14.1 Amplitude & Frequency Modulation

14.1 Amplitude & Frequency Modulation

Quick Answer: AM varies amplitude; % modulation from envelope Emax/Emin; BW ≈ 2 × highest AF; sidebands carry the intelligence. FM varies frequency; Δf set by audio level; β = Δf/fm; Carson BW ≈ 2(Δf + fm); pre-emphasis/de-emphasis improve high-frequency SNR. FM’s constant envelope resists amplitude noise better than AM.

Element 3 Topic 3-H (Signals and Emissions) starts where transmitters put intelligence onto RF. GROL work on marine, aviation, and fixed public stations means reading scope envelopes, setting deviation and modulation meters, and knowing why an A3E AM channel and an F3E FM channel behave differently under noise and overload.

What “modulation” means

A bare RF carrier is a continuous wave (CW) with fixed frequency and amplitude. Modulation impresses information by varying one or more carrier parameters in proportion to a modulating signal (voice, tone, data):

This section drills AM and FM—the two continuous-wave families that dominate pool questions for modulation index, bandwidth, and noise behavior.

Amplitude modulation (AM)

How AM works

In amplitude modulation, the amplitude (strength) of the RF carrier rises and falls in proportion to the instantaneous value of the modulating signal. Frequency of the carrier remains (ideally) fixed; the envelope of the RF sine wave traces the audio waveform.

On an oscilloscope in RF mode you see a “sausage” envelope: loud audio widens the peak-to-peak RF excursion; silence leaves a constant carrier height.

Modulation factor and percent modulation

Define carrier peak amplitude Ec (unmodulated) and modulating peak amplitude Em (the audio component of the envelope). The modulation factor (modulation index for AM):

[ m = \frac{E_m}{E_c} ]

Percent modulation:

[ %,\mathrm{mod} = m \times 100% = \frac{E_m}{E_c} \times 100% ]

From the modulated envelope peaks Emax and Emin:

[ m = \frac{E_{\max} - E_{\min}}{E_{\max} + E_{\min}} \qquad %,\mathrm{mod} = \frac{E_{\max} - E_{\min}}{E_{\max} + E_{\min}} \times 100% ]

At 100% modulation, Emax = 2 Ec and Emin = 0 for a pure sine tone on a full-carrier AM wave.

Overmodulation

If the modulator drives m > 1, the envelope is no longer a faithful copy of the audio. The RF waveform can “pinch off,” produce harmonics of the modulating signal, and radiate excessive bandwidth (adjacent-channel interference). On a service bench: reduce mic gain, check ALC/compression, and verify the transmitter’s AM modulator bias—do not leave an overmodulated AM set on the air.

Sidebands and AM bandwidth

A single-tone AM signal is not “one frequency.” Fourier analysis shows three spectral lines:

1. Carrier at fc
2. Upper sideband (USB) at fc + fm
3. Lower sideband (LSB) at fc − fm

For complex audio with highest frequency component fmax (highest AF), the occupied RF bandwidth is approximately:

[ BW_{AM} \approx 2 \times f_{\max} ]

Worked example — pool-style AM broadcast: highest AF ≈ 5 kHz → bandwidth ≈ 10 kHz. That is why standard AM broadcast channels are described with about 10 kHz bandwidth (stations spaced 10 kHz in the MW band). Both sidebands carry the same audio information in conventional double-sideband full-carrier AM—half of the sideband power is “redundant” for information transfer, which is why SSB later looks attractive.

Power note (conceptual): for classic full-carrier AM with a sine tone at 100% modulation, total sideband power equals half the unmodulated carrier power (one-sixth of total radiated power in each sideband in the classic textbook split). Most of the average power sits in the carrier, which does not carry intelligence by itself—another reason Element 3 later contrasts AM with SSB efficiency.

Frequency modulation (FM)

How FM works

In frequency modulation, the instantaneous frequency of the carrier swings above and below the resting frequency fc in proportion to the modulating signal’s amplitude. Instantaneous amplitude of the RF envelope stays (ideally) constant. Louder audio → more frequency deviation; higher audio pitch → deviation swings happen faster (more times per second), not necessarily with larger Δf.

