            f
                                     0
Normalized ^
filter     |                 
response   |                
[dB]    0 _|      _ +--------+-+----- spurs     
           |     | ||        | |
      -20 _|     | |v        v |
           |     | |           v
      -40 _|     | ||        |   
           |     | ||        | |
      -60 _|    .   .        |\|
           |   ~     ~~~~~~~~   ~~~~~
           |
           +-//---+-----------+--------------->
	          f          2f       frequency
                   0           0
                    +---------+
          _____     |   Fil-  |
 +-------|_____|----+   ter   +----------+
 |         Z        |         |          |
 |          in      +----+----+          _
(~)                      |              | | Z
 |                       |              |_|  out
 |                       |               |
 +-----------------------+---------------+

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Filter topologies

Regardless of the type of resonators used (you don't even need any in a digital implementation), there are certain filter topologies that have been in use over the years. They can be created by varying the degree of coupling between individual resonators and other parameters. For details, please refer to the respective literature.

Butterworth

A classic topology that gives a ripple-free passband at the expense of only moderately steep filter skirts.

Chebyshev

Another classic, this introduces passband ripple but has the benefit of steeper filter skirts given the same filter order and thus better selectivity (or same selectivity with reduced efforts). Group delay behavior is worse than in Butterworth filters.

Elliptical (Cauer)

Elliptical filters have the steepest skirts of all analog filters, at the expense of having both passband and stopband ripple as well as high group delay deviation. The trick basically is placing "notches" (narrow bandstops) at the passband edges.

Gaussian

Filters with a Gaussian frequency response are no shape factor kings, but have very good group delay characteristics (essentially flat).

Polyphase

Polyphase filters are interesting in that they are phase sensitive, which makes them interesting for establishing image rejection in low-IF receivers. They, however, require very tight parts tolerances for good suppression of unwanted signals, which makes them interesting mainly for integrated or digital implementation.

FIR

This kind of filter is commonly implemented in the digital domain. While they require more effort for the same selectivity when compared to their IIR colleagues, their group delay is always constant.

Filter types

There is more than one way to build filters with resonators in one of the topologies listed above. For more types than those listed here, check out the Wikipedia article on electronic filters.

LC filters

LC filters are the oldest bandpass filters used in radios. They employ resonations with coils (L) and capacitors (C). Achieved Q usually wasn't too high, making for relatively bad shape factors, and they couldn't be shrunk down to very small sizes.

Crystal filters

Filters employing piezoelectric quartz crystals date back to the 1930s. The high resonator Q allowed for lower bandwidths with better shape factors or alternatively higher IFs (they have been commonly used on IFs of several MHz to more than 70 MHz). They, however, always remained somewhat large and not inexpensive.

Mechanical filters

Mechanical filters make use of mechanical vibrations of materials like steel, which can have very high Q. Transducers (e.g. piezoelectric) are used to interface with electronic circuitry. Research on them commenced in the late 1940s, and first working samples were produced in the early / mid 1950s. (The well-known Collins R-390A was one of the first receivers to use them in 1954.) The research activities continued into the early 1960s, when miniature mechanical filters were desired. Mechanical filters were commonly used for IFs of several hundred kHz and replaced crystal filters in such applications. They never were a mass-market item and primarily found use in commercial or at least high-performance receivers. The big names in manufacturing included companies like Collins and (AEG-)Telefunken (whose 200 kHz filters had a good reputation).

You may find this 1971 overview article entitled "Mechanical Filters—A Review of Progress" interesting, authored by mechanical filter experts from three continents – R. A. Johnson (Collins; USA), M. Brner (first Telefunken, then AEG-Telefunken, later part of DASA and today EADS; Germany) and M. Konno (Yamagate University; Japan). A selection of Telefunken materials on mechanical filters (entirely in German) is to be found in the files section of my "weltempfaenger" Yahoo! Group.

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Ceramic filters

Ceramic filters are not unrelated to mechanical filters, but while the latter only used transducers with piezoelectric PZT ceramics, the former employ PZT ceramics for the resonators themselves. They became a backbone of mass-market radio receiver manufacturing in the 1970s and still are in wide use today (although sadly, production of more specialized parts for more demanding applications like high-order AM IF filters and FM IF filters with low GDT deviation has already ceased).

Here's an overview article entitled "The History of Ceramic Filters" by S. Fujishima, 2000.

While Q does not seem to be a problem anymore these days, the aging properties still require that the filters be pre-aged by the manufacturer. Cost-cutting in this department means that the filters will be less stable over time.

SAW filters

SAW (surface acoustic wave) filters, with first commercial applications in the 1970s have proven popular for filters in the VHF and UHF region. Interestingly, they are FIR filters (flat group delay, linear phase), while common analog filters are IIR (minimal phase).

When working with SAW filters, one has to be aware that they don't take very high signal levels, so e.g. building an oscillator with them requires some tricks.

The 1970s SAW filters built for FM tuners (10.7 MHz) have been reported to be subject to significant aging, btw.

Digital filters

You can also implement filters in the digital domain, of course, both IIR and FIR. You only need an ADC and DSP (FPGA, whatever) fast enough.

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Demodulators

A signal on IF level may be a good thing to have, but at some point we want to regain the carried information. This requires a demodulator, also called detector, of some kind. We will now look at those for a few common types of modulation.

AM detectors

Amplitude Modulation is about the second oldest form of modulation in radio history. (It was only preceded by CW, i.e. carrier on/off.) Nonetheless, although being considered thoroughly outdated, it still sees wide use on shortwave, mediumwave and longwave (not exactly the newest terms themselves!), as well as the VHF air band.

AM works by changing the amplitude of a high-frequency carrier, i.e. a sine wave, according to the signal amplitude. Mathematically speaking, the common AM with carrier looks like this:

VRF(t) = (1 + m * Vaudio(t) / |Vaudio, max|) * Vcarrier(t); m > 0

m is the so-called modulation index. If you see specs referring to 30% AM or 80% AM, this is exactly what they mean. In practice, it is obviously not trivial to influence m directly, one has to resort to m / |Vaudio, max| instead and make sure that the input signal never exceeds ±Vaudio, max.

If you were looking at such a signal in time domain with carrier frequency being much higher than any modulation content, you'd see "some high frequency signal" whose upper and lower border, the envelope, would vary according to some low-frequency signal.

  ^ signal voltage
  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (1 + m)
  |-- .              _    .- .             .          level 
  |#### .          .##\ _/##### .        /####.
  |###### .       /############### . _ . ###### ...
  |######## . _ . #############################_ _ _ (1 - m)
  |############################################       level
0 +-----------------------------------------------> t
  |############################################_ _ _
  |######## ---. #############################
  |######.        \###############.    ###### ...
  |####.           .##/  \#####         \####
  |--_ _ _ _ _ _ _ _ _ _-  _ _ _ _ _ _  _ _ _ _
  |

The higher m, the more do minimum amplitude 1 - m and maximum amplitude 1 + m differ, up to the point where m = 100%, which makes the carrier disappear entirely at times, namely when Vaudio(t) / |Vaudio, max| = -1. If m becomes any greater, carrier phase is inverted for part of the time, meaning that the envelope on the positive side will cross over to the negative one and vice versa. This may give problems with demodulation, as we'll see soon.

The frequency spectrum of an ordinary AM signal with carrier looks like this:

^ power density
|               |
|               |
|               |
|          __   |   __
|         /  \  |  /  \
|        /    . | .    \
|       /     | | |     \
|      /      | | |      \
+-//--+-------------------+-----> f
      |  LSB    |    USB  |
             carrier
                |<------->|
                  f
		   mod,max

What used to be a lonely spike in the spectrum (or rather two, the other one at the equally large negative frequency) has now gotten some company in the form of an upper (USB) and lower sideband (LSB) which extend ±fmod,max from the carrier, with fmod,max being the highest frequency encountered in the modulating signal. You might be wondering why this happens if we're just varying the amplitude of the signal – well, the multiplication of the carrier with the modulating signal is a mixing process again and thus shifts the baseband spectrum of the modulating signal upwards to extend around the carrier. The carrier signal itself then has to be added.

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Envelope detectors

Theoretical aspects

Now how do we recover the original signal? This is commonly done with a rectifier with following lowpass filtering as an envelope detector. This kind of detector does not need to know about carrier frequency and phase at all, only the filtering needs to be conceived such that the highest modulation frequencies pass with low distortion while the carrier frequency is suppressed well. This makes such a detector relatively simple.

There is only one limitation for this kind of detector: As we do not know about the carrier phase, demodulation will not be correct for m >= 100%. (See the previous discussion of this case.) A signal that originally looked like this:

  ^ signal voltage
  |      _
  |    .   .
  |   /     \
  |  /       \ 
  | /         \
  |/           \
0 +-------------\--------------------> t
  |              \           / ...
  |               \         /
  |_ _ _ _ _ _ _ _ \ _ _ _ / _ _ m = 100% level
  |                 \     /
  |                   ._.
  |

...would be demodulated like this:

  ^ signal voltage
  |      _
  |    .   .
  |   /     \
  |  /       \ 
  | /         \
  |/           \
0 +-------------\--------------------> t
  |              \     _     / ...
  |               \  .   .  /
  |_ _ _ _ _ _ _ _ \/_ _ _\/ _ _ m = 100% level
  |
  |
  |

...which of course amounts to bad distortion. This is why overmodulated AM stations sound so dreadful.

Diode detector operation

There are, however, practical limitations as well. Here's an envelope detector about as simple as they get:

o---------|<|-------+----+--------o
|          D        |    |        |
 \                  |    _         \
  |                ---  | |         |
  | V  (t)       C ---  | | R       | V   (t) (< 0)
 /   AM             |   |_|  load  /   out
|                   |    |        |
v                   |    |        v
o-------------------+----+--------o

To explain the basic functioning of the circuit, we will assume diode D to be ideal (i.e. a short if the voltage dropping over it is positive, no conduction in case of reverse voltage) and neglect capacitor C for now. Then there will be two cases:

1. VAM < 0: Vout = VAM 1. VAM > 0: Vout = 0

This is a half-wave rectifier, called like this because assuming sine wave input, it uses the input signal half of the time only and outputs half sine waves (other the top or the bottom half, the latter in this case).

The purpose of the capacitor is no different than that of its equivalent in a linear power supply: It smoothes the rectified signal, thus suppressing high-frequency components around the carrier frequency.

For better understanding, we'll include an additional resistor in our model, as there always is some source impedance:

               _____
o------|<|----|_____|----+----+--------o
|       D        R       |    |        |
 \                S      |    _         \
  |                     ---  | |         |
  | V  (t)            C ---  | | R       | V   (t) (< 0)
 /   AM                  |   |_|  load  /   out
|                        |    |        |
v                        |    |        v
o------------------------+----+--------o

Just like in a linear power supply, one can distinguish between two phases of operation:

  1. Charging: If the momentary input amplitude drops below Vout (which is held approximately constant by C), the diode starts conducting and C is charged. The RC time constant for this is τc = 2 RSC.
    Note that RS includes the effective series resistance of a real-life diode.
    The factor of 2 comes in because charging can only take place during one half-wave (the negative one in this case).
  2. Discharging: If no amplitude peaks reach down low enough for charging, C will become discharged by load resistance Rload with RC time constant τd = RloadC.

In case of a signal amplitude modulated with a sine, charging would occur when the sine rises and discharging when it falls.

There is still some DC offset accompanying the signal at this point – the very reason why this kind of circuit is used in power supplies – but we can easily get rid of that by using a suitably large coupling capacitor later on.

Limitations (I): Slewing distortion vs. filtering

It is clear that the demodulator will not be able to follow the signal transients arbitrarily fast. At high frequencies and amplitudes, it will invariably generate slewing distortion. Furthermore, generally τc ≠ τd. Usually τc < τd (or even τc << τd, the typical case in power supplies), so the detector will fail to follow falling transients properly first. When choosing C, a compromise must be found between high-frequency filtering and distortion.
Since it is not easy to achieve a good tradeoff between filtering and distortion in a setup like this, a number of practical implementations employ not only 1st order, but 2nd order filtering.

Limitations (II): Effects of non-ideal diodes

Even with the slewing problem being sorted out, this basic AM detector circuit still does not perform very well in practice – high distortion is encountered for low input signal levels and high modulation indices. This is because real-life diodes exhibit a finite voltage drop when conducting, with an exponential relation between current and voltage.

We can gain some insight with a still simple but a touch more realistic diode model that assumes the diode to start conducting at some finite voltage Vf, typically 0.5..0.7 V for silicon diodes. Now look at our AM signal again and imagine what happens if we reduce the amplitude of the input signal until Vf exceeds the 1 - m level and then finally the 1 + m level. The modulating signal will get clipped towards negative voltages, causing ugly distortion. At the end, there will be no output left at all!

Practical diode detectors will therefore typically use diodes with a low Vf, frequently germanium diodes in the past (Schottkys are even better still), along with a little trick:
The diode gets a little forward bias current (typically obtained from a supply voltage via a large-value resistor), so that its voltage already is near Vf with no input. Then a small input signal will be sufficient to get the diode conducting when it's supposed to. Since one doesn't want the diode to conduct overly much on the other half-waves (which would degrade performance again), this takes some optimizing – besides, it's supposed to work halfway well over a certain temperature range, and the diode characteristic is quite temperature dependent.
This trick is commonly found in sets with discrete diode detectors from the 1970s and 1980s.

In practice, it is also important that the diode used be relatively quick in turning off and on.

Obtaining better performance

Improved performance over a single diode detector can be obtained when using a full-wave rectifier or a full-wave bridge rectifier, in part due to their high-frequency components having twice the frequency when compared to a half-wave rectifier. They also deliver larger output amplitudes. The biasing trick is not applied as easily to bridge rectifiers, however, and they have a higher voltage drop about equivalent to their half-wave colleagues, but not requiring an IFT, they are more suitable for integration. Full-wave diode bridge rectifiers have historically been used in communications receivers (e.g. Telefunken E1501) and also find use in ICs (e.g. Philips TDA1072/1572, Japanese IC makers are usually tight-lipped about things like these).

Options for very well-performing AM envelope detectors include:

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Synchronous detectors

Synchronous AM detectors are basically nothing but SSB detectors with carrier-synchronous inserted BFO signal. Basically there are two ways of obtaining such a carrier-synchronous signal which may also be combined:

  1. Use a limiting amplifier to remove AM from the carrier (so-called pseudosynchronous detection); works well as long as the signal does not drop too far but fails to work on overmodulated signals, momentarily giving an inverted carrier)
  2. Use a PLL of some kind for carrier regeneration; limiting is also advisable here, else the BFO signal may become quite noisy; the DDS based PLL in the AR7030 with switchable loop filter bandwidths (this allows a looong time constant and thus a clean BFO when holding lock while permitting sufficiently quick action when locking onto a carrier) is a pretty smart solution

Sony's synchronous detectors, for example, use a PLL based system with limiting (with the VCO running at 8 times the IF; using a ceramic resonator based VCO limits pulling range and improves phase noise). Their integrated envelope detector already is a pseudosynchronous type, at least in case of the CXA1376.

