Frequency and Phase Modulation: FM and PM Explained

Frequency Modulation (FM) and Phase Modulation (PM) are angle modulation methods. In FM, the frequency of the carrier changes with the message signal, while amplitude stays constant. In PM, the phase of the carrier changes with the message. Both keep amplitude steady, which makes them resistant to noise that mainly affects amplitude.

FM and PM matter because they give high quality audio and reliable data links. FM radio sounds clearer than AM, and PM forms are used inside many digital systems. Learning how deviation and modulation index work explains their better performance.

Key Concepts

Carrier frequency (fc): Centre frequency in hertz when no message is present. Frequency deviation: Maximum shift from fc caused by peak message, in hertz. Modulation index for FM: Deviation divided by message frequency, no unit. Phase deviation: Maximum phase shift in radians in PM. Constant amplitude: Envelope does not change, so limiters can remove amplitude noise.

• FM: instantaneous frequency follows message amplitude
• PM: instantaneous phase follows message amplitude
• Both create multiple sidebands wider than AM

Formulas

FM wave (single tone): s(t) equals Ac cos(2 pi fc t plus beta sin(2 pi fm t)). Ac in volts, frequencies in hertz, beta is modulation index, no unit.

FM modulation index: beta equals frequency deviation divided by fm. Assumes sinusoidal message.

Bandwidth by Carson rule: B approx equals 2 times (deviation plus fm). In hertz, good estimate for most power contained.

PM relation: Phase shift equals kp times message voltage, kp in radians per volt. FM and PM are related because frequency is rate of change of phase.

Worked Example

An FM station has deviation 75 kHz and highest audio frequency 15 kHz. Find beta and bandwidth. Step 1: beta equals 75000 divided by 15000 equals 5. Step 2: Carson bandwidth equals 2 times (75000 plus 15000) equals 180000 Hz or 180 kHz. FM channels are spaced 200 kHz apart, so this fits well. This wide bandwidth is why FM can deliver high fidelity stereo music with low noise.

Common Misconceptions

• FM changes amplitude also: Wrong. Ideal FM keeps amplitude constant, only frequency varies.
• FM uses less bandwidth than AM: Wrong. FM uses much more bandwidth, trading spectrum for quality and noise immunity.
• FM and PM are totally unrelated: Wrong. Modulating phase indirectly changes frequency, so circuits can generate one from the other with filtering.

Real-World Applications

FM radio broadcasting between 88 MHz and 108 MHz gives music quality. Television sound, walkie talkies and old mobile systems used FM. Digital modulations like PSK are forms of phase modulation used in WiFi and satellite links. Bluetooth uses frequency shift methods related to FM.

FM varies carrier frequency and PM varies phase according to the message, both with constant amplitude. Their wider bandwidth buys excellent noise resistance, making them ideal for quality audio and modern digital communication.