Single-sideband_modulation

# Single-sideband modulation **Single-sideband modulation** (SSB), or single-sideband suppressed-carrier modulation (SSB-SC), is a refinement of [[Amplitude_modulation|amplitude modulation]] that transmits only one of the two mirror-image sidebands an amplitude-modulated [[Carrier_wave|carrier]] would otherwise produce, and drops the carrier itself. A three.js microsim built for this article lays the spectra of full AM, DSB-SC and SSB side by side and shows the filter that strips one sideband away, so the reader watches the occupied span of spectrum halve as the second sideband and the carrier disappear. The technique halves the [[Sideband|sideband]] bandwidth that carries the message and puts all of the transmitter's power into the one sideband doing the work, at the price of a receiver that must regenerate the missing carrier accurately enough to avoid a warble or a mush of static. It grew out of long-distance wired telephony and, from the mid-twentieth century, became the standard for long-range voice communication on [[Radio|radio]] links too weak, too crowded, or too battery-limited to waste a carrier and a sideband: amateur high-frequency voice, marine and aeronautical HF, and military tactical radio all still use it. ## Basic concept Ordinary amplitude modulation multiplies a message onto a carrier and, in doing so, creates two copies of the message's spectrum: one shifted up to sit just above the carrier frequency and one shifted down to sit just below it, the upper and lower sidebands. For a real-valued message the two are mirror images of each other, so each already contains everything needed to reconstruct the message; the carrier itself carries no information at all, yet in full AM it typically holds more transmitted power than either sideband alone.[^johnson146] SSB removes what is redundant: it keeps one sideband, discards the other, and suppresses the carrier, so every watt leaving the transmitter and every hertz of the channel does useful work. The result no longer has an amplitude envelope that follows the message the way an ordinary AM envelope does, so the simple [[Envelope_detector|envelope detector]] that recovers speech from full AM cannot recover it from SSB; some form of coherent mixing against a locally generated replica of the missing carrier is needed instead, as described below under Demodulation. ## History Suppressing the carrier to pack more voice channels onto a wire pair was an economic idea before it was a radio one. John R. Carson, an engineer at AT&T, filed the foundational patent on suppressed-carrier signaling on December 1, 1915; it issued in 1923 and describes both suppressing the carrier and recovering the message by mixing the received signal with a locally generated replica of it, the "homodyne" method that modern synchronous detectors still use.[^carson1915] A single-sideband signal can be built by filtering a double-sideband signal, but a filter sharp enough to remove one sideband without touching the other is hard to build at radio frequencies; Ralph Hartley, at Western Electric's engineering department (reorganized that same year as [[Bell_Labs|Bell Telephone Laboratories]]), patented an alternative in 1925 that produces one sideband directly by adding and subtracting two amplitude-modulated signals in quadrature, a scheme still called the phasing method.[^hartley1928] D. K. Weaver published a third method in 1956, in the journal that later became part of the IEEE's own lineage, that reaches the same result with ordinary [[Low-pass_filter|low-pass filters]] and a fixed quadrature shift rather than either a sharp bandpass filter or a phase-shift network that must stay accurate across the whole audio band.[^weaver1956] SSB's bandwidth and power efficiency made it the mainstay of long-distance point-to-point [[Telecommunications|telecommunications]] before satellites and undersea cable took over that role, and it remains the everyday voice mode of amateur high-frequency [[Radio|radio]] operation to this day. ## Mathematical formulation Multiplying a baseband tone by a carrier produces, by the ordinary trigonometric product-to-sum identity, a term at the sum of the two frequencies and a term at their difference: this is standard textbook Fourier analysis, and it is the whole of why amplitude modulation has two sidebands rather than one. SSB can be generated directly, without ever forming the unwanted sideband, using the [[Analytic_signal|analytic signal]] of the message: if `m_hat(t)` is the [[Hilbert_transform|Hilbert transform]] of the message `m(t)`, then `s(t) = m(t)*cos(wc*t) − m_hat(t)*sin(wc*t)` contains only the upper sideband, and the same expression with a plus sign contains only the lower one. The Hilbert