Why pseudosynchronous detection is the same as envelope detection

You may be surprised to read this. In fact, it's not exactly the same in theory but would work out identically in practice. Why?

Given this pretty input signal:

  ^ s(t) input signal
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...
0 +/-----\-----/-----\-----/-----\-----/-----> t
  |       \   /       \   /       \   / 
  |        -         -         - 
  |

...an ideal rectifier (envelope detector) for the positive half-wave would give an output like this prior to lowpass filtering:

  ^ r(t) rectified signal
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...
0 +~-----~-----~-----~-----~-----~-----~-----> t
  |
  |
  |

This can equally be described as the multiplication of the original function with a periodic rectangular waveform, as

/ s(t) * (+1), s(t) ≥ 0 r(t) = < \ s(t) * 0, s(t) < 0

Let's look at it graphically:

  ^ r(t) rectified signal
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...
0 +~-----~-----~-----~-----~-----~-----~-----> t
  |
  |
  |

                    ||
                    ||

  ^ s(t) input signal
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...
0 +/-----\-----/-----\-----/-----\-----/-----> t
  |       \   /       \   /       \   / 
  |        -         -         - 
  |

                    *     

  ^ m(t) multiplying function
  |
1 |+-----+     +-----+     +-----+     + ...
  ||     |     |     |     |     |     |
0 ++-----+=====+-----+=====+-----+=====+-----> t
  |
  |
  |

It is easy to see that for any sine or merely amplitude modulated signal s(t), m(t) will have the same periodicity and in addition be in phase with s(t).

Now m(t) is not a nice pure sine that is in phase with the carrier of s(t) – but it does contain a spectral component that is! (Just look at the Fourier series of such a signal.) Therefore at least part of the output will be equivalent to the result of mixing with a carrier-synchronous sine, which is just what happens in a pseudosynchronous detector.

The other components of m(t) are to be found at DC and odd-order multiples of the carrier frequency – but all of these generate mixing products in the vicinity of the carrier frequency or higher, which are easily filtered out presuming that the modulation bandwidth is small vs. the carrier frequency.

Note that in case of momentary carrier phase reversal as it happens with (effective) overmodulation, both envelope and pseudosynchronous detectors will also reverse the phase of the locally extracted carrier. Without any means of buffering the "real" carrier phase, distorted demodulation cannot be avoided.

In effect you can achieve equally good results with either a good envelope detector (e.g. precision rectifier circuit) or pseudosynchronous detection. Only "real" synchronous detection has an edge over both under critical conditions.

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SSB detectors

Another kind of modulation belonging to the class of amplitude modulation schemes is SSB, single sideband. Only one sideband is transmitted and the carrier is suppressed, which considerably increases efficiency and allows for narrower channel spacing. It is therefore in wide use among amateur radio operators (hams) and utility stations on shortwave. The downside is that demodulation is far less simple than for AM, and a receiver with good frequency stability und tuning resolution is needed. Therefore, plans to use it for broadcast, as proposed in the late 1970s, never got very far.

In frequency domain, the spectra of SSB signals look like this:

^ power density
|
|               |   __
|                  /  \
|               | .    \
|                 |     \
|               | |      \
+-//----------------------+-----> f
               f|    USB  |
                car
                |<------->|
                  f
                   mod,max
^ power density
|
|          __   |
|         /  \
|        /    . |
|       /     |
|      /      | |
+-//--+-------------------------> f
      |  LSB   f|
                car
      |<------->|
        f
         mod,max

In a receiver, a replacement for the missing carrier must be generated, which must match the carrier frequency on transmitter side fairly closely. For speech transmissions, an accuracy of a few 10 Hz is generally sufficient. For historical reasons, the oscillator used for carrier insertion at IF level is commonly called BFO, Beat Frequency Oscillator. This stems from the days when people would still use a BFO to enable SSB reception with an AM detector. The BFO "beats against" the received signal.

The most simple kind of SSB detector is an AM detector that is being fed both the SSB signal and a BFO signal. This generally does not work too well and requires careful adjustment of the RF gain to match signal and BFO levels. It is not sideband selective either, i.e. both sidebands below and above the BFO are demodulated. This arrangement was commonly found in communications receivers up to the 1950s, when only CW had to be made audible.

Receivers today use product detectors, which are nothing but mixers fed with the IF-level signal and the BFO signal. This is, in fact, quite similar to a direct conversion receiver – a product detector mixes things down to an "IF" of zero, i.e. into the baseband. And just like we already saw in the superhet discussion, frequencies both above and below the BFO frequency are mixed down, which in this case means that the detector reacts to both sidebands.

If we want to build a receiver which is sideband selective, we have two options:

  1. Filter out only the desired sideband by means of IF filters with suitably low bandwidth and steep skirts and set the BFO frequency to either the lower or higher end of the passband.
  2. Use a sideband selective product detector.

Both options are commonly used, possibly even the combination. Sony sets offering AM synchronous detection use the second option, while a number of communications receivers makes use of the first (good SSB filters are needed anyway).

Now what is a sideband-selective product detector? It is basically the same as an image rejection mixer, unsurprisingly given that the problem to be solved is the same. The principle is really old, which you can see from the following arrangement being called a Hartley Image Rejection Mixer (this is the same Hartley who pioneered the inductively tapped Hartley oscillator, I suppose):

                RF in
                  |
                  |
    +-------------+-------------+
    |                           |
    v                           v
 +-----+                     +-----+
 |     |             +---+   |     |
 |  X  |<---------+->|90|-->|  X  |
 |     |          |  +---+   |     |
 +-----+          |          +-----+
    |           +---+           |
    v           | ~ | LO        v
 +-----+        +---+        +-----+
 | _   |                     | _   |
 |  \  |                     |  \  |
 |   \ |                     |   \ |
 |     | LPF             LPF |     |
 +-----+                     +-----+
    |                           |
    v                           |
  +---+                         |
  |90|                         |
  +---+                         |
    |          +-----+          |
    |          |  +  |          |
    +--------->| or  |<---------+
               |  -  |
               +-----+
                  |
                  |
                  v 
               IF out

This would not be so practical for SSB demodulation, since achieving a wideband 90 phase shift (which would have to be carried out in the baseband) is not easy. (In the analog domain, that is. A DSP-based implementation can use the Hilbert transformation.) If you have a signal bandwidth small compared to the IF, that's another matter.

For SSB, typically the following topology is being used:

                IF in
                  |
                  |
    +-------------+-------------+
    |                           |
    v                           |
  +---+                         |
  |90|                         |
  +---+         +---+           |
    |           | ~ | LO        |
    v           +---+           v
 +-----+          |          +-----+
 |     |          |  +---+   |     |
 |  X  |<---------+->|90|-->|  X  |
 |     |             +---+   |     |
 +-----+    LSB/USB          +-----+
    |        select             |
    |           \               |
    |          +-\---+          |
    |          |  +  |          |
    +--------->| or  |<---------+
               |  -  |
               +-----+
                  |
                  |
                  v 
               +-----+
               | _   |
               |  \  |
               |   \ |
               |     | LPF
               +-----+
                  |
                  |
                  v 
              Audio out

I won't go too far into the math here. Basically such a mixer exploits the symmetry properties of trigonometric functions in such a way that the spectral components of one sideband have equal sign after mixing and those of the other one do not.

In practice, opposite sideband suppression depends on component matching, and the LO signals' orthogonality of course. Expect about 30..40 dB.

There are various ways of generating the two orthogonal LO signals. One can use phase shift networks, but that brings component tolerances into play. A popular method involves flip-flops, only requiring an input signal four times the desired LO in frequency (another slightly different version: Sony uses a divide-by-8 counter). For a glimpse of how this works, check out NXP appnote AN1981. There you can also see how one can use a PLL for this purpose.

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FM discriminators

Common types of FM detectors, or discriminators as they're often called (usually if limiting is also performed), include

detectors, of which you will most frequently find quadrature types today. Some preceding types worth looking at are

Some more interesting oldschool types can be found on Low Tech FM Radios.

Slope detector

This is a very primitive type of FM detector. It makes use of a tuned circuit having slopes, i.e. regions where the output drops as you move away from the circuit's center frequency. This effect can be used to convert FM into AM, then a regular AM detector serves for demodulation. Thus basically any AM receiver (preferably with less great IF filtering) can be used to make FM audible by slight mistuning.

A major disadvantage of such a detector is that it still reacts to AM and thus also to fading and all kinds of disturbances (i.e. lightning cracks). Besides, their distortion performance is hardly exciting.

Read more about slope detectors.

Foster-Seeley discriminator

The Foster-Seeley discriminator takes the idea of the slope detector a step further by using a double-tuned circuit (i.e. two coupled tuned ones) and full-wave rectifier.

This detector still is sensitive to amplitude variations and thus requires limiting in preceding stages.

Read more about Foster-Seeley detectors at tpub.com or radio-electronics.com.

Ratio detector

Ratio detectors were a common standard type in pre-IC days but still found occasional use in the 1980s and 1990s. They improve upon Foster-Seeley types by having some integrated AM rejection and lower required input levels. Telling them apart from Foster-Seeley circuits is easy: One of the diodes is reversed, and there is an electrolytic capacitor present.

Read more about ratio detectors at.tpub.com or radio-electronics.com.

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Quadrature detector

Quadrature detectors, while they already existed in the days of vacuum tubes, became very popular when the first FM radio ICs appeared in the early 1970s. While the circuitry inside was more complex than that for a ratio detector (both a limiting amplifier and a mixer are required, with the latter typically being a Gilbert cell type), externally only a single-tuned circuit is needed for the same basic functionality. (Hi-fi applications nonetheless make use of double-tuned circuits for reduced distortion.)

This CommsDesign article gives a block diagram and mathematical description for a quad detector.

We can also see a quad detector as being analogous in function to a delay line discriminator. Why? Well, here's a "truth table" for a multiplier = mixer given input signals that can either be positive (+1) or negative (-1):

x y x * y
+ + +
+ - -
- + -
- - +

Now map + --> 0 and - --> 1, and there you have the XOR truth table!

The phase shift network consisting of the series capacitor and single-tuned circuit then aims to establish a linear relation between frequency and phase shift in the vicinity of (f0, 90), where f0 is the IF and center frequency of the single-tuned circuit. This function basically simulates a delay line, except that phase shift decreases rather than increases with frequency (look here for a plot).

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PLL detector

PLL detectors are a typical choice for top-class FM tuners, as low noise and distortion are possible. They only became feasible in the early 1980s but the operating principle is actually quite straightforward:

                                   +-----+
                                   | Buf |
                                   |     |
                             +---->| |>  |----> Out
                             |     |     |
                             |     +-----+
                             |   
        +-----+     +-----+  |   +-----+
        | PD  |     | LPF |  |   | VCO |
        |     |     | _   |  |   |     |
IF ---->| Δφ  |---->|  \  |--+-->| /\/ |--+
in      |     |     |   \ |      |     |  |
        |     |     |     |      | f   |  |
        +-----+     +-----+      |  v  |  |
           ^                     +-----+  |
           |                              |
           +------------------------------+

The input serves as the reference frequency for a simple PLL. If the input frequency changes, the loop will follow it. Demodulation is by tapping off the VCO control voltage.

For obvious reasons, the VCO's control voltage vs. frequency characteristic must be fairly linear for low distortion, but then the required bandwidth of a few hundred kHz at 10.7 MHz is not that large either, making PLL detectors some of the lowest-distortion discriminators in practice. The AM rejection of such a circuit also is pretty high, which contributes to the high achieved SNRs (in excess of 80 or even 90 dB; the phase detector obviously has to have pretty low noise then).

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Pulse-count detector

This kind of detector already made an appearance in the 1950s but only really became widely used by the mid/late 1970s, when FM tuner manufacturers like Kenwood and Pioneer managed to integrate the circuitry into proprietary ICs. As a downmixing stage was required for optimum SNRs, pulse-count detectors only found their way into the better models. In the early 1980s, they were superseded by PLL detectors.

The operating principle of a pulse-count detector is quite straightforward:

    ^ limited input signal
 1 _|  _____       _____       _____       ___...
    | |     |     |     |     |     |     |
-1 _|_|     |_____|     |_____|     |_____|
    +---------------------------------------------> t
      .     .     .
      .     .     .     |  |
      .     .     .    \|  |/
      .     .     .     \  /
      .     .     .      \/
      .     .     .
    ^ pulse generating / shaping circuitry output
 1 _| .     .     .
    | |     |     |     |     |     |     |
 0 _|_|_____|_____|_____|_____|_____|_____|___...
    +---------------------------------------------> t

                        |  |
                       \|  |/
                        \  /
                         \/

    ^ integrated output signal
 1 _|       
    |
 0 _|-----------------------------------------...
    +---------------------------------------------> t

The input signal is limited and fed to some circuitry that generates pulses of equal shape and height at every zero crossing (or every second one) – this circuitry might either be quite straightforward (e.g. differentiator plus suppression of negative peaks), but also more fancy implementations with dedicated pulse shaping circuitry are feasible. Quick trigger circuits were already used for scopes in the 1970s, so the technology was there. Finally the output is sent through a lowpass filter for integration, where obviously the output level will scale directly with the pulse rate and thus the frequency.

This operating principle enables very high linearity over a large frequency range, but there is one potential problem: If the frequency deviation of the input signal is small vs. the IF, the output voltage range will be quite small, thus the obtained SNR may not be that great. Kenwood solved this problem by integrating a downmixer for downconversion to a second IF of typically about 2 MHz (800 kHz in later L-01T samples) after the signal has passed through all the filtering. Now of course a mixer rarely improves intermodulation characteristics, and there are several external components associated with it, so pulse-count detectors mainly graced more upscale models – my KT-80 was the least expensive one available from Kenwood.

There are some more pitfalls of pulse count detectors as well. Looks like as nice as they are in theory, getting them to work really well in practice is another matter!

Since pulse counters tend to like a well-limited signal, Kenwood's second generation pulse-count tuner ICs included an additional limiter stage in the middle of 1st IF filtering. While understandable, this is not such a smart idea – while it certainly works splendidly if there only is a single station in sight, the generated intermodulation distortion would mean effectively reduced selectivity (as in this example where IF amplifier nonlinearity was the culprit).

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Delay line discriminator

Delay line discriminators make use of the fact that a fixed-time delay equates to a phase shift that scales linearly with frequency:

sin(2 π f (t + τ) + φ) = sin (2 π f t + (φ + 2 π f τ)) = sin (2 π f t + φ + Δφ) I.e. Δφ = (2 π τ) f

If you then compare the phase difference of both the original and delayed signal by means of a phase detector, the output of the phase detector will grow linearly with frequency.

