Frequency Modulation (FM)
Frequency Modulation (FM) is a method of signal transmission in which the carrier wave’s frequency is varied in proportion to the amplitude of the modulating signal. The amplitude of the carrier remains constant. FM offers improved noise resistance and better signal quality compared to Amplitude Modulation (AM).
Mathematical Representation
The FM signal can be described as:
s(t) = A_c cos(ω_c t + β sin(ω_m t))
Where:
s(t) = Modulated signal
A_c = Carrier amplitude
ω_c = Angular carrier frequency
ω_m = Angular frequency of the modulating signal
β = Modulation index
t = Time
Frequency Deviation
The frequency deviation indicates how far the instantaneous frequency moves from the carrier frequency:
Δf = β × f_m
Where:
Δf = Frequency deviation
β = Modulation index
f_m = Modulating signal frequency
Modulation Index
The FM modulation index is calculated as:
β = Δf / f_m
It determines how many sidebands are generated and the resulting bandwidth.
Spectral Characteristics
FM signals generate multiple sidebands, whose amplitudes are defined by Bessel functions. Key spectral features include:
Carrier frequency
Symmetric sidebands around the carrier
Bandwidth dependent on the modulation index
Types of Frequency Modulation
Narrowband FM (NBFM)
β < 1
Small frequency deviation
Minimal sideband generation
Used in voice communication (e.g., handheld radios)
Wideband FM (WBFM)
β > 1
Large frequency deviation
Many sideband components
Used in high-fidelity audio (e.g., FM radio broadcasting)
Example Calculation
Given:
f_m = 5 kHz
Δf = 50 kHz
Then:
β = 50 kHz / 5 kHz = 10
This is an example of wideband FM, since β > 1.
Practical Considerations
Good noise immunity
Constant signal amplitude
Wider bandwidth than AM
More complex circuitry and modulation schemes
Applications
FM is used in a wide range of systems:
FM radio broadcasting
Two-way radios (e.g., aviation, police)
Telemetry and control systems
Wireless microphones
Satellite communications
Medical imaging systems
Audio synthesis (FM synthesis)
Advantages and Limitations
Advantages:
High noise rejection
Superior audio quality
Amplitude stability (resistant to fading)
Limitations:
Higher bandwidth requirements
Increased system complexity
More expensive to implement
Historical Context
Developed by Edwin Armstrong in 1933
Introduced high-fidelity audio broadcasting
Became the standard for analog audio transmission
Influential in the evolution of modern communication
Comparison with Other Modulation Techniques
More resistant to noise than AM
Wider bandwidth than AM, but more efficient than phase modulation in many cases
Preferred for audio applications
Forms the basis of modern analog and digital modulation schemes