transform shifts every frequency component of the message by 90 degrees without changing its amplitude, which is exactly the operation a phasing-method modulator performs with an analogue network instead of a digital filter. ### Lower sideband The sign in front of the quadrature term is the whole difference between the two sidebands: a minus sign cancels the lower sideband's contribution and leaves the upper, and a plus sign does the reverse. Because the message and its Hilbert transform have the same energy, the lower and upper sideband signals built this way carry identical power for the same message, so the choice between them is a matter of band-plan convention, not physics. ## Practical implementations and considerations Three distinct engineering routes reach the same signal, and each trades a different piece of complexity for a different limitation. ### Bandpass filtering The most direct approach mixes the message onto a carrier to form an ordinary double-sideband signal and then removes one sideband with a sharp bandpass [[Filter_(signal_processing)|filter]]. The filter must reject a sideband that sits immediately next to the one being kept, which is easy at audio-derived intermediate frequencies of a few hundred kilohertz using a crystal or mechanical filter, and correspondingly harder the higher the carrier frequency, because a filter's required sharpness scales with its centre frequency divided by the gap to be rejected. ### Hartley modulator The phasing method avoids a sharp filter entirely. Two balanced modulators, fed with the message and the carrier ninety degrees apart in each path, produce two double-sideband signals whose unwanted sidebands are equal and opposite; summing them cancels the unwanted sideband and reinforces the wanted one. Its accuracy depends entirely on how well the ninety-degree phase shift is held across the whole audio band, which is the method's practical weakness. ### Weaver modulator The third method sidesteps that weakness by needing a quadrature shift at only one fixed audio frequency rather than across a whole band. It mixes the message with quadrature audio oscillators, filters each product with an ordinary [[Low-pass_filter|low-pass filter]], and mixes the pair up to the final frequency in quadrature a second time; the two stages of quadrature mixing do the same cancellation the Hartley method does, without the wideband phase-shift network. ### SSB tuning Because SSB carries no carrier for a receiver to lock onto, its local oscillator must be set within a few tens of hertz of the transmitter's suppressed carrier or the recovered speech shifts in pitch and starts to sound unnatural; too far off and it becomes unintelligible. This single-hertz-scale demand on frequency stability, trivial for a modern synthesized [[Oscillation|oscillator]], was SSB's main obstacle in the vacuum-tube era and the reason wide adoption waited for stable, easily tuned local oscillators. ## Demodulation SSB is recovered by mixing the received signal with a locally generated carrier at (or very near) the frequency that was suppressed at the transmitter, a step called product detection, and low-pass filtering the result back down to the message band; this is the same "homodyne" idea Carson's original patent described. Because the receiver's oscillator is never exactly the transmitter's missing carrier, the recovered audio is shifted uniformly in frequency by the difference between the two, which is what SSB tuning trades against. In practice the product detector is one stage of an otherwise ordinary [[Superheterodyne_receiver|superheterodyne receiver]] or a [[Direct-conversion_receiver|direct-conversion receiver]], with the detector's local oscillator standing in for the missing carrier. ## SSB as a speech-scrambling technique Because an SSB signal can be shifted, inverted or split in frequency without losing any of the message it carries, the same building blocks used to generate it were long used to build simple analogue speech scramblers: mixing speech up and back down through an offset carrier inverts the spectrum, so high frequencies become low and low become high, leaving a signal that sounds like noise to an ordinary receiver but unscrambles cleanly with the matching offset. The scheme protects against a casual listener rather than a determined one; frequency inversion is a fixed, guessable transformation; and it says nothing about how SSB itself is transmitted, only that its architecture is reusable for the purpose. ## Suppressed carrier (SSB-SC), double-sideband suppressed carrier (DSB-SC), and vestigial sideband (VSB) Four related schemes sit on a single spectrum-versus-simplicity trade-off. Full [[AM_broadcasting|AM broadcasting]] keeps both sidebands and the whole carrier, occupying a bandwidth of twice the baseband width for a real message, because that redundant carrier lets a cheap [[Envelope_detector|envelope detector]] recover the programme without any local oscillator at all.