Link_budget - Wikiparency

# Link budget A **link budget** is an accounting of every power gain and loss a signal experiences on its way from a transmitter to a receiver, tallied in decibels to predict how much power will actually arrive. It is a design tool rather than a measurement: an engineer adds the transmitter's power and every antenna gain, subtracts every loss the path and the hardware introduce, and compares the result against the smallest power a receiver needs to recover the signal. The gap between the two is the link margin, the safety allowance a design keeps in reserve against losses that can only be estimated rather than measured in advance. A three.js companion sketch renders the same idea as a running tally, carrying each gain and loss to a final margin. Because the same bookkeeping applies wherever a signal travels, from a [[Radio_wave]] crossing open space to a pulse of light inside a fibre, a link budget's individual terms change with the medium even though its logic does not. The sections below follow that pattern, treating radio propagation, guided transmission lines and optical fibre in turn, each substituting its own loss mechanism for the last. ## In radio systems In a radio link the accounting begins with the power the transmitter delivers to its [[Antenna_(radio)|antenna]], is increased by that antenna's gain toward the receiver, is reduced by the loss the wave suffers crossing the path between the two antennas, and is increased again by the receiving antenna's own gain. Two further deductions almost always apply: the loss of the feedline that connects each antenna to its radio, and a scatter of smaller losses that a careful design lists individually rather than folding into one guess. Everything gained is added and everything lost is subtracted, all in decibels, so the whole calculation is a sum: received power equals transmitted power plus transmit gain minus path loss minus miscellaneous loss plus receive gain. The path-loss term is usually the free-space value from the [[Friis_transmission_equation]], also called [[Free-space_path_loss|free-space path loss]], increased for any additional attenuation the specific path adds. The number the budget is compared against is not fixed either. A receiver's required input power is set by the noise it must work above, and that noise floor is a small calculation of its own: cascading each amplifying stage's noise figure by the standard formula, in which later stages matter less the more the first stage has already amplified the signal, gives the receiver's overall noise figure and hence the smallest usable signal.[^cascade] Background radio noise adds to the same total from outside the receiver: galactic and atmospheric emission raise the effective temperature an antenna delivers to the front end, and near the ground in crowded bands, man-made noise from electrical equipment can dominate that figure by several orders of magnitude.[^antennatemp] A budget that ignores either is compared against too generous a target. Consider a modest example: a transmitter delivering 30 dBm (1 W) into an antenna with 10 dBi of gain, a path loss of 120 dB, 3 dB of feedline and miscellaneous loss, and a receiving antenna with 10 dBi of gain leaves 30 + 10 − 120 − 3 + 10 = −73 dBm at the receiver's input. Against a receiver needing −90 dBm to work reliably, the link closes with 17 dB of margin, comfortable enough to absorb a fade or an optimistic gain figure without failing. ### Line-of-sight vs non-line-of-sight transmission A link with an unobstructed [[Line-of-sight_propagation|line of sight]] between the two antennas is the easiest case: the path loss sits close to the free-space value, changes slowly and predictably as the antennas move, and needs only a modest margin. Once the path is obstructed, by terrain, buildings or foliage, the signal instead arrives by reflection, diffraction and scattering around the obstacles, a regime engineers call non-line-of-sight. [[Multipath_propagation|Multipath]] arrivals combine constructively and destructively as the geometry or the atmosphere shifts, producing [[Fading|fading]] that is properly described only in statistical terms rather than by a single loss figure. Under such fading the received envelope varies randomly rather than sitting at its average value, so a margin sized only for that average will be exceeded on some fraction of the time; the deeper the fade a design must tolerate for an acceptable outage rate, the larger the margin it needs.[^fading] [[Radio_propagation|Propagation]] models for non-line-of-sight paths are consequently empirical, fitted to measurements in the environment of interest, rather than derived from geometry alone. ### Further losses Beyond the path loss itself, a careful budget lists every smaller deduction by name instead of guessing at a single allowance. Gaseous absorption and, at microwave frequencies, rain along the path both add loss that grows with frequency; a receiving antenna not pointed exactly at the transmitter loses some of its peak gain; and two antennas whose polarizations are not aligned lose power to a mismatch that can be severe if they are crossed at right angles. Connectors, filters and an imperfect impedance match between a radio and its feedline each cost a further fraction of a decibel to a few decibels. None of these is large on its own, but a design that omits several of them can find a real link performing noticeably worse than its headline budget promised. ### Earth–Moon–Earth communications The most extreme ordinary radio path is one that leaves Earth entirely and returns: an Earth–Moon–Earth link bounces a signal off the Moon's surface to reach a station beyond the horizon or, among radio amateurs, simply to make contact across arbitrary distances by way of a target roughly a quarter of a million miles away. The path was first closed in an experiment usually called Project Diana, in January 1946, when a United States Army radar set detected its own pulse reflected back from the Moon.