Question

12 A function generator can be angle modulated with various 7-2 waveforms. Based on a 50-Hz sinusoid before modulation is applied, the output signal with modulation is v(t) 20 cos(100mt+6t) Determine (a) instantaneous signal phase and (b) instanta- neous signal frequency (radian and cyclic). (c) Sketch the forms of the instantaneous signal phase and frequency

Answer 1

The angle modulated signal is v (t) = 20 cos (100 pi t) + 6 pi t (a) Instantaneous signal phase in v (t) is theta_i (t) = 100 pi t + 6 pi t in rad theta_i = 106 pi (b) The instantaneous signal angular frequency w_i (t) = d theta_i (t)/dt w_i (t) = d/dt {100 pi t + 6 pi } c w_i (t) = d/dt {106 pi t} w_i (t) = 106 pi rad/s The instantaneous signal frequency f_i (t) = 1/2 pi w_i (t) f_i (t) = 1/2 pi 106 pi f_i (t) = 53 Hz (c) theta_i = 106 pi t f_i (t) = 53 Hz for all t