Amplitude Modulation

Amplitude modulation — AM — was the first practical method for transmitting voice over radio, and it remains in widespread use today on the shortwave broadcast bands, the medium wave AM broadcast band (530–1700 kHz), the aviation VHF band (118–137 MHz), and on the 10-meter amateur band. Every other voice modulation technique — SSB, FM, digital modes — is ultimately a refinement developed to overcome AM's inherent inefficiencies. To understand why those improvements matter, you must first understand AM completely: how the modulated waveform is constructed, what the sidebands are, how power is distributed, what happens when modulation goes wrong, and how a receiver extracts the audio. This lesson covers all of that from first principles.

What AM Does to the Carrier

In amplitude modulation, the amplitude (peak voltage) of the carrier wave is made to vary in direct proportion to the instantaneous voltage of the audio (modulating) signal. The carrier frequency remains perfectly constant throughout — it is only the size of the carrier's peaks and troughs that changes. The result is a waveform whose overall outline, traced by connecting the peaks of the RF waveform, mirrors the shape of the audio signal exactly. That outline is called the envelope of the AM signal.

Mathematically, the AM waveform is written as:

Let's unpack what this equation is telling you. The carrier sin(2πf_ct) oscillates rapidly at the radio frequency. The term [1 + m·sin(2πf_mt)] is a slowly varying multiplier that swings between (1 − m) and (1 + m) as the audio tone oscillates. When the audio is at its positive peak, the multiplier reaches its maximum of (1 + m), and the carrier amplitude is at its highest. When the audio is at its negative peak, the multiplier reaches its minimum of (1 − m), and the carrier amplitude is at its lowest. When the audio is at zero, the multiplier is exactly 1, and the carrier is at its unmodulated amplitude.

Visualizing this: the RF waveform looks like a perfectly normal high-frequency sine wave that has been "squeezed" and "expanded" in a rhythmic pattern by the audio. At 100% modulation (m = 1), the carrier amplitude swings between zero and twice the unmodulated value. At 50% modulation (m = 0.5), it swings between half and one-and-a-half times the unmodulated value. At 0% modulation (m = 0), it is simply a constant-amplitude carrier with no information.

Three AM waveforms showing 50%, 100%, and 120% (over)modulation. At 100%, the carrier amplitude just reaches zero on negative audio peaks. At 120%, the envelope would go negative — but the RF waveform cannot follow, so it clips to zero, causing severe distortion and unwanted sidebands (splatter).

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The Modulation Index

The modulation index m (also called the modulation depth or modulation factor) is the single number that describes how deeply the audio signal is modulating the carrier. It is defined as the ratio of the peak amplitude of the modulating audio signal to the peak amplitude of the unmodulated carrier:

The modulation index tells you what fraction of the carrier amplitude is being contributed by the audio signal. At m = 0.5 (50% modulation), the audio signal's peak amplitude is half of the carrier's peak amplitude. At m = 1.0 (100% modulation), the audio signal's peak amplitude exactly equals the carrier's peak amplitude — this is the maximum recommended modulation for standard AM without distortion.

Why is 100% modulation the maximum? Look at the AM equation again: when m = 1 and the audio is at its negative peak (sin(2πf_mt) = −1), the multiplier becomes [1 + 1 × (−1)] = 0. The carrier amplitude reaches zero. This is exactly the ideal limit — the carrier momentarily disappears at the deepest negative audio excursion, then returns. If m exceeds 1.0, the term (1 + m·sin(2πf_mt)) would go negative, which means the carrier would be required to reverse phase. An ordinary AM transmitter cannot do this — instead, the output simply goes to zero and stays there while the audio tries to push negative, causing the envelope to clip. This clipping generates spurious sidebands that spread across wide sections of the band, a phenomenon called splatter.

Measuring Modulation from the Waveform

In practice, you can measure the modulation index of an AM signal using an oscilloscope connected to the transmitter output (via an attenuator or pickup). On the oscilloscope, the AM waveform displays as a "double envelope" — the outline traced by the positive peaks (upper envelope) and the outline traced by the negative peaks (lower envelope). The maximum amplitude of the envelope is V_max and the minimum amplitude is V_min.

For a 100% modulated signal (m = 1): V_max = 2V_c and V_min = 0. Substituting: m = (2V_c − 0) / (2V_c + 0) = 1.0. This confirms the formula. For a 50% modulated signal: V_max = 1.5V_c and V_min = 0.5V_c. Substituting: m = (1.5 − 0.5) / (1.5 + 0.5) = 1.0 / 2.0 = 0.5. Correct.

