Common Compact Shortwave Antennas

Loop, whip or dipole?

I have been fascinated by electrically small loop antennas (circumference 2πr << λ/2) for a long time. Then one day I decided to find out what it is that makes them perform so well, at least for receiving purposes. A number of Google searches, a good bit of reading and some calculations later, here's what I found on small antennas in general. (Y'know, trying to explain a subject you don't understand properly is a brilliant way of learning a lot about it.)

Basics

You have to keep one thing in mind when physically small antennas (<<λ/2, typically <λ/10) are concerned: TANSTAAFL. Or as AA5TB so neatly puts it,

You can have any TWO of the following antenna parameters:

You cannot have all three.

Thus we will have to decide between efficiency and broadband operation later on.

It is useful to distinguish between transmission and reception applications. The reason is that on the shortwave ranges, noise levels are quite high, so that the RSGB Communication Handbook stated a receiver noise figure of 10 dB to be quite sufficient even for the highest ranges decades ago, assuming a fullsize dipole. On the lower bands, requirements are much more relaxed still, with atmospheric noise easily equalling 20 to 30 dB. Therefore you could easily get away with either a receiver with relatively modest sensitivity on a fullsize antenna or a more sensitive receiver with an antenna that has considerable loss. Therefore an antenna with 20 dB loss (a modest 1% radiation efficiency) may very well be able to hear everything. However, the signal levels produced when transmitting with it will be rather pitiful (as in 20 dB below those of a fullsize dipole with decent height).

Monopoles (vertical / whip) and dipoles

Relations between monopoles and dipoles

The dipole probably is the most fundamental type of antenna out there from a theoretical point of view, going right back to Heinrich Hertz himself. It is also commonly used for transmission purposes, while the average SWL has certainly seen its monopole relatives, notably telescopic whips.

Now this is not the place to reiterate short dipole theory – you can find enough of that on the web (here's an example). However, once you have that, a vertical or whip is not hard to understand.

A whip antenna is nothing but a short and comparatively thick monopole (vertical) over receiver ground. Any monopole needs a counterpoise at constant potential (typically, ground) that serves as a "mirror" and thus completes a dipole of twice the length. The impedance seen by a connected receiver will only be half as high as between two dipole halves, but other than that the theory for dipoles will apply. (Of course if you want to connect something to a monopole, you'll need an unbalanced connection, while for a dipole it would be balanced.)

A look at short dipoles

Now it is known that a short dipole (less than one tenth the wavelength) is predominantly capacitive. Let's have a look at the commonly used equivalent circuit as given in the book "Antenna Handbook: Antenna theory" by Y. T. Lo and S. W. Lee (you may notice this is actually unbalanced so would apply to a monopole, but as we've seen it can be treated in the same way):

      ____     ____     ____
 +---|____|---|____|---|####|---||-----o----+
 |     R        R        L      C           | 
 |      r        o        d      d          | 
 |                                          | 
 |    rad R   loss R    ind    cap          _
 |                                    load | | Z
(~) src                                    |_|  L
 |                                          |  
 |                                          | 
 +-------------------------------------o----+

Only the radiation resistance actually contributes signal. It increases with the square of dipole length to wavelength ratio, i.e. (l/λ)▓, so it'll get pretty small for very short dipoles. It's barely 2 Ω for l/λ=1/10, and at l/λ=1/50 it drops to a measly 80 mΩ. (But wait until you've seen the numbers for loops!)

Loss resistance originates in the dipole material's finite conductivity and increases with frequency due to skin effect (approximately Ro ∝ √(f) once skin depth is smaller than conductor radius/thickness). It usually is much smaller than radiation resistance for a "full-grown" dipole, but can easily become as big or bigger than radiation resistance for short dipoles with low conductor diameter and/or non-ideal materials (e.g. steel wire).

In a short dipole, the effect of inductance is rather negligible.

That leaves us with capacitance. This turns out to be quite small, commonly in the single-digit pF range or not far beyond. Thus it contributes a large reactance (imaginary part of the impedance) in series, with a magnitude well in the kΩ range for the lower shortwave ranges. Thus it obviously dominates the whole antenna impedance.

      ____ 
 +---|____|----||-----o----+
 |     R       C           | 
 |      s       d          | 
 |                         | 
 |    sum R   cap          _
 |                   load | | Z
(~) src                   |_|  L
 |                         |  
 |                         | 
 +--------------------o----+

Implications on efficiency and bandwidth

      ____ 
 +---|____|----||-----o----+
 |     R       C           | 
 |      s       d          | 
 |                         | 
 |   sum R << |X |         _
 |            | C|   load | | Z
(~) src                   |_|  L
 |                         |  
 |                         | 
 +--------------------o----+

Now try getting any noteworthy amount of RF power through that. Not easy! Here we have to remember that power transfer is highest if load impedance is the conjugate complex of source impedance. Therefore what we have to do is cancelling out the cap's large negative reactance by an equal amount of positive reactance, usually by inserting an inductance in series or in parallel (with the parallel version having the advantage of transforming the very small radiation and loss resistance up, easily in the hundreds of kΩ, which gives much higher voltages and invites use of a JFET or MOSFET based amplifier).

