The periodic voltage source in the circuit shown in Fig. P16.47(a) has the waveform

Chapter 16, Problem 16.47

(choose chapter or problem)

The periodic voltage source in the circuit shown in Fig. P16.47(a) has the waveform shown in Fig. P16.47(b).

a) Derive the expression for \(C_{n}\).

b) Find the values of the complex coefficients \(C_{o}, C_{-1}, C_{1}, C_{-2}, C_{2}, C_{-3}, C_{3}, C_{-4}\), and \(C_{4}\) for the input voltage \(v_{g}\) if \(V_{m}=54 \mathrm{~V}\) and \(T=10 \pi \mu \mathrm{s}\).

c) Repeat (b) for \(v_{o}\).

d) Use the complex coefficients found in (c) to estimate the average power delivered to the \(250 \mathrm{k} \Omega\) resistor.

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