Now an analog delay line, while it has been used (the most common application is probably in analog PAL TV sets), is somewhat cumbersome to implement. Real-life delay line discriminators use digital electronics these days, so we will look at how they work next.

The second digital type after the pulse count detector, this kind of delay discriminator takes the input signal in a well-limited "digital" form and XORs this with a copy passed through a delay line consisting of an even number of inverters. Any digital circuit has a finite propagation delay, which is made use of here. The total delay is dimensioned such that approximately a 90 phase shift is obtained at 10.7 MHz (or whatever the IF used).

    +---+                            +-----+    +-----+ 
--->| 1 |--+------------------------>|     |    | LPF |
    +---+  |                       x |     |    | _   |
IF   cmp   |                         | XOR |--->|  \  |--->
in    =    |   +---+        +---+  y |     |    |   \ | Out
     lim   +-->| 1 |o-....->| 1 |o-->|     |    |     |
               +---+        +---+    +-----+    +-----+

For why this works, let's recall the truth table for an XOR:

x y x XOR y
0 0 0
0 1 1
1 0 1
1 1 0

The output goes high when either of the input signals is high, but not if both of them are.

Now how can this be used as a frequency-selective detector?

Assuming both input signals are exactly in phase – which would be the case at very low frequencies – the output would always remain low:

   ^ x input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t

   ^ y input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ XOR output
1 _|
   |
0 _|_________________________________________...
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ LPF output
1 _|
   |
0 _|_________________________________________...
   +---------------------------------------------> t

Now assume that the delay corresponds to 180, i.e. the signals are always out of phase. In this case the output would remain high all the time:

   ^ x input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t

   ^ y input
1 _|_       _____       _____       _____    
   | |     |     |     |     |     |     |
0 _| |_____|     |_____|     |_____|     |___...
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ XOR output
1 _|_________________________________________...
   |
0 _|
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ LPF output
1 _|_________________________________________...
   |
0 _|
   +---------------------------------------------> t

Now for a slightly more interesting case, a 90 phase shift:

   ^ x input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t
     .     .     .
   ^ y input     .
1 _| .   _____   .   _____       _____       ...
   | .  |  .  |  .  |     |     |     |     |
0 _|____|  .  |_____|     |_____|     |_____|
   +---------------------------------------------> t
     .  .  .  .  .  .
     .  .  .  .  .  .  |  |
     .  .  .  .  .  . \|  |/
     .  .  .  .  .  .  \  /
     .  .  .  .  .  .   \/
   ^ XOR.output  .  .
1 _| .__.  .__.  .__.   __    __    __    __
   | |  |  |  |  |  |  |  |  |  |  |  |  |  |
0 _|_|  |__|  |__|  |__|  |__|  |__|  |__|  |...
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ LPF output
1 _|
   |_________________________________________...
0 _|
   +---------------------------------------------> t

There's a bit more going on in this case. When averaged in the following lowpass filter, the XOR output becomes 0.5. We'll call this frequency our nominal center frequency f0.

Now for a less than 90 phase shift, like you'd find if the instantaneous frequency were lower than f0:

   ^ x input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t
     .     .     .
   ^ y input     .
1 _| .  _____    .  _____       _____       ...
   | . |   . |   . |     |     |     |     |
0 _|___|   . |_____|     |_____|     |_____|
   +---------------------------------------------> t
     . .   . .   . .
     . .   . .   . .   |  |
     . .   . .   . .  \|  |/
     . .   . .   . .   \  /
     . .   . .   . .    \/
   ^ XOR output  . .
1 _| ._.   ._.   ._.    _     _     _     _ 
   | | |   | |   | |   | |   | |   | |   | |
0 _|_| |___| |___| |___| |___| |___| |___| |_...
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ LPF output
1 _|
   |
0 _|-----------------------------------------...
   +---------------------------------------------> t

A-ha! Our pulses have become narrower. The averaged value drops to less than 0.5.

And finally, here's a case with somewhat more than 90 phase shift, like you'd find if the instantaneous frequency were higher than f0:

   ^ x input
1 _|  _____       _____       _____       ___...
   | |     |     |     |     |     |     |
0 _|_|     |_____|     |_____|     |_____|
   +---------------------------------------------> t
     .     .     .
   ^ y input     .
1 _| .    _____  .    _____       _____
   | .   | .   | .   |     |     |     |
0 _|_____| .   |_____|     |_____|     |_____...
   +---------------------------------------------> t
     .   . .   . .   .
     .   . .   . .   . |  |
     .   . .   . .   .\|  |/
     .   . .   . .   . \  /
     .   . .   . .   .  \/
   ^ XOR output  .   .
1 _| .___. .___. .___.  ___   ___   ___   ___...
   | |   | |   | |   | |   | |   | |   | |
0 _|_|   |_|   |_|   |_|   |_|   |_|   |_|
   +---------------------------------------------> t

                       |  |
                      \|  |/
                       \  /
                        \/
   ^ LPF output
1 _|
   |-----------------------------------------...
0 _|
   +---------------------------------------------> t

Now the pulses are wider. Our averaged value obviously becomes larger than 0.5.

So overall we can say that the filtered detector output would become larger as frequency increases, at least up to the point where the phase difference becomes 180, i.e. at 2 f0. Moreover, the relationship between phase difference and pulse width (and therefore output level after lowpass filtering) is extremely linear, limited only by finite signal rise and fall times (these would shorten very short pulses or gaps). The phase difference in turn also scales with frequency in a linear fashion, as outlined earlier:

Δφ = 2 π f (t + τ) - 2 π f t = 2 π f τ ~ f

This means that excellent linearity can be achieved with such a detector.

The phase detector is made up by the XOR plus following lowpass filtering in this case.

Like in the pulse count detector, the output voltage range obtained scales inversely with the IF chosen.

Delay line discriminators find use in modern-day Accuphase tuners, including the T-1000 with its DSP based stereo decoder. They do not appear to use downmixing, so obtainable SNR appears to be good enough as-is.

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Baseband processing

Treatment of receivers usually stops after demodulation. However, that doesn't mean that the following stages would be irrelevant, quite the contrary. The recovered signal may need further demodulation by itself, with a typical example being the multiplex stereo system most commonly used for FM broadcasting and TV audio. Even if the signal is useful as-is, further filtering may be useful.

Deemphasis

As the receiver noise on weaker FM signals increases in amplitude with rising frequency, one commonly uses preemphasis on the transmitter side and deemphasis on the receiver side. This means that the usually weaker high-frequency audio components are amplified on the transmitter side using a circuit with a PD type frequency response, which is flat up to a certain frequency and then rises at 6 dB per octave. The receiver contains a 1st-order lowpass filter which has a complementary response. These tend to be specified in terms of RC time constant τ, where

       1
τ  = ------
     2 π f
          c

fc is the filter corner frequency.

In FM broadcasting, there are two different values of τ in use for historic reasons. In North America where the first such system was established (originally from 42 to 50 MHz), you'll find 75 s preemphasis. This was later found to be too heavy in practice, restricting deviation too much, so the rest of the world uses 50 s.

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FM stereo demodulation

FM stereo modulation is quite straightforward: A stereo signal is lowpass filtered at about 15 kHz, and then a multiplex signal is obtained by rapidly switching between the two channels at a 38 kHz rate. This gives a mono baseband signal, plus two sidebands containing the difference signal (L-R) which are symmetric around 38 kHz, for a total bandwidth just short of 54 kHz. Finally a 19 kHz tone which is phase synchronous to the 38 kHz switching rate is added, the so-called pilot tone.

Demultiplexing this therefore would seem easy: All you need to do is recover the 38 kHz switching frequency by locking a PLL to the pilot tone and then switch audio between the left and right output channels again. Apply deemphasis, finished. Well, it basically does work like that, but there is a problem that needs resolving:

38 kHz switching action means that we have a switching mixer there, which will duly respond not only to sidebands around 38 kHz, but also the corresponding odd-order harmonics (114 kHz, 190 kHz, …). Those additional sidebands are filtered out at the transmitter side in order to conserve bandwidth, so all that's to be received there is noise, interference from stations on frequencies nearby and funny intermodulation products e.g. from multipath propagation. Not what you want in your output signal! So how is this problem commonly tackled?

In practice, the phase shift between 19 and 38 kHz caused by lowpass filtering and limited IF bandwidth needs to be taken into account if optimum channel separation is to be achieved. When you are doing things by DSP, it is even possible to adjust phase shift dynamically so best stereo separation is achieved for each station!

Another problem is the pilot tone, which may generate high-frequency intermodulation distortion in following amplifier stages and in the olden days liked to interference with high-frequency tape biasing. Most any hi-fi tuner has high-Q notch and general lowpass filtering at the output that suppresses the pilot tone and other remaining high-frequency content, but the aforementioned "super decoders" commonly employed pilot tone cancellation as well.

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Frequency readout

For many decades, frequency readout was a major design issue in any receiver, especially if you wanted to achieve any kind of accuracy. There are two basic types of frequency readout:

  1. Mechanical. Here the readout facilities are mechanically coupled to the component that controls tuning, usually a rotating variable capacitor or less commonly inductor.
  2. Electronic. Here the readout is derived from either a frequency counter or the programmable divider setting(s) in a PLL.

Mechanical readouts

Mechanical frequency readouts can be traced back pretty much as far as radios themselves. As they evolved over a number of decades and were used in receivers for all kinds of purposes and in all kinds of price ranges, there is considerable variety to be noted. While those in cheap and nasty sets typically aren't exciting, the more complex ones can be fascinating wonders of precision mechanical engineering. Basic types include:

Obviously the more interesting ones tend to be types manufactured for higher demands, as in (not uncommonly military or commercial) communications receivers.

For example, you'll find a horizontal dial with moving loupe pointer on the Telefunken E104 (here's a 1959 article describing the mechanics, in German), while a R&S EK07 of similar vintage employs an additional vernier dial in the ranges that wouldn't allow sufficient resolution.

Concentric scales with moving pointer weren't too typical of "full-blown" communications receivers, but you'll find them in the Telefunken E127 with its "rainbow dial", which was a more down-to-earth receiver for maritime use when compared to the aforementioned E104.

Moving circular dials were quite popular in amateur radio equipment in the 1960s and 1970s, whether it's some fine Drake gear, a Kenwood TS-520(S), or a more basic and affordable Allied receiver from the Radio Shack stable.
A very interesting variation is found in the WWII-era Telefunken E52 "Kln", arguably the world's most advanced shortwave receiver at the time: Microfilm on a rotating glass disc contains tiny dial markings which then are projected onto a screen (more on this). Resulting readout accuracy is remarkable. This readout system was copied in the Russian R-250 receiver originally conceived in the late 1940s (it uses a Collins-style frequency conversion concept, by the way), whose last updated version R-250M2 was manufactured up to the early 1980s.
It will appear that the very first projection scales with glass dial were used in the 1934 vintage Sachsenwerk "Olympia" radios, with the company consistently marketing radios with them until 1939. In these sets, they were used to provide an isolated, larger and thus better-readable station name. The feature was called Kinoskala, "cinema scale", thereby referring to the use of projection. As you can see, the idea certainly didn't come out of nowhere.

Rotating dial drums could be found in 1970s amateur equipment such as the venerable Yaesu FRG-7 (one of the better consumer-level Wadley loop implementations), a Kenwood R-300 (some good pics of this set), similar-looking but more basic Realistic DX-200 or this nice Denon TU-500 FM tuner.

Film scales were quite common in more advanced Japanese shortwave portables in the early / mid 1970s. The aforementioned Sony CRF-230 used them, as did the classic ICF-5900W for its main dial (with a separate dial for bandspread tuning over ±125 kHz that allowed a frequency resolution of ±1 kHz, an excellent result for a mid-'70s consumer-level set). The origins of film scales, however, lay in professional equipment, like the late-'50s Racal RA17.

In terms of receivers with mechanical numeric frequency readouts, one comes to mind immediately: The classic Collins R-390(A) (check out the picture of the mechanics). Within its 1 MHz segments, frequency is displayed to 1 kHz, with accuracy better than this on a well-aligned sample. For the 1950s, this was absolutely phenomenal – consumer-level receivers were commonly stuck with far less accurate scales well into the 1970s, especially on the higher bands (look at the Kenwood R-300 pictures above). But believe it or not, there are some "boatanchor" type receivers that still beat this by an order of magnitude – an early-'60s Siemens E311 pulls off 100 Hz accuracy and ±20 Hz stability over 24 hours. That one has a very interesting concept using grid-locked oscillators plus thermostats for crystal oscillator and VFO.

More advanced receivers would usually allow dial calibration. For this purpose, commonly a marker feature was included (such marker generators were also sold as aftermarket additions later on). Based on a stable crystal oscillator, this would output a spectrum with many harmonics, maybe every 500, 250 or 100 kHz. These are easily made heard on anything that can demodulate SSB.

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Electronic readouts

There are two different ways of implementing electronic frequency readouts:

Since electronic readouts have been around for a few decades now, display technology has changed quite a bit, too:

However, frequency readout does not necessarily have to be visual – with the advent of voice synthesizers in the 1980s, optional voice output for frequency and operation parameters also became available. Together with direct frequency input as afforded by PLL synthesizers, this made communications receivers a lot more accessible to blind users.

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Receiver design issues

RF tracking

RF tracking designates the process of synchronously varying LO and frontend filtering center frequencies. Due to the nonlinear relation between either capacity or inductance and frequency of an LC circuit, aforementioned equation

         1
f  = ----------   (1)
 0   2 π √(L C)

..., tracking is generally imperfect, with it being spot on at no more than three discrete points. Deviations then have to be minimized through component value selection and alignment. In general, tracking errors scale with the ratio of minimum and maximum covered frequency (obviously so, given that the influence of the nonlinearity grows accordingly).

It be noted that RF tracking can be implemented regardless of whether air cap, varicap diode or permeability tuning is employed. The case of PLL synthesized sets with RF tuning tends to leave people slightly confused, but one merely needs to understand that the PLL's VCO is a varicap diode tuned LO like any other, with an accompanying tuning voltage which in turn can be tapped off to serve for tuning tracking circuits. The tuning voltage basically has the same function as the (multi-gang) air cap's shaft that rotates all sections synchronously.

It does get a little tricky when LO and RF have to track at very different rates – imagine you have a receiver with a high 1st IF of e.g. 55.845 MHz that implements RF tracking on mediumwave. Going from 522 to 1620 kHz is a change of about 1.6 octaves, while at the same time the LO has to move no more than 0.03 octaves. In such cases, some level shifting may be applied to compensate for such grave differences in LO and RF tracking rates.

