# Phase Modulation and its application

Phase Modulation (PM) is a type of modulation technique used for embedding information or message signal on a carrier wave by varying the phase of the carrier wave. In PM, the phase of the carrier wave is changed in proportion to the amplitude of the modulating signal. For this a phase modulator circuit is used. The carrier signal and information signal are fed into the phase modulator and as the amplitude of the information signal the phase of the carrier signal is changed proportionally. That is greater the information signal amplitude the greater will be the phase shift in the carrier signal and vice versa.

Imagine that the message signal is a sine wave, carrier are usually sine wave in analog modulation, then during the positive excursion of the message sine wave, the phase modulator causes lagging phase shift in the carrier signal and negative excursion of message sine wave, the phase modulator causes leading phase shift in the carrier signal. This lag and lead phase shifting of carrier signal in accordance to the amplitude of the message signal is shown below.

Phase modulation(PM) can be achieved from frequency modulation(FM) and vice versa. In both PM and FM the amplitude of the carrier signal is constant(not changing). In fact in phase modulation there is also frequency shift in the carrier signal and thus FM signal is also produced.

Phase modulation and frequency modulation falls into broader category of modulation called angle modulation. The equation for general angle modulated wave is as follows.

$$s(t) = A_c cos[\theta(t)]$$       ---------------->(1)

where the modulated signal amplitude $$A_c$$ is maintained constant and the angular argument $$\theta(t)$$ is varied linearly with the message signal $$m(t)$$ as follows,

$$\theta(t) = 2 \pi f_c t + k_p m(t) dt$$    ------------->(2)

where $$f_c$$ is the unmodulated carrier frequency and $$k_p$$  represents the phase sensitivity of the modulator expressed in radian/Hz.

From(1) and (2) a phase modulated signal is represented as follows,

$$s(t) = A_c cos[2 \pi f_c t + k_p m(t) ]$$       ---------------->(3)

Phase modulation can be achieved using direct phase modulator or indirect phase modulator. Direct phase modulator is equivalent to indirect frequency modulator and indirect phase modulator is equivalent to direct FM modulator(see frequency modulation with varactor diode). Direct phase modulation is achieved by applying modulating signal voltage to carrier signal oscillator which changes the capacitance in the oscillator circuit and thereby changes the phase of the carrier signal. A varying voltage dependent capacitor such as varactor diode or reactance modulator is often used.

Following shows an example of phase modulator implemented with varactor diode, inductor and resistor.

To create a PM signal, the modulating signal is first passed through a phase shifter or a variable phase delay line made using the varactor diode and resistor R2. The carrier signal is fed through the capacitor C1 and then into the circuit consisting of the resonant circuit consisting of varactor diode capacitor and the inductor. During the mixing process, the phase of the carrier signal is varied in accordance to the input message or modulating signal. The output of the phase shifter is then added to the carrier signal, resulting in a PM signal.

One of the key advantages of phase modulation is its immunity to amplitude variations in the signal. Since PM encodes information in the phase of the carrier wave, it is less sensitive to variations in the amplitude of the signal. This makes it a popular modulation technique for applications where signal distortion due to amplitude variations is a concern. That is phase modulation has better noise immunity than amplitude modulation.

#### Applications of Phase Modulation

• Telecommunications: Phase modulation is widely used in telecommunications, especially in digital communication systems. In digital communication, Phase Shift Keying (PSK) is a type of phase modulation that is commonly used for encoding digital information on a carrier wave. PSK is used in applications such as satellite communication, digital broadcasting, and wireless communication.
• Radar: Phase modulation is also used in radar systems for measuring the distance and velocity of objects. In radar systems, a modulated signal is transmitted and then reflected back from the object being measured. The reflected signal is then analyzed to determine the distance and velocity of the object.
• GPS: Global Positioning System (GPS) uses phase modulation to determine the location of an object. In GPS, a modulated signal is transmitted from a satellite, and the signal is received by a GPS receiver on the ground. By analyzing the phase of the received signal, the GPS receiver can determine the distance between the satellite and the receiver, which is used to calculate the receiver's location.
• Optical Communication: Phase modulation is also used in optical communication systems, where it is used to encode information on a light wave. In optical communication, Phase Shift Keying (PSK) and Differential Phase Shift Keying (DPSK) are popular modulation techniques used for encoding digital information on an optical signal.

In conclusion, Phase Modulation is a versatile modulation technique used in various applications ranging from telecommunications to radar and GPS systems. Its immunity to amplitude variations makes it an attractive option for applications where signal distortion due to amplitude variations is a concern.

References: