530 The circuit in Fig P530 is excited by the source wavefor

5.30 The circuit in Fig. P5.30 is excited by the source waveform shown in Fig. P5.25(b) R1 i(t) s() (t Figure P5.30: Circuit for Problem 5.30 (a) Derive Fourier series representation of i(t) b) Calculate the first five terms of using Ri R2 100 , L = l mH, and C = I «F c) Plot i(t) and vs() using nmax-100

Solution

a) i(t) = vs/( R1 + R2*sc /(R2 + sC)

fourier transform = vs( 1 - e^-t/(R1+R2)C)

B) v(t) = 100 + 0.1s/( 1000 + s^{2 )}