In general there are two methods of RF tracking alignment, two-point and three-point.

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Limiting in FM receivers

A limiter is an amplifier (generally with high gain) that clips the peaks of the amplified waveform. This turns a nice sine...

  ^ s(t) input signal
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...      ___ 
0 +/-----\-----/-----\-----/-----\-----/-----> t ___ lim
  |       \   /       \   /       \   /              levels
  |        -         -         - 
  |

... into a rectangular waveform:

  ^ l(t) limited signal
  |
  |+-----+     +-----+     +-----+     +...
  ||     |     |     |     |     |     |
0 +|-----|-----|-----|-----|-----|-----|-----> t
  ||     |     |     |     |     |     |
  |+     +-----+     +-----+     +-----+
  |

A good limiter will have low limiting levels and thus accept a wide range of input amplitudes with identical output. This can be used to strip amplitude modulation, which turns out to be handy for (improved) suppression of AM like lightning crashes.

However, one must not forget that limiting is severe nonlinear distortion of the input signal. This does not matter if there only is one single lonely signal in sight, but as soon as multiple ones arrive all at once, funny things tend to happen due to intermodulation distortion (potentially up to fairly high orders). For example, intermod generated in IF amplification stages between filters degrades effective selectivity. This is why concepts with limiting in the middle of filtering, as encountered e.g. with Kenwood's second-generation pulse-count detector tuners, should be looked at critically.

In cases where the budget for tubes or transistors was limited, some limiting in IF amplification stages was accepted in order to get decent AM rejection characteristics, but when this wasn't an issue, the IF strip was kept linear until after filtering. This can be seen in receivers as early as the early-1950s REL model 646 "Precedent", a tuner coming from a manufacturer of pro gear, which shows. In this rx, a manual RF gain control is included to keep the IF strip in linear operation at all times, the limiting is then carried out in following dedicated pre-limiter and limiter stages. BTW, when I saw the schematics (dated 1951 if I'm not mistaken), I was fairly impressed – a 5-gang (permeability tuned) frontend with dual RF amplifiers, the respectable number of 10 LC circuits for selectivity with 5 IF gain stages, followed by three pre-limiter and two limiter stages, finally being demodulated by what appears to be an early ratio detector. This level of effort was only found in consumer tuners about 20..25 years later, with some help from IC technology and ceramic filters.

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Mixer types and performance

As outlined under Intermod and spurs, real-life mixers are not pure multipliers. They vary widely in all kinds of (partly interdependent) performance parameters – port isolation, signal handling, intermodulation and dynamic range, conversion loss or gain and noise figure, LO drive levels, impedance matching. See 'Mixers, part 1' in Vol. 8 of the archived WJ tech notes (part 2 is equally worth reading).

Let me highlight an interesting correlation between intermodulation and noise related performance parameters, which ultimately finds expression in dynamic range: Say you have two mixers with very similar nonlinear characteristics, but one being noisier than the other (or more lossy, which amounts to the same), and a certain desired sensitivity level. Now the noisier mixer would have to be fed with higher signal levels (e.g. more amplification beforehand), and that in turn means that its undesired mixing products will rise in a non-linear manner (of course).
A mere 3 dB higher signal levels would increase 2nd-order intermod by 6 dB and 3rd-order intermod by 9 dB, degrading the respective intermodulation-free dynamic ranges by these amounts.

In practice, you'll also find this the other way round: Unspectacular-looking but low-noise mixers giving surprisingly good IMD performance due to low signal levels possible.

One can generally distinguish between additive and multiplicative mixers. Among additive mixers, ones with a dedicated oscillator or self-oscillating ones exist.

Basics: Switching mixers

When dealing with mixer theory, we have been assuming sinusoidal signals that are being multiplied. However, this multiplication can also be performed by one signal switching the other one on and off. Such a switching mixer can be treated as a linear multiplier mixer fed with a clipped (rectangular instead of sinusoidal) LO signal, as illustrated:

  ^ sine multiplying function
  |
  |  .-.         .-.         .-.         
  | /   \       /   \       /   \       ...
0 +/-----\-----/-----\-----/-----\-----/-----> t
  |       \   /       \   /       \   / 
  |        -         -         - 
  |
                    |  |
                   \|  |/
                    \  /
                     \/

  ^ switching multiplying function (1)
  |
1 |+-----+     +-----+     +-----+     + ...
  ||     |     |     |     |     |     |
0 ++-----+=====+-----+=====+-----+=====+-----> t
  |
  |
  |
                    —OR—

  ^ switching multiplying function (2)
  |
+1|+-----+     +-----+     +-----+     + ...
  ||     |     |     |     |     |     |
  +|-----|-----|-----|-----|-----|-----|-----> t
  ||     |     |     |     |     |     |
-1|+     +-----+     +-----+     +-----+
  |

The second type of multiplying function would be encountered in case of two-way switches, e.g. diode ring mixers.

Why can this type of function serve the same purpose? For this, we best take a look at the Fourier series of such a signal. In "Taschenbuch der Mathematik" (Bronstein, Semendjajew et.al.), we find for a 2π-periodic function of type (2) with amplitude a:

    4a  /         sin(3x)   sin(5x)       \
y = -- | sin(x) - ------- + ------- - ...  |
     π  \            3         5          /

For comparison, a sine with the same metrics would be

y = a sin(x)

So as you can see, there is one component in the rectangular signal that corresponds to the sine, so it can obviously be used for a mixer. What's the rest then?

Substituting x by ω t = 2 π f t, we find the other components to be at frequencies 3f, 5f, ... – these are odd-order harmonics. As outlined under LO Harmonics, these components will also generate mixing products, so RF signals that might cause trouble must be filtered out beforehand.

With a switching function of type (1), an additional DC component is present, which means that the RF signal is also let through as-is.

Practical examples for switching mixers include H-Mode mixers or regular FET, differential amplifier or diode ring mixers with a sufficiently high LO insertion level.

Why may switching mixers be preferred to linear mixers? Well, this has to do with conversion loss. If you see a mixer as kind of a variable gain amplifier (or attenuator) controlled by the LO signal that has a certain adjustment range, the switching case will enable a much larger amplitude of the LO fundamental when compared to linear operation, and thus also stronger desired mixing products, reducing mixer loss and noise figure. This, of course, comes at the cost of the mixer now also responding to LO harmonics, as outlined above.

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Additive mixers

Additive mixers are mixers that employ the nonlinear transfer characteristic of some device to generate the desired mixing products when fed with both RF and LO signals on the same port, similar to what we've seen with 2nd order intermod. However, they frequently take it one step further, basically implementing a switching mixer. How is this done? Consider a device with e.g. an approximately exponential transfer characteristic, like IB(VBE) in a bipolar transistor:

       ^ output
       |
       |                      .
       |                     .
       |                    .
       |                   /
       |                  /
       |                 /
\/\/\..|................/.
       |               / .
       |              /  .
       |            _'   .
       |          _-     .
_____..|_____..--       .
       +--+--------------+-------> input
          |              |
          A              B
          .              .
          .              .

          ^              ^
          |              |
          |              |

          /              /
          \              \
          /              /
          \              \
          /              /

Now presume that our RF signal is small, so small that it doesn't see the nonlinearity at whatever point on this curve it ends up on. Then imagine you add another signal of much greater amplitude that our RF signal "rides upon" – you guessed it, the LO signal. As this stronger signal sweeps a larger range of the transfer characteristic, for example between marked points A and B, small-signal gain for the RF signal varies. It is obvious that the small-signal gain δoutput / δinput at the marked points A and B is quite different: At point B you get quite a bit of output, while there's next to nothing at A.

This effect can be used to implement a switching mixer. You merely need an LO signal that has a fairly rectangular waveform and well-chosen LO amplitude and operating point (which determines the offset; for a symmetric LO signal it would be just in the middle between A and B in this example). The LO signal then switches RF signal gain dynamically, effectively performing a multiplication with a shifted rectangular waveform whose low and high levels correspond to the small-signal amplifications at points A and B.

There are several consequences we can draw from these considerations:

Best switching and strong signal handling capabilities would be achieved with a device having a transfer characteristic like this:

       ^ output
       |
       |                      .
       |                     .
       |                    .
       |                   /
       |                  /
       |                 /
\/\/\..|................/.
       |               / .
       |              /  .
       |             /   .
       |            /    .
_____..|___________/     .
       +--+--------------+-------> input
          |              |
          A              B
          .              .
          .              .

          ^              ^
          |              |
          |              |

          /              /
          \              \
          /              /
          \              \
          /              /

This kind of ideal device is, however, a little hard to find in practice. ;)
(Common emitter and common base circuits come reasonably close though.)

Typical real-life additive mixers are those found in the AM sections of 1960s/1970s transistor portables. Those generally use a bipolar transistor in a common emitter circuit for mixing, and the oscillator is either executed separately with a dedicated transistor or implemented by using the mixer itself for amplification (the aforementioned self-oscillating mixer). They are characterised by:

Ironically, in tube sets an additive mixer could actually have better noise and intermod properties than a multiplicative counterpart. This is because lower noise meant less preamplification required, and the difference in signal levels more than made up for the worse intermod characteristics.

A note on self-oscillating mixers: These are not easy to get right and optimize for dynamic range, as e.g. strong signals or capacitive loading of the antenna circuit (i.e. touching the antenna) may pull the LO, plus the interaction between RF and LO circuits makes alignment difficult. Nonetheless they remained common in FM frontends – where they were used in common base configuration together with an RF amp – up to the 1980s, especially when space and budget were tight.

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Multiplicative mixers

It is also possible to build true multiplicative mixers. This is typically done with J-FETs, dual-gate MOSFETs (or a cascode arrangement) or diode ring mixers, though single bipolar transistors can also be used. Amplifier-type multiplicative mixers (transistor in common emitter circuit or FET in common source circuit, or differential amplifier) are quite easy to understand – their amplification is modulated dynamically.

Let's look at this bipolar transistor in common emitter configuration with current feedback through an emitter resistor, for example:

               ...
               |
         .     +---- output
         .     |
         .    /
         |  |/ 
signal --+--|
            |\  
              \|
               |
               +------> LO input
               |
               _
              | |
              |_| R
               |   E
               |
              ---
               - 

Its small-signal voltage gain is approximately

        R
         C         1
A  ≈ -------- ~ --------
 V   1 + S R    1 + S R
            E          E

Which means that it decreases if the emitter resistor increases. Now imagine that additional current is pushed through RE from the LO input drawn. The voltage over RE increases, but the transistor still runs at about the same current, so it appears like RE has momentarily gotten bigger, with the respective effect on AV.

This gain control function can also be implemented in a more direct way. You can use a transistor as a variable current source for a differential amplifier, for example. (An approximation for a current source is a large resistor, and a transistor can be used as sort of a variable resistor after all. The differential amplifier's differential voltage gain depends directly on the sum current through both its transistors.) It is also easy to build a switching mixer this way, as a differential amplifier's halfway linear differential input voltage range is quite limited (assuming no emitter degeneration to be present) – so the LO signal would go to the differential amplifier and the RF input would control the current source.
If you look at the schematics of 1970s Panasonic shortwave portables like RF-2200 and RF-4800, you will find just such an arrangement for the first mixer. It is equally useful if you need a gain controlled amplifier for IF-level AGC. A Gilbert cell is an extension of the same concept that employs two such gain controlled differential amplifiers. for mixing.

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Single-balanced mixers

It is possible to suppress certain unwanted mixing products when using a mixer arrangement that accepts balanced (rather than single-ended) input or gives balanced output on one port.

For example, the gain-controlled differential amplifier arrangement outlined earlier can be used as a single-balanced mixer or modulator – unbalanced RF and LO inputs, balanced IF output.

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Double-balanced mixers

Double-balanced mixers take the idea of single-balanced mixers a step further. They use two mixers, and two of the three ports are balanced.

Here's one drawn with balanced RF input and IF output, but unbalanced LO input (other combinations are equally possible, for example the 1st mixer in the Sony ICF-6700W/L middle-class shortwave receiver or Onkyo T-4711 FM tuner had a balanced LO and unbalanced RF port).

                RF in
                  |
  |               |
| |----ccccccccc--+
  |    ---------
    +--ccccccccccc+ccccccccccc--+
    |             |             |
    |             |             |
    |           -----           |
    |             -             |
    |                           |
    |           +---+           |
    |           | ~ | LO        |
    v           +---+           v
 +-----+          |          +-----+
 |     |          |          |     |
 |  X  |<---------+--------->|  X  |
 |     |                     |     |
 +-----+ M        -          +-----+ M 
    |     2     -----           |     1
    |             |             |
    |             |             |
    +--ccccccccccc+ccccccccccc--+
  |    ---------
| |----ccccccccc--+
  |               |
                  |
                  v 
                IF out

Eliminating the input and output transformers (which tend to be handy for impedance matching as well) for a more abstract view, we arrive at something like this:

                RF in
                  |
                  |
    +-------------+-------------+
    |                           |
    v                           |
 +-----+                        |
 | 180|                        |
 +-----+                        |
    |                           |
    v                           v
 +-----+         LO          +-----+
 |     |        +---+        |     |
 |  X  |<-------| ~ |------->|  X  |
 |     |        +---+        |     |
 +-----+ M                   +-----+ M 
    |     2                     |     1
    v                           |
 +-----+                        |
 | 180|                        |
 +-----+                        |
    |           +---+           |
    +---------->| + |<----------+
                +---+
                  |
                  |
                  v 
                IF out

We can see that the two mixers receive the RF signal with opposite phase, likewise their outputs are effectively subtracted later on.

Now look at our nonlinear mixer model from the advanced intermodulation cases again.

We can describe the RF signal voltage after the respective nonlinearity as:

VRF' = k0 + k1 VRF + k2 VRF + k3 VRF + ...

Same goes for the LO signal.

When these are multiplied, we get all possible combinations of terms and coefficients. That looks pretty messy. We are not, however, interested in those original coefficients at all, but rather those of the components encountered after mixing, which are a function of the former. The latter coefficients can be written in matrix form:

1 VRF VRF VRF VRF4 VRF5 ...
1 a00 a01 a02 a03 a04 a05 ...
VLO a10 a11 a12 a13 a14 a15 ...
VLO a20 a21 a22 a23 a24 a25 ...
VLO a30 a31 a32 a33 a34 a35 ...
VLO4 a40 a41 a42 a43 a44 a45 ...
VLO5 a50 a51 a52 a53 a54 a55 ...
... ... ... ... ... ... ... ...

In other words, our output looks like:

Vout = a00 + a01 VRF + a02 VRF + a03 VRF + ... + a10 VLO + a11 VLO VRF + a12 VLO VRF + ... + a20 VLO + a21 VLO VRF + a22 VLO VRF + ... + ...

I think you get the point. a11 VLO VRF is our desired term.

