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.
Applying KCL at node a,
Substituting these in Equation.(1) yields
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.
This is a differentiator with
For 0 < t < 4 ms, we can express the input voltage in Figure.(2b) as
This is repeated for 4 < t < 8 ms. Using Equation.(2), the output is obtained as
Thus, the output is as sketched in Figure.(3).