Amplitude modulation is the process of varying the amplitude of a high-frequency carrier wave in proportion to the instantaneous value of a low-frequency message (modulating) signal. In the conventional form of AM, known as full-carrier AM or AM-DSB (Double Sideband full carrier), the transmitted signal contains not only two sidebands carrying the information but also a carrier component that does not itself carry any message information.
The carrier, however, consumes a large share of the transmitted power. For typical voice transmission the carrier alone absorbs about two-thirds of the total transmitted power, while each sideband carries only about one-sixth of the information-bearing energy. Since the message exists only in the sidebands, the carrier is, from an information point of view, wasted power.
Suppressed-carrier amplitude modulation techniques were developed to remove this inefficiency. In these schemes, the carrier is suppressed either partially or completely at the transmitter, and the receiver is made responsible for re-inserting a local carrier for demodulation. The two principal suppressed-carrier methods are:
These techniques are fundamental to analog communication practice. SSB, in particular, became the international standard for long-distance shortwave telephony and is still the dominant mode in high-frequency (HF) radio, land-mobile, and some microwave systems. Understanding them is essential for the 4th-year student because they illustrate the trade-off between spectral efficiency, power efficiency, and receiver complexity that underlies all modern communication system design.
| Term | Definition |
|---|---|
| Carrier wave | A high-frequency sinusoidal signal, c(t) = Accos(2πfct), whose amplitude, frequency, or phase is varied in accordance with the message signal. |
| Message (modulating) signal | The low-frequency information-bearing signal m(t), band-limited to frequency fm, that one wishes to transmit. |
| Sideband | A frequency band adjacent to the carrier produced by modulation. The upper sideband (USB) lies above fc; the lower sideband (LSB) lies below fc. |
| Suppressed carrier | A modulation scheme in which the carrier component is attenuated (ideally to zero) at the transmitter so that it carries no transmitted power, leaving only the sidebands. |
| Modulation index (μ or m) | The ratio of the peak message amplitude to the peak carrier amplitude, m = Am/Ac. In suppressed-carrier schemes the envelope is proportional to |m(t)|, so a different measure, the percentage modulation, is often used. |
| Synchronous (coherent) detection | Demodulation achieved by multiplying the received signal by a locally generated carrier whose frequency and phase match the original carrier exactly. |
| Balance modulator | A circuit (often a diode ring or differential pair) that cancels the carrier and produces a DSB-SC output. |
| Sideband filter | A highly selective filter (crystal, ceramic, or mechanical) used to pass one sideband and reject the other in SSB generation. |
| Phasing method | SSB generation using Hilbert transformers (90° phase shifters) and balanced modulators to cancel one sideband arithmetically. |
| Vestigial Sideband (VSB) | A compromise technique in which one sideband is transmitted fully and a vestige (portion) of the other is retained to ease filtering; used in analog TV. |
| Peak envelope power (PEP) | The average power over one RF cycle at the crest of the modulation envelope; the standard power rating for SSB transmitters. |
Amplitude modulation was demonstrated experimentally in the first years of the 20th century and first used for voice transmission by Reginald Fessenden in 1906. Commercial AM broadcasting began in the 1920s using the full-carrier, double-sideband format because it allowed simple, inexpensive envelope (diode) detection in receivers — an important consideration when most listeners used simple home-built sets.
By the 1920s and 1930s, engineers recognized that the full-carrier format squandered power and spectrum. Radio amateurs and point-to-point telegraphy operators sought more efficient modes. The suppressed-carrier concept emerged: if the carrier is removed at the transmitter, all of the power can be concentrated in the sidebands that actually carry information.
The single-sideband principle was patented and developed in the early years of radio telephony. A landmark was the long-wave telephone link between the United States and Britain in the late 1920s, which used SSB to conserve both spectrum and power over transatlantic distances. During and after the Second World War, SSB equipment matured rapidly for military and commercial HF telephony, using improved crystal filters for sideband selection and stable frequency synthesizers for carrier re-insertion.
Through the mid-20th century the International Telecommunication Union and national regulators adopted SSB as the standard for HF point-to-point telephony and aeronautical mobile services. In broadcasting, the need to keep receivers cheap delayed suppressed-carrier adoption; instead, Vestigial Sideband (VSB) was chosen for analog television, transmitting a full carrier, one full sideband, and a vestige of the other to save 6 MHz of channel bandwidth.