[^diana] Because the Moon is a distant and imperfectly reflective target rather than a mirror, the round-trip loss is far larger than a same-distance free-space calculation would suggest, and closing the link at all has historically demanded the largest antennas, the most sensitive receivers and, in recent decades, narrow-band digital modes built to pull a signal from well under the noise. ### Voyager program [[NASA]]'s Voyager probes, launched in 1977 and still transmitting from beyond the outer planets, push the same accounting to its practical limit: a spacecraft transmitter of a few tens of watts, radiated through a high-gain dish a few metres across, must close a link across a path loss that grows every year as the distance grows.[^voyager] The budget balances on the receiving end rather than the transmitting one: dish antennas tens of metres across, cooled low-noise amplifiers, and heavy error-correcting coding all lower the power the ground station needs, so a margin of only a few decibels remains where an ordinary terrestrial link would carry many times as much. ## In waveguides and cables A link budget for a guided path is simpler than a radio path because the medium's loss is a fixed, predictable quantity rather than a statistical one: a [[Coaxial_cable|coaxial cable]] or a metal waveguide attenuates by a characteristic number of decibels per unit length that rises with frequency, chiefly because the conductor loss that dominates at lower frequencies worsens as the signal is pushed closer to the surface of the conductor. The budget then subtracts that per-length attenuation, multiplied by the run's length, plus every connector and splice loss along the way, from the source power, and compares the result against the receiver's input requirement exactly as in the radio case. Because none of these losses depends on weather or multipath, the margin a guided link needs is smaller than a radio link's for the same confidence: the main uncertainty is manufacturing tolerance and ageing rather than a randomly varying channel. The same [[Transmission_line|transmission-line]] theory that describes a cable's attenuation also governs the impedance match between a radio and its feedline, so a link budget for a guided path and the input-impedance analysis of the antenna at its far end are, in practice, two views of the same circuit. ## In optical communications An optical link replaces antenna gain with the optical power launched into a fibre and replaces free-space or cable loss with the fibre's own attenuation, typically quoted in decibels per kilometre and, in the low-loss window used for long-haul systems, as little as a few tenths of a decibel per kilometre, orders of magnitude lower than any radio-frequency cable achieves. The budget adds every splice and connector loss along the route, subtracts them from the launched power, and compares the result against the receiver's sensitivity, a figure usually only a little above the noise level of the photodetector itself. Because fibre loss is so low, long-haul systems are often limited less by the budget closing at all than by the accumulated distortion of the pulses that carry the data, a separate concern from the power accounting a link budget performs. The same margin logic still applies, sized to cover component ageing and connector wear over the system's service life rather than a randomly fading channel. ## Microsims A three.js companion sketch, part of the same framework family as the [[Free-space_path_loss]] visualisation, extends it into a full link budget: every gain and loss the "In radio systems" section lists above appears as its own running term, carried to a total that shows whether the link closes with margin to spare. It is presented separately from this text rather than embedded in it. The same decibel bookkeeping this article describes for radio, cable and fibre links has close cousins elsewhere in this framework. *Try:* in the [[Sonar]] sketch, follow its own term-by-term accounting of source level, transmission loss, target strength and noise, the same kind of sum this article performs for gain and loss, applied to whether an echo clears a detection threshold instead of whether a radio link closes. *Try:* in the [[Doppler_effect]] sketch, set the source moving and watch the received frequency drift; a link like the Voyager program's must track exactly this kind of shift before any of its budgeted power can be captured at all. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Link_budget) : [Wikitube](https://en.wikitube.io/wiki/Link_budget) Skeleton mirrored at revision 1372158277. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Friis_transmission_equation]] - [[Free-space_path_loss]] - [[Radio_receiver]] - [[Signal-to-noise_ratio]] - [[Radio_propagation]] - [[Transmission_line]] ## References The additive decibel form of the link-budget equation, and the free-space path-loss term it usually contains, are standard radio-engineering results and are not separately footnoted, per Wikitube style guide §6.1. Page numbers below are PDF pages of the open editions. [^cascade]: Ellingson, S. *Radio Systems Engineering - Revised First Edition*. 2023, pp. 99-103 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^antennatemp]: Ellingson, S. *Radio Systems Engineering - Revised First Edition*. 2023, pp. 104-107 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^fading]: Ellingson, S. *Radio Systems Engineering - Revised First Edition*. 2023, pp. 163-167 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^diana]: Citation needed: a contemporary 1946 U.S. Army Signal Corps report or press account confirming the date and personnel of the first Earth-Moon-Earth radar echo (the "Project Diana" experiment). [^voyager]: Citation needed: a NASA/JPL Voyager mission fact sheet confirming current transmitter power, high-gain antenna diameter and link margin. ## External links No independent external links accompany this article; its three.js companion sketch is embedded in the Microsims section above.