A series RLC circuit is connected to a voltage source x(t). The output y(t) is taken across the capacitor. The negative side of x(t) and y(t) is the common ground. The values of the elements are: R=8.1250 Ohms, C= 1 farad, and L= 1.0 Henry.
Derive an ordinary differential equation relating y to x. Specify the poles of the circuit. Derive a transfer function H(s) for the circuit, using impedance and voltage divider concepts.
Specify the DC gain of the above circuit. Justify your answer. Specify the high frequency gain of the circuit. Justify your answer Based on 2.1 and 2.2 what kind of filter is this filter?
Write a matlab program to compute the gain and phase of this filter for 0 < w < 15 and plot the gain and phase versus frequency Label your plots accurately. Attach your commented program.