Sideband - Wikiparency

# Sideband A **sideband** is a band of frequencies, higher or lower than a carrier frequency, produced when that carrier is modulated by a message signal; the sidebands, not the carrier itself, are what carry the information a transmission delivers. A three.js microsim built for this article lights up the upper and lower sideband of a simple amplitude-modulated tone individually, so the reader can see each one as a distinct piece of spectrum rather than as an unlabelled bump either side of the carrier line. Every common analog scheme creates sidebands by this same mechanism, but not the same pattern of them: [[Amplitude_modulation|amplitude modulation]] produces exactly two, [[Frequency_modulation|frequency modulation]] produces an unbounded family of them, and [[Single-sideband_modulation|single-sideband modulation]] keeps only one and throws the rest away on purpose. How far the sidebands spread from the carrier sets how much of the [[Radio_spectrum|radio spectrum]] a transmission occupies, which is the figure a service like [[AM_broadcasting|AM broadcasting]] must fit inside its licensed channel. The idea predates radio broadcasting by decades and applies just as directly to a modulated light beam or an ultrasonic pulse as to a carrier at medium-wave frequencies: any process that varies one signal's amplitude, frequency or phase in step with a second signal necessarily pushes some of that second signal's energy away from the first signal's own frequency, and the resulting displaced energy is a sideband whether or not the word is used to describe it. ## Sideband creation Modulating a carrier means multiplying it, in some fashion, by a message signal, and multiplication in time is what creates new frequencies: by the ordinary trigonometric product-to-sum identity, a carrier at `fc` multiplied by a single tone at `fm` yields components at `fc + fm` and `fc − fm`, the upper and lower sideband, and none at `fc` or `fm` themselves unless the modulator deliberately leaves one in. This is the same arithmetic that describes two nearby tones added together rather than multiplied: summing a component at `fc + fm` with one at `fc − fm` reproduces a signal at `fc` whose amplitude rises and falls once every `1/fm` seconds, exactly the slow pulsing, or "beating," heard when two close pitches sound together.[^beat] A sideband pair and a beat are the same mathematics looked at from opposite ends: one asks what two tones sound like when added, the other asks what a single tone looks like once it has been split in two by modulation. Nothing in this arithmetic depends on `fc` being a radio-frequency carrier rather than an audible pitch; the split is a property of multiplication in time, and the name "sideband" is simply what engineers call the split when the two components sit close enough together, and far enough from zero frequency, to be handled as a pair riding on a carrier rather than as two independent tones. ### Sideband Characterization A real message is not a single tone but a continuous band of frequencies, so each sideband is itself a band rather than a line: the whole message spectrum is shifted bodily up to sit just above the carrier, and a second, mirrored copy is shifted down to sit just below it. The width of either sideband is set by the highest frequency present in the message, and the two sidebands of an unfiltered modulator are always mirror images of each other, because a real-valued message has no way to tell the modulator to treat positive and negative offsets from the carrier differently. Only once the modulator, or a filter after it, is allowed to treat the two sides asymmetrically — as [[Single-sideband_modulation|single-sideband]] and vestigial-sideband systems do on purpose — does that mirror symmetry break, and the two sidebands stop being interchangeable copies of the same information. ## Amplitude modulation Ordinary amplitude modulation is the plainest case: it produces exactly two sidebands, one on each side of the carrier, each a full, undistorted copy of the message spectrum, and it usually leaves the carrier itself fully present so that a simple [[Envelope_detector|envelope detector]] can recover the message without any local oscillator. Because both sidebands are transmitted, the occupied bandwidth is twice the highest frequency in the message.[^johnson124] The trade is power: at full, 100 percent modulation depth on a single tone, the two sidebands together carry exactly one third of the total transmitted power, and less at any shallower depth or with a typical, less-than-full-scale message, while the remaining two thirds sits in a carrier that conveys nothing.[^johnson146] A 5 kHz voice baseband therefore needs a 10 kHz channel under ordinary AM, one sideband's width on each side of the carrier; [[Single-sideband_modulation|single-sideband modulation]] exists precisely to keep only one of those 5 kHz sidebands and none of the wasted carrier power, halving the channel and, on a single tone, tripling the fraction of transmitted power that is doing useful work. ## Frequency modulation Frequency modulation builds its sidebands differently, and the difference is qualitative rather than a matter of degree. Because the modulation acts on the carrier's instantaneous frequency rather than its amplitude, even a single modulating tone produces, in principle, an unbounded family of sideband pairs spaced at every integer multiple of the modulating frequency, with amplitudes that fall off according to a Bessel function of the modulation index rather than stopping after one pair. In practice only a limited number of these pairs carry enough power to matter, and an engineering rule credited to John Carson — the same engineer whose 1915 patent underlies single-sideband transmission — approximates the bandwidth holding nearly all of an FM signal's power as twice the sum of the peak frequency deviation and the highest modulating frequency.