Prelab 10: Op-Amp Differentiators and Integrators

1. Use time-based methods (i.e., differential equation representations) to confirm the input-output voltage relationships given for the ideal op-amp integrator and differentiator shown in figure 1 of the lab.

2. Use sinusoidal steady-state analysis to show the phasor input-output voltage
relationship is *H(jw) =
V _{o}/V_{in} = -jwRC* for the
ideal differentiator and

3. Figure 2 of the lab shows a practical implementation of a
differentiator. Derive the transfer function
*H(jw) = V _{o}/V_{in}* for
this circuit. For what frequencies does the circuit act as a differentiator?
What effective operation is performed by the circuit at high frequencies?

4. Figure 3 of the lab shows a practical implementation of an integrator.
Derive the transfer function
*H(jw)=V _{o}/V_{in}* for
this circuit. For what frequencies does this circuit act as an integrator?
How does the circuit respond to low frequencies?