SDCs are at a disadvantage relative to LDCs, right?
Correct. Brainfade on my part. Must be getting old or something.
Doubling the area of the diaphragm doubles the signal but less-than-doubles the noise, because the noise in one half of the diaphgragm is uncorrelated with the noise in the other half, and partly cancels. The signal gets 6 dB louder but the noise only gets 3 dB louder, so you get a net 3 dB improvement in SNR.
Quadrupling the area, like when going from 12 mm SDC to 24 mm LDC diaphragms, gives you 6 dB improvement in SNR.
Absolutely correct.
And "how much noise"?
NOTE, originally the numbers were off due to a unit conversion error!
Measurements on a circular electret microphone with a radius of 1.8 cm and a sensitivity of 5 mV/µbar yield Brownian‐motion noise voltages of about 9 nV|/Hz in the frequency range between 1 and 5 kHz.
So an LDC capsule (36mm Diaphragm) with
-46dB -26dB sensitivity had around 1.3uV noise from Brownian motion, or around
-72dB -92dB.
Common LDC Capsules are around 20mV/Pa so noise will be also lower by a factor 2.5, for around 0.52uV noise or 3.6nV|/Hz. So any J-Fet with < 3.6nV|/Hz at ~ 5kHz and up will degrade the flat band noise by less than 3dB, above 5kHz.
Trivial to scale from here for capsule size and sensitivity to get a first approximation of Brownian Motion noise.
Capsule capacitance and Resistor noise give us the LF noise function. A low leakage diode for biasing leads to less noise than a 1GOhm resistor and is likely easier to purchase for a DIY Enthusiast.
If our capsule above is 65pF and our effective resistance 500M (1G Bias and 1G after a coupling capacitor like commonly seen) will produce 410uV noise, but with a lowpass of ~ 5Hz (65pF x 500MOhm = 32500uS = 4.89Hz).
So 3uV|/Hz without lowpass becomes 300nV|/Hz at 50Hz, 30nV|/Hz at 500Hz and 3nV|/Hz at 5kHz. So we intersect the flat line Brownian motion noise at around 2
5kHz. We usually call noise with this behavior "1/LF" noise.
So our circuit noise is 3.6nV|/Hz for the flat (Brownian motion) part of the noise spectrum rising from ~ 5kHz to 300nV|/Hz at 50Hz and 530nV|/Hz at 20Hz.
That is for capsule, 1G bias resistor, 1nF coupling capacitor and 1G to ground, for a 20mV/PA or -34dB sensitivity capsule
With 3.6nV|/Hz in the flat band above 5kHz I must say I have few concerns that any sensible J-FET noise whatsoever will be of consequence for the complete microphone.
Note, all noise figures unweighted. For A weighting overlay this curve (which shows why A-weighted noise in microphones so low despite there being a ton of it):
I guess we can kill Brownian noise by using our microphones in a Vacuum and the resistor noise by doing it at very low temperatures close to absolute zero... 555
Thor
PS, this is not a high precision analysis of microphone noise, more a quick first order approximation that allows us to get a handle on the general magnitude of noise, not an 0.001dB accurate prediction.