This at the same time already is the output of the first mixer, M1:

Vout,1 = a00 + a01 VRF + a02 VRF + a03 VRF + ... + a10 VLO + a11 VLO VRF + a12 VLO VRF + ... + a20 VLO + a21 VLO VRF + a22 VLO VRF + ... + ...

The second mixer, M2, is fed an inverted RF but the same LO signal, so all the odd powers of VRF get a negative sign:

Vout,2 = a00 - a01 VRF + a02 VRF - a03 VRF + ... + a10 VLO - a11 VLO VRF + a12 VLO VRF - ... + a20 VLO - a21 VLO VRF + a22 VLO VRF - ... + ...

After the second inversion, M2's output obviously looks like this:

Vout,2' = -a00 + a01 VRF - a02 VRF + a03 VRF - ... - a10 VLO + a11 VLO VRF - a12 VLO VRF + ... - a20 VLO + a21 VLO VRF - a22 VLO VRF + ... - ...

Since the two mixers are assumed to be identical, the magnitudes of the coefficients are exactly the same. What differs are the signs. Therefore we'll be looking at matrices of coefficient signs now. For M2's output after the second inversion (the one we just looked at), we get this stripe pattern:

1 VRF VRF VRF VRF4 VRF5 ...
1 - + - + - + ...
VLO - + - + - + ...
VLO - + - + - + ...
VLO - + - + - + ...
VLO4 - + - + - + ...
VLO5 - + - + - + ...
... ... ... ... ... ... ... ...

For the first mixer, M1, the same matrix obviously is quite unexciting:

1 VRF VRF VRF VRF4 VRF5 ...
1 + + + + + + ...
VLO + + + + + + ...
VLO + + + + + + ...
VLO + + + + + + ...
VLO4 + + + + + + ...
VLO5 + + + + + + ...
... ... ... ... ... ... ... ...

The addition performed equals a matrix addition in this representation, which makes the whole process very simple to deal with. Imagining "+" to be +axy and "-" to stand for -axy, the addition results in the following matrix of factors:

1 VRF VRF VRF VRF4 VRF5 ...
1 0 +2 0 +2 0 +2 ...
VLO 0 +2 0 +2 0 +2 ...
VLO 0 +2 0 +2 0 +2 ...
VLO 0 +2 0 +2 0 +2 ...
VLO4 0 +2 0 +2 0 +2 ...
VLO5 0 +2 0 +2 0 +2 ...
... ... ... ... ... ... ... ...

We find that all the terms involving even-order powers of VRF cancel out! Not bad. A bunch of mixing products less to worry about. In addition, not one LO harmonic makes it to the output, though the RF does.

When swapping the roles of RF and LO port, this can be used to get rid of mixing products stemming from even-order LO harmonics. Especially the 2nd one may be bothering in practice. Now no RF makes it to the output (good if the IF chosen is in the tuned reception range), but the LO signal and its odd-order harmonics do (which generally is less dramatic, as the LO usually runs above the IF and can be filtered out). The matrix of coefficient scaling factors for this case:

1 VRF VRF VRF VRF4 VRF5 ...
1 0 0 0 0 0 0 ...
VLO +2 +2 +2 +2 +2 +2 ...
VLO 0 0 0 0 0 0 ...
VLO +2 +2 +2 +2 +2 +2 ...
VLO4 0 0 0 0 0 0 ...
VLO5 +2 +2 +2 +2 +2 +2 ...
... ... ... ... ... ... ... ...

Practical examples of double-balanced mixers include diode ring mixers and the Gilbert cell mixers widely used in ICs up to microwave regions (as a radio geek, you might encounter the NE602 or TA7358AP, or the mixer in the TDA1072/1572 or TA8132AN; just about any newer quadrature detector or analog PLL stereo decoder would contain one as well). A Gilbert cell mixer basically uses a pair of differential amplifier mixers (see Multiplicative mixers) whose variable current source transistors in turn form a differential amplifier stage themselves.

You might have guessed it – one can also build a triple-balanced mixer. This takes two dual-balanced ones which in turn are used in a dual-balanced configuration. All ports – RF, LO and IF – are balanced then. The effort and high LO drive levels involved generally mean that triple-balanced mixers tend to be used for very high-performance applications only. Some Gilbert cell implementations, however, like the Motorola MC1496 modulator, also allow for triple balanced operation.

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Sampling mixers

Sampling a signal at a certain frequency (by means of sample-and-hold circuitry) can also be used to form a mixer. This is due to the inherent frequency periodicity of a sampled signal. Both upmixing of f0 to f = n * fS ± f0 and downmixing of f0 = n * fS ± f to f are possible. The latter can be employed to implement a modulo-f phase detector and ultimately PLL.

Frontend concepts and gain distribution

The frontend for a given application will be strongly influenced by the signal handling requirements associated with it. A few examples:

It is clear that an application with very low signal levels will benefit from lots of gain from a low-noise amplifier up front. Typically there is a low-noise amplifier with moderate gain first, then another one with more gain, which in total gives an amplifier whose noise figure is dominated by the LNA but which has a good bit of gain, so its noise figure in turn dominates the rest of the receiving system.

This same setup would, however, be absolutely deadly when used in frequency ranges with high signal and noise levels. The low noise figure would be of no use since external noise would dominate everything, but the poor mixer would see very high signal levels and generate intermod like crazy.

Therefore a practical receiver needs to find its place somewhere between these extremes. Thankfully there is an instrument that makes it possible to find a good balance, namely the noise figure and Friis' formula for the noise figure of multiple cascaded stages. Surprisingly little RF gain may be needed for a pretty low noise figure, especially when low-noise devices are used, explaining why a relatively humble-looking frontend on paper may still give good performance, as in this case. The only variable remains antenna noise figure, i.e. how much noise the antenna "sees". This, of course, would depend strongly on the type of antenna used, which on shortwave might vary from a telescopic aerial to a big loop or Beverage. A receiver that adapts well to a wide range of antennas remains a non-trivial task.

When both weak and strong signal handling are required, i.e. a large input dynamic range is needed, there are two basic approaches between which real-life receivers tend to be found:

  1. Classic approach: Use whatever (usually relatively weak) mixer you have, filter out unwanted mixing products and reduce sum signal levels by extensive RF tracking. This was typically found in analog-tuned receivers up to the 1960s. Up to five tracking RF circuits were used in those days.
  2. Modern-day brute-force approach: Use minimal frontend filtering and employ the best mixer you can get a hold of. This kind of concept started to appear with PLL synthesized sets with high 1st IFs, understandably so since frontend tracking became a nontrivial task with these. In addition, this approach allows very wide tuning ranges.

In practice, neither extreme tends to give ideal results – the first one has its share of problems with in-band intermod, while the second one still shows some 2nd-order intermod. Therefore most current shortwave communications receiver / transceiver designs employ good mixers with an array of band filters to bring sum signal levels down (with the bottleneck in terms of 2nd-order intermodulation not uncommonly being the switching diodes used…). FM broadcast receivers have always stayed closer to the first approach, with only occasional appearances of balanced mixers in the 1980s and 1990s; the use of RF AGC has made life a good bit easier for their mixers.

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Choice of IF bandwidths

While the first mixer tends to be a critical spot, it is important not to neglect following stages. Intermodulation distortion generated in them may still worsen selectivity (as CW operators or the owners of some FM tuners may be able to tell you) and degrade performance on intermodulation-sensitive modulation types (OFDM! – see this example with DRM). (It's not like AM would be intermod insensitive, but first many regular AM demodulators have pretty lousy distortion specs anyway and second the human ear is quite tolerant.)

In practice, one would usually try to keep IF bandwidths on the first IF(s) as narrow as possible, as this gives the mixer afterwards less choice among signals to generate intermod from, along with reducing overall sum signal levels, which equally benefits strong signal handling. There are a few concepts which violate this rule, i.e. use wideband IFs (i.e. classic Wadley Loop, Sony's "dual conversion light"), but these are generally not known for highest dynamic range in return. Several 1950s-vintage pro-grade receivers with wider IF ranges (used to provide better frequency readout accuracy) used tracking filters to tackle this problem.

Interestingly it is possible to make IF bandwidths too narrow, as some amateur radio transceiver manufacturers using high 1st IFs (70+ MHz) found out the hard way. In these cases the crystal IF filter starts limiting in-band intermodulation performance, rather than the mixer following it (there have also been cases where narrower roofing filters have degraded out-of-band performance, at least that's how I'd interpret the FT-2000 measurements; even John Thorpe got bitten by this problem). I assume the high circuit Qs required increase voltage levels this much that the quartz crystals become appreciably nonlinear (and those already are something a little different from your average clock crystal). Therefore some recent designs have reverted to 1st IFs of around 10 MHz, at least for the classic shortwave amateur radio bands.

This example shows how basically any component in the signal path may degrade linearity once the classic trouble spots (mixers and amplifiers) are out of the way. For example, you better make sure that ferrite cores in band filters and transformers don't saturate. Essentially all the components need to be evaluated carefully if dynamic range is to be maximized.

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Pitfalls of diode-switched bandpass filters

An array of switched bandpass filters at the input is commonly seen in shortwave communications receivers and transceivers. Its purpose is quite obvious, reducing sum signal levels for the preamplifier (if any) and first mixer. While some receivers employ relays to select one of these filters, most designs make use of diode switching. It is obvious that a diode as a nonlinear component may potentially generate intermodulation, and manufacturers tend to make sure that bias currents in such a switching application are generous (for the diode may stop conducting if peak RF current equals or exceeds bias current) and dynamic impedances kept low. However, there is an interaction between filter topology and diode-related nonlinearity that must have eluded most receiver designers back in the 1980s and 1990s.

There are two ways you can build a bandpass filter (duality), one has low stopband impedance and the other has high stopband impedance. It's easy to tell which one you're looking at, the first has a parallel element (e.g. parallel LC) to ground at the ends, the second has a series element (e.g. series LC) in series.

So how do these cases relate to the use of band switching diodes?

  1. High stopband impedance: Signal currents at the filter input are maximum in-band, and there's not much happening outside. Voltage levels at the input may rise to twice the in-band levels, more if a high-impedance antenna is connected, but that's a problem for the passives at most and usually won't be sufficient to get any of the other bands' switching diodes out of reverse bias (which would take several volts).
  2. Low stopband impedance: Signal currents at the filter input (through the diode) are minimum in-band and maximum outside. (Outside, the 50 Ω source feeds a short, which doubles current vs. a 50 Ω load.) In such a low-impedance environment, the dynamic impedance of the switching diode is not negligible, and worse yet, the high RF current levels will do their best to modulate it. If any in-band mixing products result, the diode will happily give these off to the 50 Ω load presented by the filter there. Oops!
    For another side effect, any RF amplifier in front of the band filters has to work into a very low impedance out of band, which is not likely to do its intermodulation performance any good.

Thus you'd be well advised to pick your filter topology wisely! (Circuit simulation is likely to be helpful for tweaking, too.) If you want to compare the two filter topologies using LTspice, here's a sample octave bandpass (Chebyshev, 0.1 dB).

For a good example of how this can go wrong, take the Sony ICF-SW55 receiver. It uses 50 Ω filters, but its designers forgot to adjust switching diode biasing to this low impedance (they run these VHF switching diodes at a modest 0.6 mA). In addition, the filters use a topology with low stopband impedance, which amuses neither the diodes nor the whip antenna RF preamplifier. Here are schematics of both the original highest octave shortwave bandpass and same converted to dual topology, again for LTspice.

Suppose you have an existing filter topology that works well, but happens to be of the low stopband impedance type. How do you convert it to dual topology while keeping the same nominal impedance? That's quite simple if you keep in mind that normalized impedance z = Z/Z0 becomes normalized admittance y' = Y'/Y0 = Y'Z0 in the dual filter. Therefore it follows that dual impedance is

       2
      Z
       0        2
Z' = --- = Y * Z
      Z         0

This means that parallel and series circuits as well as inductors and capacitors exchange their roles, with new values of

      2
L' = Z * C
      0

      L
C' = ---
      2
     Z
      0

It's always a good idea to check simulated filter response in case you have miscalculated something. If things get a little tricky topologically, just exchange "series" and "parallel". For example, a series connection of two parallel LC circuits in series becomes a parallel connection of two series LC circuits in parallel.

Things become a little more complicated if the filter has to perform an impedance transformation. After all, the dual filter works the same for admittance and would transform in the wrong direction. You have to turn the filter around and normalize original filter components to original output impedance (so the simple L' and C' formulas given above no longer apply and will need to be re-derived), then it should work again.

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What's the deal with these intercept points?

In a nutshell, intercept points are one (very popular) means of characterising nonlinearity performance of components in the signal path. They can be quite useful assuming you know about their little ifs and buts. So let's look at this topic a little more closely.

Here's the commonly used means of specifying performance in RF components:

A component could be just about anything – an amplifier, a mixer, a diode-switched bandpass filter, an attenuator, whatever. Even harmless-looking passive devices are more or less nonlinear – while a resistor network may prefer to burn up before developing significant nonlinearity, inductors or transformers with ferrite cores are quite a different story.

Noise figure is one of those classic textbook topics. If you're not familiar with it, here's a nice intro. Now you may want to interface this with classic input-referred voltage and current noise densities in a circuit – then look no further than the Wikipedia entry on thermal noise, and don't forget your impedance transformations.

Intercept points are obtained by plotting logarithmic output levels (usually in dBm) vs. logarithmic input levels of both a wanted signal and resulting nth-order nonlinear components. As we have seen when looking at intermodulation distortion in mixers, the amplitude of these nonlinear components grows more quickly than wanted signal amplitude, but both traces are straight lines when plotted loglog. (2nd-order products rise 2 times as fast, 3rd-order ones 3 times, etc.) Therefore it is possible to extrapolate them to some intersection point. The coordinates of this point are – you guessed it – the nth-order input and output intercept points.

Which ones you'll find specified for a particular kind of device is usually governed by "bigger is better". Thus you may find output IP3 for an amplifier, while a passive diode mixer with its inherent loss will have input IP3 specified. Converting between the two is easy, just subtract gain to go from output to input IPn.

Now for the little ifs and buts:

Speaking of dynamic range, this is usually defined for each order of nonlinearity. In a "well-behaved" system, it's the difference between wanted signal and distortion product when the latter is just starting to rise out of the noise floor. But what is "the noise floor"? As SM5BSZ points out, that depends on measurement (noise!) bandwidth. That's the B factor in the 3rd-order SFDR formula presented in this blog entry (note that the factor of G is the result of his IP3 being OPIP3; then it's consistent with this appnote). Oops. If you want to make comparisons between different receivers, it's a good idea to determine noise bandwidth and refer everything to, say, 1 Hz.

