Question

Problem 24: (18 points) 1. (6 points) Figure 2 shows an RC circuit with input f(t) and output y(t) Function Generator R, v, (r) y1) Figure 2: RC circuit. (a) (1 point) Sketch the circuit in the phasor domain by replacing the capacitor with its impedance represen- (b) (3 points) Using circuit analysis techniques, show that the frequency response function is Specify the DC gain, K, and the time constant, T, in terms of the parameters R, R, and C (c) (2 points) Determine the magnitude. H w) and phase angle. LHC w) of the frequency response function in part (b) in terms of the parameters R, R, and C 2. (5 points) In part1 you obtained the frequency response function by applying circuit analysis techniques to the phasor domain representation of the crcuit In applications other than electronic circuits, for example control systems engineering, it is necessary to obtain the frequency response function directly from the ordinary differential equation that describes the input-output behavior of the system. Consider a system with input f(t), output y(t), and the ODE representation Q(D)y(t) P(D)f(t) d"" f = dtn dtn Suppose that the sinusoidal inp generates the sinusoidal steady-state response where the phasor representation of f(t) and y(t) are

Answer 1