Today, suppressed-carrier methods remain embedded in modern systems: SSB dominates amateur radio and HF aeronautical communication; balanced (suppressed-carrier) modulators are the building block of every I/Q modulator in digital radios; and the mathematics of Hilbert transforms and synchronous detection underlies digital single-sideband, QAM, and OFDM systems.
In DSB-SC, the modulated wave is simply the product of the message and the carrier. If the carrier is c(t) = Accos(2πfct) and the message is m(t), then:
For a tone message m(t) = Amcos(2πfmt):
Unlike full-carrier AM, the envelope of a DSB-SC signal is proportional to |m(t)| and crosses zero whenever the message passes through zero. The envelope therefore no longer resembles the message; the phase of the carrier reverses by 180° at each message zero-crossing. This is why a simple envelope detector cannot recover the message.
Applying the product-to-sum identity to the tone case:
The spectrum contains only two components: one at fc + fm (upper sideband) and one at fc − fm (lower sideband). The carrier at fc is absent. For a general message band-limited to B Hz, the spectrum of s(t) occupies fc − B ≤ |f| ≤ fc + B, a total transmission bandwidth of 2B — the same as full-carrier AM — but with no power wasted in the carrier.
For the tone case with normalized 1 Ω resistance, the total average power is:
All of this power resides in the two sidebands. Compared with full-carrier AM at the same peak envelope, DSB-SC delivers the same information power with up to two-thirds less total power, i.e. a power efficiency gain that approaches a factor of 3 (4.8 dB) as the modulation index approaches unity.
A DSB-SC signal contains two sidebands that are mirror images of each other: the upper sideband carries the message spectrum shifted up to fc, and the lower sideband carries the same information shifted down. Because either sideband alone contains the complete message, one of them can be discarded. SSB-AM transmits only one sideband (upper or lower) with the carrier suppressed.
For a tone message Amcos(2πfmt), choosing the upper sideband:
For a general message m(t), SSB can be written compactly using the Hilbert transform m̂(t) of the message:
SSB requires a transmission bandwidth of only B Hz for a message band-limited to B Hz — half that of DSB-SC or full-carrier AM. For voice (300–3400 Hz), an SSB channel occupies only about 3 kHz instead of 8 kHz, more than doubling the number of channels available in a congested HF band.
With the carrier suppressed and one sideband removed, SSB concentrates all transmitted power into information. Relative to full-carrier AM, SSB achieves a power saving of up to 9 dB (a factor of about 8) at 100% modulation, and reduces transmitted bandwidth by 50%. These gains are obtained at the cost of greater transmitter and receiver complexity.
Any device or circuit whose output is proportional to the product of the message and the carrier can serve as a DSB-SC generator. The practical methods fall into two broad classes: balanced modulators (carrier cancellation in a nonlinear circuit) and multiplier-based modulators (analog or digital multiplication).
The classic DSB-SC generator uses four diodes connected in a ring, with the carrier applied to one pair of opposite nodes and the message to the centre tap of an input transformer. The diodes act as polarity reversers switched by the carrier:
The output is therefore m(t)·square-wave(at fc) = m(t)·s(t) in effect a multiplication. Because the circuit is symmetric, any carrier leakage to the output cancels (the two halves carry equal and opposite carrier currents), while the message is multiplied. The Fourier series of the square-wave switching function contains only odd harmonics of fc, so the output contains products at fc ± fm, 3fc ± fm, etc. A bandpass filter centred at fc selects the desired DSB-SC term and rejects the odd-harmonic products.
Two identical amplifiers (bipolar transistors or FETs) are driven in push-pull by the carrier so that their carrier components cancel at the combined output, while the message, applied to both, appears as a product term. The FET version is preferred because the square-law portion of the FET characteristic produces the product m(t)·c(t) with only even-order distortion terms that are easily filtered.
Integrated-circuit balanced multipliers (e.g. the Gilbert cell, as in the 1496-type IC) produce an output proportional to the product of two input voltages:
These circuits offer excellent carrier suppression (often ≥ 60 dB with proper trimming of the balance potentiometer), low distortion, and stable operation, and are widely used in instrumentation and low-power transmitters.
