Standing_wave_ratio - Wikiparency

# Standing wave ratio The **standing wave ratio** (SWR), most often quoted as the voltage standing wave ratio (VSWR), is a measure of how well a load's impedance matches the characteristic impedance of the [[Transmission_line|transmission line]] feeding it, computed from the standing wave that any mismatch sets up along the line. A perfectly matched load absorbs every watt sent toward it and reflects none, leaving no standing wave and an SWR of exactly 1; a badly mismatched load reflects a large fraction of the incident wave, and the resulting standing wave's ratio of maximum to minimum amplitude climbs well above 1, growing without bound as the mismatch approaches a total short or open circuit. SWR is a direct, if less immediately intuitive, restatement of the [[Reflection_coefficient|reflection coefficient]] `Gamma`, the complex ratio of the reflected wave's amplitude to the incident wave's amplitude at the load; every [[Antenna_(radio)|antenna]] feed line, cable run and connector in a radio system is checked against SWR precisely because it is easy to measure directly with a simple in-line meter, without needing the reflection coefficient's separate magnitude and phase. Elsewhere on this page, a three.js companion sketch stands a forward and a reflected wave together on a mismatched line and reads out both the VSWR and the reflection coefficient as the mismatch changes; the neighbouring [[Radar]] article's sketch shows a related, if physically distinct, kind of reflection: an echo returning from a distant target rather than a wave reflected at a nearby connector. ## Impedance matching A transmission line's characteristic impedance is fixed by its geometry, commonly 50 ohms for [[Coaxial_cable|coaxial cable]] used throughout [[Radio-frequency_engineering|radio-frequency engineering]] and 75 ohms for cable used mainly for video and broadcast reception; a load is matched when its own impedance at the operating frequency equals that same value, resistive part and reactive part alike. Matching matters for two largely separate reasons. First, only a matched load draws the maximum power a given source and line can deliver; any mismatch reflects part of the incident wave back toward the source instead of delivering it to the load, so an unmatched antenna radiates less power for the same transmitter output than a matched one would. Second, and often the more urgent concern in practice, a badly mismatched load returns reflected power to the transmitter's own output stage, where it can raise voltages and currents inside the amplifier well above their normal operating levels, degrade the linearity of the amplification, or in a severe case damage the output transistor or tube outright; many transmitters include protection circuitry that automatically reduces power, or shuts down entirely, once the SWR at the output rises past a set threshold. Where a load's own impedance cannot be changed, a separate matching network, built from reactive components such as [[Inductor|inductors]] and [[Capacitor|capacitors]], a transformer, or a length of transmission line used as an impedance transformer, is inserted between the source and the load to present a matched impedance to the line even though the load itself remains mismatched. ## Relationship to the reflection coefficient For a load impedance `Z_L` on a line of characteristic impedance `Z0`, the voltage reflection coefficient at the load is `Gamma = (Z_L - Z0) / (Z_L + Z0)`, a complex number whose magnitude never exceeds 1 for a passive load and whose phase describes how the reflected wave is shifted relative to the incident one at the load itself. The standing wave ratio follows directly from the magnitude alone: `SWR = (1 + |Gamma|) / (1 - |Gamma|)`, and the same relationship inverted, `|Gamma| = (SWR - 1) / (SWR + 1)`, recovers the reflection magnitude from a measured SWR. Because SWR depends only on `|Gamma|`, it discards the reflection coefficient's phase entirely: two loads with the same mismatch magnitude but different phase, for instance a purely resistive mismatch and a purely reactive one of the same size, produce the same SWR on the line even though their reflected waves are shifted quite differently relative to the incident one. This loss of phase information is exactly what a [[Smith_chart|Smith chart]] restores: plotting the complex reflection coefficient directly on the chart shows a perfect match at the centre and total reflection, `|Gamma| = 1`, all the way around the outer rim, with every circle of constant radius in between corresponding to one fixed SWR regardless of phase.