A sawtooth waveform f(t) shown in Figure 1 has amplitude A = 1 V and period T0 = 1 ms. The sawtooth signal f(t) is applied to a circuit shown in Figure 2. The output of the circuit is y(t). Let R = 800?, L = 100mH.
(a) Find the numerical values of an, bn, cn, ?n for 0 ? n ? 3.
(b) Represent f(t) as a sum of dc component, fundamental component, 2nd harmonic component, and 3rd harmonic component. The coefficients must be numbers.
(c) Find the transfer function H(?) of the circuit shown in Figure 2.
(d) Find the numerical values of |H(n?o)| and ?H(n?o) for 0 ? n ? 3. ?0 = 2?/T0.
(e) Find the magnitude ycn and phase y?n of the trigonometric Fourier coefficients of the output y(t).
(f) Represent y(t) as a sum of dc component, fundamental component, 2nd harmonic component, and 3rd harmonic component. The coefficients must be numbers.
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