## Friday, November 27, 2020

### Audio Amplifier Feedback - Inverting and Differential OpAmp

This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.

Last week, I examined how the basic feedback theory applies to a non-inverting opamp.

Let's look at the other common way of connecting an opamp - the inverting amplifier:

In the diagram:
• $A$ is the gain of the amplifier with no feedback applied (its open loop gain)
• $x$ is the input signal
• $y$ is the output signal
The feedback network consists of two resistors $R_1$ and $R_2$. The gain $B$ of the feedback network is that of a voltage divider: $$B=-{R_1 \over R_1+R_2}$$The minus sign here accounts for the fact that the feedback is applied to the inverting input of the opamp. This is the same as in the non-inverting configuration.

Unlike in the non-inverting configuration, the input signal arrives at the amplifier's input via a divider consisting of the same resistors $R_1$ and $R_2$. Effectively, the inverting configuration is a superposition of two circuits, one for feedback:
and one for the input signal:

The gain of the input divider is: $$-{R_2 \over R_1+R_2}$$As before, the minus sign here accounts for the fact that the attenuated input signal is applied to the inverting input of the opamp.

Now we can write down the Signal Transfer Function, the Error Transfer Function and the Loop Gain:
$$STF=-{A*{R_2 \over R_1+R_2} \over (1+A*{R_1 \over R_1+R_2})}$$
$$ETF={1 \over (1-A*B)}={1 \over (1+A*{R_1 \over R_1+R_2})}$$
$$LG=A*B=A*{R_1 \over R_1+R_2}$$
As $A$ (and hence $LG$) increases, $STF$ approaches the familiar $-{R_2 \over R_1}$.

The differential connection with R1=R3 and R2=R4 has the same STF and ETF as the inverting: