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--- standing_wave_ratio [2026/10/02 16:22] – Organise Wikiham as an encyclopedia of individual articles 127.0.0.1
+++ standing_wave_ratio [2026/10/02 21:06] (current) – Add technical encyclopedia coverage, formulas, examples and primary references admin
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 ====== Standing wave ratio ======
-**Standing wave ratio** (**SWR**) describes the standing-wave pattern associated with impedance mismatch along a transmission line. It is often measured when evaluating an amateur radio antenna system.
+**Standing wave ratio (SWR)** describes the standing-wave pattern produced when a load reflects part of an incident wave on a [[transmission_line|transmission line]]. Antenna work commonly uses **voltage standing wave ratio (VSWR)**, the ratio of maximum to minimum voltage amplitude along the line.
-===== Interpretation =====
+===== Reflection coefficient =====
-A low SWR indicates a good match at the measurement point. It does not by itself show that the antenna radiates efficiently. A dummy load can present a good match while intentionally converting most transmitted energy into heat.
+For a line with real characteristic impedance Z0 and load impedance Z_L:
-The measurement point, operating frequency and feed-line configuration matter when interpreting a result. Include these details with the instrument and test conditions in any published measurement.
+<code>
+Γ = (Z_L - Z0) / (Z_L + Z0)
+VSWR = (1 + |Γ|) / (1 - |Γ|)
+Reflected power fraction = |Γ|²
+</code>
-===== See also =====
+Γ is the voltage-wave reflection coefficient at the stated reference plane. These expressions assume the relevant travelling-wave model and reference impedance. For a passive load on a lossless line, a perfect match gives Γ = 0 and VSWR = 1:1.
-  * [[antenna|Antenna]]
+===== Worked example =====
-  * [[transmission_line|Transmission line]]
-  * [[radio_experiment|Radio experiment]]
+A purely resistive 100 Ω load on a 50 Ω line gives:
+<code>
+Γ = (100 - 50) / (100 + 50) = 1/3
+VSWR = (1 + 1/3) / (1 - 1/3) = 2:1
+Reflected power fraction = (1/3)² ≈ 11.1%
+</code>
+The reflected power fraction is 11.1%, not 33.3%. This is not automatically the percentage of transmitter power permanently lost: feed-line losses, source behaviour and repeated reflections affect the complete system.
+Return loss expresses the same local reflection using [[decibel|decibels]]:
+<code>
+Return loss = -20 log10(|Γ|)
+</code>
+The example gives approximately 9.54 dB return loss. Larger positive return loss means a smaller reflection.
+===== What SWR does not show =====
+A low SWR indicates a good match at the measurement point, not necessarily good radiation efficiency. A dummy load can have a near-perfect match while converting RF into heat. A lossy feed line can also make the transmitter-end SWR look better than the antenna-end value.
+A tuner can transform the impedance seen by a transmitter without removing cable or antenna losses. Record frequency, reference impedance, measurement point, cable arrangement and instrument settings when comparing results.
+===== References =====
+  * [[https://www.arrl.org/files/file/Technology/tis/info/pdf/0505qex044.pdf|Frank Witt, AI1H: transmission-line loss, SWR and return-loss measurements]].
+  * [[https://www.arrl.org/files/file/Technology/tis/info/pdf/q1106037.pdf|ARRL QEX: reflected waves and the interpretation of SWR]].