FM makes a message control the carrier’s instantaneous frequency; PM makes it control the carrier’s phase. Because instantaneous frequency is the rate at which phase changes, the two methods are closely related—but their bandwidth estimates, demodulator implementations, and practical trade-offs depend on the signal and system, not just the modulation label.
How FM and PM encode a message
Both frequency modulation (FM) and phase modulation (PM) vary the angle of a constant-amplitude carrier. A useful representation is s(t) = A cos(2πfct + φ(t)), where A is carrier amplitude, fc is carrier frequency, and φ(t) is the time-varying phase contribution.
In FM, the message determines the instantaneous frequency deviation. Since frequency is the time derivative of phase, the phase contribution accumulates as the message changes. In PM, the message determines phase deviation directly; consequently, instantaneous frequency deviation follows the rate of change of the message. The relationship is summarized in the NTIA Manual of Regulations and Procedures for Federal Radio Frequency Management and the Loyola course material.
A held message level makes the distinction clear
If a message is held at a constant level for a period, FM produces a constant frequency offset during that interval, so the carrier phase ramps steadily. PM instead produces a fixed phase displacement while the message remains constant; its frequency changes principally while the message is changing. With a sinusoidal message, both can look similar because differentiation or integration changes the sinusoid’s scale and phase, but not its sinusoidal form.
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FM vs. PM at a glance
| Comparison | FM | PM |
|---|---|---|
| Quantity controlled directly | Instantaneous frequency deviation tracks the message. | Phase deviation tracks the message. |
| Message-to-frequency relationship | Frequency deviation is proportional to the message; phase contribution is its integral. | Frequency deviation follows the message’s derivative. |
| Common single-tone parameter | Modulation index β = Δf/fm, where Δf is peak frequency deviation and fm is tone frequency. |
Phase index h depends on peak message amplitude and phase sensitivity. |
| Bandwidth estimate | Carson-style estimate depends on peak frequency deviation and highest modulating frequency. | NTIA’s analog-PM expression depends on phase index and highest modulating frequency. |
| Implementation context | Used in a range of analog applications; receiver design and performance depend on the system. | NTIA describes analog PM as rarely used because receiving hardware is more complex. |
| Noise comparison | No universal advantage can be stated without matched signal, receiver, and noise conditions. | No universal disadvantage can be stated without matched signal, receiver, and noise conditions. |
How to estimate bandwidth
Neither FM nor PM has a single fixed bandwidth. The estimate depends on message bandwidth and modulation settings. For engineering estimates, Carson’s rule for FM is often written B ≈ 2(Δf + fm), with Δf the peak frequency deviation and fm the highest modulating frequency.
NTIA’s 2021 edition of its handbook, revised in 2023, gives analog necessary-bandwidth expressions as follows:
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| Modulation | NTIA expression | Parameters |
|---|---|---|
| Analog FM | Bn = 2M + 2KD |
M is highest modulating frequency; D is peak frequency deviation; K is normally 1 in the fundamental Carson form. |
| Analog PM | Bn = 2(h + 1)M |
M is highest modulating frequency; h is phase modulation index. |
These formulas are not directly interchangeable: the FM expression uses frequency deviation, while the PM expression uses phase index. For a single-tone FM signal, β = Δf/fm. For PM, phase index is proportional to peak message amplitude and phase sensitivity; with a multi-frequency message, the resulting frequency deviation is affected by how quickly the message changes. Keep units consistent and identify the signal assumptions when making a calculation.
What the estimate does—and does not—mean
Carson’s rule is an approximate necessary-bandwidth estimate, not a hard edge beyond which no spectral energy exists. NTIA notes that the fundamental form uses K = 1, while an adjusted factor may be appropriate in measured cases. Actual occupied or necessary bandwidth also depends on the applicable definition, system, filters, and any subcarriers or composite modulation. Use the relevant regulatory or system specification when compliance, channel spacing, or emission limits matter.
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Does FM or PM have better noise immunity?
There is no defensible universal winner from the available comparison. Both methods encode information in carrier angle rather than amplitude, and a receiver can limit amplitude variations before angle demodulation. That is why FM is often described as resistant to amplitude noise, but it does not establish that FM always performs better than PM.
A fair comparison has to specify the message spectrum, deviation or phase index, received carrier-to-noise ratio, receiver architecture and bandwidth, and the noise or interference being considered. Random additive noise, amplitude disturbances, adjacent-channel interference, and distortion from a nonideal demodulator can affect recovered information in different ways. The result should also be measured consistently—for example, as recovered audio signal-to-noise ratio or digital bit error rate. The cited technical material provides no matched numerical FM-versus-PM noise result.
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Where FM and PM are used
NTIA’s handbook describes analog PM as rarely used because the receiving hardware is more complex. It also gives typical highest-modulating-frequency categories for analog FM, including commercial-quality voice, broadcast-quality high-fidelity voice and music, frequency-division multiplex, and standard-definition video links. These are engineering examples in a government handbook, not evidence that every listed link remains common in current deployments. For example, the handbook lists up to 15 kHz for broadcast-quality high-fidelity voice and music as a typical value, not a universal limit.
In digital communications, distinguish these analog methods from their keyed relatives: frequency-shift keying (FSK) and phase-shift keying (PSK) use discrete frequency or phase states. The Loyola course material discusses FSK and PSK examples, but the terms are not synonyms for analog FM and PM.
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Choosing what to compare in a real system
- For bandwidth, compare the actual message bandwidth and deviation or index, using the definition required by the system or regulator.
- For noise, compare receivers under matched carrier-to-noise ratio, signal conditions, filtering, and performance metric.
- For implementation, account for the receiver and demodulator complexity; NTIA identifies this as a practical reason analog PM is rare.
- For digital designs, identify whether the scheme is analog FM/PM or keyed FSK/PSK before comparing performance.
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