[^carsonfm] A wider deviation therefore buys a cleaner signal only by spending more sidebands, and so more bandwidth, than amplitude modulation ever needs for the same message. Broadcast FM illustrates the trade with round numbers: a peak deviation of 75 kHz and an audio bandwidth of 15 kHz put Carson's rule at 2 x (75 + 15) = 180 kHz, close to the 200 kHz channel spacing broadcasters actually use, next to the 10 kHz an AM channel needs for a much narrower 5 kHz baseband. This is also why an FM signal tolerates far more noise for a given transmitter power than AM does over the same path: spreading the message over many sideband pairs, rather than concentrating it in one pair close to the carrier, is what lets an FM receiver's discriminator trade the extra bandwidth back for a better signal-to-noise ratio once the received carrier is strong enough to stay above the receiver's capture threshold. ## Effects Sidebands are not a footnote to a transmission; they are the practical reason a modulated signal needs any bandwidth at all, and every channel plan, from an [[AM_broadcasting|AM broadcasting]] band to an amateur voice segment, exists to keep one transmitter's sidebands from overlapping its neighbour's. A modulator that is not perfectly linear generates extra, unwanted sidebands beyond the ideal pair or family, a form of [[Distortion|distortion]] that can splatter energy into an adjacent channel even when the intended sidebands are well behaved. Because sidebands carry the whole message and are mirror images of one another in ordinary amplitude modulation, either one can be discarded without losing information, which is the starting observation behind single-sideband and vestigial-sideband transmission alike; and because a sideband is nothing more than energy sitting at an offset from a carrier, the same offset can be produced by reflection from a moving object as readily as by a modulator, which is the connection the Doppler-shift microsim below makes visible. A receiver's own [[Filter_(signal_processing)|filter]] shapes which of these effects the listener ever notices: a filter matched to the wanted sideband's width passes the message and rejects most out-of-band splatter, while one cut too narrow clips the sideband itself and distorts the very message it was meant to protect. ## Microsims A three.js companion built for the Wikitube framework, rather than carried over from an existing sketch, lights the upper and lower sideband of a simple amplitude-modulated carrier separately, letting the reader see each sideband as a distinct band of spectrum instead of an unlabelled shoulder next to the carrier line; it is described here only in outline, without its own controls or readouts, since those belong on its own page. The idea it isolates — a sideband as energy sitting at a fixed offset from a carrier — recurs in the two neighbouring sketches below, each built around a different kind of offset. *Try:* in the [[Radar]] sketch, read the diagnostics for an approaching or receding target: the Doppler-shifted echo it reports is, in effect, a single sideband sitting off to one side of the transmitted frequency by the shift `f_d`, with no mirror-image partner on the other side, because reflection from one moving target has no way to create the second, opposite offset a modulator produces. *Try:* in the [[Doppler_effect]] sketch, move the source speed control and watch the two observer markers report different frequencies at the same instant: one sits above the source frequency and one below it, the same up-and-down straddling of a centre frequency that a pair of sidebands shows around a carrier, produced here by motion rather than by modulation. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Sideband) : [Wikitube](https://en.wikitube.io/wiki/Sideband) Skeleton mirrored at revision 1337313290. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Amplitude_modulation]] - [[AM_broadcasting]] - [[Single-sideband_modulation]] - [[Frequency_modulation]] - [[Carrier_wave]] - [[Radio]] - [[Radio_spectrum]] ## References [^beat]: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2016 ed., pp. 32-33 (PDF pages): two phasors at nearby frequencies sum to a slow envelope, "beating," at their difference frequency. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. [^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 sideband power equals half the power of the message `s(t)`; for a full-scale single tone this works out to one third of the total transmitted power. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^carsonfm]: Engineering and Technology History Wiki. "John R. Carson." Biographical entry noting the 1922 "Carson bandwidth rule" for estimating the bandwidth of a frequency-modulated signal. https://ethw.org/John_R._Carson