Question

3. (35 pts) Consider a standard RLC circuit with a resistor R, inductor L and capacitor C all in series driven by a voltage source v(t). The voltage source gives pulses of 5 volts that last 1 msec every 10 msec, i.e. a square wave with period 10. We are interested in the output y(t) which is the current flowing through the circuit at time t. (a) Find a general expression for the frequency response H(jw) of this system (b) Let R-5, C 0.1, L-02. Plot by hand using straight-line approximations the gain lH(jw)| in dB vs. ω using a log scale for the x-axis. Use a range ofw E (10-2, 104) (c) Now, plot the gain in Python over the same range. Some functions you might find useful for this are: np.logspace), np.abs), and plt.semilogr(). Turn in both the code and plot (d) Find the Fourier series representation of the output current y(t) (e) Using this representation and the synthesis equation, plot y(t) in Python for the first 20 harmonics. Turn in both the code and plot

Answer 1

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