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.

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

Multiplying by 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 is the point
in time when the integrator goes into operation.
We will usually take 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.

Fri Mar 14 11:57:03 CST 1997