Building a microphone amplifier

You should consider the PSRR of the mic amp stage itself when considering system noise. If you have say 25nV/rt Hz spot noise but the amplifier itself has 80 dB PSRR then you will be ok - the input referred noise will be negligible.

Why? Why wouldn't the mismatch between the phantom supply resistors and the microphone output impedances affect the transfer from phantom supply noise to the differential signal?

By the way, we were discussing a supply with 14.4 microvolt per root hertz of noise.
 
Even though resistors might have a ±1% tolerance band, in any batch they are usually quite tightly matched not all over the place like your example. But in any case when I worked in professional audio nobody would just use 1% resistors out of a box for phantom power, they were always selected as matched pairs using a decent resistance bridge; likewise the input resistors for differential circuits. It's a no-brainer really.

I think I would be sacked immediately if I suggested using hand selected parts at work, but it is feasible for a DIY project. You also have to select the microphone for good output impedance balance, though, or just add a cheap RC filter.
 
I think I would be sacked immediately if I suggested using hand selected parts at work, but it is feasible for a DIY project. You also have to select the microphone for good output impedance balance, though, or just add a cheap RC filter.
In any modern production facility the process is (or should be) automated, likewise for the microphone manufacturer; just buy reputable brands, not shonky brothers' best price audio.
 
Input of the mic preamp, you mean?
Nope, not at all. The 48 volts is DC power for the microphone amplifier, not for the microphone capsule. Look at the attached example schematic.

A moving-coil capsule needs no DC power at all, and phantom power never goes anywhere near it.

If you have a condenser microphone capsule, it will most likely have an electret to provide it - no external power needed.
I've never seen a condenser microphone with 6.8 ohm output impedance, 100 ohm is more typical.
You have to work hard to take an op-amp with an open loop gain of 100,000, a closed-loop gain of 100, and still screw up the circuit enough to get a 100 ohm output impedance from it.

But let's say you've added 100 ohm series resistors to ensure stability when driving long cables, as in the attached schematic. One hundred ohms is roughly one order of magnitude bigger than 6.8 ohms, so you get roughly one order of magnitude less filtering, or 20 dB less. That still leaves a lot of filtering. Worrying about it being inadequate is pretty nit-picky.

But let's humour the nit-picking, and calculate more exactly. With a 100 ohm output resistance, fed through a 6.8k resistor, ripple and noise on the 48V line is still attenuated by 36 dB, just by the preamp output impedance alone. That drops the 1.4 mV total noise voltage down to about 20 microvolts.

And the mic signal at this point is likely to be line level, say 100 mV. S/N ratio will be 74 dB, already greater than actual acoustic S/N ratio in the room itself (typically set by cooling fans, air conditioner, distant traffic, the 'fridge humming in the kitchen, et cetera.)

But, as PRR said, it is easy to add a little bit of extra filtering (100 ohm / 100 uF + 10uF) and knock that down a lot more, especially if you use a 48 V switching supply with a high switching frequency. You get another 76 dB of filtering with that combination, if the ripple is from a 100 kHz switching power supply.

Power supply noise is now at -150 dB relative to microphone signal, and that is so low as to not even be on the list of things to worry about. Input hiss from the microphone preamp will be a lot larger than the phantom power hiss.

There is another thing we've been ignoring. A competently designed mic preamp will invariably have its own power supply rail filtering, in addition to the stuff we've been considering.

For example, in the attached schematic (taken from A Texas Instruments app note), notice that the mic preamp itself includes a 5.1V zener that will itself considerably attenuate any noise voltage coming in via the 48 V phantom power. The zener is followed by a 100 ohm / 33 uF low-pass filter to attenuate any noise voltage on the DC even more.

We can run endlessly in circles arguing about this and that minor detail, but it is a waste of breath time. PRR put it succinctly and accurately: "...the 48V has almost no effect on 'sound'..." (if the rest of the circuitry is designed by someone with at least minimal competence. )

-Gnobudddy
 

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We can run endlessly in circles arguing about this and that minor detail, but it is a waste of breath time. PRR put it succinctly and accurately: "...the 48V has almost no effect on 'sound'..." (if the rest of the circuitry is designed by someone with at least minimal competence. )

-Gnobudddy

I could go into three things I disagree with in your latest post, but I won't. Actually the main reason why I was arguing with you is not technical at all. It's the way you implicitly insulted everyone but PRR in post #12. If PRR is the voice of reason, then apparently everything waijin, johnmath, Enzo and I wrote in posts #1...#10 is unreasonable, even though we were converging on essentially the same solution as PRR: some sort of regulated supply with a bit of RC filtering.
 
Thank you for your suggestion. I read the manual of 317hv. Its 10hz-10khz output noise is 0.003% of the output voltage, 48V x 0.003 = 144mv square root Hz. It seems that the output noise is still very large. I don't think IC output seems to be a good scheme. Maybe I need to consider the scheme of voltage reference + power tube current expansion?
TPS7A4001 is a better choice because noise is about 60µV (really < noise of LM317H) and PSSR is same as LM317H. However the package is CMS 😉