You'll need a mighty big inductor there, which will contribute a healthy share of loss resistance on its own, but it'll improve things considerably nonetheless. Loss resistance for a fixed coil can be optimized by using the right size and material of iron powder or ferrite core, depending on frequency range and required power levels.

      ____                             
 +---|____|----||----o------+-------------+
 |     R       C            |             | 
 |      s       d           |             | 
 |                          |             | 
 |   sum R << |X |          _             _
 |            | C|  tuning |#| L    load | | R
(~) src                ind |#|  t        |_|  L
 |                          |             |  
 |                          |             | 
 +-------------------o------+-------------+

But alas, this introduces a new problem: The impedance of an inductor increases with frequency while for the capacitor it's the other way around, so the cancellation will work for one frequency only! In practice this will be an area that might be a few 10 or 100 kHz wide depending on losses, but still this is quite narrowband. Remember we have to decide between high efficiency and broadband operation?

We could make the whole affair work over a certain frequency range by simply using a variable inductor. However, these aren't exactly common, though you will find them in some antenna tuners and power amplifiers. Alternatively, one could use a parallel LC network with multiple taps on the L and a more common variable capacitor. (Simple whip antenna tuners like the ADDX-PRE-1 work like that.)

If we are trying to use this antenna over a really wide bandwidth (like 100 kHz to 30 MHz), just about all we can do is make sure that our input impedance is reasonably high towards the lower frequencies. Using some JFET or MOSFET amp would be one possible option (as it would be for the parallel-L-tuned dipole). The noise figure of the whole shebang will probably be rather lousy in some places.

Further problems of monopoles

In order for a monopole to be completed to a full dipole, a good ground is required. That's why vertical antennas are commonly used with radials which greatly increase conductivity. Now unfortunately any battery-operated receiver with a whip antenna has a problem in this very area: The ground connection is arbitrarily lousy! Unless an explicit ground connection is established, pretty much all you have is some capacitive coupling from circuit ground to the surface underneath. The whole affair could include a good bit of old-fashioned resistance, too, depending on the conductivity of things in the path to ground potential (typically furniture, walls and such). So what does this look like in the equivalent circuit diagram?

      ____
 +---|____|----||-----o----+
 |     R       C           | 
 |      s       d          | 
 |                         | 
 |                         _
 |                   load | | Z
(~) src                   |_|  L
 |                         |  
 |    ____                 | 
 +---|____|----||-----o----+
       R       C  
        g       g  

Like this. Redrawn in a more conventional way:

      ____        
 +---|____|---||---||-----o----+
 |   R >> R   C    C           | 
 |    g    s   g    d          | 
 |                             | 
 |                             _
 |                       load | | Z
(~) src                       |_|  L
 |                             |  
 |                             | 
 +------------------------o----+

Oh dear. Reactance gets even larger, and even if we managed to cancel this out, only a teeny tiny part of the remaining resistance is actually made up by radiation resistance. As any owner of a portable shortwave receiver will be able to attest, whip sensitivity on batteries is rather lousy and much improves upon establishing an explicit ground connection or merely attaching an external power supply.

Field impedance

Short dipoles and monopoles are also called "electric" antennas because they primarily react to the electric component of the electromagnetic field, i.e. their field impedance is high. As W8JI points out, this only applies for distances up to about λ/10, but that's usually sufficient to include a large number of in-house interference generators with their respective "antennas", also of the "electric" variety in many cases.

That being said, monopoles, improperly balanced dipoles (more common than you may think) and various other unbalanced forms of antennas may be better in terms of noise than commonly given credit for. A few common-mode chokes in the feedline may work wonders (yet more improvement is to be had with more of them on the "antennas" of RFI generators). Of course grounding should only be either at the antenna or at the receiver, not both. If there is a ground loop, part of the signal current will be common mode.

The field impedance of free space is 120π Ω ≅ 377 Ω btw.

