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; % Sampling frequency in Hertz
time = 0:1/sampling_frequency:1; % Time vector

% Generate the message signal (a sine wave)
message_signal = sin(2 * pi * message_frequency * time);

% Generate the carrier signal (a cosine wave)
carrier_signal = cos(2 * pi * carrier_frequency * time);

% Perform Amplitude Modulation (AM)
am_signal = (1 + 0.5 * message_signal) .* carrier_signal;

% Plot the signals
subplot(3,1,1);
plot(time, message_signal);
title('Message Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(3,1,2);
plot(time, carrier_signal);
title('Carrier Signal');
xlabel('Time (s)');
ylabel('Amplitude');

subplot(3,1,3);
plot(time, am_signal);
title('Amplitude Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');

% Perform Amplitude Demodulation
demodulated_signal = am_signal .* carrier_signal;

% Apply low-pass filter to remove high-frequency components
cutoff_frequency = 2 * message_frequency;
[b, a] = butter(6, cutoff_frequency / (sampling_frequency/2), 'low');
demodulated_signal_filtered = filtfilt(b, a, demodulated_signal);

% Plot the demodulated signal
figure;
plot(time, demodulated_signal_filtered);
title('Demodulated and Filtered Signal');
xlabel('Time (s)');
ylabel('Amplitude');
web('https://www.salimwireless.com/search?q=modulation%20techniques', '-browser');

Output

Fig 1: Amplitude Modulation and Demodulation

Q & A and Summary

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

Amplitude Modulation (AM) is a modulation 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 mathematically represented as:

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

A_c is the carrier amplitude
K_a is the amplitude sensitivity
m(t) is the modulating signal
f_c is the carrier frequency

2. What is the role of the modulation index \( \mu \) in AM, and how is it calculated?

The modulation index quantifies the extent of carrier amplitude variation. It is calculated as:

\( \mu = K_a A_m \)

Or alternatively:

\( \mu = \frac{A_{\text{max}} - A_{\text{min}}}{A_{\text{max}} + A_{\text{min}}} \)

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

3. How does the frequency domain representation of an AM signal reveal its spectral characteristics?

Applying the Fourier Transform to the AM signal reveals:

Impulse functions at \( \pm \omega_c \)
Shifted replicas of the message spectrum at \( \omega_c \pm \omega_m \)
Bandwidth determined by message signal's frequency range

This analysis helps visualize where the signal energy is concentrated in the frequency spectrum.

4. What is the formula for calculating the bandwidth of an AM signal?

The AM bandwidth is twice the highest frequency in the message signal:

BW = 2 × f_m

5. How does synchronous (coherent) demodulation work in AM, and what is the role of the low-pass filter (LPF)?

Synchronous demodulation multiplies the AM signal with a locally generated carrier:

\( v(t) = s(t) \cdot \cos(2\pi f_c t) \)

This yields a signal with both baseband and high-frequency components:

\( v(t) = \frac{A_c}{2} [1 + K_a m(t)] + \frac{A_c}{2} [1 + K_a m(t)] \cos(4\pi f_c t) \)

The LPF removes the high-frequency term, leaving:

\( v_{LPF}(t) = \frac{A_c}{2} + \frac{A_c K_a}{2} m(t) \)

The DC component is removed, and the signal is amplified to restore \( m(t) \).

6. What is the significance of the Fourier transform in analyzing the frequency spectrum of AM signals?

The Fourier transform shows the frequency components present in an AM signal, including:

Carrier components at \( \pm \omega_c \)
Sidebands representing the message signal shifted around the carrier

This helps in efficient design of filters and bandwidth allocation in communication systems.

7. Explain the process of amplitude modulation in terms of signal representation and its impact on bandwidth.

AM modifies a carrier wave’s amplitude according to a message signal. Represented as:

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

This causes the signal to occupy a bandwidth of \( 2f_m \), effectively doubling the message signal’s bandwidth.

8. How does over-modulation in AM affect the transmitted signal?

Over-modulation occurs when \( \mu > 1 \). It results in signal distortion due to carrier inversion and clipping. This leads to:

Loss of message signal fidelity
Increased bandwidth and interference
Demodulation errors

Also Read about

2. Digital Modulation Techniques:

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

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