1. FM MODULATION AND DEMODULATION

2. A NGLE M ODULATION To generate angle modulation, the amplitude of the modulated carrier is held constant and either the phase or the time derivative of the phase is varied linearly with the message signal.

3. G ENERAL F ORMS The expression for an angle modulated signal is: The instantaneous phase of s(t) is: The instantaneous frequency of s(t) is:

4. P HASE M ODULATION For phase modulation: Where; kp : sensitivity in rad/v Hence, the general form of the PM signal is:

5. For frequency modulation: By then Where; kf : sensitivity in Hz/v Hence, the general form of the FM signal is: F REQUENCY M ODULATION

6. I NSTANTANEOUS F REQUENCY The instantaneous frequency for FM signals is: Note: The instantaneous frequency; fi(t) will have the same shape of that of the message since the message is hidden in the frequency.

7. FM M ODULATION I NDEX & B ANDWIDTH The FM modulation index β is defined as the peak frequency derivation divided by the message frequency. It is given by the following formula: Carson’s rule: A 98% power bandwidth can be obtained using the simple formula:

8. G ENERATION OF FM SIGNALS In a direct FM, the instantaneous frequency of the carrier is varied in accordance with m(t) by means of a voltage – controlled oscillator ( VCO ). VCO is a linear frequency modulator. It is an oscillator with a voltage reactance that controls the oscillator output frequency The instantaneous frequency of the VCO is given by: The VCO Characteristics :

9. - The VCO output is: - The VCO output represents the FM signal.

10. FM D EMODULATION Phase Locked Loop: - PLL is a negative feedback control loop in which the feedback signal is used to lock the output frequency and phase of any input signal. - The block diagram of PLL:

11. PLL C OMPONENTS 1. Phase detector ( phase comparator): It is a mixer (multiplier) followed by a low pass filter. The output voltage of the PD is a function of the phase difference between the two input signals. - If xi(t) represents the FM signal and xo(t) represents the VCO output : Hence:

12. - The low pass filter suppresses the high frequency term. Hence, the PD output is given by: - When the difference between the two phases is very small: Where; Kǿ is the PD sensitivity.