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## FM MODULATION AND DEMODULATION

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**Angle Modulation**• 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.**General Forms**• The expression for an angle modulated signal is: • The instantaneous phase of s(t) is: • The instantaneous frequency of s(t) is:**Phase Modulation**• For phase modulation: Where; kp : sensitivity in rad/v • Hence, the general form of the PM signal is:**Frequency Modulation**• For frequency modulation: By then Where; kf : sensitivity in Hz/v • Hence, the general form of the FM signal is:**Instantaneous Frequency**• 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.**FM Modulation Index & Bandwidth**• The FM modulation index β is defined as the peak frequency derivation dividedby the message frequency. • It is given by the following formula: • Carson’s rule: A 98% power bandwidth can be obtained using the simple formula:**Generation 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 :**- The VCO output is:**- The VCO output represents the FM signal.**FM Demodulation**• 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:**PLL Components**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:**- 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 .