Wireless 101
M04 · L01
Module 4

Frequency Modulation

Instead of changing the amplitude, FM changes the frequency of the carrier. The result: better noise immunity, richer audio, and the backbone of FM radio worldwide.

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Wireless 101
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Core Idea

Encoding in Frequency

In AM, louder signals mean bigger waves. In FM, louder signals mean faster oscillation. The amplitude stays constant — only the frequency wobbles up and down, tracking the message signal.

AM
Amplitude varies
FM
Frequency varies
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Wireless 101
M04 · L01
Mathematics

The FM Equation

The message signal x(t) controls the instantaneous frequency. The integral of the message becomes the phase of the carrier.

FM Signal
s(t) = A_c \cos\!\left(2\pi f_c t + 2\pi k_f \int_0^t x(\tau)\,d\tau\right)
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Wireless 101
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Key Concept

Instantaneous Frequency

At any moment, the frequency is the carrier frequency plus a shift proportional to the message. When x(t) is positive, frequency rises; when negative, it falls.

Instantaneous Frequency
f_i(t) = f_c + k_f \, x(t)
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Wireless 101
M04 · L01
Parameter

Frequency Deviation

Δf is the maximum shift away from the carrier frequency. It tells you how far the frequency swings. Commercial FM radio uses Δf = 75 kHz — the frequency can swing 75 kHz above or below fc.

Deviation
\Delta f = k_f \cdot \max|x(t)|
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Wireless 101
M04 · L01
Key Ratio

Modulation Index

The modulation index β is the ratio of frequency deviation to message frequency. It determines the signal bandwidth and whether FM is narrowband or wideband.

Modulation Index
\beta = \frac{\Delta f}{f_m}
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Wireless 101
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Classification

Narrowband vs. Wideband

When β << 1, FM is narrowband (bandwidth ≈ 2fm, similar to AM). When β >> 1, it becomes wideband (bandwidth ≈ 2Δf). Commercial FM radio is wideband: β ≈ 5.

Narrowband
β << 1
Wideband
β >> 1
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Wireless 101
M04 · L01
Spectrum

Bessel Functions & Sidebands

An FM signal produces infinite sidebands spaced at multiples of fm. Their amplitudes are governed by Bessel functions Jn(β). As β grows, more sidebands carry significant energy.

FM Spectrum
s(t) = A_c \sum_{n=-\infty}^{\infty} J_n(\beta)\,\cos\!\left(2\pi(f_c + n f_m)t\right)
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Wireless 101
M04 · L01
Interactive

FM Wave Explorer

Adjust Δf and fm to see how the FM waveform changes.

Δf2.0
fm0.5
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Wireless 101
Knowledge Check

Check what stuck

Four questions from this lesson. Answer to see why — the explanation appears whether you were right or wrong. Nothing is scored or saved.

Question 1 of 0
Score 0/0

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Wireless 101
M04 · L01
Advantages

Why FM Matters

  • Noise immunity: noise affects amplitude, not frequency
  • Capture effect: stronger station suppresses weaker ones
  • Constant envelope: efficient power amplifiers
  • High fidelity: wider bandwidth = richer audio
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Wireless 101
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Coming Up

Next: FM Bandwidth

Now that we understand the FM signal, we will derive its bandwidth using Carson's Rule and compare narrowband vs. wideband FM trade-offs.

Next Lesson
FM Bandwidth & Carson's Rule →
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