operational amplifier - Benefits of multiple op-amp gain stages in series?

I'm a bit lost in regards to how multiple op-amps in series will perform. My use case would be the amplification of low-voltage audio signals (4-50mVRMS) to roughly 8VRMS.

I only found documentation on how gain will influence the bandwidth-product of the amp, but I'm lost when it comes to noise and distortion. I was hoping to achieve better performance regarding amplification of the signal when using multiple gain-stages in series, but didn't find any documentation that would suggest an improvement in performance when doing so.

Is there any benefit in chaining multiple amps together in series other than improving the bandwidth-product of the circuit?

Answer

Noise:

Say your opamp has GBW of 10MHz and noise of 1µV (to keep things simple). The source has 1µV RMS noise also.

Each opamp will amplify its own noise by the circuit noise gain, plus the noise of everything upstream, of course, by the circuit's gain. So you want the gain of the first stage to be high enough (say, at least 10) so that the noise of the source and the first opamp (which are now amplified 10x) dominates the noise added by the other opamps downstream.

So, here:

• say we want a gain of 100, 1st opamp has gain G1=10, 2nd has gain G2=10.

1st opamp amplifies source noise (1µV), plus its own (1µV) by G1, this adds up in RMS so at the output of OPA1 we got 14µV, this is then amplified by G2 and we have 141.7µV noise at the output.

• G1=1, G2=100

1st opamp simply adds its own noise to the source (1.4µV at output), then second opamp adds its own noise and amplifies 100x. We get 172µV noise at the output.

This only matters if the source is low-noise. If source noise is higher than what OPA1 will add, then it matters much less.

Note: This also applies to offset voltage, which may be the dealbreaker sometimes.

Distortion:

Your opamp has GBW of 10MHz. You want a gain of 160-2000.

With one opamp, you spend 2000 off your GBW on gain. So only 10M/2000=5kHz GBW remains for correcting distortion and, even more important, actually processing the signal!

Here, the circuit will have a closed-loop bandwidth of around 5kHz, and horrid distortion above a few hundred hertz, since there is very little loop gain to correct opamp nonlinearities.

If both opamps are identical, the best distortion will be achieved by having them share the gain equally, ie both with a gain of 44, the product of which is 1936.

This may interfere with noise considerations, but in this case, it should not.

If this is for precision DC, remember closed loop gain accuracy depends on available open loop gain (GBW divided by Gain).

Gotchas

The first opamp need not be rail to rail, nor high output current, which gives a wider choice of low-noise or precision opamps. Its output current drive and slew rate matter less than the second opamp (see Null's answer).

The second amp need not have a high precision input stage, doesn't need to be FET either, as it is driven from a low impedance. It can have strong output drive, or rail to rail, if needed. Or it can just be cheaper...

But... input stage common mode distortion in non-inverting mode will be worse in the second opamp (good thing it's not JFET then).