Noise Gain

The term "noise gain" is used a lot in designs with opamps.  So what is noise gain and how is it useful?

If we model the opamp noise with a noise source at its non-inverting input, the noise gain is the closed-loop gain of the circuit (with signal sources disabled).  Note that the noise gain is the same as the signal gain in the canonical non-inverting configuration.  In the standard feedback configuration, the opamp open-loop gain is A and the feedback factor is b, then the closed-loop gain is A/(1+Ab), which reduces to 1/b when A is large.  The stability of the circuit is depended on Ab; if we denote the noise gain n, we can analyze the stability from A/n, and in a Bode plot, the point of interception of the magnitude of A and n is where the magnitude of A/n equals to 1.  The amount of phase shift at this point determines the stability.  We can do a quick stability check by looking at the rate of closure of A and n: if A and n intercept with 20dB per decade, the circuit is stable; if A and n intercept at 40dB per decade, the circuit is likely unstable because it would have 2 poles contributing total180 degrees phase shifting.

We just consider the non-inverting configuration; for other configurations, the noise gain is not the same as the signal gain, but the noise gain plays the same role in determining the stability.  There are ways to increase the noise gain without changing the signal gain to achieve greater level of stability.