Background: Develop a Simulink model for an FM modulator whose output is describ

Question

Background: Develop a Simulink model for an FM modulator whose output is described by x_FM(t) = A_c cos[2 pi f_c t + 2 pi k_f integral_-infinity^t s(alpha)d alpha] Assume k_f = 5 Hz/V, f_c = 10 Hz, and modulating waveform s(t) = cos(2 pi t). Display the message and modulator output waveform. Procedure: The message signal is processed by the cascade of Discrete-Time Integrator block (from the Simulink Discrete library) and Gain block (from Math Operations Library) to generate the k_f integral_-infinity^t s(alpha)d alpha. A Ramp block from Simulink Sources library is used to produce the f_ct. The combined signal f_ct + k_f integral_-infinity^t s(alpha)d alpha is applied to an Fen block from the User-Defined Functions library to produce the FM signal. The sample time parameter value of 1/100 is selected.

Explanation / Answer

1. Go to sin block and put frequency =1 and phase = 90 and sample time parameter is 1/100

2. use integrator block and connect with sin block.

3. Now gain block and gain is 5.

4. Now use ramp block with function 5t

5. Now use adder block to add gain block output and ramp block o/p as input of adder.

6. Now use function block with cos(2*pi*f(t)). where f(t) is output of adder.

7. now use scope block with 2 input. first is sin block with phase 90 and frequency 1. and other is output of fcn block

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