[^steer-smith-match] A purely resistive load plots on the chart's horizontal axis, an inductive load plots in the upper half of the chart and a capacitive load in the lower half,[^steer-smith-polar] and adding a length of matched line to the load rotates its point clockwise around the corresponding constant-SWR circle without changing the SWR itself.[^steer-smith-rotate] ## The standing wave pattern Along the line itself, the standing wave is what results from adding the incident and reflected [[Sine_wave|sinusoidal waves]] at every point: where the two arrive in phase, their amplitudes add and the local voltage reaches an antinode, a local maximum that repeats every half wavelength back toward the source; where they arrive exactly out of phase, the amplitudes subtract and the voltage falls to a node, a local minimum spaced exactly halfway between two antinodes. For a purely resistive mismatch, the pattern's first voltage maximum sits right at the load if the load resistance exceeds the line's characteristic impedance, or the first minimum sits at the load if it is lower; any reactive part in the load shifts the whole pattern along the line by a distance set by the reflection coefficient's phase, without changing the ratio between the maximum and minimum values anywhere along it. At the extreme of a short-circuit or an open-circuit load, the incident and reflected waves have equal amplitude everywhere, so the voltage pattern falls to an exact zero at every node, current does the same at the antinodes staggered a quarter wavelength away, and the standing wave ratio is formally infinite, a limit no real line quite reaches because some loss is always present. Because the pattern repeats every half wavelength regardless of what the load is, a measurement taken anywhere convenient along a sufficiently long line, not necessarily right at the load, is enough to determine the SWR, though not the load impedance itself without also noting where the pattern's minimum falls relative to the load. ## Practical implications of SWR A real transmission line is never perfectly lossless, and a standing wave raises both the peak [[Voltage|voltage]] and the peak [[Electric_current|current]] the line must carry compared with a matched line carrying the same net power, which increases the [[Electrical_resistivity_and_conductivity|resistive]] and dielectric losses the line's own imperfections extract; a mismatch that would cost only a negligible fraction of a decibel on a short, low-loss line can cost several decibels of the transmitted power outright on a long or lossy run at a high SWR. The peak voltage a standing wave produces also matters on its own, independent of loss: at high transmitter power, the voltage antinode of a badly mismatched line can approach or exceed the line's dielectric breakdown rating, risking an arc inside a connector or the cable itself that a matched line at the same average power would never approach. Because of these two effects together, most radio equipment specifies a maximum tolerable SWR, commonly around 1.5:1 to 2:1 for solid-state transmitters, above which the manufacturer no longer guarantees either full power output or long-term reliability, and many amateur and commercial installations treat keeping the feed line's SWR comfortably inside that figure as a routine, ongoing maintenance concern rather than a one-time setup check. ## Methods of measuring standing wave ratio The oldest direct method, the slotted line, exposes a short gap in the outer conductor of a special section of transmission line so a small sliding probe can sample the electric field at any point along it; sliding the probe by hand or by motor across at least half a wavelength traces out the standing wave pattern directly, and the ratio of the largest reading to the smallest gives the SWR without ever computing a reflection coefficient explicitly. A slotted line is precise but mechanically inconvenient and progressively impractical at low frequencies, where half a wavelength can run to metres, so most modern SWR meters instead use a directional coupler, a passive network that samples a small, separate fraction of the forward wave and the reflected wave individually as they pass a fixed point on the line, typically rectifying each sample with a [[Diode|diode]] detector to a DC voltage that a meter or a digital readout converts directly into forward power, reflected power and SWR. A vector network analyzer goes a step further, measuring the complex reflection coefficient itself, magnitude and phase together, at every frequency across a swept band rather than the single SWR number a simple in-line meter reads at one frequency and one power level, at the cost of a far more expensive instrument than a hand-held or in-line SWR meter. ## Power standing wave ratio Power standing wave ratio (PSWR) is defined simply as the square of