Helpful Audio-Related Calculators

Originally featured on my blogalike, these now inhabit a page of their own here.

Overview

RMS Summing and Unsumming Calculator

RMS summing

This calculator will RMS sum the contributions of up to three voltage noise sources, each arbitrarily given either in ÁV, dBV, dBu, a voltage noise density at a given bandwidth, or a resistance value at a given ambient temperature and bandwidth.
Currently temperature and bandwidth cannot be set individually; if you need something more advanced, consider badgering the author.

Enter individual sources


kHz
K

Change any value or click "Go!" to proceed.
*) Only needed if any resistor values or noise densities (in or out)
**) Only needed if any resistor values (in or out)

Result

RMS unsumming

This calculator allows subtracting the contributions of up to two additional noise sources from a total combined (RMS summed) voltage noise value to arrive at the contribution of the remaining noise source, each of them arbitrarily given either in ÁV, dBV, dBu, a voltage noise density at a given bandwidth, or a resistance value at a given ambient temperature and bandwidth. So if you've always wanted to know what the input noise density is for a microphone preamp given with an EIN of -128.5 dBu under the conditions of 20 kHz bandwidth and 150 ohm source, this is the one for you!
Currently temperature and bandwidth cannot be set individually; if you need something more advanced, consider badgering the author.

Data entry


kHz
K

Change any value or click "Go!" to proceed.
*) Only needed if any resistor values or noise densities (in or out)
**) Only needed if any resistor values (in or out)

Result

Back to topics

Entry last modified: 2020-03-13 – Entry created: 2020-02-15

Headphone Output Impedance Calculator

Here's a little JS-based online adaptation of one of my spreadsheets. With this you can determine how much a given amplifier output impedance will warp frequency response with a variable-impedance load like headphones or speakers when compared to an ideal 0-ohm output (or optionally, when compared to a given baseline output resistance). You can also have output resistance estimated if you have determined a certain amount of frequency response deviation. Headphone impedance plots can be obtained from various places.

Determine frequency response deviation

Data entry ohms * **
ohms *
ohms
ohms (optional)

*) within audible range, ~40 Hz .. 15 kHz recommended
**) May be same as nominal impedance |Z_n|

Results dB peak-peak
dB peak-peak

And now the inverse:

Determine output resistance

Data entry ohms * **
ohms *
dB peak-peak

*) within audible range, ~40 Hz .. 15 kHz recommended
**) May be same as nominal impedance |Z_n|

Results ohms

Technical background

When a load whose impedance varies over frequency is attached to an amplifier with a given output resistance, a complex voltage divider is formed. As a result, the signal received by the load becomes frequency-dependent, with higher impedance giving higher levels. For example, many big open headphones have an impedance peak in the 80-100 Hz vicinity, which thus results in increased bass levels. The impedance response of multi-driver balanced armature IEMs can even be a real rollercoaster (e.g. Triple.fi 10s, varying betwen about 7 and 65 ohms), potentially resulting in significant coloration. See the Headphone Outputs That Suck article for more information.

A few headphones actually sound their best when operated with a nonzero output resistance. Thus the option for a baseline Rout as a reference point.

My rule of thumb is that you're doing fairly well if the deviation from the ideal response is about 1 dB maximum. Perfectionists will want to shoot for about 0.3 dB (the approximate limit of audibility), especially if the critical region is found somewhere from midbass to several kHz.

Back to topics

Entry last modified: 2020-02-15 – Entry created: 2013-09-22

Output noise calculator for opamp-based amplifiers

Say you want to build an opamp-based headphone amp or preamplifier (or a power amp or literally anything else with something that behaves like an opamp) and would like to know what sort of output noise levels to expect in the audible range. Here's a little online calculator for you.

[Schematic: Example noninverting amplifier]
Noninverting amplifier with part names. (Current noise source at inverting input is missing.)

Data entry

Opamp noise specs (optional) nV/√(Hz)
pA/√(Hz)
nA
Part values kOhms
kOhms
kOhms (optional)
kOhms (optional)
kOhms (optional)
Misc. K
kHz

Change any value or click "Go!" to proceed. – Also see notes.

Results

Gain
dB
Minimum noise floor @ low volume nV/√(Hz)
ÁVrms

nV/√(Hz)

nV/√(Hz)
Maximum noise floor w/ source nV/√(Hz)
ÁVrms

Maximum noise floor, no source nV/√(Hz)
ÁVrms

Notes

Note 1: If you fill in input bias current, a lower boundary of input noise density will be calculated. It's the shot noise contribution √(2*q*2Ib) ("fudge factor" of 2 currently under investigation). For obvious reasons, this only gives sensible results for parts without input bias current cancellation. Parts employing this may actually show substantially higher current noise density than spec when confronted with unbalanced impedances, e.g. more than twice in the LT1028 or LT1115.

Note 2: If you need a unity gain follower, enter some very large number for Rg (at least a factor of 1000 greater than Rf or so).

Note 3: For a circuit without a volume pot, enter its source resistance into the Rseries field. Sources are assumed noiseless, which may not be the case in practice.

Note 4: A parallel resistor Rpar to ground at the input is not taken into account as its contribution to noise is usually negligible in practice, being much larger than highest source impedance seen by the opamp with a source connected (which usually is (Rpot + Rsource)/4 + Rseries, while that parallel resistor tends to be in the order of Rpot or greater). If this is not the case yet accurate worst-case (no source) results are desired, input a value of Rpar || Rpot in the Rpot field.

Note 5: You can also use this calculator for determining the noise of a basic inverting circuit (minus the Rpot and Rsource related niceties). After all, that one only swaps the signal (voltage) source and ground reference when compared to its noninverting cousin, and voltage sources are shorts in a small-signal model, so signal input is totally equivalent to ground here.

What it does

The calculator first computes the impedances that the opamp sees at its inverting and noninverting inputs for 3 different cases (minimum volume, maximum source impedance with a source connected, and maximum source impedance with the input left open). Then these are added (a little trick, equivalent to RMS summing their voltage noise) and their corresponding thermal voltage noise density is computed. The same value times opamp in gives the current noise contribution. Finally the previous two terms and opamp en are RMS summed, giving total input-referred noise density. (Equivalent opamp voltage noise density is the RMS sum of en and the in-related contribution.) Applying noise gain gives output noise density, which times √(20000 Hz) gives total output noise within 20 kHz. That value referred to 1 V in dB gives dBV.

It is assumed that any coupling capacitors are big enough for their effect to be neglected.

Back to topics

Entry last modified: 2020-03-21 – Entry created: 2013-09-16

A few useful spreadsheets

These are mainly geared towards the headphone user. OpenDocument format.

Back to topics

Entry last modified: 2012-06-03 – Entry created: 2010-07-01


© Stephan Gro▀kla▀ 2020. Commercial duplication of this content, including eBay descriptions and similar, with prior permission only.

Contact me

Created: 2020-02-21
Last modified: 2020-03-13