[ProAudio] Microphones question

[Bill Whitlock]

You realize, of course, that the nominal impedance, 150 Ω or 200 Ω, of a mic is just that.  It's an ideal approximation that's useful to compare relative noise performance of preamplifiers - much like 4 Ω or 8Ω is for speakers. In reality, these impedances are quite frequency dependent and not purely resistive.  I did the analysis once for an SM57 but can't locate it at the moment.  I don't remember the exact numbers but the analysis runs something like this:  The mic has a dynamic capsule, whose "voice coil" has both DC resistance and inductance.  This is followed by a small transformer (a 1:3 step-up turns ratio in the SM57) and it has a parallel inductance and DC resistances on primary and secondary.  The goal is to calculate from these values to determine a first-order equivalent circuit at the mic output terminals.  The resistance and inductance (in series) of the capsule, plus the primary DCR of the transformer, values will be reflected through the transformer, multiplied by the square of the turns ratio, to the secondary side.  The open-circuit inductance of the transformer (as measured on the secondary) is now in parallel with the output as well.  From this, the purely electrical portion of the output impedance can be calculated. Of course, the mechanical resonances of the capsule will make the apparent inductive reactance of the capsule change with frequency, so the best course is to actually measure the impedance at the microphone output across frequency - for the purpose of determining how much noise voltage will be created by the preamp's noise current flowing in this impedance.  To calculate the thermal noise voltage created by the mic itself, only the equivalent DC resistance as calculated above is necessary - the reactive (inductive) components of impedance do not generate thermal noise.
If you have access to an LCR impedance bridge, it can resolve the impedance into resistive and inductive reactance components - a much quicker process.
Bill WhitlockAES Life Fellow(former Jensen Transformers owner)


-----Original Message-----
From: Dan Lavry via ProAudio <proaudio at bach.pgm.com>
To: proaudio at bach.pgm.com
Sent: Fri, Jun 11, 2021 12:44 pm
Subject: Re: [ProAudio] Microphones question

My question is about mic output impedance, in relation to noise:

Both the mic and the micpre contribute to noise. The micpre generates 
some noise voltage which can be measured by replacing the mic with a 
short (0 Ohm). But there is also mipre generated noise current, which is 
no problem for 0 Ohm, but real mics have some impedance...

At some point, it was decided to model a mic noise with replacing the 
mic with 150 Ohm resistor.  I am not proposing to change it, just trying 
to understand why 150 Ohm.

The value 150 Ohm makes 1.568nV/sqrtHz (at room temp), so for 20H-20KHz 
noise voltage of .225uV. Given that we are interested in noise power, we 
can use the dBu scale to realize that the resistor itself sets a limit 
on the noise floor at -130.9dBu. But say the impedance is 1K, then we 
have -122.8dBu.

I assume that the resistor modeling is a simplification. I would be 
interested in comments from the mic experts here.

Thank You

Dan Lavry


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