Integrator

A circuit diagram of an opamp in a integrator configuration is shown in Figure 17.

**Figure 17:** Integrating amplifier.
$\begin{figure} \begin{center} \epsfig{file=images/opampimg5.eps}\end{center}\end{figure}$

The basic input-output relationship for the integrator circuit is

$\begin{displaymath}v_{out}(t) = -\frac{1}{RC} \int_0^t v_{in}(\tau) d\tau + v_{out}(0^-) . \end{displaymath}$

(16)

Exercise. Derive formula (15). Hint: Make use of Ohm's law for capacitors to work out the capacitor current, equation (17).

PSPICE file: inta1.sch. (For practical reasons, a 50 M $\Omega$ resistor is included in series with the capacitor.)

ANU Engineering - ENGN2211