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EE 212 Lab

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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(jω) = V*_{o}/V_{in} =
-jωRC for the ideal differentiator and *H(jω) =
V*_{o}/V_{in}= -1/(jωRC) for the ideal integrator.

3. Figure 2 of the lab shows a practical implementation of a
differentiator. Derive the transfer function *H(jω) =
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(jω)=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?