Deviation and modulation index

Peak frequency deviation Δf (or fd): maximum amount the instantaneous frequency departs from fc.

Modulation index for FM (often denoted β or mf):

[ \beta = \frac{\Delta f}{f_m} ]

where fm is the modulating frequency of a single-tone test.

Deviation ratio (related, for system design with maximums):

[ \mathrm{Deviation\ ratio} = \frac{\Delta f_{\max}}{f_{m,\max}} ]

Worked example — FM broadcast (pool classic): maximum deviation 75 kHz, highest modulating frequency 15 kHz:

[ \mathrm{Deviation\ ratio} = \frac{75}{15} = 5 ]

That 5 is a standard Element 3 number for broadcast FM. Narrowband land-mobile / marine FM voice uses much smaller deviation (historically ±5 kHz class systems; modern narrowband is even tighter)—the formula stays the same; only the design numbers change.

Carson’s rule — FM bandwidth estimate

FM spectra have many Bessel sidebands, not just two. A practical estimate of occupied bandwidth is Carson’s rule:

[ BW \approx 2(\Delta f + f_m) ]

For systems using the highest AF fmax and peak deviation Δfmax:

[ BW \approx 2(\Delta f_{\max} + f_{m,\max}) ]

Worked example — broadcast FM: Δf = 75 kHz, fm = 15 kHz → BW ≈ 2(75 + 15) = 180 kHz. Channel spacing is 200 kHz with guard band so adjacent stations do not overlap—Element 3 sometimes frames that spacing as interference prevention between neighbors.

Worked example — communications FM: Δf = 5 kHz, fm = 3 kHz → BW ≈ 2(5 + 3) = 16 kHz, which is why wideband FM phone IF filters near 15 kHz appear in receiver topics.

Pre-emphasis and de-emphasis

FM demodulation noise density rises with frequency (triangular noise spectrum after the discriminator). To improve high-frequency SNR without simply cranking deviation forever:

1. Transmitter pre-emphasis — intentionally boost higher audio frequencies before modulation.
2. Receiver de-emphasis — apply complementary high-frequency rolloff after demodulation.

Net result: flat audio response plus reduced high-frequency noise. Element 3 wording: pre-emphasis boosts highs to improve the signal-to-noise ratio; de-emphasis is the complementary receiver stage. Standard broadcast pre-emphasis time constants (e.g., 75 µs in U.S. FM broadcast practice) are the engineering implementation of that RC boost curve.

If you hear overly bright, hissy audio on FM, check whether de-emphasis is present/correct—not just volume.

AM vs FM — noise immunity and operating traits

Why FM has better noise immunity (pool idea): amplitude noise and many ignition/static spikes ride on the amplitude axis. An FM receiver limits (clips) amplitude before frequency detection, so constant-envelope FM plus limiting rejects much of that noise. AM must preserve envelope shape, so amplitude noise rides through the detector. That is the commercial reason marine VHF and land-mobile phone standardized on FM (F3E) for short-range voice, while HF long-haul preferred SSB for spectrum and power—not because AM “cannot work,” but because each mode fits its environment.

Service-bench AM/FM checklist

1. AM scope: set % modulation from Emax/Emin; stay ≤ 100%; stop overmodulation splatter.
2. AM bandwidth: ≈ 2 × highest AF (10 kHz class for 5 kHz AF broadcast).
3. FM deviation: set with a deviation meter or Bessel-null method; know β = Δf/fm.
4. FM bandwidth: estimate with Carson’s rule 2(Δf + fm).
5. Broadcast anchors: 75 kHz / 15 kHz → deviation ratio 5.
6. Pre-emphasis TX + de-emphasis RX for FM SNR.
7. Noise: FM constant envelope + limiting → better amplitude-noise immunity than AM.

Master AM percentage and FM deviation math, and most Topic 3-H continuous-wave questions collapse to formula recognition. Next section covers single-sideband—half the bandwidth and far better power efficiency than full-carrier AM.