## Friday, November 20, 2020

### Audio Amplifier Feedback - Non-Inverting OpAmp

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

Let us see how the feedback theory from my last week's post applies for a opamp in a typical non-inverting configuration:

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.

Using the formulas from last week's post:
$$STF={A \over (1-A*B)}={A \over (1+A*{R_1 \over R_1+R_2})}$$
$$ETF={1 \over (1-A*B)}={1 \over (1+A*{R_1 \over R_1+R_2})}$$
$$LG=A*B=A*{R_1 \over R_1+R_2}$$
As $A$ (and hence $LG$) increases, $STF$ approaches the familiar ${R_1+R_2 \over R_1}=1+{R_2 \over R_1}$.

One special case here is an opamp connected as a unity gain buffer:

This is equivalent to the general non-inverting connection with $R_1$ open and $R_2$ shorted. In this case, $B=-1$ and
$$STF={A \over (1-A*B)}={A \over (1+A)}$$
$$ETF={1 \over (1-A*B)}={1 \over (1+A)}$$
$$LG=A*B=A$$
$LG$ equals $A$ - in this configuration, all available open loop gain is applied to reduce the output error. As $A$ increases, $STF$ approaches unity.

In the next post, I will look at the opamp in the inverting configuration.