LECT-17: ANGLE MODULATION ( PM & FM )

Summary

This video covers the concept of angle modulation, a nonlinear process in which the angle of the carrier wave is varied in accordance with the message signal, unlike amplitude modulation (AM) where the amplitude changes. It explains the advantages of angle modulation, such as better noise immunity, though at the cost of increased complexity and higher transmitter/receiver costs. The video then delves into the mathematical expressions for angle modulated waves, discussing phase modulation (PM) and frequency modulation (FM) as two main types. A comparison of AM, PM, and FM concludes the discussion, highlighting the differences in their waveform behaviors.

Takeaways

• 😀 Angle modulation is a nonlinear process where the angle of the carrier wave is varied according to the message signal.
• 😀 Unlike amplitude modulation, in angle modulation, the amplitude of the carrier remains constant while the angle varies.
• 😀 Angle modulation offers better noise performance and resistance to interference compared to amplitude modulation.
• 😀 The primary disadvantage of angle modulation is the increased complexity of the transmitter and receiver, which raises costs.
• 😀 The angle modulated wave is mathematically expressed as s(t) = AC cos(θ_i(t)), where AC is the carrier amplitude and θ_i(t) is the instantaneous angle.
• 😀 The instantaneous frequency in angle modulation is derived from the rate of change of the instantaneous angle with respect to time.
• 😀 The average frequency over a small time interval ΔT can be calculated using the formula: f_ΔT(t) = (θ(t+Δt) - θ(t)) / (2πΔT).
• 😀 Instantaneous frequency, represented by f_i(t), is calculated as the derivative of the instantaneous angle: f_i(t) = (1 / 2π) * dθ_i/dt.
• 😀 In the case of an unmodulated carrier, the angle of the carrier is θ_c(t) = 2πF_c * t + Φ_c, where F_c is the carrier frequency.
• 😀 Angle modulation can be classified into two types: phase modulation (PM) and frequency modulation (FM). In PM, the instantaneous angle varies linearly with the message signal, while in FM, the instantaneous frequency varies linearly with the message signal.

Q & A

What is the key difference between amplitude modulation and angle modulation?

The key difference is that in amplitude modulation (AM), the amplitude of the carrier wave varies according to the message signal, while in angle modulation, the amplitude of the carrier wave remains constant, and only the angle (or phase/frequency) varies according to the message signal.

Why do we use angle modulation instead of amplitude modulation?

Angle modulation offers better performance against noise and interference compared to amplitude modulation. It improves noise performance by using channel bandwidth effectively, but at the cost of increased system complexity and higher transmitter and receiver costs.

How is the angle modulated wave mathematically expressed?

The angle modulated wave is mathematically expressed as s(t) = AC * cos(θ_i(t)), where AC is the carrier amplitude, and θ_i(t) is the instantaneous angle, which is a function of the message signal.

What is the difference between average frequency and instantaneous frequency in angle modulation?

Average frequency is calculated over a small time interval (ΔT) and is given by the formula f_ΔT(t) = (θ(t + ΔT) - θ(t)) / (2πΔT). Instantaneous frequency, on the other hand, is the frequency at any given instant and is obtained by taking the derivative of the instantaneous angle with respect to time, expressed as f_i(t) = (1 / 2π) * (dθ_i / dt).

What is the concept of the instantaneous angle in angle modulation?

The instantaneous angle in angle modulation, denoted as θ_i(t), varies over time according to the message signal. It represents the phase change of the carrier wave and is crucial for understanding both phase modulation and frequency modulation.

What are the two types of angle modulation discussed in the script?

The two types of angle modulation discussed are phase modulation (PM) and frequency modulation (FM). In phase modulation, the instantaneous angle varies linearly with the message signal, while in frequency modulation, the instantaneous frequency varies linearly with the message signal.

What is phase sensitivity factor (Kp) in phase modulation?

The phase sensitivity factor (Kp) in phase modulation is a proportionality constant that represents how much the phase of the carrier changes with respect to the message signal. It is measured in radians per volt.

How is frequency modulation related to instantaneous angle?

In frequency modulation, the instantaneous frequency is related to the instantaneous angle by the equation f_i(t) = (1 / 2π) * (dθ_i / dt). To obtain the instantaneous angle, the instantaneous frequency is integrated over time, resulting in a phase shift proportional to the message signal.

What is the equation for phase modulated signal?

The phase modulated signal is given by s(t) = AC * cos(2πF_c * t + K_p * m(t)), where F_c is the carrier frequency, K_p is the phase sensitivity factor, and m(t) is the message signal.

What happens to the carrier wave in case of amplitude modulation?

In amplitude modulation, the amplitude of the carrier wave varies instantaneously according to the message signal, resulting in a waveform that has an envelope. This causes the carrier signal to be modulated in amplitude, as shown in the double sideband suppressed carrier version of AM.