Op Amp Differentiator Circuit and Equation

Differentiator has the same logic as the integrator. We only need to switch the capacitor position with the resistor, and vice versa.

Op Amp Differentiator Circuit


A differentiator is an op amp circuit whose output is proportional to the rate of change of the input signal.

In Figure.(1a) in the “Integrator Circuit“, if the input resistor is replaced by a capacitor, the resulting circuit is a differentiator, shown in Figure.(1) below.

op amp differentiator
Figure 1. An op amp differentiator.

Applying KCL at node a,

op amp differentiator


op amp differentiator

Substituting these in Equation.(1) yields

op amp differentiator

showing that the output is the derivative of the input. Differentiator circuits are electronically unstable because any electrical noise within the circuit is exaggerated by the differentiator. For this reason, the differentiator circuit in Figure.(1) is not as useful and popular as the integrator. It is seldom used in practice.

Op Amp Differentiator Circuit Example

Sketch the output voltage for the circuit in Figure.(2a), given the input
voltage in Figure.(2b). Take
vo = 0 at t = 0.

op amp differentiator
Figure 2

This is a differentiator with

op amp differentiator

For 0 < t < 4 ms, we can express the input voltage in Figure.(2b) as

op amp differentiator

This is repeated for 4 < t < 8 ms. Using Equation.(2), the output is obtained as

op amp differentiator

Thus, the output is as sketched in Figure.(3).

op amp differentiator
Figure 3

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