Amplitude, Frequency, and Phase Modulation Techniques (AM, FM, and PM)

• 📘 Overview
• 🧮 Amplitude Modulation (AM)
• 🧮 Online Amplitude Modulation Simulator
• 🧮 MATLAB Code for AM
• 🧮 Q & A and Summary
• 📚 Further Reading

Amplitude Modulation (AM):

The carrier signal's amplitude varies linearly with the amplitude of the message signal.

An AM wave may thus be described, in the most general form, as a function of time as follows:

When performing amplitude modulation (AM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 90 Hz (100 - 10 Hz), 100 Hz, and 110 Hz (100 + 10 Hz).

Figure: Frequency Spectrums of AM Signal (Lower Sideband, Carrier, and Upper Sideband)

A low-frequency message signal is modulated with a high-frequency carrier wave using a local oscillator to make communication possible. DSB, SSB, and VSB are common amplitude modulation techniques. We find a lot of bandwidth loss in DSB. The bandwidth of SSB is half that of DSB. Because of its low bandwidth, SSB is ideal for audio transmission. VSB has a little higher bandwidth than SSB, making it appropriate for video transmission.

MATLAB Code for Amplitude Modulation

% The code is written by SalimWireless.Com % Amplitude Modulation (AM) and Demodulation clc; clear all; close all; % Define parameters carrier_frequency = 100; % Carrier frequency in Hertz message_frequency = 10; % Message signal frequency in Hertz sampling_frequency = 10 * carrier_frequency; time = 0:1/sampling_frequency:1; % Generate signals message_signal = sin(2 * pi * message_frequency * time); carrier_signal = cos(2 * pi * carrier_frequency * time); % Perform Amplitude Modulation (AM) am_signal = (1 + 0.5 * message_signal) .* carrier_signal; % Plotting subplot(3,1,1); plot(time, message_signal); title('Message Signal'); subplot(3,1,2); plot(time, carrier_signal); title('Carrier Signal'); subplot(3,1,3); plot(time, am_signal); title('Amplitude Modulated Signal'); % Demodulation demodulated_signal = am_signal .* carrier_signal; cutoff_frequency = 2 * message_frequency; [b, a] = butter(6, cutoff_frequency / (sampling_frequency/2), 'low'); demodulated_signal_filtered = filtfilt(b, a, demodulated_signal); figure; plot(time, demodulated_signal_filtered); title('Demodulated and Filtered Signal');

Output Results

Fig 1: Amplitude Modulation and Demodulation Plots

Q & A and Summary

1. What is Amplitude Modulation (AM), and how is it mathematically represented?

Amplitude Modulation (AM) is a technique in which the amplitude of a high-frequency carrier signal is varied in proportion to the baseband message signal. The modulated signal s(t) is represented as:

\( s(t) = A_c \left[ 1 + K_a m(t) \right] \cos(2\pi f_c t) \)

2. What is the role of the modulation index \( \mu \) in AM?

The modulation index quantifies the extent of variation. Calculated as \( \mu = K_a A_m \). Values include:

• \( \mu < 1 \): Under-modulation
• \( \mu = 1 \): 100% modulation
• \( \mu > 1 \): Over-modulation (distortion)

3. Spectral characteristics in the frequency domain?

Fourier Analysis reveals components at \( \pm \omega_c \) (carrier) and shifted replicas at \( \omega_c \pm \omega_m \) (sidebands).

4. What is the formula for AM Bandwidth?

BW = 2 × f_m

5. How does synchronous demodulation work?

It multiplies the AM signal with a local carrier. The resulting signal passes through a Low Pass Filter (LPF) to remove high-frequency terms, leaving the original message.

6. Significance of Fourier transform?

It helps in efficient design of filters and bandwidth allocation by showing carrier and sideband energy distribution.

7. Impact on bandwidth?

AM effectively doubles the message signal’s bandwidth because it creates two sidebands (USB and LSB).

8. How does over-modulation affect the signal?

It results in signal distortion, carrier inversion, and clipping, leading to a loss of fidelity and increased interference.

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Differences Between FM and PM

s(t) = A_c cos[ ω_ct + k_pm(t) + k_f∫m(t)dt ]

Parameters

• A_c = Carrier amplitude
• ω_c = Carrier angular frequency
• m(t) = Message signal
• k_p = Phase sensitivity constant
• k_f = Frequency sensitivity constant

Phase Modulation (PM)

s_PM(t) = A_c cos( ω_ct + k_pm(t))

Frequency Modulation (FM)

s_FM(t) = A_c cos( ω_ct + k_f∫m(t)dt)

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Further Reading

1. Frequency Modulation (FM)
2. Phase Modulation (PM)
3. AM Demodulation
4. FM Demodulation
5. PM Demodulation
6. Modulation Indices for AM, FM, and PM
7. DSB and SSB-SC
8. Online Simulator for Amplitude Modulation

2. Digital Modulation Techniques:

Examples of digital modulation techniques are ASK, FSK, PSK, QPSK, QAM, PCM, etc.