Differentiation Circuit

To obtain a differentiation circuit we replace the input resistor of the inverting amplifier with a capacitor as shown in figure 6.9.

 
Figure 6.9:  Differentiation circuit.

Replacing with in the voltage gain gives

or

Using dV/dt=I/C gives

and thus the same result as above.

The frequency response is shown in figure 6.10.

 
Figure 6.10:  Differentiation circuit frequency response.