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In this subsection, we'll only look at integrating a single input signal. However, the circuit and analysis given here can be extended as above to create a circuit that will integrate a weighted sum. The integrator is shown in Figure 7.

Figure 7:  An Integrator

Following the same type of analysis given above, the equating of input and feedback currents gives


Multiplying by tex2html_wrap_inline1346 and integrating both sides gives


Those in whose minds Calculus is fresh will notice that we've been a bit sloppy here. It is much more accurate to write


where c is an initial condition and tex2html_wrap_inline1350 is the point in time when the integrator goes into operation. We will usually take tex2html_wrap_inline1352 and always discuss time relative to that ``beginning of time.'' We'll have to be more careful if the computer causes itself to be reset with new initial conditions at various points during the computation. In those cases, we'll call the beginning of the whole computation time 0 and talk in relative terms about the intervals between resets.

Brian L. Stuart
Fri Mar 14 11:57:03 CST 1997