How do I plot noise gain of an op amp circuit in SPICE?

Question

How is an AC analysis of the noise gain of an op amp circuit plotted in LTspice?

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This is a follow-on question to a prior question here: What is noise gain, really? And how is it determined in the general case?

Answer 1

Plotting the noise gain of an op amp circuit is not too challenging if that's the only trace you want. You simply insert an AC voltage source at the non-inverting terminal, remove (short) any other signal source, and perform an AC analysis.

For a simple non-inverting amplifier circuit this is simply changing the signal source to an AC source and plotting V(out)/V(v+). If you use an AC amplitude of 1, it's simply V(out).

The violet trace below exactly overlays the yellow trace beneath it, showing that the simpler V(out) expression is equivalent when the test signal is AC 1.

If the \$+\$ terminal is grounded, as it is in an inverting amplifier circuit, you simply insert the V_test signal source between the \$+\$ terminal and ground.

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Things get trickier when we want to plot another gain at the same time. However, if we want to plot noise gain against loop gain, we can take advantage of the relationship between the two:

\begin{align} \\ NG & = \frac{A_o}{1 + A_o\beta} \\ \\ LG & = A_o\beta \\ \\ NG & = \frac{A_o}{1 + LG} \end{align}

Expressions for both \$A_o\$ and \$LG\$ are available in a loop gain analysis:

\$A_o\$: V(out) / (V(v+) - V(v-))

\$LG\$: V(fb) / V(v-)

Combining them we get this expression (note the minus sign in the denominator to account for application to inverting terminal):

\$NG\$: (V(out) / (V(v+) - V(v-))) / (1 - (V(fb)/V(v-)))

Using this expression we can plot noise gain (cyan) on the same chart as loop gain (violet) and open loop gain (yellow). Note that SPICE shorts V_sig during this .AC analysis; V_sig can be omitted (shorted) if desired without affecting the plot.

A note on the setup for the loop gain analysis: The AC 1 signal source provides the perturbation into the high-impedance inverting input. The loop response appears on its other side, the node labeled fb. The loop gain is plotted with the expression V(fb)/V(v-) in an .AC analysis.