[ProAudio] Microphones question

Dan Lavry dan at lavryengineering.com
Sat Jun 12 07:42:19 PDT 2021

Hi again,

Impedance is one thing, but my question is about circuit generated 
noise, not impedance. The noise generated by a theoretical resistor is 
sqrt(4*K*T**R** BW). It is NOT sqrt(4*K*T**Z**BW)  where R is a pure 
resistor, Z is the impedance.

Here is a simple example is a single 300 Ohm resistor in parallel with a 
capacitor 17pF capacitor. The 300 Ohm resistor generates around 3.13uV 
at room temp and 20KHz BW. The capacitor generated noise (BW*K*T/C) is 
only 0.034uV. Capacitor generated noise is very tiny unless you use very 
small cap values (such as in semiconductor switched cap filters in sigma 

The capacitors may impact the frequency response. In this simple example 
In the example (300 Ohm, 17pF), the BW is limited by single pole at 
31MHz. Take a 6mH in series which that translate into around 753 Ohm at 
20KHz. It may alter the impedance significantly, and impact flatness 
response some, but the *higher* impedance in series, against say 6.8Kohm 
Phantom load resistors, actually *attenuates* the noise and the signal.

The capacitors and inductors of the mic (equivalent circuit) together 
with the load (micpre input) may shape the frequency response, thus 
indirectly impact the noise (and the signal) over the BW of interest, 
but higher impedance is not a direct cause of generated noise. Resistors 
are the thermal noise generators.

While I simplified things a lot, accounting for noise begins with 
figuring the individual components contributions over the BW of 
interest, and then accounting for frequency response (integral of noise 
over freq). It gets easier for flat response. This is very different 
then figuring impedance. Analyzing noise is about multiple noise sources 
at each component interacting with the circuit.  Analyzing impedance is 
about circuit interaction with signals and not about generating the 

The 300 Ohm Bill suggested for SM57 seems like a good estimate (ignoring 
the cap and inductance). Even at 20KHz, with the 800 Ohm series 
impedance against the 6.8K input, the impact (attenuation) is small, and 
actually reduces the signal and noise slightly.

It seems to me that suggested LCR and impedance measurements are not 
appropriate for noise estimation, and the old single resistor model 
works better. The question is still the resistance value...


Dan Lavry

On 6/11/2021 11:46 PM, Bill , via ProAudio wrote:
> My analysis of the SM57 appeared in the chapter I co-wrote with 
> Michael Pettersen of Shure. It's in the Ballou "Handbook for Sound 
> Engineers" 3rd edition, Chapter 21 "Preamplifiers and Mixers," pages 
> 601-602.  It may be in a different chapter and page number in the 4th 
> and 5th editions.  Anyway, the parameters for the equivalent circuit are:
> (capsule) =12 Ω and 157 µH in series, feeding the primary of a
> transformer = 1:4.5 ratio, DCRs 1.2 Ω pri and 24 Ω sec, sec L = 2.75 mH
> which, impedance converted through the transformer, becomes equivalent 
> to 6 mH in series with 300 Ω across pins 2 and 3 (each having 17 pF of 
> capacitance to the case.
> The measured impedance, not surprisingly, never goes below 300 Ω and 
> broadly peaks at 530 Ω at 150 Hz, again returning to 300 Ω between 1 
> and 2 kHz, then rising to 500 Ω at 10 kHz and 800 Ω at 20 kHz.
> If I had to choose, a 300 Ω resistor would be a fair approximation for 
> calculating noise in the frequency range (about 1 to 5 kHz) where 
> noise is most audible at low levels.
> Bill Whitlock
> AES Life Fellow
> Ventura, CA
> -----Original Message-----
> From: Bill Whitlock via ProAudio <proaudio at bach.pgm.com>
> To: proaudio at bach.pgm.com <proaudio at bach.pgm.com>
> Sent: Fri, Jun 11, 2021 10:03 pm
> Subject: Re: [ProAudio] Microphones question
> I'll be showing my age here, but the EIA or Electronic Industries 
> Association set standards for components used in consumer gear back in 
> the 50s, when I was young repair tech. They defined speaker impedance 
> as the value on the impedance vs frequency curve as the first minimum 
> after the first maximum as frequency is increased ... and the most 
> common standard was 3.2 ohms.  In most cases, it represented the 
> lowest impedance over the audio frequency range.
> And I think you're right that I published both the equivalent circuit 
> and the impedance curve for the SM57 in the Ballou book.  Today, I 
> only checked the version posted at the Jensen website, which I think 
> is the 3rd edition.  I'll check my manuscripts for the piece in the 
> 4th or 5th edition.  If I find it, I'll post it here. I'm guessing 
> that there are a lot of impedance plots that are never published by 
> mic manufacturers.
> Bill
> -----Original Message-----
> From: Jim Brown via ProAudio <proaudio at bach.pgm.com>
> To: proaudio at bach.pgm.com
> Sent: Fri, Jun 11, 2021 8:25 pm
> Subject: Re: [ProAudio] Microphones question
> On 6/11/2021 6:47 PM, Bill Whitlock via ProAudio wrote:
> > As I recall from my tests of the SM57, its impedance varied from under
> > 150 Ω at very low frequencies to over 300 Ω at resonance - and 
> continued
> > to rise at higher frequencies.  I'll try to find the data - I did the
> > tests as research before writing Jensen AN-005 about mic splitters.
> I remember seeing that data, perhaps in your chapter in the Ballou
> Handbook for Sound Engineers.
> To others -- it's important to realize that the impedance of a dynamic
> mic is complex, because it's equivalent circuit is complex. Remember
> that a dynamic mic is the analog of a single driver loudspeaker. If I
> remember correctly, the nominal impedance of a mic is defined by the
> manufacturer as 1/5 of the minimum load impedance. Someone will correct
> me if my memory has failed me. For loudspeakers, it's the minimum value
> of its impedance when plotted vs frequency, and it's impedance typically
> varies by at least two orders of magnitude over its operating range.
> Jim Brown
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