[^johnson124] DSB-SC keeps both sidebands but removes the carrier, halving the transmitted power for the same sideband information while still occupying the full double bandwidth and still needing a coherently generated local carrier to demodulate. SSB-SC removes the carrier and one whole sideband, halving the bandwidth again on top of the DSB-SC power saving. Vestigial sideband keeps nearly all of one sideband, a full carrier, and only a fragment of the other sideband, a compromise chosen when a signal's low-frequency content is large enough that a true single-sideband filter cannot cut cleanly next to the carrier; historically this was the choice for [[Signal_modulation|modulating]] video rather than voice, where sharp cutoff of a wide, DC-rich baseband is impractical. ## Compatible single side-band A handful of systems from the 1950s through the 1980s tried to get some of SSB's efficiency while still working, at reduced quality, on an ordinary AM [[Radio_receiver|receiver]] with no product detector: they transmit a full sideband on one side and a reduced or independent sideband on the other, together with enough carrier for an envelope detector to track. The approach traded some of SSB's bandwidth and power saving for backward compatibility, and none of these compatible schemes displaced full SSB where a matched receiver could be assumed. ## Frequencies for LSB and USB in amateur radio voice communication Amateur operators follow a fixed, purely conventional split rather than a technical rule: lower sideband on the high-frequency voice bands below 10 MHz, and upper sideband above it, including on the VHF and UHF bands. Nothing about propagation or receiver design requires this particular split; it exists so that two stations tuned to the same dial frequency, with no other information exchanged, already agree on which sideband to expect and can understand each other immediately. ## Extended single sideband (eSSB) Standard voice SSB restricts the audio passband to roughly the 300 Hz to 3 kHz band that carries intelligible speech with minimum bandwidth. Extended SSB widens that passband, sometimes to 5 kHz or more of audio, trading the bandwidth SSB otherwise saves for higher fidelity, an option some amateur operators use within their allocated band segments when spectrum crowding allows it. ## Amplitude-companded single-sideband modulation (ACSSB) ACSSB adds a low-level pilot tone alongside the sideband and applies [[Companding|companding]], compressing the signal's dynamic range before transmission and expanding it back afterward, so that a weak signal buried near the receiver's noise floor is still intelligible once expanded. Land-mobile and marine VHF systems explored ACSSB in the 1980s as a way to fit narrower channels into crowded bands while keeping usable range, at the cost of the extra companding hardware and the pilot tone's own small slice of bandwidth. ## Controlled-envelope single-sideband modulation (CESSB) Ordinary SSB transmitters are limited by peak envelope power: an amplifier sized for the occasional loud syllable spends most of a conversation working well below its capability. CESSB, described by David Hershberger in 2016, shapes the modulating waveform so that its peaks are held to a controlled ceiling without the sideband splatter that simply clipping the audio would cause, letting the same amplifier deliver a higher average power for the same peak rating and the same occupied bandwidth.[^hershberger2016] The technique is implemented in digital signal processing rather than analogue circuitry, and has appeared in amateur [[Software-defined_radio|software-defined radio]] transceivers built after that date. ## ITU designations International frequency-allocation practice identifies emissions by a short code rather than a name: full-carrier AM is designated A3E, and single sideband is J3E when the carrier is fully suppressed, R3E when a small "pilot" carrier is left for the receiver to lock onto, and H3E when the full carrier is kept, matching the compatible schemes described above. The letters and digits describe the modulation type, the nature of the modulating signal, and the type of information carried, in a scheme meant to be read the same way regardless of the language of the [[Radio_spectrum|licence]] issuing it. ## SSB bandwidth reduction The earliest motive for shrinking SSB's already-halved bandwidth further was commercial rather than technical: a long-distance telephone carrier that could pack more voice channels onto one cable pair or one radio band earned more revenue per route, and Carson's original suppressed-carrier patent was aimed at exactly that, stacking many single-sideband voice channels back to back on a single [[Transmission_line|transmission line]] with only a narrow guard band between them.