How this instrument works
In any RF or transmission-line system, power only transfers efficiently from source to load when their impedances match. When they don't, some of the signal reflects back toward the source instead of being absorbed by the load — wasted power, standing waves on the line, and in high-power systems, potential damage to the source. Impedance matching calculations quantify exactly how bad a mismatch is, using two closely related numbers: the reflection coefficient (Gamma) and the voltage standing wave ratio (VSWR).
The reflection coefficient Gamma is the fraction of the signal's voltage that reflects back from the load, calculated directly from the load and source impedances: Gamma = (Z_L - Z_0) / (Z_L + Z_0). Gamma ranges from -1 (a dead short) through 0 (a perfect match, no reflection at all) to +1 (an open circuit). Gamma is a signed quantity that also tells you whether the load is higher or lower impedance than the line, but for characterizing mismatch severity, engineers usually work with its absolute value.
VSWR takes the absolute value of Gamma and converts it into the ratio of maximum to minimum standing-wave voltage that would actually be measured along the transmission line: VSWR = (1 + |Gamma|) / (1 - |Gamma|). A perfect match gives VSWR = 1.0 (no standing wave at all); as the mismatch worsens, VSWR climbs toward infinity. VSWR is the number most commonly quoted on antenna, connector and cable datasheets because it's directly measurable with a standing-wave meter, unlike Gamma, which usually has to be calculated.
The classic case that makes this concrete is video and broadcast coax: 75-ohm systems (cable TV, video) connecting into 50-ohm RF equipment (most general-purpose radio gear) produce a small but real mismatch — Gamma = 0.2, VSWR = 1.5 — modest enough to often be ignored in low-power hobbyist setups, but worth correcting with a proper matching transformer in demanding professional systems.
- Enter Load impedance Z_L in ohms — the impedance of the antenna, cable or device the signal is feeding into.
- Enter Source / line impedance Z_0 in ohms — the characteristic impedance of the transmission line or the source's own output impedance.
- Read Reflection coefficient (Gamma) for the signed fraction of voltage reflected back toward the source.
- Read Voltage standing wave ratio (VSWR) for the standing-wave ratio a meter would measure on the line — 1.0 means a perfect match, with no upper bound as the mismatch worsens.
- Try setting Z_L equal to Z_0 to confirm Gamma = 0 and VSWR = 1.0, the ideal reference case with zero reflected power.
Worked example — 75-ohm load on a 50-ohm source
Enter Load impedance Z_L = 75 ohms and Source / line impedance Z_0 = 50 ohms — the standard mismatch between 75-ohm video/RF coax and 50-ohm general RF equipment. Reflection coefficient (Gamma) reads 0.2, from (75-50)/(75+50) = 25/125 = 0.2.
Voltage standing wave ratio (VSWR) reads 1.5, from (1 + 0.2)/(1 - 0.2) = 1.2/0.8 = 1.5. A VSWR of 1.5 is a mild, commonly tolerated mismatch — it's the textbook example used across RF engineering courses precisely because 50-ohm and 75-ohm systems are both extremely common, and understanding the modest reflection between them is a rite of passage for anyone doing RF or video signal work.
Questions
What is a 'good' VSWR value?
VSWR = 1.0 is a perfect match with zero reflected power, and in practice a VSWR below about 1.5 is generally considered good for most RF systems — it corresponds to roughly 4% of the power being reflected rather than delivered to the load. A VSWR of 2.0 (about 11% reflected power) is often the maximum many transmitters or amplifiers tolerate before their protection circuitry intervenes, and VSWR above about 3.0 usually signals a mismatch that needs correcting before running significant power through the system.
Why does a 75-ohm load on a 50-ohm system produce VSWR 1.5, not something worse?
The mismatch severity depends on the ratio between the two impedances, not just their difference. 75 and 50 ohms differ by only 25 ohms but their ratio is 1.5:1, which the Gamma formula converts to a modest 0.2 reflection coefficient — a 25-ohm difference matters much more if the smaller impedance is, say, 5 ohms rather than 50, because the formula normalizes by the sum of the two impedances. That's part of why the 50/75-ohm mismatch is tolerable enough that many consumer systems don't bother correcting it, while a raw open or short circuit (Gamma = +/-1) reflects 100% of the power.
What does a negative reflection coefficient mean?
A negative Gamma means the load impedance is lower than the source or line impedance (Z_L < Z_0) — the reflected wave's voltage is inverted relative to the incident wave at the load. A positive Gamma means the load impedance is higher (Z_L > Z_0). The sign doesn't affect VSWR, which always uses the absolute value of Gamma, but it matters for phase-sensitive calculations like the exact position of standing-wave voltage maxima and minima along the line.
What happens at the extremes: a short circuit or an open circuit load?
A dead short (Z_L = 0) gives Gamma = -1: the reflection coefficient's magnitude is 1, meaning 100% of the incident voltage reflects back, and VSWR becomes mathematically infinite (undefined division by zero in the VSWR formula, since |Gamma| = 1). An open circuit (Z_L approaching infinity) gives Gamma approaching +1, the same 100%-reflection result from the opposite direction. Both extremes represent total mismatch — no power at all reaches a genuine load, because there effectively isn't one.
Why do RF engineers care about VSWR instead of just using Gamma?
VSWR is what a standing-wave meter actually measures on a live transmission line — the ratio between the highest and lowest voltage points along the standing wave pattern created by the reflected signal interfering with the incident signal. Gamma is a cleaner number for calculation and clearly shows direction (positive or negative), but VSWR is the practical, directly-measurable, always-positive number quoted on antenna and cable datasheets, which is why it's the industry-standard spec for describing how well a real RF connection is matched.