A circuit has transfer function H (s) = . The circuit is excited by a sinusoidal

Question

A circuit has transfer function H (s) = . The circuit is excited by a sinusoidal input vin(t) = 2cos(omega t)u(t) V. Compute the magnitude and phase of the STEADY STATE output voltage at omega = 0, 100, and 1000 rad/s. Write down the steady slate output voltage sinusoid for each case. Which evaluations can be done approximately by inspection. A circuit with transfer function H(s) = is excited by the input Vin = 5cos(500t + 45 degree ) V. Compute the magnitude and phase of the STEADY STATE output voltage at omega = 200, 500,1000 and 10000 rad/s. Write down the steady state output voltage sinusoid in each case.

Explanation / Answer

(a) (1) When w = 0 rad/s, Output magnitude is 5 and phase is 0. Output is 5cos(wt)u(t) (2) When w = 100 rad/s, Output magnitude is 20.5132 and phase is - 81.6743. Output is 20.5132cos(wt - 81.6743)u(t). (3) When w = 1000 rad/s, Output magnitude is 141.4655 and phase is - 133.568. Output is 141.4655cos(wt - 133.568)u(t). (b) (1) When w = 200 rad/s, Output magnitude is 4.953 and phase is 37.1467. Output is 4.953cos(500t + 37.1467). (2) When w = 500 rad/s, Output magnitude is 4.953 and phase is 33.69. Output is 4.903cos(500t + 33.69). (3) When w = 1000 rad/s, Output magnitude is 4.9372 and phase is 35.91. Output is 4.9372cos(500t + 35.91). (4) When w = 10000 rad/s, Output magnitude is 4.999 and phase is 43.857. Output is 4.999cos(500t + 43.857).

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