ArticleslgStudy

physics

Standing wave ratio

Standing wave ratio is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Standing wave ratio rather than just read about it. In short: In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line.

Standing wave ratio — main illustration
Standing wave ratio — illustration

Key takeaways

  • Standing wave ratio belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Standing wave ratio to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Standing wave ratio from memory before moving on to harder problems.

Reference excerpt

In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the partial standing wave's amplitude at an antinode (maximum) to the amplitude at a node (minimum) along the line. Voltage standing wave ratio (VSWR) (pronounced "vizwar") is the ratio of maximum to minimum voltage on a transmission line . For example, a VSWR of 1.2 means a peak voltage 1.2 times the minimum voltage along that line, if the line is at least one half wavelength long. A SWR can be also defined as the ratio of the maximum amplitude to minimum amplitude of the transmission line's currents, electric field strength, or the magnetic field strength. Neglecting transmission line loss, these ratios are identical. The power standing wave ratio (PSWR) is defined as the square of the VSWR, however, this deprecated term has no direct physical relation to power actually involved in transmission. SWR is usually measured using a dedicated instrument called an SWR meter. Since SWR is a measure of the load impedance relative to the characteristic impedance of the transmission line in use (which together determine the reflection coefficient as described below), a given SWR meter can interpret the impedance it sees in terms of SWR only if it has been designed for the same particular characteristic impedance as the line. In practice most transmission lines used in these applications are coaxial cables with an impedance of either 50 or 75 ohms, so most SWR meters correspond to one of these. Checking the SWR is a standard procedure in a radio station. Although the same information could be obtained by measuring the load's impedance with an impedance analyzer (or "impedance bridge"), the SWR meter is simpler and more robust for this purpose. By measuring the magnitude of the impedance mismatch at the transmitter output it reveals problems due to either the antenna or the transmission line.

Impedance matching

SWR is used as a measure of impedance matching of a load to the characteristic impedance of a transmission line carrying radio frequency (RF) signals. This especially applies to transmission lines connecting radio transmitters and receivers with their antennas, as well as similar uses of RF cables such as cable television connections to TV receivers and distribution amplifiers. Impedance matching is achieved when the source impedance is the complex conjugate of the load impedance. The easiest way of achieving this, and the way that minimizes losses along the transmission line, is for the imaginary part of the complex impedance of both the source and load to be zero, that is, pure resistances, equal to the characteristic impedance of the transmission line. When there is a mismatch between the load impedance and the transmission line, part of the forward wave sent toward the load is reflected back along the transmission line towards the source. The source then sees a different impedance than it expects which can lead to lesser (or in some cases, more) power being supplied by it, the result being very sensitive to the electrical length of the transmission line. Such a mismatch is usually undesired and results in standing waves along the transmission line which magnifies transmission line losses (significant at higher frequencies and for longer cables). The SWR is a measure of the depth of those standing waves and is, therefore, a measure of the matching of the load to the transmission line. A matched load would result in an SWR of 1:1 implying no reflected wave. An infinite SWR represents complete reflection by a load unable to absorb electrical power, with all the incident power reflected back towards the source. It should be understood that the match of a load to the transmission line is different from the match of a source to the transmission line or the match of a source to the load seen through the transmission line. For instance, if there is a perfect match between the load impedance Zload and the source impedance Zsource = Z*load, that perfect match will remain if the source and load are connected through a transmission line with an electrical length of one half wavelength (or a multiple of one half wavelengths) using a transmission line of any characteristic impedance Z0. However the SWR will generally not be 1:1, depending only on Zload and Z0. With a different length of transmission line, the source will see a different impedance than Zload which may or may not be a good match to the source. Sometimes this is deliberate, as when a quarter-wave matching section is used to improve the match between an otherwise mismatched source and load. However typical RF sources such as transmitters and signal generators are designed to look into a purely resistive load impedance such as 50Ω or 75Ω, corresponding to common transmission lines' characteristic impedances. In those cases, matching the load to the transmission line, Zload = Z0, always ensures that the source will see the same load impedance as if the transmission line weren't there. This is identical to a 1:1 SWR. This condition (Zload = Z0) also means that the load seen by the source is independent of the transmission line's electrical length. Since the electrical length of a physical segment of transmission line depends on the signal frequency, violation of this condition means that the impedance seen by the source through the transmission line becomes a function of frequency (especially if the line is long), even if Zload is frequency-independent. So in practice, a good SWR (near 1:1) implies a transmitter's output seeing the exact impedance it expects for optimum and safe operation.

Relationship to the reflection coefficient

… excerpt ends here. Continue reading the full article.

Illustrations

Standing wave ratio: SWR of a vertical HB9XBG Antenna for the 40m-band as a function of frequency
SWR of a vertical HB9XBG Antenna for the 40m-band as a function of frequency
Standing wave ratio: Incident wave (blue) is fully reflected (red wave) out of phase at short-circuited end of transmission line, creating a net voltage (black) standing wave. Γ = −1, SWR = ∞.
Incident wave (blue) is fully reflected (red wave) out of phase at short-circuited end of transmission line, creating a net voltage (black) standing wave. Γ = −1, SWR = ∞.
Standing wave ratio: Standing waves on transmission line, net voltage shown in different colors during one period of oscillation. Incoming wave from left (amplitude = 1) is partially reflected with (top to bottom) Γ = 0.6, −0.333, and 0.8 ∠60°. Resulting SWR = 4, 2, 9.
Standing waves on transmission line, net voltage shown in different colors during one period of oscillation. Incoming wave from left (amplitude = 1) is partially reflected with (top to bottom) Γ = 0.6, −0.333, and 0.8 ∠60°. Resulting SWR = 4, 2, 9.
Standing wave ratio: Example of estimated bandwidth of antenna according to the schedule VSWR by the help of the Ansys HFSS[4]
Example of estimated bandwidth of antenna according to the schedule VSWR by the help of the Ansys HFSS[4]
Standing wave ratio: Slotted line. The probe moves along the line to measure the variable voltage. SWR is the maximum divided by the minimum voltage
Slotted line. The probe moves along the line to measure the variable voltage. SWR is the maximum divided by the minimum voltage

Worked examples

Example 1 — a first encounter with Standing wave ratio

Start with the simplest possible case. Write down what Standing wave ratio claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Standing wave ratio before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Standing wave ratio ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Standing wave ratio

In research
Standing wave ratio appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Standing wave ratio in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Standing wave ratio is common in secondary-school and first-year university syllabi. It links to neighbouring topics Antennas (radio), Electronics concepts, Engineering ratios, so understanding it makes those chapters shorter.
In everyday life
Look for Standing wave ratio outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Standing wave ratio in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Standing wave ratio means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Standing wave ratio out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Standing wave ratio in simple terms?

In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transmission line, and SWR is defined as the ratio of the p…

Why does Standing wave ratio matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Standing wave ratio?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Standing wave ratio.

Tags

  • Antennas (radio)
  • Electronics concepts
  • Engineering ratios
  • Radio electronics
  • Wave mechanics

Keep exploring