Carrier_wave - Wikiparency

# Carrier wave Several names attach to the same idea: **carrier wave**, carrier signal, and simply "carrier" all refer to one steady, usually sinusoidal waveform that carries no information of its own until something else varies one of its properties. The *Carrier signal* microsim on this page draws that message-free wave alongside a modulated version of itself, and lets the reader switch between amplitude, frequency, and phase modulation to see what a bare carrier looks like next to one actually doing work. A carrier is deliberately the simplest possible periodic waveform: one amplitude, one frequency, one phase, and nothing else changing in time. That simplicity is the point. [[Signal_modulation|Modulation]] needs a stable, predictable reference to vary; a carrier supplies exactly that reference and nothing more, leaving amplitude, frequency, and phase as the only three knobs any modulation scheme can turn. ## Overview A carrier is written `c(t) = A·cos(2π f_c t + φ)`, the same rotating-phasor picture that describes any [[Sine_wave|sinusoid]]: an amplitude, an [[Angular_frequency|angular frequency]] 2π f_c, and a starting phase, none of which move on their own.[^john021] Left alone, this waveform's spectrum is a single pair of impulses at ±f_c and nowhere else — in the sketch, setting the modulation depth to zero collapses the spectrum panel to exactly that one line, a visible demonstration that a bare carrier, however much power it carries, carries zero information. The same three quantities that describe it — amplitude, frequency, and phase — are exactly the three a modulator can act on, the basis for the whole family of related techniques running from [[Amplitude_modulation|amplitude modulation]] through [[Frequency_modulation|frequency modulation]] to phase modulation; a carrier is also the special, undamped case of a broader family: the same complex-exponential formula that describes a signal decaying or growing in amplitude over time reduces to a carrier precisely when that decay rate is set to zero, leaving a wave that neither strengthens nor weakens as it repeats.[^john022] The carrier's frequency is chosen for reasons that have nothing to do with the message it will eventually carry. Radio-frequency engineering treats that choice as bounded by physics: an antenna radiates efficiently only once its length is a substantial fraction of the carrier's wavelength, so a message that would need a [[Dipole_antenna|dipole antenna]] kilometers long at its own low frequency can instead ride a carrier whose much shorter wavelength fits an antenna a few meters or even centimeters across. A carrier also gives a communication system a dial to turn, since two transmitters on two different carrier frequencies can share the same air or cable without colliding; informally, the carrier frequency is a station's dial number, and retuning a radio to a different one is the whole act of choosing what to listen to, independent of anything that station happens to be modulating onto it. Locating and locking onto that carrier is the first job of almost any receiver, from a simple crystal set to a modern [[Superheterodyne_receiver|superheterodyne receiver]] tuning stage; everything the receiver reports afterward, including the [[Signal-to-noise_ratio|signal-to-noise ratio]] it can offer, is measured relative to that one reference tone. ## Carrierless modulation systems Not every communication system needs a sinusoidal carrier at all. Digital signals sent directly over a wire — the pulses on a [[Transmission_line|transmission line]] inside a piece of equipment, or the line code an Ethernet cable carries between two ports — vary voltage levels in a baseband pattern that is transmitted exactly as generated, with no sinusoidal tone underneath it to modulate. The terminology can mislead here: Ethernet's channel-access method is named "carrier-sense multiple access" for its habit of listening for any signal energy already on the wire before transmitting, a sense of "carrier" that means only "something is currently on the line," not the steady sinusoid this article otherwise describes. Ultra-wideband impulse radio is the wireless counterpart of the same idea. Rather than modulating a continuous sinusoidal tone, it radiates a stream of extremely short pulses, each one so brief in time that its own spectrum is inherently very wide, spreading the transmitted energy thinly across a broad swath of spectrum instead of concentrating it around one narrowband carrier frequency. Both cases still fit the wider frame of [[Signal_modulation|signal modulation]] — a message is still being impressed on a transmitted waveform — but neither needs the one clean spectral line that gives an ordinary carrier its name. Both also still belong squarely to [[Telecommunications|telecommunications]] and to the same [[Electronics|electronics]] that builds conventional carrier-based radios; what changes is only whether a single steady tone sits underneath the information, not whether the underlying idea of modulating a message onto a transmitted waveform still applies. A plain analog telephone line is carrierless in the same sense: the voice waveform a microphone produces travels the copper pair essentially as generated, riding no shifted-up sinusoidal tone at all. A wire tolerates a low-frequency message that the open air will not, because a wire does not have to radiate anything — the antenna-length reasoning that pushes