Calculator: AM Modulation Index

Sidebands: Where the Information Lives

The most important thing to understand about AM — and the thing that connects AM theory to everything else in this module — is the sideband structure. When you expand the AM equation mathematically using a trigonometric identity, you discover that the modulated signal is not just a single frequency but a sum of three distinct frequency components:

This is remarkable: modulating a carrier with a single audio tone does not "smear" the carrier across a range of frequencies. It creates exactly three discrete spectral lines — the carrier and two sidebands symmetrically placed above and below it. The spacing between the carrier and each sideband equals the audio frequency exactly. A 1,000 Hz tone modulating a 7,295 kHz carrier creates a carrier at 7,295.000 kHz, an LSB component at 7,294.000 kHz, and a USB component at 7,296.000 kHz.

Now consider what happens with a real voice signal, which contains audio frequencies spanning roughly 300 Hz to 3,000 Hz. Each frequency in that voice signal creates its own pair of sidebands. The collection of all the USB components forms the upper sideband — a band of frequencies extending from f_c + 300 Hz to f_c + 3,000 Hz. The collection of all the LSB components forms the lower sideband — a mirror image extending from f_c − 3,000 Hz to f_c − 300 Hz. Together with the carrier in the middle, the full AM signal occupies a bandwidth of twice the highest audio frequency.

The key insight about sidebands and information: the carrier itself carries zero information. It is a fixed-frequency, constant-amplitude tone. All of the information — the voice, the music, the Morse code — is encoded entirely in the sidebands. Furthermore, the upper sideband and lower sideband contain identical information (they are mirror images of each other in the frequency domain). This redundancy is what SSB exploits: by transmitting only one sideband and suppressing the other (and suppressing the carrier entirely), SSB achieves the same information transfer using less than half the bandwidth and far less power.

Spectrum of an AM voice signal. The carrier at fc is flanked by the lower sideband (LSB) and upper sideband (USB). For voice spanning 300–3,000 Hz, the total bandwidth is 2 × 3,000 Hz = 6 kHz. Both sidebands carry identical information — the audio content. The carrier in the middle carries no information.

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AM Bandwidth

The bandwidth of an AM signal is determined entirely by the highest audio frequency present in the modulating signal:

The AM broadcast band stations in North America are spaced 10 kHz apart because each station can transmit audio up to 5 kHz, producing sidebands 5 kHz wide on each side, for a total of 10 kHz occupied bandwidth. In practice, some AM broadcasts push audio up to 10 kHz (20 kHz total bandwidth) but with careful filtering to avoid interference to adjacent channels 10 kHz away.

On amateur radio, when AM is used on HF (primarily 10 meters and as an optional mode on other bands), the signal bandwidth is limited by the audio bandwidth of the microphone and transmitter audio chain. Most AM-mode transceivers restrict audio to about 2.5–3 kHz (for 5–6 kHz total AM bandwidth) to avoid occupying excessive spectrum. The FCC Part 97 rules for amateur radio specify that you must use the minimum bandwidth necessary for the information being sent.

Calculator: AM Bandwidth

Power Distribution in an AM Signal

Understanding power distribution in AM reveals why it is so inefficient compared to SSB. The total power in a modulated AM signal depends on the carrier power and the modulation index:

This power breakdown is striking. Even at the maximum recommended modulation depth of 100%, two thirds of the transmitter's output power goes into the carrier — which carries no information. Only one third of the power is in the sidebands where the voice actually lives. And because AM sends both sidebands (which contain identical information), only one sixth of the total transmitted power is in each information-bearing sideband.

The carrier power never changes with modulation level — it stays fixed at P_c regardless of m. Only the sideband power changes. This is why AM transmitters are designed to handle significantly more power than the carrier rating: a 100 W carrier AM transmitter must safely handle 150 W output at 100% modulation. The power supply, finals, and output network must all be sized for the peak modulated power.

Overmodulation and Splatter

Overmodulation occurs when the modulation index exceeds 1.0 (100%). This happens when the audio level fed to the transmitter's modulator is too high — either because the microphone gain is set too high, the operator is shouting, or the audio processing is incorrectly adjusted. Overmodulation is one of the most serious operating problems in AM, and one of the most common complaints received by operators on AM calling frequencies.

When m exceeds 1.0, the term (1 + m·sin(2πf_mt)) goes negative during the peaks of negative audio excursion. The carrier voltage would be required to reverse polarity, which most AM transmitters cannot do — they simply switch off. The result is that the carrier is cutoff (clipped to zero) during the negative audio peaks, creating flat spots in the RF envelope. These flat spots represent an abrupt change — a sharp step — in the waveform. Any sharp step in a time-domain waveform corresponds to a very wide range of frequencies in the frequency domain. These unwanted frequency components appear as sidebands far removed from the carrier — they extend across adjacent channels and interfere with other stations' communications.

This interference is called splatter or key clicks (for CW). Splatter from an overmodulated AM station can render completely unusable several kilohertz of spectrum on both sides of the overmodulated carrier. FCC Part 97.307 prohibits spurious emissions and requires amateur stations to avoid unnecessary bandwidth. Overmodulation is therefore not only technically harmful but also illegal in amateur radio operation.

