Phase Modulation & Demodulation

Principle of Phase Modulation

In Phase Modulation, the modulating signal is used to vary the phase of the carrier signal.

The instantaneous phase of the carrier signal is given by:

φ(t) = φc + kpm(t)

where φc is the phase of the unmodulated carrier signal, k is the sensitivity of the phase modulator, and pm(t) is the modulating signal.

Expression for Phase Modulation

The Phase Modulation can be mathematically expressed as:

s(t) = Ac cos[2πfct + kpm(t)]

where s(t) is the modulated signal, Ac is the amplitude of the carrier signal, fc is the frequency of the carrier signal, and k is the sensitivity of the phase modulator.

$v(t) = A_c \cos\left(2\pi f_c t + k_p \int_{-\infty}^t m(\tau) d\tau\right)$

Where:

v(t) is the phase modulated waveform
A_c is the amplitude of the carrier signal
f_c is the frequency of the carrier signal
k_p is the phase sensitivity constant
m(t) is the message signal

Phase Modulation Equation

φ(t) = φ_msin(2πf_mt + K_psin(2πf_mt))

Phase Demodulation

Phase Demodulation is the process of recovering the modulating signal from the Phase Modulated signal.

The most commonly used phase demodulation techniques are:

Coherent Detection
Non-Coherent Detection

Demodulation is a process to recover the original signal. It is function at the receiving end. It converts the signal into its original form. Demodulation of PM is also related to the demodulation of FM. Let the output of the FM demodulator be y(t). The modulated signal is directly proportional to the output of the FM demodulator

m(t) ∝ y(t)

Where, m(t) is the modulated signal

m(t) ∝ θ(t)

The message is also proportional to the phase angle of the modulating system. It is the condition for the phase modulated signal.

y(t) ∝ dθ(t)/dt

y(t) = kdθ(t)/dt

A constant is always substituted in place of the proportionality symbol. Where, K is the proportionality constant Thus, we get a recovered message signal from the phase modulated input by placing the integrators after the frequency discriminator or frequency demodulators in FM.

The phase demodulation formula is:

$\hat{m}(t) = \frac{1}{k_p}\frac{d}{dt} \left[\sin\left(2\pi f_c t + \phi(t)\right)\right]$

The formula for phase demodulation is:

Δθ = arctan Δf f_m

where:

Δθ = phase deviation
Δf = frequency deviation
f_m = modulating signal frequency
arctan = inverse tangent function

Phase Demodulation Equation

V_d(t) = 2K_pf_mcos(2πf_mt) + 2K_pf_mcos(2πf_mt)sin(2πf_mt)

Phase Deviation Formula

Δφ = K_pA_c

Applications of Phase Modulation

The applications of Phase Modulation are listed as follows:

Sound Synthesis
PM is less susceptible to noise interference and popping sounds than AM. Hence, it is suitable for sound broadcasting, commonly referred to as sound synthesis.
Digital Synthesizers
PM is used in digital synthesizers for the generation of signals and waveform.
Telephone communication
PM is widely used in telephone communication due to its high-speed transmission.

Advantages of Phase Modulation

The advantages of Phase Modulation are as follows:

High speed
Phase modulation is considered as one the fastest modulation technique. It is due to the pulse generation at high speed.
Low signal power consumption
PM requires low signal power consumption due to its better efficiency and fast speed.
Simple circuit design
The components required in the phase modulated circuit are less as compared to FM. Hence, it has a simple circuit design.
Easy modulation and demodulation
Phase modulation and demodulation is easy as compared to PM due to its simple circuit design..

Disadvantages of Phase Modulation

The disadvantages of Phase Modulation are as follows:

Low noise immunity
PM has less noise immunity than FM. It is because the frequencies are less affected by external disturbances than phase. Hence, PM has low noise immunity than FM.
Complex circuitry during conversion from FM to PM
The conversion process from frequency modulation to phase modulation is complex. It is due to the additional components required for the conversion.
Low signal to noise ratio
PM has a low signal to noise ratio than FM. It is due to the higher bandwidth of FM.