the voltage standing wave ratio, `PSWR = VSWR^2`, a relic of an era when some instruments displayed the squared quantity directly because it was easier to derive from a simple [[Diode|diode]]-detector circuit than the unsquared ratio was. Despite the name, PSWR is not itself a ratio of two powers actually flowing anywhere on the line, and no meaningful physical power measurement corresponds to it directly; the terminology persists mainly in older equipment documentation and is now generally considered obsolete, with VSWR reported directly wherever a modern instrument or specification has a choice. ## Implications of SWR on medical applications [[Radio-frequency_engineering|Radio-frequency]] energy delivered into the human body, whether for diathermy, tissue ablation, or another therapeutic use, is delivered into a variable, lossy load whose impedance shifts with the tissue's own electrical properties, its size, and the exact placement of the applicator against it. A poor match between the RF generator and that tissue load reflects power back toward the generator in exactly the way an antenna mismatch does, wastes energy the treatment is meant to deliver, and can concentrate unintended heating at the connector or applicator itself rather than at the intended treatment site.[^cite-medical-swr] Because the load's impedance in this setting is neither fixed nor entirely predictable in advance, medical RF equipment commonly monitors SWR, or the equivalent reflected-power fraction, continuously during treatment and reduces or interrupts power automatically if the reading rises past a safe threshold, the same protective role an SWR-triggered power fold-back plays in an ordinary radio transmitter. ## Microsims This article carries no p5.js sketch of its own. A three.js companion elsewhere on this page stands a forward and a reflected wave together on a mismatched transmission line and reads out the VSWR and the complex reflection coefficient together as the load impedance changes. *Try:* in the [[Radar]] sketch, note that the modelled echo voltage already falls as 1/R² from spreading alone; a real radar's own feed line is held to a low SWR for the same underlying reason a matched line is held to one anywhere else — so that a reflection at a mismatched connector does not throw away more of that same signal before spreading loss ever gets a chance to.  **Microsim — three.js (Wikitube framework), pending deploy:** *Standing wave ratio: mismatch, reflection and VSWR* will play here once `https://wikitube-3d-microsims.netlify.app/radio/Standing_wave_ratio.html` is live.  *Built from `MICROSIM_GUIDE/specs/sims/Standing_wave_ratio.json`; part of the [[PORTAL_Radio|Radio]] set.*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Standing_wave_ratio) : [Wikitube](https://en.wikitube.io/wiki/Standing_wave_ratio) Skeleton mirrored at revision 1364248521. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Reflection_coefficient]] - [[Coaxial_cable]] - [[Antenna_(radio)]] - [[Transmission_line]] - [[Smith_chart]] - [[Radio-frequency_engineering]] ## References The reflection-coefficient definition, the SWR-from-gamma formula, and the physics of a standing wave on a transmission line are standard results covered in essentially every transmission-line or RF-engineering textbook and are not separately footnoted here, per the Wikitube style guide §6.1. Page numbers below are PDF pages of the open edition linked in Further reading. [^steer-smith-match]: Steer, M. *Microwave and RF Design: Networks*. 2019, p. 67 (PDF page). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/microwave-and-rf-design-networks . CC BY-NC. [^steer-smith-polar]: Steer, M. *Microwave and RF Design: Networks*. 2019, pp. 67, 70, 78 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/microwave-and-rf-design-networks . CC BY-NC. [^steer-smith-rotate]: Steer, M. *Microwave and RF Design: Networks*. 2019, pp. 72, 79-85 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/microwave-and-rf-design-networks . CC BY-NC. [^cite-medical-swr]: Citation needed: a specific medical-device standard or clinical-engineering source establishing SWR or reflected-power monitoring practice in therapeutic RF equipment has not been identified in this pass. ## Further reading - Michael Steer. *Microwave and RF Design: Networks* (2019). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/microwave-and-rf-design-networks - Steven Ellingson. *Radio Systems Engineering*, Revised First Edition (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering ## External links This article carries no sketch of its own yet. The three.js companion named in the lead is placed on the live page by the site's build process and will list its own link here once published.