Exercise 6.1 Opamp configurations with reactive components

The figure below shows 2 circuits consisting of an opamp with a feedback network. In this exercise you may assume that the opamps are ideal, with infinite voltage gain.

a)

Derive a relation for the signal transfer $H(\mathit{j\omega })$ of the circuit with the capacitor, in figure (a).

b)

Derive a relation $\frac{v_{\mathit{out}}}{v_{\mathit{in}}}(t)$ of circuit (a) - the one with the capacitor. Note that this is a time domain transfer.

c)

Derive a relation for the signal transfer $H(\mathit{j\omega })$ of the circuit with the inductor, in figure (b).

d)

Derive a relation $\frac{v_{\mathit{out}}}{v_{\mathit{in}}}(t)$ of circuit (b): the one with the inductor. Note that this is a time domain transfer.