Frequency Modulation (FM)

Table of Contents

Introduction to Frequency Modulation (FM)

Frequency Modulation (FM) is a method of impressing data onto an alternating-current (AC) wave by varying the instantaneous frequency of the wave. This contrasts with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency remains constant. In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal.

Frequency Modulation (FM) Radio is what most music stations use for broadcasting.

Basic Principle of Frequency Modulation

Modulation Process

The basic equation for a sinusoidal carrier signal is:

$s(t) = A_c \cos(2 \pi f_c t)$

where $A_c$ is the amplitude of the carrier signal, $f_c$ is the frequency, and $t$ is time.

In frequency modulation, the frequency $f_c$ is varied according to the information signal. The equation for an FM signal is:

$s(t) = A_c \cos(2 \pi f_c t + \beta \sin(2 \pi f_m t))$

where $f_m$ is the frequency of the modulating signal, and $\beta$ is the modulation index.

The change in frequency in response to the information signal (the modulation) is what encodes the information in the carrier wave.

Modulation Index

The modulation index $\beta$ is a key parameter in the frequency modulation process. It is defined as the ratio of the frequency deviation (the maximum departure of the instantaneous frequency from the carrier frequency) to the frequency of the modulating signal:

$\beta = \dfrac{\Delta f}{f_m}$

where $\Delta f$ is the frequency deviation.

Advantages and Applications of Frequency Modulation

Advantages

FM is known for its ability to provide high fidelity sound in broadcasting applications. One significant advantage is its resilience to signal-level variation and noise. This makes FM ideal for mobile radio communication and broadcasting where signal levels are likely to vary considerably.

Applications

FM is widely used in audio signal broadcasting like FM radio, sound synthesis, telemetry, radar, seismic prospecting, and monitoring newborns for seizures via EEG.

Frequency Modulation: Advanced Topics

Bandwidth of FM Signals

The bandwidth of FM signals is significantly larger than that of amplitude modulated signals. It is dependent on both the frequency deviation and the frequency of the modulating signal.

Carson’s Rule

Carson’s Rule estimates the bandwidth for an FM signal as:

$B = 2(\Delta f + f_m)$

where $B$ is the bandwidth, $\Delta f$ is the peak frequency deviation, and $f_m$ is the maximum baseband message frequency.

Carson’s rule provides a reasonably accurate estimate for the bandwidth of an FM signal, especially for the case of wideband FM.

Conclusion

Frequency modulation is a key technique in modern communication systems providing several advantages over amplitude modulation, particularly in mobile applications. The resilience to signal level variations and noise, along with high fidelity, makes FM ideal for many applications, notably in broadcasting and telemetry.

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Frequency Modulation (FM)

Introduction to Frequency Modulation (FM)