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Loop antennas

Small loops

A small loop antenna (circumference 2πr << λ/2) is essentially an inductor with a cross-section big enough to pick up electromagnetic fields (predominantly the magnetic part) halfway well. It's basically the magnetic counterpart to a short dipole. Practical ones are frequently tuned, and we'll see why this is shortly. Here's an equivalent circuit:

      ____     ____     ____             
 +---|____|---|____|---|####|-------+------o----+
 |     R        R        L          |           | 
 |      r        o        d         |           | 
 |                                  |           | 
 |    rad R   loss R    ind   par  ___          _
 |                            cap  ___    load | | Z
(~) src                             |  C       |_|  L
 |                                  |   p       |  
 |                                  |           | 
 +----------------------------------+------o----+

Radiation resistance (which is the only part actually contributing our signal during reception) differs noticeably from that of the short dipole: It increases with the 4th power of the circumference to wavelength ratio, i.e. (2πr/λ)4. One could also say it increases with loop area A squared. In fact, as long as the loop remains reasonably thin, adding more turns N leads to an effective loop area of N*A since from far away, it looks like a single turn with N times the current. Small loops have very small radiation resistances – a one-turn circular loop with 2πr/λ=1/10 (that's about 3 m in diameters at 3 MHz) can offer only 20 mΩ, and for 2πr/λ=1/50 this shrinks to a modest 30 ÁΩ. Yep, that's microohms.

As an inductor typically involves a conductor of some length (which could be a wire or a copper tube), some losses in there are obviously inevitable. If the antenna is supposed to have any kind of efficiency later on, they have to be made very small due to the modest radiation resistance.

Any inductance also has a parasitic parallel capacitance, typically inter-winding capacitance (which can be less than 1 pF to multiple pF depending on the loop). This leads to the phenomenon of self-resonance and limits the maximum frequency of a tuned loop. Note that for a given inductance, the lower-diameter loop with more windings will generally exhibit the higher inter-winding capacitance.

That leaves us with the inductance itself. Its value tends to range between a few ÁH for a typical single-turn SW loop to several hundred ÁH for their MW and LW brethren. For example, a 3 m dia. single-turn loop has an inductance of about 6..7 ÁH, equivalent to a reactance XL ≅ +120 Ω at 3 MHz. (Radiation resistance is about 20 mΩ then.) That sure seems easier to tune out than the values far in the negative kOhm range that we saw with short dipoles.
A small 9" dia. loop with 25 windings occupying about 1" like the Tecsun AN-200 has about 250 ÁH (going by the Bob's Tesla Web Lab formula), giving an XL of about 800 Ω to 2.7 kΩ across the MW band. Since my sample will tune up to pretty much exactly 2 MHz, that means minimum capacitance (including inter-winding) is about 25 pF, down from a maximum of about 400 pF. Not a bad little tuning cap there, and wire routing seems quite solid, too.

Implications on efficiency and bandwidth

As in the case of short dipoles and monopoles, we will have to decide between efficiency and bandwidth. If we want a decent kind of efficiency, the large positive reactance has to be cancelled out. This can be done with a series capacitor or the more useful impedance-transforming parallel capacitor variant.

      ____     ____     ____             
 +---|____|---|____|---|####|-------+------o----+
 |     R        R        L          |           | 
 |      r        o        d         |           | 
 |                                  |           | 
 |    rad R   loss R    ind   sum  ___          _
 |                            cap  ___    load | | R
(~) src                             |  C       |_|  L
 |                                  |   s       |  
 |                                  |           | 
 +----------------------------------+------o----+

The parallel capacitor version is particularly neat, since the tuning capacitance, parasitic (inter-winding) capacitance and input capacitance of a following FET amplifier stage (whose input impedance typically is in the hundreds of kOhms in parallel to a few pF) are all in parallel and can be lumped together. This makes determining minimum sum capacitance and thus highest tunable frequency rather easy. Again, this kind of circuit transforms our radiation and loss resistance up. Obviously the tuning capacitor will also contribute some losses, not terribly much for sure but remember that our signal-contributing radiation resistance is pretty low to begin with. (And to bust some myths, no, a mechanical varicap is not per se better than a varicap diode in that regard. Not the usual AM radio ones with wipers at least. You can build very high-Q mechanicals though.)

Of course one does not need to attach a FET amplifier there, part of the loop can also be used to form a balun for impedance transformation to e.g. a 50 Ω system. Single-turn shortwave loops typically have a small coupling winding at the side opposite of the tuning capacitor, where currents are highest. If you have ever used an external tuned loop to boost signal levels on a portable receiver with an internal ferrite rod using "inductive coupling" (in which case you can probably attest to the effectiveness of this method), that's the same effect. A ferrite rod is nothing but a loop would on a high permeability (Ár) core after all. Here's something for you if you feel like simulating inductive coupling in LTspice.

As already with the short dipole, broadband use is a bit of a mess as antenna impedance is rather non-constant. At least reactance becomes smaller as frequency decreases, but that advantage is eaten up by the more quickly decreasing radiation resistance, so in the end Q = |XL|/Rr behaves about the same (Q ∝ 1/f│).