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More spurious signals

In Intermod and spurs we have seen that a receiver may generate unwanted signals through a combination of RF and LO harmonics. However, other spurious signals may be appearing even without any received signal whatsoever, i.e. they're purely internally generated artifacts. We'll look at some typical ones now.

DC/DC converter radiation

Battery operated equipment with a PLL synthesizer has to employ a DC/DC converter (essentially a cross between an oscillator and switch-mode power supply) to generate a supply voltage high enough for meaningful varactor diode tuning, usually 13..15 V. It works at a high frequency (typically around 2..3 MHz) which enables it to use a small transformer. For obvious reasons, this means that its input and output must be appropriately choked and filtered and it should be shielded. Some receivers skimp on the filtering and then have some PCB traces radiate the DC/DC frequency and its harmonics – easily noticed if it's a shortwave set employing a telescopic antenna. Thrifty designers will at the very least choose the DC/DC frequency such that the desired reception bands are not affected.

LO-related mixing products

Without RF input, a well-executed single conversion superhet (without DC/DC noise and such) won't exhibit any spurious signals. This changes as more IFs come into play. Here we have multiple mixers and LO signals that may interact.

Now in an ideal receiver, all sections are well shielded and signals only go where they're supposed to. In real life, things can be quite different, especially in compact and / or inexpensive portable receivers. Here you may find LO signals everywhere. What does that mean in a dual conversion set with high 1st IF, for example?

2nd mixer

Let's say the 1st LO signal with its associated harmonics got into the 2nd mixer which in turn is fed with an LO signal that is not free from harmonics either. For a spur to be noticeable, it would have to end up on 2nd IF level:

 
m * f    ± n * f    = ±f    , m,n ∈ {1, 2, 3 ...} 
     LO1        LO2     IF2

Now in this case, you typically have an inverting 1st mixer and non-inverting 2nd mixer:

f   = f  + f
 LO1   R    IF1

f   = f   - f
 LO2   IF1   IF2

This gives us

 
m * (f  + f   ) ± n * (f    - f   ) = ±f
      R    IF1          IF1    IF2      IF2

Taking into account that typically fIF1 >> fIF2, we find that the left side will never become much smaller than fIF1 in the "+" case, so its chances of eqally with the right side are pretty slim. Therefore we'll discard this option now:

 
m * (f  + f   ) - n * (f    - f   ) = ±f
      R    IF1          IF1    IF2      IF2

This result can be solved for fR:

      1   /                                \
f  = --- | (n - m) * f    + (±1 - n) * f    |
 R    m   \           IF1               IF2/

Please note that fR is the frequency that the receiver is set to. If it became negative, we'd be looking at a different receiver (non-inverting 1st mixer), so all such results are out. This affects all the cases in which m > n, and most m = n. The only interesting m = n case remaining is m = n = 1, where one result is left:

fR = 0

A receiver that goes down to zero Hz like an AOR AR7030 really lets you tune this one in. You'd also find it in a single conversion receiver actually, as there always is some LO-IF leakage. Thus if you want to get into ULF reception, better use something that is not a classic superhet, maybe a direct conversion receiver or sampling + FFT based setup.

Let's look at some of the other spurs (with m < n) in an example. Say we have a shortwave portable with fIF1 = 55.845 MHz, fIF2 = 455 kHz and a reception range of like 3 MHz to 30 MHz. Then these are the first few spurs you'll find:

m n m + n fR / kHz
2 3 5 27467.5
27012.5
3 4 7 18160
17856.66...
4 5 9 13506.25
13278.75
4 6 10 27353.75
27126.25
5 6 11 10714
10532
6 7 13 8852.5
8700.833...

The author compared four receivers employing this sort of concept – Sony ICF-SW7600, ICF-SW7600G, Redsun RP2000 and Eton/Lextronix E100 "new version". The two Sony models did the best job in terms of spur suppression, with only the first two spurs ((m,n) = (2,3) case) qualifying as strong. The Redsun model came in behind, showing all but the last four, and the E100 placed last, still detecting the 8700.833... kHz spur weakly. Generally the spur frequency seemed to have at least as large an influence on strength as the order.

When examining things manually, you are likely to miss a few spurs. A spreadsheet, like this one, can be quite helpful in finding them. In case of the E100, this allowed for finding several more spurs, especially around 27 MHz, the highest-order one being 27285.5 kHz with (m,n) = (10,15).

1st mixer

Spurs may just as well be created in the first mixer, meaning that the 2nd LO leaks back into the RF input. This came to the author's attention by the signal strength of some of the spurs in a couple of receivers (e.g. DE1102, ICF-SW7600) depending on RF attenuator setting.

The math is quite similar to the previous case here:

 
m * f    ± n * f    = ±f    , m,n ∈ {1, 2, 3 ...} 
     LO1        LO2     IF1
      1   /                             \
f  = --- | (n - m ± 1) * f    - n * f    |
 R    m   \               IF1        IF2/

In fact, we can show that the spurs generated will be the very same ones. Defining n' = n ± 1 and rewriting the expression for fR yields:

      1   /                                    \
f  = --- | (n' - m) * f    + (-/+1 - n') * f    |
 R    m   \            IF1                  IF2/

+/- becomes -/+, but other than that the expression has the same shape as for the 2nd mixer case. So unsurprisingly, our spreadsheet shows the same spurs, just in the other table and shifted a column to the left or right.

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Ensuring optimum frequency stability

Topological approaches

As a rule of thumb, the more independent reference oscillators a receiver has, the more it can drift (either in the short term or due to aging). This is why one tries to reduce their number to a minimum in higher-grade receivers – up to the point where every oscillator signal in the receiver is derived from a single master clock! The advantages are obvious – adjust one item during realignment, and everything is back on frequency, plus you may be able to afford using a more stable oscillator type to begin with.

The "single reference clock" approach is typically used in high-grade communications receivers and transceivers, the pro stuff may also include an input for an external reference. As an example from the "semi-pro" class, I'll mention the venerable AOR AR7030. This receiver employs a temperature compensated crystal oscillator at an odd 11.13625 MHz, exactly one fourth the 2nd LO but also controlling the DDS (with 1st LO generation including premixing, and BFO) and even the microprocessor.

A notable preceding approach is drift cancellation, which can be employed in multiple conversion superhets. The basic idea is to make use of a potentially drifty oscillator signal in both an upmixing stage and a following downmixing stage, so that overall its influence cancels out. The filtering in between the mixers must allow for a slight frequency variation, of course. One of the oscillator signals is usually mixed upwards or downwards using another, relatively stable oscillator.
As outlined earlier, the idea was first employed in the Wadley Loop concept. Drift cancellation was, however, also implemented in receivers using PLL frequency synthesis, particularly ones employing premixing in the PLL – both "semi-synthesized" sets (where this was quite natural) like the Kenwood R-1000 or Yaesu FRG-7700 and "regular" PLL sets like the Sony ICF-2001D/2010 and ICF-SW77. Here the 2nd LO frequency (from some crystal oscillator) also enters into 1st LO frequency generation, so their difference remains constant, and any frequency inaccuracy or drift in the 2nd LO only shifts signals around on the 1st IF, which is easily wide enough to tolerate this. Effective frequency stability is the same as for a single-conversion receiver using the 2nd IF!

Incidentally, the "single reference clock" approach has the same effect on frequency stability, so it includes drift cancellation.

Drift cancellation also has other uses, like dedicated IF shift (filter passband shift). A single-conversion SSB receiver is basically a dual conversion receiver with a final IF of zero, so one can easily apply the same trick to shift the filter passband around (single passband tuning, PBT). Various Kenwood transceivers around 1980 made use of this, like TS-120, TS-130 and TS-530, with the bigger dual conversion TS-830 having IF shift on both IFs and thus allowing a variable bandwidth (dual PBT). If there is any drift in the oscillators, this only affects filtering (not reception frequency stability) and is easily corrected by the operator if needed. (The main source of reception frequency drift in these units is the analog PTO, either directly due to temperature stability or indirectly due to supply voltage variation, with the latter addressed by several modifications and maintenance procedures to ensure a stable voltage and reliable ground connection.)

If the drifty oscillator in question also happens to contribute significant amounts of phase noise (e.g. in a Wadley Loop receiver), drift cancellation has another advantage: It also cancels part of that phase noise! Obviously if a PLL is involved in the canceling loop, the cancellation will only be effective within its bandwidth, but even so it may well achieve a significant improvement.

[TS-530 frequency configuration diagram]
Frequency configuration of Kenwood TS-530 HF transceiver using IF shift / drift cancellation.

(excerpt from service manual as available online)

Enhancing reference stability

If the number of reference oscillators is already down to one, what more can one do to improve stability even further?

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Automatic Gain Control (AGC, AVC)

AGCs are a fairly special topic and not widely understood well. Maybe the following sections help in improving this for both the reader and the author.

Motivation

The need for AGCs came about when amplitude modulation (AM) became more widely used. The problem was that a weaker received signal would also have less amplitude variation (absolutely speaking) and thus give weaker output. With a non-ideal AM detector it would be worse still. Not too much fun if your signal strength varied considerably over time! This, however, is common e.g. on shortwave. Lots of volume knob action there – provided your set had one at all.

There are other uses of AGCs as well, of course. They also tend to be handy for keeping gain stages or mixers in their linear range, reducing intermodulation distortion at the potential cost of higher noise or less sensitivity. You may have wondered why AM receivers with limited AGC range tend to become very distorted and ultimately "speechless" on very strong stations – well, if an IF stage runs into clipping, you have a nice limiter there, a fine tool for stripping off AM.

A first look

The basic idea of an AGC for an AM receiver goes like this:
Your envelope detector, being a rectifier, happens to give you a DC component – otherwise discarded – that grows with increasing signal strength (quite linearly so if it does a good job).
Now what if you had some amplifier or attenuator stage earlier in the receiver which is voltage controllable? Feeding our DC component to this could be used for accomodating varying signal strength. If the output were weaker than desired, the gain would be turned up or the attenuation reduced, and vice versa.

/|\
 |   +-----+    +-----+    +-----+    +---------+
 |   |     |    | VCA |    |     |    |   Det   |
 |   |     |    |     |    |     |    |         |
 |   |     |    |   /||    |     |    |    |    |
 +---| ... |--->|  α  |--->| ... |--->| _|\|___ |--+--> Out
     |     |    | /   |    |     |    |    |    |  |
     |     |    |     |    |     |    |    |    |  |
     |     |    |     |    |     |    |         |  |
     +-----+    +-----+    +-----+    +---------+  |
                   ^                               |
                   |           +-----+             |
                   |           | LPF |             |
                   |           | _   |             |
                   +-----------|  \  |<------------+
                               |   \ |
                               |     |
                               +-----+

This basic approach applies to pretty much any AGC, even if it's not an AM receiver we're looking at. The only major difference is that other applications typically don't give you an AM detector for free and it has to be added manually.

In practice, usually some "translation" is required for the VCA stage, and in addition it is beneficial to "blow up" the voltage range, so you'll typically also find an amplifier stage in the feedback loop.

/|\
 |   +-----+    +-----+    +-----+    +---------+
 |   |     |    | VCA |    |     |    |   Rect  |
 |   |     |    |     |    |     |    |         |
 |   |     |    |   /||    |     |    |    |    |
 +---| ... |--->|  α  |--->| ... |--->| _|\|___ |--+--> Out
     |     |    | /   |    |     |    |    |    |  |
     |     |    |     |    |     |    |    |    |  |
     |     |    |     |    |     |    |         |  |
     +-----+    +-----+    +-----+    +---------+  |
                   ^                               |
                   |     +-----+                   |
                   |     | Amp |      +-----+      |
                   |     |     |      | LPF |      |
                   |     |  /| |      | _   |      |
                   +-----| / | |------|  \  |<-----+
                         | \ | |      |   \ |
                         |  \| |      |     |
                         | K   |      +-----+
                         |  A  |
                         +-----+

Now this very much looks like an exercise in control theory, doesn't it? It is, however, not a trivial one, as the concept is inherently nonlinear. We will look at both linear and nonlinear models later on.

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Ideal and real-life AGC action

How should the AGC be behaving anyway? Here it's useful to distinguish between two cases:

  1. Static AGC characteristic
  2. Dynamic AGC characteristic
Static

The static characteristic for an AM receiver would typically look like this:

  1. For most of the input signal strength range, output should be as constant as possible.
    (In practice it does tend to rise a little. This is a function of AGC loop gain and VCA characteristics.)
  2. It typically does not make much sense to bring up background noise to the same level as a "real" signal. Therefore the AGC only needs to do anything when a half-decent SNR is reached (a typical value being about 3 dB).
    The location of this point, commonly called "AGC knee", is usually governed by available overall maximum gain in the receiver. Under the AGC knee, output will scale linearly with input.
  3. In practice, there will also be a maximum signal strength above which the AGC can no longer keep the level constant. This is because real-life variable gain (attenuation) stages always have a minimum gain and thus a finite gain adjustment range (typically about 40..60 dB per stage). The overall AGC range is therefore governed by the product (or sum if in dB) of the gain adjustment ranges of all the variable gain stages in the receiver.

Want to see some real-life static AGC measurements? Here are some at Clifton Laboratories, and you can also find signal and noise plots for JRC NRD-525, AOR AR7030 and Sat-Schneider DRT1.

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Dynamic

In the dynamic case, the AM receiver designer has to find a compromise between the elimination of fading and the preservation of real modulation. Consider what would happen if the AGC were very fast (i.e. no lowpass filtering whatsoever) – the AGC would attempt to level out any kind of AM. Quite unfortunately, fading and AM are exactly the same. Fortunately, fading in practice frequently is not too fast, and there typically isn't any really deep bass on AM stations. However, it is clear that a choice of multiple AGC speeds may be of use – slower for less bass distortion during stable conditions, faster for accomodating quick fading.

Now let's investigate the role of the lowpass filter. The rectifier – filter setup should seem quite familiar from the discussion of AM diode detectors, and in fact this is pretty much the same thing. Only the time frames are different – here it's not the tradeoff between tracking the fastest-slewing modulation components and suppression of IF-level components, but between tracking signal strength changes well and not reacting too much to the lowest-frequency components of the modulation.
Our charging and discharging time constants τc and τd make an appearance here as attack time and decay time.
In order to achieve a steeper transition between "fading" and "bass" frequency ranges and therefore either better signal change tracking or less bass distortion (or both), higher-order filtering may be used. For the effect of 2nd vs. 1st order filtering on low-frequency distortion in what seems to be a linear AGC, see Fig. 5 in the TDA1572(T) datasheet.

Depending on what the AGC is supposed to be used for, τc and τd may or may not be equal. (When receiving speech in SSB, a short attack and long decay time tend to be useful, while an FM signal affected by random fading can be treated just as well with symmetric attack and decay times.) When using a high-bandwidth AM detector and following it up with a buffer, a following filter will show symmetric action for attack and decay. In order to make things unsymmetric again, inserting a diode is needed.