wireless systems toward a high carrier frequency simply has nothing to act on when the signal never leaves the conductor it was launched into. ## Carrier leakage A modulator built to suppress the carrier entirely, as in double-sideband suppressed-carrier or single-sideband transmission, relies on canceling the carrier term exactly, and real circuits never do that perfectly. Component mismatches inside a balanced modulator leave a small residual carrier riding along with the sidebands it was supposed to travel alone; this residue is carrier leakage, also called carrier feedthrough. It wastes a little transmitted power on a component that, by design, was meant to carry no information, and it can bias a receiver's synchronous detector, which is often trying to synthesize its own local reference at exactly the frequency the leaked carrier now also occupies. A related leakage shows up inside the receiver rather than the transmitter. In a direct-conversion design, the local oscillator that a mixer uses to bring the carrier down to baseband can leak backward out through the mixer toward the antenna and radiate weakly on the carrier's own frequency, or leak forward and mix with itself to produce a spurious [[Distortion|distortion]] right at the center of the band the receiver is trying to listen to. Neither fault is total; both are a matter of how well isolated the local oscillator's port is from the signal path, a specification every mixer and modulator carries and no real one reaches perfectly, quoted as an isolation figure in [[Decibel|decibels]] because the semiconductor [[Diode|diodes]] or [[Transistor|transistors]] that do the switching are never matched to each other quite exactly.[^cnleak] Balancing the circuit better, or adding a filter tuned to reject the carrier frequency specifically, reduces the leaked tone but essentially never removes it altogether. Spectrum regulators that police out-of-band emissions treat a leaked carrier the same way they treat any other unwanted emission from a transmitter, since it occupies real spectrum next to a transmission whether or not it was ever meant to be there. ## Microsims The *Carrier signal* sketch stacks three panels — the message, the bare carrier, and the modulated output — behind a selector that switches the modulation between amplitude, frequency, and phase. Carrier frequency f_c (1–20 Hz) and message frequency f_m (0.2–5 Hz) set the two tones, and a single modulation-index slider (0–2) reshapes whichever scheme is currently selected; a readout below the panels names the type in use alongside the two frequencies and the index. *Try:* Keep the frequencies fixed and step the selector from amplitude to phase modulation at the same index, and watch the second and third panels change shape completely even though the message driving them never does. The *Carrier wave* sketch narrows the focus to amplitude modulation alone, adding an explicit spectrum view. Carrier frequency f_c (4–30 Hz), message frequency f_m (0.5–5 Hz), and modulation depth mu (0–1.3) are draggable sliders, and two buttons add an envelope overlay and start a slow horizontal scroll so the carrier's own motion, rather than a single frozen snapshot of it, is visible. The spectrum panel drops a stem for the carrier at f_c and one stem for each sideband at f_c ± f_m, sized by the fraction of power each one carries — the same kind of power distribution a continuous [[Spectral_density|spectral density]] describes, concentrated here at three discrete lines instead of spread smoothly — with a bracket marking the occupied bandwidth B = 2 f_m; a beat-style product of two nearby tones is exactly what puts those sideband stems at f_c ± f_m in the first place.[^stib032] *Try:* Start at mu = 0, where the spectrum shows one bare line and the diagnostics report a flat, message-free carrier; raise mu and watch two sideband stems grow at f_c ± f_m while the time-domain envelope appears, then push mu past 1 and watch that envelope fold through zero. A three.js companion renders the same bare carrier as a helix, with no modulation applied at all, whose radius, pitch, and starting phase are exactly the three parameters this page's equation exposes. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Carrier_wave) : [Wikitube](https://en.wikitube.io/wiki/Carrier_wave) Skeleton mirrored at revision 1372268677. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Signal_modulation]] - [[Superheterodyne_receiver]] - [[Amplitude_modulation]] - [[Frequency_modulation]] ## References [^john021]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 21 (PDF page), Eq. 2.19: `A·cos(2π f0 t + φ) = Re[A·exp(jφ)·exp(j2π f0 t)]`. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^john022]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 22 (PDF page), Eq. 2.22: the decaying (or growing) complex exponential `A·exp(jφ)·exp((−1/τ + j2πf)t)`, of which an undamped carrier is the zero-decay-rate case. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^stib032]: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2016 ed., pp. 32–33 (PDF pages), Eq. 1-16: `a1·exp(jωt) + a2·exp(j(ω+δ)t) = (a1 + a2·exp(jδt))·exp(jωt)`, the same product-to-sum step that places a carrier's sidebands at f_c ± f_m. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. [^cnleak]: Citation needed: typical local-oscillator-to-signal-port isolation figures, in decibels, for a double-balanced mixer or modulator have not been pinned to a source here.