An operational amplifier configured as an inverting amplifier is one of the most widely used configuration. Hence we must study how the feedback resistors affects the overall gain. In this section we shall study how to calculate the gain of inverting amplifiers.

Let us look at the circuit diagram of inverting amplifier. Observe how the current from the source divides into base current and the current through the feedback resistor.

Analysing the current through the feedback loop

We apply Kirchoff’s current law at the node. The current from the signal source iin divides into iF(current through the feedback resistor) and the base current IB.

Hence iin = iF  + IB

Here the base IB current is very small. Typical value of base current is 0.5μA for 741C operational amplifier. For the sake of simplicity, we neglect base current in comparison with iin and iF. Hence the above equation may simply be written as

iin ≅ iF

Let us simplify the above equation. From the figure given above, we can write the equation as follows.

equation 1

However, since the non-inverting terminal of the op-amp is connected to ground, the inverting terminal is approximately at the ground potential. The inverting terminal is said to be at virtual ground.  Rewriting the above equation, we get the following expression.

equation 2

Rearranging the above equation, we get.

equation of gain of inverting amplifier

Hence the gain of inverting amplifier is equal to the ratio of feedback resistance RF to the input resistance R1. We can conclude from the above equation that the gain of inverting amplifier is independent of the open loop gain of op-amp. The gain of inverting amplifier is dependent on external components (resistors). Thus we can control the gain of inverting amplifier using external resistors. In the sections to follow, we shall also see how to select the value of those resistors in the inverting amplifiers.