An additional function of the loop filter is keeping the loop from becoming unstable. (Open-loop gain must be down to 1 before open loop phase shift reaches -180!) See compensation in audio amplifiers.

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VCAs

The types of VCAs used include voltage controlled amplifiers and voltage controlled attenuators. In a shortwave portable, you'd typically find PIN diode attenuators in the frontend (which does not have to deal with huge signal levels) and voltage controlled IF amplifiers in ICs. You can find more on various kinds of VCAs in this term paper.

AGC modelling

dB-linear AGC

A central problem in the description of AGCs is the presence of a voltage-controlled amplifier, an inherently nonlinear device (it is, after all, a multiplier). There is a trick, however, that allows getting rid of this problem: Use logarithmic signal levels, a logarithmic amplifier after the detector and a VGA with an exponential (i.e. dB-linear) control characteristic as the VCA. You will find an explanation in this term paper. (BTW: The explanation for V2 on p.II is not correct; it arguably applies to V1 where all gain stages are at maximum gain.)

This is what the dB-linear model of the AGC loop outlined in the paper looks like (with some extra signal gain included):

                    G
                     dB
                    |
i                   |                 o
 dB                 v                  dB
----->(+)----------(+)----------+--------> 
       ^                        |
       |                        |
       |                        |
     +---+                      |
     | a |                      |
     +---+                      |
       ^                        |
       |       +------+         |
       |       |      |       - v
       +-------| F(s) |<-------(+)
               |      |         ^ 
               +------+         |
                                |
                          +-----------+
                    V --->| 20 log(e) |
                     R    +-----------+
          i               G         20*log(e) * a * F(s) * V
           dB              dB                               R
o   = ------------ + ------------ + -------------------------
 dB   1 + a * F(s)   1 + a * F(s)         1 + a * F(s)

That looks fairly tame – however, there is a catch: Here the filter, represented by its Laplace transform F(s), must be dB-linear! In other words, this model does not apply to your average straightforward rectifier – filter – amplifier setup since it requires that a logarithmic amplifier (for linear → dB conversion) be present in front of the filter. Here's a sample application of a dB-linear AGC that includes log amp and dB-linear amp/att ICs.

Something quite easily done in the dB-linear AGC model is an extension of the number of VCAs, commonly carried out in practice to increase AGC range and loop gain.

             G                    G
              1dB                  2dB
              |                    |
i             |                    |                 o
 dB           v                    v                  dB
----->(+)----(+)---->(+)----------(+)----------+--------> 
       ^              ^                        |
       |              |                        |
       |              |                        |
     +---+          +---+                      |
     | a |          | b |                      |
     +---+          +---+                      |
       ^              ^                        |
       |              |       +------+         |
       |              |       |      |       - v
       +--------------+-------| F(s) |<-------(+)
                              |      |         ^ 
                              +------+         |
                                               |
                                         +-----------+
                                   V --->| 20 log(e) |
                                    R    +-----------+
            i               G   + G   
             dB              1dB   2dB
o   = ---------------- + ----------------
 dB   1 + (a+b) * F(s)   1 + (a+b) * F(s)

        20*log(e) * (a+b) * F(s) * V  
                                    R
      + ----------------------------- 
              1 + (a+b) * F(s)                      

You can see that it is obviously irrelevant for AGC action where exactly the signal gain stages (G1, G2) are located – they might even be in front of the whole AGC loop. It is not irrelevant, of course, when looking at noise figure and the signal levels at various stages! (See Frontend concepts and gain distribution.)

It may be worth noting that a dB-linear AGC does not do an overly great job when it comes to levelling out input level variation, as you see in the static input – output characteristic (back to one VCA here):

          i               G         20*log(e) * a * F(0) * V
           dB              dB                               R
o   = ------------ + ------------ + -------------------------
 dB   1 + a * F(0)   1 + a * F(0)         1 + a * F(0)

Changes are merely attenuated by a factor of 1 + a * F(0). That's how you can determine the type of AGC in AM IF IC datasheets – the dB-linear type would have a slight linear increase of output level (in dB) above the AGC knee, while for a linear AGC it may be pretty much entirely flat. (Of course it gets more difficult to tell if there's a dB-linear AGC with high loop gain a * F(0) involved.)

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Linear AGC (I)

The classic way of building AGCs is not dB-linear but truly linear – at least linear in the sense that the VCA (as kind of a multiplier) is the only nonlinear component present.

Typical implementation
                       +-----+ 
      +-----+          | IF  | 
      | VCA |          | Amp | 
i (t) |     |          |     |                 o (t)
 RMS  |   /||          | |\  |                  RMS
----->|  α  |--------->| | \ |-------------+--------> 
      | /   |          | | / |             |
      |     |          | |/  |             |
      +-----+          |     |             v
         ^             +-----+        +---------+
         |                            |   Rect  |
         |                            |         |
         |                            |    |    |
         |                            | _|\|___ |
         |                            |    |    |
         |                            |    |    |
         |                            |         |
         |                            +---------+
         |     +------+                    |
         |     | Diff |       +-----+      |
         |     | Amp  |       | LPF |      |
         |     |      |       | _   |      |
         +-----|   /| |<------|  \  |<-----+
               |  / | |       |   \ |
               |  \ | |       |     |
               |   \| |<-- V  +-----+
               |      |     R 
               +------+      

This is how it might look like in practice. Again, there is some extra signal gain included (following IF amplifier).

Linear AGC model
i (t)  +-------+          +-----+                 o (t)
 RMS   |       |          |     |                  RMS
------>| α(V ) |--------->|  G  |-------------+--------> 
       |    C  |          |     |             |
       +-------+          +-----+             |
           ^                                  |
           |                               +-----+
           |                               |     |
           |                               |  K  |
           |                V              |   D |
           |                 R             +-----+
           |                |                 | V
           |   +------+     |     +------+    |  D
           |   |      |   - v     | f(t) |    |
           +---|  K   |<---(+)<---|  ~   |<---+
            V  |   A  |        V  | F(s) |
             C +------+         F +------+

That's how the various components were modelled:

The VCA is described with its controllable attenuation α, i.e. sout = sin / α(VC).

Trying to compute the output yields:

oRMS * α( KA * ( f(t) (∗) (KD * oRMS) - VR ) ) = G * iRMS

...which in the static case becomes:

oRMS * α( KA * ( F(0)*KD * oRMS - VR ) ) = G * iRMS oRMS * α( KA*F(0)*KD * oRMS - KA*VR ) = G * iRMS

Before we continue here, we'll generalize things some more, writing

oRMS * α(oRMS) = G * iRMS

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General AGC modelling
Abstract model
i (t)  +---------+     +-----+        o (t)
 RMS   |         |     |     |         RMS
------>| α(o   ) |---->|  G  |----+--------> 
       |    RMS  |     |     |    |
       +---------+     +-----+    |
            ^                     |
            |                     |
            |                     |
            +---------------------+

In the last section, we wrote:

oRMS * α(oRMS) = G * iRMS

The corresponding model, which has a number of components lumped with the VCA, is given above.

Note that the expression holds in any case, dynamic included. As the dynamic description includes a convolution, however, expect it to be an order of magnitude more difficult in general; the dB-linear case is one of few exceptions, so even if the AGC loop is not a truly dB-linear one, one would generally prefer to "dB-linearize" the model in a certain operating point and look at the behavior for small changes around it. If that is not sufficient, numeric simulation is required. What's easy to build may be quite hard to treat theoretically and vice versa.

Focusing on static description for now, we can rewrite things as

o    * α(o   )
 RMS      RMS
-------------- = G = const 
     i
      RMS

If we want oRMS to change very little over a wide iRMS range in the static case, obviously α(oRMS) must show a strong monotonous increase with oRMS in order to "catch up" with the growing iRMS. It is also clear that levelling out oRMS will work all the better the steeper the increase is.

The same relation can also be expressed in dB:

o  + α  (o  ) - i  = G
 dB   dB  dB     dB   dB

This makes computing the input – output transfer characteristic for the dB-linear case dead easy. (Try it with an αdB = K * (odB - C) approach, and you'll see.)

VCA considerations

There are a few kinds of VCA characteristics that you might encounter:

While the attenuators can be used out of the box with a control voltage that grows with oRMS, the amplifiers require that their control voltage decrease with oRMS.

Practical VCAs will have minimum and maximum values of α. The minimum in attenuators is obviously reached when everything is let through (i.e. α = 1), in amplifiers it's nothing but the inverse of the maximum gain. A real system will not be able to achieve infinite attenuation either.

When αmin is reached, the system has run out of gain, colloquially speaking. This occurs at low input levels, then the output is:

       G
o   = ---- * i 
 RMS  α       RMS
       min

If the VCA is an amplifier, we unsurprisingly obtain

o   = G       * G * i 
 RMS   VCA,max       RMS

For an attenuator with αmin = 1, this is

o   = G * i 
 RMS       RMS

The same happens when attenuation hits αmax:

       G
o   = ---- * i 
 RMS  α       RMS
       max
o   = G       * G * i 
 RMS   VCA,min       RMS
Effect on α

The α(oRMS) characteristic in a dB-linear AGC might look something like this:

    α   ^
     dB |
        |
α      -+ - - - - - - - .------...
 max,dB |             .
        |            /
        |           /.
        |          / .
        |         /  .
        |        /   .
        |       /    .
        |      /     .
        |     /      .
α      _|____/       .
 min,dB +------------+---------> o
                     o            dB
                      nom,dB

In this example, αmin is hit fairly suddenly. Under these conditions, the transition from the region with AGC action to the "out of gain" region will be quite sharp, resulting in a well-defined AGC knee. In practice, this may be different, of course, as real-life AGC characteristics show.

The concept of delayed AGC is best understood when looking at a voltage controlled attenuator. If the argument of α has the shape of oRMS - C, then the attenuator characteristic is shifted to the right by C and attenuation is reduced accordingly. This can be used to set the output level, for example.

AGC effectiveness

Now that we know what happens when α tops or bottoms out, you may be wondering what the result is in the normal working range. In order to answer this, we look at our input – output relation again...

oRMS * α(oRMS) = G * iRMS

...and differentiate by iRMS, which gives us:

do       /                dα(o   ) \
  RMS   |                     RMS   |    
----- * | α(o   ) + o   * --------- | = G
di      |   RMS      RMS   do       |     
  RMS    \                   RMS   /      
do
  RMS               G
----- = ------------------------ 
di      d      /              \
  RMS   ----- | o    * α(o   ) |
        do    |  RMS      RMS  |
          RMS  \              /

Neat! We now have an expression that will give us the slope of oRMS(iRMS) for any given oRMS and does not depend on iRMS at all. As a good AGC should minimize this very expression within its working range, it is now possible to look for functions which maximize the term in the denominator and to determine the differential output level variation remaining when using different kinds of real-life α(oRMS) characteristics.

(The more mathematically inclined will identify the above result as the derivative of the inverse, where the original function was iRMS(oRMS).)

Ideal α

What would be an ideal α(oRMS) characteristic? It would be useful if it had a pole at some oRMS = onom as that would mean that the output level would stay near onom pretty well, and it should be monotonously increasing with oRMS ∈ [0, onom). Within this range, its values should be inhabiting [0, +∞). An approach that fulfills these conditions is

             m
       (o   )
         RMS
α = -------------- , m ∈ {0, 1, 2, ...}
                n    n ∈ {1, 2, ...}
    (o   - o   )
      nom   RMS

It turns out that an amplifier with linear control characteristic preceded by a differential amp doing level adaptation according to Vout = KA * (VR - Vin) produces exactly that kind of behavior.

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Linear AGC (II): Examples
Linear amplifier VCA

Now let's examine a few examples. First we'll take a look at a setup involving a linear amplifier VCA and differential amplifier for level adaptation. The components are going to be modelled as follows for static considerations:

       1
α = -------
    K  * V
     V    C 

VC = -KA * (VF - VR), KA > 0

VF = F(0) * VD

VD = KD * oRMS

So overall α(oRMS) becomes

                         1 
α(o   ) = ---------------------------------
   RMS    K  * (-K ) * (F(0)*K  * o   - V )
           V      A           D    RMS   R

                         1                 
        = ---------------------------------
          K  * (-K ) * (F   (0) * o   - V )      
           V      A      eff       RMS   R       
                                       

...with F(0)*KD =: Feff(0).

We can see that the nominal output level (where the denominator has a pole) becomes

        V     
         R    
o   = -------
 nom  F   (0) 
       eff
    
    ≈ V  , F   (0) ≈ 1     
       R    eff

This allows writing α(oRMS) as:

                1               1
α(o   ) = -------------- * -----------
   RMS    -K *K *F   (0)   o    - o
            V  A  eff       RMS    nom

                1              1
        = ------------- * -----------
          K *K *F   (0)   o    - o
           V  A  eff       nom    RMS

Therefore our input – output relation becomes

                   o
      1             RMS   
------------- * ----------- = G * i
K *K *F   (0)   o    - o           RMS
 V  A  eff       nom    RMS

In this case we can even determine oRMS(iRMS) analytically by inversion of the input – output relation (either in a straightforward manner or by seeing it as a Mbius transformation). If we define KV*KA*Feff(0) =: K, it becomes

        K * G * i
                 RMS
o   = ---------------- * o 
 RMS  K * G * i    + 1    nom
               RMS

And indeed, for a large enough K * G, this will approach onom pretty quickly. What's interesting is the inherent highpass characteristic – even with arbitrarily high maximum amplification in the VCA, signal gain at very low levels will never exceed K * G. In practice this means that in order to obtain a well-defined AGC knee, one should make sure that α hits αmax before this effect reduces output level considerably, i.e.

iRMS(oRMSmin)) >> i6dB

...where iRMS(oRMSmax)) =: iRMS(omin) is the input level at which α hits αmin and i6dB is the level where the inherent highpass characteristic would lead to a 6 dB drop in output level, the latter being:

        1
i   = -----
 6dB  K * G

iRMS(omin) := imin is the minimum input level still covered within the regular AGC working range.

                1
o   = o    - --------
 min   nom   K * α
                  min
                 o
        1         min
i   = ----- * -----------
 min  K * G   o    - o
               nom    min
        1  
    = ----- * (K * o   * α    - 1)         
      K * G         nom   min 

Therefore what should be ensured is:

K * o   * α    - 1 >> 1 ⇒
     nom   min          

K * o   * α    >> 1
     nom   min          

With the expressions for K and oRMS, this can be written as:

K * K * V * α    >> 1
 V   A   R   min          

This is the condition that needs to be fulfilled for a well-defined AGC knee level, provided αmin is reached fairly suddenly. Of the four parameters involved, two are given by the VCA and another one by desired output level, so the only one we can really influence is KA, the differential amplifier's differential gain. This should therefore be as large as possible.