Left: properly modulated AM at 85% — clean envelope, no clipping. Right: overmodulated at 130% — the envelope clips to zero during negative audio peaks, creating flat spots that generate broad spurious sidebands (splatter) spread across adjacent channels. Overmodulation is both technically harmful and a violation of FCC rules.

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To avoid overmodulation in a ham shack AM station:

• Use an oscilloscope to monitor the RF envelope and verify the envelope never touches zero (for a single-tone test)
• Set microphone gain so that your average voice level produces approximately 70–85% modulation, leaving headroom for voice peaks
• Use an audio speech processor or compressor with a hard limiter set at 100% — never higher
• Speak at a consistent level and distance from the microphone
• Have another station on the frequency listen for any reports of distortion or splatter

The Envelope Detector: How AM Is Demodulated

The enormous advantage of AM over other modulation schemes is the simplicity of the detector circuit needed to recover the audio. An AM signal can be demodulated with a circuit containing a single diode, a capacitor, and a resistor — three components costing pennies. This circuit is called an envelope detector (also called a diode detector or peak detector).

The envelope detector works in two phases:

Charging phase: When the incoming AM signal is at a positive peak, the diode conducts and charges the capacitor up to the peak voltage of the RF signal. The capacitor charges very quickly — the RC time constant is short enough to follow the rapid rise of the RF peaks.

Discharge phase: When the RF signal passes through zero and into the negative half-cycle, the diode blocks and the capacitor discharges slowly through the load resistor. The time constant RC is chosen to be short enough to follow the audio-frequency variations in the envelope (decay time of about 1/f_audio) but long enough to not follow the rapid RF oscillations (much shorter than 1/f_c).

The result is that the capacitor voltage follows the envelope of the AM signal — it rises and falls with the audio frequency modulation. This voltage, after removing any DC offset with a coupling capacitor, is the recovered audio signal. It is then amplified and fed to the loudspeaker.

The envelope detector: one of the simplest radio demodulator circuits. The diode rectifies the AM signal, the capacitor averages over the RF cycles to follow only the audio envelope, and the coupling capacitor removes DC to leave the recovered audio. The circuit works because the RC time constant is chosen to be much longer than the RF period but shorter than the audio period.

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The envelope detector has one important limitation: it requires the carrier to be present in the received signal. If you try to use an envelope detector to demodulate an SSB signal (which has no carrier), you get an unintelligible output — the envelope of an SSB signal does not correspond to the original audio waveform. This is why SSB and CW require a different type of detector (the product detector, covered in the Detectors and Demodulators lesson).

AM vs SSB: The Key Tradeoffs

Since SSB is derived from AM by suppressing the carrier and one sideband, comparing them directly reveals exactly what improvements SSB makes and what costs it imposes.

The 9 dB advantage of SSB over AM deserves explanation. Consider a 100 W carrier AM transmitter. At 100% modulation it produces 150 W total, of which 50 W (1/3) is in the sidebands. The useful power in one sideband is only 25 W. A 100 W SSB transmitter puts the full 100 W into one sideband. The ratio is 100/25 = 4 times = 6 dB in power. But because SSB uses half the bandwidth of AM, the power spectral density is also doubled, which contributes an additional 3 dB advantage in a bandwidth-limited receiver. Combined, SSB has approximately 9 dB advantage over full AM under typical operating conditions. For a ham operator trying to make contact with a distant station on 40 meters at the edge of propagation range, 9 dB is an enormous margin — it is the difference between making the contact and not.

AM in Amateur Radio

Despite the dominance of SSB on HF amateur bands, AM retains an enthusiastic following in the amateur community, particularly on the 10-meter band (29.0–29.2 MHz for AM voice) and the 160-meter band among vintage radio enthusiasts. AM on HF is often called "vintage" or "classic" AM and appeals to operators who enjoy the distinctive warm audio quality of high-fidelity AM audio and the camaraderie of the "AM community" that gathers on specific calling frequencies.

The 10-meter band is particularly suited to AM because at 10 meters the available spectrum is wide (1.7 MHz total bandwidth for amateurs), propagation can support worldwide contacts during periods of high solar activity, and a 6 kHz AM signal is a much smaller fraction of the total band than on the narrower HF bands. Additionally, 10 meters shares the frequency band with the citizens band (CB radio), and many CB rigs use AM, making 10-meter AM a natural bridge for operators upgrading from CB to amateur radio.

The aviation VHF band (118–137 MHz) uses AM for an important historical reason: AM allows multiple transmitters (aircraft and ground stations) to be heard simultaneously on the same frequency if they transmit at the same time, because their envelopes add together. With FM and its capture effect, only the strongest signal would be heard — in aviation where simultaneous transmissions by multiple aircraft could carry critical safety information, this would be dangerous. AM's linearity — the fact that two AM signals on the same frequency add linearly at the receiver — is an important safety feature in aviation communication.