Question 6.3.4: Integration with Op Amps Determine the transfer function Vo(...

The impedance of a capacitor is 1/Cs. Thus, the transfer function of the circuit is found from (6.3.5) with Z_{i}(s) = R and Z_{f} (s) = 1/Cs. It is
\frac{V_{o}(s)}{V_{i}(s)} = − \frac{Z_{f} (s)}{Z_{i}(s)} = − \frac{1}{RCs}
Thus in the time domain, the circuit model is
v_{o} = − \frac{1}{RC} \int^{t}_{0}  {v_{i}  dt}            (1)
Thus the circuit integrates the input voltage, reverses its sign, and divides it by RC. It is called an op-amp integrator, and is used in many devices for  computing, signal generation, and control, some of which will be analyzed in later chapters.