## Angle ModulationAngle modulation is the combination of The spectral components of the modulated signal depend on the frequency and amplitude of the components in the baseband signal. Angle modulation is non-linear, while amplitude modulation is a The signal has the form of V(t) = A cos [ω Where, ω A is the amplitude constant ϕ (t) is the phase angle, which is not constant. It is a function of the baseband signal. ## Types of Angle ModulationAngle modulation is the combination of phase and frequency modulation. It is the modulation where both the frequency and phase of the carrier vary with the amplitude of the message signal, as discussed above. Angle Modulation is categorized as ## Frequency ModulationIf the frequency of the carrier varies with the amplitude of the message signal, it is known as frequency modulation. The amplitude of the modulated signal depends on the frequency difference between the carrier frequency and the center frequency. FM is a type of both analog and digital modulation. The applications of analog frequency modulation are ## Phase ModulationIf the carrier phase varies with the amplitude of the message signal, it is known as phase modulation. In angle modulation, it is together used with frequency modulation. It is also an integral part of both analog and digital communication. In analog communication, phase modulation is used for transmitting The waveforms of frequency modulation and phase modulation are shown below: ## Relationship between Frequency and Phase ModulationThe block diagram of frequency modulation consists of an integrator and a phase modulator, as shown below: The modulating signal is applied to the integrator, which is further sent to the phase modulator. The output of the combination of the integrator and the phase modulator is the frequency modulated signal. Let the message signal and the frequency constant be m(t) and K Where, K The output of the phase modulator is given by: The block diagram of the phase modulation consists of a differentiator and a frequency modulator, as shown below: The modulating signal is applied to the differentiator, which is further sent to the frequency Let the phase constant be K The output can be represented as: V(t) = A cos [ω Where, ω A is the amplitude constant m(t) is the instantaneous value of the message signal The instantaneous angular frequency is the differentiation of the output of the frequency modulator. It is given by: ω = ω The maximum frequency component of the message signal and instantaneous value of the message signal is F ## Modulation IndexThe deviation of the total angle from the carrier angle is defined as phase deviation. The deviation of the total angle from the carrier angle is defined as The frequency of the message signal is represented as ω ω The angle modulated signal is given by: V(t) = A cos [ω Where, ω A is the amplitude constant ω B is the peak amplitude of the phase constant ϕ (t) The instantaneous frequency is represented as ω. ω = d/dt [ϕ] ω = d/dt [[ω ω = ω We know, ω = 2πF Substituting the value of ω = 2πF, we get: 2πF = ω F = ω F = F Where, F F The maximum frequency deviation is represented as Δf = BF Thus, equation (1) can be represented as: In the next section, we will discuss FM (Frequency Modulation) and Phase Modulation (PM) in detail. ## Numerical ExamplesLet's discuss some numerical examples based on the angle modulation.
Given: Phase ϕ (t)= 2π 10 Instantaneous frequency = dϕ (t)/dt = d/dt [2π 10 = 2π 10 At, t = 0.8ms t = 0.8 x 10 Substituting the value of t, we get: = 2π 10 = 2π 10 = 2π 10 (cos16 π = 1) = 2π 10 = 2π 10 = 2π 10 = 6.47 ×10 = 6.47M Hz Thus, the instantaneous value is 6.47M Hz.
Instantaneous frequency = dϕ (t)/dt = d/dt [2π 10 = 2π 10 At, t = 0.5ms t = 0.5 x 10 Substituting the value of t, we get: = 2π 10 = 2π 10 = 2π 10 (cos 10 π = 1) = 2π 10 = 2π 10 = 2π 10 = 6.314 ×10 Thus, the instantaneous value is 6.314 ×10 Next TopicPhase Modulation |