The op amp shown in Fig. 10.65 has an infinite input impedance, zero output impedance
Chapter 10, Problem 59(choose chapter or problem)
The op amp shown in Fig. 10.65 has an infinite input impedance, zero output impedance, and a large but finite (positive, real) gain, \(A=-\mathbf{V}_{o} / \mathbf{V}_{i}\). (a) Construct a basic differentiator by letting \(\mathbf{Z}_{f}=R_{f}\), find \(\mathbf{V}_{o} / \mathbf{V}_{s}\), and then show that \(\mathbf{V}_{o} / \mathbf{V}_{s} \rightarrow-j \omega C_{1} R_{f}\) as \(\mathbf{A} \rightarrow \infty\). (b) Let \(\mathbf{Z}_{f}\) represent \(C_f\) and \(R_f\) in parallel, find \(\mathbf{V}_{o} / \mathbf{V}_{s}\), and then show that \(\mathbf{V}_{o} / \mathbf{V}_{s} \rightarrow-j \omega C_{1} R_{f} /\left(1+j \omega C_{f} R_{f}\right)\) as \(\mathbf{A} \rightarrow \infty\).
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