EE 212
Lab 9: Op-Amp Differentiators and Integrators


Op-amp circuits are often designed and implemented for signal differentiation and integration. Until recently (before computer-based control), control algorithms (such as PID) containing differentials and integrals were implemented in discrete circuit components. Differentiation is also useful for obtaining velocity measurements from a signal representing a position or determining a signal's frequency (recall the amplitude of the time derivative of a sinusoid is scaled by its frequency). Figure 1 below shows an ideal op-amp integrator and differentiator with input-output relationships that are theoretically correct, but have practical implementation issues discussed below. In this lab, practically realizable differentiators and integrators will be built using op-amps, resistors and capacitors.

1. The Differentiator

2. The Integrator

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