Operational Amplifier / Op Amp Gain

- a simple summary of the gain given by various operational amplifier or op-amp, opamp circuits showing the formulas, formulae used for the calculations.

The gain of an operational amplifier or op-amp (opamp) circuit depends upon a variety of factors including the circuit configuration as well as the components around the operational amplifier chip itself. This page gives a summary or overview of the gain of the different operational amplifier circuits available.

Inverting op-amp gain

The circuit for the inverting op-amp circuit is shown below. This circuit has the output 180 degrees out of phase with the input and also provides a virtual earth input.

Basic inverting operational amplifier circuit

It is easy to derive the calculation for the op-amp gain. The input to the op-amp itself draws no current and this means that the current flowing in the resistors R1 and R2 is the same. Using ohms law Vout /R2 = -Vin/R1. Hence the voltage gain of the circuit Av can be taken as:

Av       =       - R2 / R1

As an example, an amplifier requiring a gain of ten could be built by making R2 47 k ohms and R1 4.7 k ohms.

Non-Inverting Op-Amp gain

The circuit for the non-inverting op-amp is shown below. It offers a higher input impedance than the inverting opamp circuit.

Basic non-inverting operational amplifier circuit

The gain of the non-inverting circuit for the operational amplifier is easy to determine. The calculation hinges around the fact that the voltage at both inputs is the same. This arises from the fact that the gain of the amplifier is exceedingly high. If the output of the circuit remains within the supply rails of the amplifier, then the output voltage divided by the gain means that there is virtually no difference between the two inputs.

As the input to the op-amp draws no current this means that the current flowing in the resistors R1 and R2 is the same. The voltage at the inverting input is formed from a potential divider consisting of R1 and R2, and as the voltage at both inputs is the same, the voltage at the inverting input must be the same as that at the non-inverting input. This means that Vin = Vout x R1 / (R1 + R2)Hence the voltage gain of the circuit Av can be taken as:

Av       =       1 + R2 / R1

As an example, an amplifier requiring a gain of eleven could be built by making R2 47 k ohms and R1 4.7 k ohms.

Summary

Op-amp gain or opamp gain is very easy to determine. The gain calculations for the different circuits is slightly different, but essentially both circuits are able to offer similar levels of gain, although the resistor values will not be the same for the same levels of op amp gain.