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) = Vo/Vin = -jωRC for the ideal differentiator and H(jω) = Vo/Vin= -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) = 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(jω)=Vo/Vin for this circuit.
For what frequencies does this circuit act as an integrator? How does the
circuit respond to low frequencies?