The circuit in Figure P15.23 is a switched-capacitor integrator. Let (C_{F}=) (30 mathrm{pF}) and (C_{1}=5 mathrm{pF}), and

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The circuit in Figure P15.23 is a switched-capacitor integrator. Let \(C_{F}=\) \(30 \mathrm{pF}\) and \(C_{1}=5 \mathrm{pF}\), and assume the clock frequency is \(100 \mathrm{kHz}\). Also, let \(v_{I}=1 \mathrm{~V}\).

(a) Determine the integrating \(R C\) time constant.

(b) Find the change in output voltage during each clock period.

(c) If \(C_{F}\) is initially uncharged, how many clock pulses are required for \(v_{O}\) to change by \(13 \mathrm{~V}\) ?

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