In modern equipment the message is digitized; a digital multiplier (or a lookup-table DDS mixing stage) computes the product, followed by a DAC and reconstruction filter. Digital generation gives precise balance, perfect reproducibility, and easy integration with digital signal processing chains.
Residual carrier appears at the output whenever the two halves of the balanced circuit are not identical (component tolerances, transformer asymmetry, drive imbalance). A balance adjustment (a trimmer or bias potentiometer) is provided to null the carrier. A figure of merit is the carrier suppression ratio, typically required to exceed 40–60 dB below the sidebands.
SSB generation combines a DSB-SC signal with a mechanism that removes one sideband. There are three classical methods:
The most widely used method. A balanced modulator produces a DSB-SC signal; a highly selective bandpass filter then passes one sideband and rejects the other.
This method cancels one sideband arithmetically instead of filtering it. Two DSB-SC signals are formed:
where m̂(t) is the Hilbert transform of m(t), obtained by passing the message through a −90° phase-shift network. Subtracting gives the upper sideband; adding gives the lower sideband:
The Weaver method overcomes the wideband phase-shift problem by first translating the message to a low quadrature band where a fixed 90° shift is easy, and was historically important in generating high-quality SSB for telephony multiplex systems.
Practical transmitters often combine both ideas: a wideband phasing stage with relaxed phase accuracy provides coarse sideband cancellation, followed by a modest filter that cleans up the residual unwanted sideband. This relaxes the demands placed on both the phase networks and the filter, giving high sideband suppression (>60 dB) at reasonable cost.
| Method | Sideband selection by | Main advantage | Main limitation |
|---|---|---|---|
| Filter | Crystal/ceramic bandpass filter | High sideband suppression; simple concept | Difficult at high fc with wide message; needs low IF translation |
| Phasing | Hilbert (90°) networks and addition/subtraction | Works at any carrier frequency; no sharp filter | Critical wideband 90° phase accuracy; lower sideband suppression |
| Hybrid | Coarse phasing + cleanup filter | High suppression with relaxed components | More complex design |
Because the carrier is absent, the SSB receiver must supply its own carrier. Two families of demodulators exist:
The received SSB signal is multiplied by a locally generated carrier that must match the original carrier in both frequency and phase. For an USB signal s(t) with local carrier cos(2πfLOt + φ):
Since the carrier is suppressed, the receiver must reconstruct it:
If a local carrier is added to the SSB signal before a diode envelope detector, the resulting waveform approximates an AM signal whose envelope follows the message:
This is the basis of synchronous envelope detection in some SSB receivers and of the "carrier re-insertion" beat-frequency practice. If ALO is too small, diagonal distortion and audio distortion appear; if too large, dynamic range is wasted.
Conventional superheterodyne SSB receivers use a BFO: an oscillator at the intermediate frequency, offset slightly from the IF centre, mixed with the SSB signal so the difference tone at audio is produced. In practice the BFO is the "carrier" that the product detector needs, and its tuning dial lets the operator peak the voice quality by ear.
Like SSB, DSB-SC requires a coherent carrier. The principal methods are:
The received signal is multiplied by a local carrier and low-pass filtered:
With φ = 0 the message is recovered exactly, scaled by the path gain. This is the standard demodulator for DSB-SC and is also the first stage in many SSB demodulators.
A diode envelope detector recovers the envelope |s(t)| = |m(t)|, which equals ±m(t) but has lost the sign of the message — the output is a rectified version with 180° phase reversals of the carrier unrepresented. Hence the envelope detector is unsuitable for DSB-SC unless a strong carrier is deliberately re-inserted first (turning the signal into near-AM). This is exactly the option used in carrier re-insertion receivers, but it wastes the power advantage of carrier suppression and is avoided where link budget matters.
| Method | Needs transmitted pilot? | Complexity | Performance |
|---|---|---|---|
| Product detector + Costas loop | No | Moderate | Excellent; locks at low SNR |
| Squaring loop | No | Moderate | Good; 180° phase ambiguity |
| Product detector + pilot | Yes | Low | Very good if pilot SNR high |
| Envelope detector with carrier re-insertion | Effectively local only | Low | Poor power efficiency; simple receivers |