[^carson1915] Radio SSB has been pushed the same way since, mainly by processing the message rather than the carrier: companding, as in ACSSB, and envelope shaping, as in CESSB, both narrow the effective demand on the channel without changing the sideband-and-suppressed-carrier idea underneath. Digital modes push the same goal further still by compressing the message itself before it ever reaches a modulator, the same principle behind ordinary audio [[Data_compression|data compression]], at the cost of no longer being SSB at all. ## Microsims A three.js companion piece, built for the Wikitube framework rather than carried over from an existing sketch, renders the spectra of full AM, DSB-SC and SSB together and shows the filter that a bandpass or phasing method uses to cut one sideband away; it is described here only in outline, without its own controls or readouts, because those belong on its own page. *Try:* in the [[Doppler_effect]] sketch, change the source speed and watch every frequency in the wavefront shift by the same additive amount — the same uniform shift an SSB receiver's product detector introduces when its local oscillator sits a few hertz off the suppressed carrier, described above under SSB tuning.  **Microsim — three.js (Wikitube framework), pending deploy:** *Single-sideband modulation: fewer lines, a harder filter* will play here once `https://wikitube-3d-microsims.netlify.app/radio/Single-sideband_modulation.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Single-sideband_modulation.json`; part of the [[PORTAL_Radio|Radio]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Single-sideband_modulation) : [Wikitube](https://en.wikitube.io/wiki/Single-sideband_modulation) Skeleton mirrored at revision 1370561815. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Sideband]] - [[Radio]] - [[Amplitude_modulation]] - [[Carrier_wave]] - [[Frequency_modulation]] - [[Superheterodyne_receiver]] - [[Software-defined_radio]] - [[Companding]] ## References [^carson1915]: Carson, J. R. "Method and Means for Signaling with High-Frequency Waves." U.S. Patent 1,449,382, filed December 1, 1915, granted March 27, 1923, assigned to American Telephone and Telegraph Co. https://patents.google.com/patent/US1449382A/en [^hartley1928]: Hartley, R. V. L. "Modulation System." U.S. Patent 1,666,206, filed January 15, 1925, granted April 17, 1928, assigned to Western Electric Co. https://patents.google.com/patent/US1666206A/en [^weaver1956]: Weaver, D. K. "A Third Method of Generation and Detection of Single-Sideband Signals." Proceedings of the IRE, 1956. https://ieeexplore.ieee.org/document/4051946/ [^hershberger2016]: Hershberger, D. L. "Controlled Envelope Single Sideband." QEX (American Radio Relay League), January/February 2016. https://www.arrl.org/files/file/QEX_Next_Issue/2016/January_February_2016/Hershberger_QEX_1_16.pdf [^johnson124]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 124 (PDF page): AM bandwidth is twice the baseband width for a baseband much narrower than the carrier frequency. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^johnson146]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 146 (PDF page): for an AM signal `[1 + s(t)]*cos(2*pi*fc*t)`, the power in the sidebands equals half the power of the message `s(t)`, with the carrier itself carrying the rest. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. ## Sources Page numbers above are PDF pages of the open editions linked under Further reading. Claims about the trigonometric structure of amplitude modulation and the Fourier shift theorem underlying it are standard results in signal theory and are not separately footnoted, per house style §6.1; the patent, journal and QEX citations above are the primary and near-primary sources for who built each variant and when. ## Further reading - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to Filtering: Theory*. 2026. CC BY. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory - Don Johnson. *Fundamentals of Electrical Engineering I*. 2014. CC BY. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 - Steven Ellingson. *Radio Systems Engineering*, Revised 1st ed. 2023. CC BY-NC. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain*. 2020. CC BY-SA. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain - Allen Downey. *Think DSP: Digital Signal Processing in Python*. 2012. CC BY-NC. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/think-dsp-digital-signal-processing-in-python