EE 212 Lab
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) = Vo/Vin = -jwRC for the ideal differentiator and H(jw) = Vo/Vin= -1/(jwRC) for the ideal integrator.







3. Figure 2 of the lab shows a practical implementation of a differentiator.  Derive the transfer function H(jw) = Vo/Vin 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)=Vo/Vin for this circuit.  For what frequencies does this circuit act as an integrator? How does the circuit respond to low frequencies?