PIN diode attenuator VCA

Next we'll look at a PIN diode attenuator in shunt configuration as discussed in the paper mentioned earlier. In a higher-impedance environment (for which it's suited best) and for moderately high frequencies (e.g. shortwave), the circuitry might look like this:

        _____
 +-----|_____|-------+--------------------+
 |        R          |                    |
 |         S         |                    |
 |                  ---                   |
 |                C ---                   |
 |                   |                    - 
 |                   |                   | |
(~)   +------+--|<|--+--|<|--+-----+     | | R 
 |    |      |   D       D   |     |      -   L
 |    |      |               |     |      |
 |    |     ---             ---    |      |
 |    |   C ---           C ---    |      |
 |    |      |               |     |      |
 |    |      |               |     |      |
 +-----)-----+-------+-------+------)-----+
      |              |             |
      |              |             |
      -             ---            -
     | |             -            | |
     | | R                        | | R
      -   2                        -   1
      |            /\              |
      |           /  \             |
      +----------/-  +\------------+
                / Diff \
               /  Amp   \
              / -      + \
              --+------+--
                |      |
                |      |
          V ----+      +-------> To AGC Filter
           R

In fact, this is exactly the kind of setup found in the Sony ICF-7601. You can also use a differential amplifier with only a single output and connect the other line to ground (-) or supply (+), that doesn't make a significant difference (an amplifier with a current output would allow for a more linear relation of input voltage and diode current though).

C are capacitors chosen large enough that they're transparent to RF, RS is the signal source resistance seen and RL is the load resistance seen.

In order to describe the attenuation, we can derive a high-frequency small-signal model from this:

       _____
 +----|_____|----+---------------+
 |    R          |               |
 |     S         |               |
 |               |               - 
 |               |              | |
(~)      +--|<|--+--|<|--+      | | R
 |       |   r   |   r   |       -   L
 |       |    D  |    D  |       |
 |       +---||--+--||---+       |
 |       |   C      C    |       |
 |       |    D      D   |       |
 +-------+-------+-------+-------+
                 |
                 |
                ---
                 -

Here the diodes are described via their small-signal resistance rD and parasitic capacitance CD. Since the diodes are to be assumed identical, we can treat them as a single diode...

       _____
 +----|_____|----+---------------+
 |    R          |               |
 |     S         |               |
 |               |               - 
 |               |              | |
(~)      +--|<|--+              | | R
 |       |   r'  |               -   L
 |       |    D  |               |
 |       +---||--+               |
 |       |   C'                  |
 |       |    D                  |
 +-------+-------+---------------+
                 |
                 |
                ---
                 -

...with:

      r
       D
r' = ---
 D    2

C' = 2 C
 D      D

We will call r'D || C'D (|| designating the parallel circuit) the equivalent small-signal diode impedance z'D:

      r
       D
z' = --- || 2 C 
 D    2        D

Since RS and RL are assumed to be there even without the attenuator present, there is a certain basic attenuation. As that is not the attenuator's fault, we'll want to obtain a description with αmin = 1.

         R + R
          S   L
α      = ------
 basic     R
            L
    s
     in      1
α = ---- * ------
    s      α
     out    basic

    R  + r' || R
     S    D     L     1
  = ------------- * ------
      z' || R       α
       D     L       basic

    R  * (z' + R ) + z' * R      R
     S     D    L     D    L      L
  = ------------------------ * ------
           z' * R              R + R
            D    L              S   L

        R  || R
         S     L
  = 1 + --------
           z'
            D

With the expression for z'D, this becomes:

                            / 1        \
α = 1 + 2 * ( R  || R  ) * | --- + jωC  |
               S     L     |  r       D |
                            \  D       /

As to be expected, using two diodes instead of only one allows obtaining a maximum attenuation that is up to twice as large, thereby increasing the control range. However, the minimum attenuation in particular depends on frequency.

Similar to the aforementioned term paper, we'll use this model for rD as found on Wikipedia:

     n * V
          T
r  ≈ ------
 D     I
        DC

...where IDC is the DC current through the diode, VT is the temperature voltage (a typical 26 mV at room temp) and n is the exponential correction factor as found in the silicon diode model.

This gives us

                            /  1               \
α ≈ 1 + 2 * ( R  || R  ) * | ------ * I  + jωC  |
               S     L     | n * V     DC     D |
                            \     T            /

What about minimum and maximum attenuation?

α   = 1 + 2 * ( R  || R  ) * jωC
 min             S     L        D      

For low frequencies ω = 2πf, this becomes 1 as intended. However, the parasitic capacitance leads to a lowpass characteristic, limiting the minimum attenuation at higher frequencies. (For RS || RL = 1 kOhm and a worst-case CD of 4 pF as specified for the 1SS123 diode used in the ICF-7601, the -3 dB cutoff is at about 20 MHz, while for RS || RL = 25 Ohm it increases to about 800 MHz.)

                              /  1                   \
α   ≈ 1 + 2 * ( R  || R  ) * | ------ * I      + jωC  |
 max             S     L     | n * V     DC,max     D |
                              \     T                /
           
                           1
    ≈ 2 * ( R  || R  ) * ------ * I
             S     L     n * V     DC,max
                              T

For low frequencies, the control range αmax / αmin is αmax itself. It is larger in a higher-impedance environment – when comparing RS || RL = 1 kOhm and RS || RL = 25 Ohm, we find a difference of about 32 dB. For higher frequencies, a lowpass characteristic becomes apparent, as discussed for αmin, i.e. the control range decreases accordingly.

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Digital AGC

Delay

Contemporary receivers with IF DSP also need AGC systems, of course. While very high AGC loop gain and large VGA adjustment ranges are less of a problem there, they have to face an additional difficulty: Delay introduced by processing and possibly digital filters inside the A/D and D/A converters (e.g. when using common audio converters). Delay not only makes theoretical treatment a lot more difficult, it can also worsen transient response and even cause instability (oscillation) if large enough.

I would estimate delays of one or two ms to be absolutely possible (typical digital filter delays in audio converters tend to be in the order of 10..60/fs or about 1/4 ms to over 1 ms at 48 kHz). For the delay to have minimum effect, I would choose time constants an order of magnitude larger, so maybe 10 or 20 ms. Now the AGC attack time for an AR7030 (conventional all-analog rx) is stated to be about 8 or 4 ms, respectively – oops! So if you want an AGC with an attack time as quick as this given a delay of 2 ms, there's no comfortable safety margin, and you have to expect negative effects. (Decay is usually a lot slower and thus not an issue.)

An approach to circumvent this problem would be using two cascaded AGCs, a very slow hardware AGC to keep the A/D converter out of clipping (with a nominal A/D input level of like -10..-20dBFS for some headroom) and another all-digital AGC which can be much faster, and which would have lower delay than one having to "reach out" into the analog domain. This is apparently followed in the Elecraft K3 ham transceiver (see measurements). The bigger Icoms also employ a dual loop AGC, albeit with the primary aim of avoiding clipping.

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Unusually noisy DSP receivers

A common complaint about contemporary DSP-based ham radio transceivers in particular is that they make the bands appear noisier than older analog models. This has to do with part or all of the following:

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Audio in communications receivers

Introduction

Even the best receiver in the world is of limited use when it frustrates the operator. Yet, topics such as style and ease of operation and audio quality do not always get the kind of attention they deserve. This is all the worse since especially in well-supplied markets like the one for ham radio transceivers it is generally these that determine user preference of one model over another – most models do a reasonably good job on the receiver side these days, with limitations commonly only becoming visible under very specific conditions. So let's look at the audio side of things, with emphasis on shortwave gear.

In general, we have to distinguish between two different types of applications:

  1. Data communications, intended to be machine / PC decoded. Think RTTY, SSTV, PSK31, whatever.
  2. Content which is supposed to be decoded by humans. This includes speech, music, but also CW.

Data communications applications tend to be relatively insensitive. Decoders usually have reasonably well-defined and uncritical input levels, demands in terms of nonlinear distortion are rarely extreme (OK, so OFDM based schemes are somewhat more picky), and things usually work best when frequency response isn't tampered with.

By contrast, humans are somewhat more picky. So let's take a closer look at the factors influencing audio quality in a receiver:

Nonlinear distortion

Nonlinear distortion in the audio chain used to be frequently ignored back in the 1980s. After all, who cares about a bit of amplifier distortion if the received material is pretty low-fi to begin with? Well, there is distortion, and there is distortion. If demodulator distortion is predominantly low-order and the following amplifier has significant amounts of high-order distortion products (typical for heavily fed-back amplifiers with weak or underbiased output stages), the result may indeed be noticeably worse than when using a low-distortion amplifier. In particular, distortion products above the intended audio passband may be audible.

For example, there is a small but audible difference between the external loudspeaker output and the headphone output of the AOR AR7030, even when using headphones of a rather high 600 ohm nominal impedance. The former (which sounds a tad fuller and nicer overall) is fed by an audio power amplifier IC, while the latter employs an opamp-based circuit that neatly violates several audio engineering rules (uses an antiquated 741-class general purpose opamp that sees input impedances and input impedance unbalance in the hundreds of kOhms, and the output series resistors seem a little small given the opamp's current driving capabilities and not overly luxurious coupling capacitors), with more than sufficient gain not making things any better in the distortion department.

Amplifier hiss

Noise is the most critical when it's wideband, as typical for AF amplifier stages. Wideband hiss can be extremely annoying when it can't be masked by program material and should therefore be kept to a minimum. Tests with real-life headphone loads are mandatory. Sensitivity levels of around 110 dB SPL per 1 Vrms aren't that uncommon, with extreme cases up to 130 dB SPL in the IEM department, so noise at low volume settings shouldn't be more than a few V over the audio bandwidth (20 Hz .. 20 kHz). Less sensitive high-impedance cans might be in the 90s, so ideally there should be a maximum output of around a Vrms or so. That's quite some dynamic range there, and most real-life receivers fail to provide it.
Series resistors have to be used with care as headphone impedance variation over frequency may lead to considerable alteration of frequency response (and a bass hump of like 10 dB is not negligible even in the low-fi realm of the short waves).

AGC characteristics

As explained under Ideal and real-life AGC action, a fast AGC response may degrade low-frequency linearity in AM. In SSB, it can cause intermodulation distortion to appear, as you'd expect from any compressor. Since fast AGC action does tend to be useful under certain conditions, selectable AGC time constants are desirable.

Frequency response

This brings us to audio frequency response. While audio processing for narrow-band FM communications is pretty well-defined, things become rather fuzzy when AM, SSB and CW are concerned. There apparently is a NAB pre/deemphasis standard for AM that applies to mediumwave broadcasting in the US, but that pretty much seems to be it.

Optimum audio frequency response is a matter of modulation, taste (we all have slightly different hearing and signal processing) and reception conditions.

Many of these considerations assume near-ideal audio playback via hi-fi headphones or loudspeakers. Communications receivers commonly ship with tiny no-fi speakers somewhere in the front, or sometimes with bigger ones on top. Weak low-frequency response and case resonance effects are common, degrading the experience even for speech. Fortunately the availability of suitable headphones and active speaker systems can be considered good nowadays. The author would estimate the optimum (low/mid) driver size for an external "shortwave" speaker to be in the 13 cm (5") to 25 cm (10") range, depending on required SPL, speaker driver performance, box type and enclosure volume.

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ANFSCD – Software defined radio (SDR)

Introduction

An SDR receiver is quite unlike a "conventional" radio – it basically is an A/D converter fast enough for the highest frequency received (with some anti-alias filtering in front of it), attached to a fast DSP / FPGA / whatever. All the filtering and demodulation is then performed in software, which gives just about unlimited possibilities (provided you have unlimited computing power, hi). Practical implementations usually allow output of part of the spectrum as I and Q signals.

As an example, let's look at the Perseus SDR that seems to be popular among radio enthusiasts right now, for good reason. (Too bad they have such a spectacularly crappy website to go with such a fine receiver. Obviously it's not common knowledge yet that WYSIWYG and the web just don't go together, regardless of what software manufacturers claim. </rant>)
This receiver uses an 80 megasamples per second 14-bit ADC and claims a dynamic range of up to 105 dB in CW. But wait, don't 14-bit ADCs only have about (14 * 6) dB = 84 dB of dynamic range (certainly less in practice)? Sure, but that refers to the whole bandwidth, 40 MHz in this case! Signals encountered up to this frequency can be considered wide if they occupy 10 or 20 kHz, and if you only look at a small part of the spectrum, you'll catch far less noise, too, thus effectively increasing dynamic range. For a 500 Hz CW filter, the gain would amount to no less than 49 dB.

Pluses of SDRs include:

Any caveats? There are a few, of course. As with any ADC, one has to take care not to overdrive the input, or else there will be bad nonlinear distortion (read: intermod) very quickly. And since a SDR typically has a wideband frontend (and that's really wideband in this case, including everything from DC to half the sampling frequency), this refers to the sum signal level. You also have to stay away from the other end of the signal strength range to ensure that the A/D converter is dithered properly, and you better make sure that A/D converter output doesn't leak back into the input.

Considering this, a dynamic range of 100 dB doesn't seem like all that much either. Imagine the input has to accept both all the strong longwave, mediumwave and shortwave signals (which can develop sum signal levels well in the hundreds of mV on a reasonably large antenna) and DX in the single-digit V region at the same time. Therefore some preselection and a variable RF preamplifier definitely seem useful, and indeed people have recognized that a "naked" SDR is not too practical if high performance is required. The Perseus employs a 10-band frontend filter bank to keep signal levels at bay, for example. (Which I was, however, unable to read at my minimum font size of 16px since the px-fixed page layout of the website breaks for anything much larger than the suggested 11px.)

A receiver that basically is one big ADC will behave like one, obviously. This makes traditional figures of merit like 3rd-order intercept point rather useless or at least requires re-evaluation. Note that an unconventional (linear) increase of intermodulation products with signal levels may also be rooted in (IF-level) amplifier stages with heavy negative feedback; those into simulating audio power amplifiers will no doubt have noticed that this kind of behavior is quite typical (calculated THD remains almost constant but the amplitude of the more critical higher-order harmonics rises with input level).

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SDR "light"

Another approach not uncommonly seen in the real world uses a direct conversion frontend, which allows the use of high performance, relatively inexpensive audio ADCs (and on the transmitter side, DACs) and significantly reduces computing power requirements at the expense of much less instantaneous bandwidth (typically in the 10s of kHz). Of course the mixer may degrade intermodulation performance, so one will typically employ an overload-resistant (FET) switching mixer design such as the I/Q arrangement pioneered by Dan Tayloe N7VE. As with any SDR, some band filters won't hurt either. The FlexRadio FLEX-1500 transceiver is one such design.

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Created: 2008-05-15
Last modified: 2011-07-20