# 20. The differential amplifier¶

This amplifier circuit has two symmetrical inputs. The voltage difference between these two inputs is amplified to produce an output with the difference amplified. Hence the name differential amplifier.

The circuit feedback is negative and comes from resistor R2.

## Profit calculation¶

The gain formula for this amplifier is as follows:

Taking into account that the resistance R1' = R1 and that the resistance R2' = R2.

In practice, it is important that the resistors R1 and R1' as well as R2 and R2' have a value as similar as possible to each other, to prevent the common input voltages from being amplified and only the difference between the input voltages being amplified. entrance.

## Input and output resistance¶

The input resistance at the common input voltage is:

And the input resistance to input voltage differences is:

The output resistance will be very low, ideally zero, because the output is directly connected to the output of the op amp.

## Simulation¶

In the following simulation we can see a differential amplifier to which two input voltages arrive. A sinusoidal input voltage, V1, is common to both inputs and its voltage is not amplified. The other triangular voltage, V2, represents the difference between the two input voltages and is amplified at the output.

## Exercises¶

Draw the schematic of an ideal differential amplifier. Add the differential gain formula below the drawing.

What type of feedback does the differential amplifier have? What resistance determines it?

What function does a differential amplifier perform? What does a differential amplifier not amplify?

Using the gain formula, calculate the gain that the simulated differential amplifier should have.

Modify the differential amplifier simulation so that resistor R1 has a slightly lower value, 9k. What happens to the output voltage of the circuit?

With the help of the circuit simulator draw a differential amplifier based on an ideal operational amplifier. The differential input resistance must be 100k ohms. The differential gain must be worth 10.

Add a 0.1 volt peak sinusoidal voltage generator between the inputs. Check that the voltage output is 1 volt peak.