Amplitude Modulation (AM)
Amplitude Modulation (AM) is a technique used to encode information by varying the amplitude of a carrier wave while keeping its frequency constant. It has been foundational to radio communications and remains relevant in RF testing, modulation analysis, and specific broadcast and communication applications.
Mathematical Definition
The basic equation for amplitude modulation is:
s(t) = A_c[1 + m(t)] cos(ω_c t)
Where:
s(t) = The modulated signal
A_c = The carrier amplitude
m(t) = The modulating signal (message signal)
ω_c = The angular carrier frequency (ωc = 2πfc, where f_c is the carrier frequency)
t = Time
The modulation index (m) quantifies the relative amplitude of the modulating signal and is also referred to as modulation depth when expressed as a percentage.
Modulation Index and Depth
The modulation index is defined by:
m = Am / Ac
Where:
m is the modulation index
Am is the amplitude of the modulating signal
Ac is the amplitude of the carrier wave
A modulation index of 1 corresponds to 100% modulation. When m > 1, the signal is overmodulated.
Overmodulation and Distortion
Overmodulation occurs when the modulation index exceeds 1, causing the envelope of the modulated signal to overlap and distort. This leads to significant degradation in signal clarity and spectral integrity.
Frequency Spectrum in AM
Amplitude modulation produces three main spectral components:
Carrier frequency: fc
Upper sideband: fc + fm
Lower sideband: fc - fm
Where fm is the frequency of the modulating signal. The total bandwidth of an AM signal is twice the highest frequency of the modulating signal.
Power Distribution in AM Signals
Power in AM is not evenly distributed. A typical breakdown is:
Carrier: ~67% of total power (no information content)
Sidebands: ~33% of total power (contain the information)
This results in low power efficiency, as most energy is used to transmit the carrier.
Types of Amplitude Modulation
Double Sideband (DSB): Full carrier and both sidebands; simple but inefficient.
Single Sideband (SSB): One sideband is suppressed; improves bandwidth and power efficiency.
Vestigial Sideband (VSB): Partial sideband suppression; used in TV broadcasting to balance efficiency and demodulation simplicity.
Example Calculation
Consider a carrier wave with the following parameters:
Carrier amplitude: 5 V
Modulating signal amplitude: 2 V
Modulation index formula: Modulation Index = Modulating Amplitude / Carrier Amplitude
Calculated modulation index: 2 V / 5 V = 0.4
Modulation depth: 40%
Practical Considerations
AM is highly susceptible to noise interference.
Power efficiency is low due to the constant transmission of the carrier.
It remains simple to implement and cost-effective for basic communication needs.
AM systems have limited bandwidth efficiency.
Applications of AM
Amplitude modulation is used in:
AM radio broadcasting
Aircraft and maritime communication
Amplitude Shift Keying (ASK) in digital communication
QAM-based modem technologies
Low-frequency RF applications
Advantages and Limitations
Advantages:
Simple modulation and demodulation circuits
Cost-effective implementation
Suitable for low-frequency signal transmission
Limitations:
Poor noise immunity
Inefficient in power and bandwidth
Limited data capacity
Historical Context
Amplitude modulation was first demonstrated by Reginald Fessenden in 1906 and became a cornerstone of commercial radio in the 1920s. While largely replaced by more efficient digital techniques, AM is still used in aviation and niche communication systems due to its simplicity and reliability.