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Linear and Nonlinear Modulation

 

1. What is Modulation?

Modulation is the process of varying a carrier signal according to the amplitude, frequency, or phase of the information (message) signal.

A high-frequency carrier wave is modified using a low-frequency message signal for transmission.

Carrier Signal: c(t) = Ac cos(2Ï€fct)
Message Signal: m(t)

2. Linear Modulation

A modulation system is called linear if the output signal is linearly proportional to the message signal.

Superposition property is satisfied in linear modulation.

Characteristics

  • Output is directly proportional to input
  • Uses linear devices and linear filtering
  • Amplitude of carrier changes according to message signal
  • Easy mathematical analysis

General Equation

s(t) = Ac[1 + k m(t)] cos(2Ï€fct)

where:

  • Ac = carrier amplitude
  • k = modulation index constant
  • m(t) = message signal

Examples of Linear Modulation

Modulation Type Description
AM Amplitude Modulation
DSB-SC Double Sideband Suppressed Carrier
SSB Single Sideband Modulation
VSB Vestigial Sideband Modulation
Example:

In AM, the carrier amplitude changes according to the message signal.

s(t)=Ac[1+m(t)]cos(2Ï€fct)

Since the signal depends linearly on m(t), AM is linear modulation.

3. Nonlinear Modulation

A modulation system is called nonlinear if the output signal is not linearly proportional to the message signal.

Superposition property does NOT hold in nonlinear modulation.

Characteristics

  • Output is nonlinear function of input
  • Angle of carrier changes
  • Uses nonlinear devices
  • Better noise immunity

Examples of Nonlinear Modulation

Modulation Type Description
FM Frequency Modulation
PM Phase Modulation
Example:

In Frequency Modulation (FM), the carrier frequency changes according to the message signal.

s(t)=Accos[2Ï€fct + kf∫m(t)dt]

Since frequency variation is nonlinear with respect to the message signal, FM is nonlinear modulation.

4. Comparison Between Linear and Nonlinear Modulation

Feature Linear Modulation Nonlinear Modulation
Carrier Parameter Changed Amplitude Frequency or Phase
Superposition Property Satisfied Not Satisfied
Noise Immunity Lower Higher
Bandwidth Requirement Lower Higher
Examples AM, DSB, SSB, VSB FM, PM

5. Summary

Linear modulation changes the amplitude of the carrier in direct proportion to the message signal.

Nonlinear modulation changes the frequency or phase of the carrier in a nonlinear manner.

AM-based systems are linear, while angle modulation systems like FM and PM are nonlinear.

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