In fact, when taking a look into formal small antenna theory (as in this book chapter by Chalas, Fujimoto, Volakis, Sertel), we find that there are fundamental limits as to how low antenna Q (or how high relative bandwidth for a tuned version) can actually go even for superconducting antennas, and while people still haven't agreed entirely on the details, you usually find Qmin ∝ 1/(ka)│ if the antenna is contained within a sphere of radius a; k = 2π/λ = 2πf/c, so there's our 1/f│ dependency again.

Balance and directivity

A small loop, much like a short dipole, is a "complete" antenna – and that applies even when it is run unbalanced. Therefore it exhibits a workable amount of directivity (nulling ability), not being restricted to "vertical" operation like typical monopoles are. A properly balanced loop will, however, do better in terms of directionality, especially on the higher frequencies. I presume common-mode signal pick-up by the feedline to be the root cause, which would be in line with the "filter unit" provided with Sony's AN-LP1 active loop, but if anyone knows better, let me know.

Field impedance

Small loop antennas are also called "magnetic" antennas because they primarily react to the magnetic component of the electromagnetic field, i.e. their field impedance is low. As W8JI points out, this only applies for distances up to about λ/10, but that's usually sufficient to include a large number of in-house interference generators with their respective "antennas" of the "electric" variety. Loops therefore tend to keep off noise from nearby RFI sources better than their "electric" cousins, which is a big plus for in-house operation.

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Online loop inductance calculators

Bruce Carter originally implemented the following two JS calculators for determining loop inductance on his loop antenna site, but that has been inaccessible much of the time lately (archive.org may help). So here's a modernized metric version of the Joe Carr and UMR EMC Lab formulas, with an implementation of the Bob's Tesla Web Lab formula thrown in for good measure.

First in line is the formula from Joe Carr's Tech Notes, which is used for square loops with wide-spaced windings:

Enter data for Joe Carr formula:
cm
cm

pF
pF
Results ÁH
MHz
MHz
m

Note: Inter-winding capacitance can upset the calculation. If that happens – decrease the number of turns! – Bruce Carter

For my homebrew MW loop, this formula gave an inductance about 15% too low. The difference dropped to about 5% after rewinding to a lower shortwave loop with twice the wire spacing, at least once I took the correct loop depth into account – it has to be (turns - 1) * spacing. Insulation with non-negligible εr (like PVC) increases capacitance and decreases effective spacing a bit.

Next in line is the UMR EMC lab formula, which can be used for rectangular loops with closely-spaced windings.

Enter data for UMR EMC lab formula: cm
cm
cm

pF
pF
Results ÁH
MHz
MHz
m

For my homebrew MW loop, this formula gave an inductance about 25% too high. After rewinding to a lower SW loop with twice the wire spacing, the deviation became much smaller, now less than 10% high.

Finally, here's an implementation of the Bob's Tesla Web Lab formula, which is suited for round (cylindrical) loops. It apparently goes back to Wheeler (1928) and is particularly accurate for long coils.

Enter data for Bob's Tesla Web Lab formula: cm
cm

pF
pF
Results ÁH
MHz
MHz
m

If you want to compare circular and rectangular loops, best shoot for same length of wire and same wire spacing.

You want even more of this? No problem:

No wonder tx loops are comparatively rare on the lower bands – if you want any kind of reasonable efficiency, you'll need a good bit of copper tubing and a variable capacitor that can take like 6..10 kV even on 100 W, plus remote tuning (you don't want this kind of fieldstrengths in your shack for sure) and a rotor. Not exactly a beginner's project. It all gets considerably more relaxed in the vicinity of 20 m, where a 1 or 1.5 m dia. loop and ~60 pF, 5 kV varicap on a short mast should already do a pretty good job e.g. as a mobile antenna.

RJELOOP3 (for multi-turn loops) also takes conductor thickness and losses into account and works pretty well, once you get it running that is. I have far from the latest and greatest PC hardware and software but still needed the DOSBox emulator. Thankfully the computing power requirements are very modest.

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Comparison time: Short dipole / monopole vs. small loop

First of all, the best small antenna is one that isn't small. Since, however, rotating your array of widely spaced Beverages is just a wee bit cumbersome (hi), and many people don't remotely have the space for anything close, compact antennas do have their place. So let's examine a few cases:

Common-mode chokes in the feedline may be helpful in any case. (Of course grounding should only be either at the antenna or at the receiver, not both. If there is a ground loop, part of the signal current will be common mode.)

Let's sum it up:

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Created: 2010-10-30
Last modified: 2010-12-18