# 14.1 Introduction

Up to this point, we have examined a number of different op amp circuits and applications. Viewed from a purely mathematical perspective, the circuits perform basic functions. Amplifiers multiply an input quantity by a constant. Voltage-controlled or transconductance amplifiers can be used to multiply a quantity by a variable. Absolute value and logarithmic functions can also be produced. There is no reason to stop with just these tools; higher mathematical functions may be enlisted. In this chapter we shall examine circuits that perform integration and differentiation. Although these circuits may appear to be somewhat esoteric at first glance, they can prove to be quite useful. Integrators perform the function of summation over time. They may be used whenever an integration function is required, for example, to solve differential equations. The differentiator is the mirror of the integrator and may be used to find rates of change. One possible application is finding acceleration if the input voltage represents a velocity.

Integrators and differentiators may be combined with summing amplifiers and simple gain blocks to form analog computers, that can be used to model physical systems. This can be a valuable aid in the initial design and testing of such things as mechanical suspension systems or loudspeakers. Unlike their digital counterparts, analog computers do not require the use of a programming language, per se. Also, they can respond in real-time
to an input stimulus.

Besides the obvious use as a direct mathematical tool, integrators and differentiators can be used for wave shaping purposes. As an example, the square/triangle generator of Chapter Nine used an integrator. With the exception of simple sinusoids, both the integrator and differentiator will change the fundamental shape of a waveform. This might be contrasted with a simple amplifier that only makes a wave larger and does not alter the basic shape. For practical work, certain alterations will be required to the ideal circuits. The effects of these changes, both good and bad, will also be studied.