VSWR Explained: Reflection Coefficient and Mismatch Loss

What VSWR is

VSWR is the voltage standing wave ratio. When a source drives a load through a transmission line, the load may not absorb all of the power. The part it does not absorb travels back toward the source. The forward and the reflected waves add up along the line, and the result is a standing wave: the voltage rises and falls with position instead of staying constant.

VSWR is the ratio of the largest voltage on that line to the smallest one:

With no reflection there is no standing wave, the voltage is the same everywhere, and the ratio is 1. That is the best possible value. A larger number means a larger reflection. VSWR is never below 1.

SWR and VSWR name the same number. Some texts write "SWR" and others "VSWR". Both mean the ratio of the largest to the smallest voltage along a line that has a standing wave. The extra V only records that the ratio is taken from voltages. There is no second quantity hiding behind the shorter name.

From reflection coefficient to VSWR

The reflection coefficient, written G (capital gamma), describes the reflected wave relative to the incident wave at the load. For a load impedance Z_L on a line of characteristic impedance Z_0, the textbook definition is:

G is a complex number. Its magnitude |G| runs from 0 (perfect match) to 1 (total reflection, for example an open or a short). At the voltage maximum, the forward and reflected waves add in phase, so the voltage is proportional to 1 + |G|. At the minimum they subtract, giving 1 - |G|. Dividing the two gives the VSWR formula:

The formula inverts cleanly:

A perfect match has |G| = 0 and VSWR = 1. As |G| approaches 1, VSWR grows without limit. A VSWR of 1.5 means |G| = 0.2. A VSWR of 2 means |G| = 0.333.

From return loss to VSWR

Return loss states the same information in decibels. It is the level of the reflected wave below the incident wave:

A large return loss means a small reflection. To go from return loss to VSWR, first recover the magnitude, then apply the VSWR formula:

The factor is 20 because |G| is a voltage-type ratio. Return loss is a positive number in this convention. A VNA that shows S11 in dB shows the same value with a minus sign, so S11 = -13.98 dB corresponds to a return loss of 13.98 dB. The page on return loss versus insertion loss covers the sign convention and how this number differs from loss through a device.

The figure below plots VSWR against return loss, computed from these formulas. Note how flat the curve becomes at high return loss: the last few tenths of VSWR cost many dB of return loss.

Reflected power and mismatch loss

Power goes with the square of voltage. The fraction of incident power that is reflected is therefore |G|^2. The fraction that reaches the load is 1 - |G|^2.

Mismatch loss expresses the power that does not get through, in decibels:

Mismatch loss is small for good matches and grows quickly only at poor ones. A VSWR of 1.5 reflects 4 % of the power and loses 0.177 dB. A VSWR of 2 reflects 11.1 % and loses 0.512 dB. These numbers are computed from the formulas above. The table lists more values.

VSWR	abs(G)	Return loss (dB)	Power reflected	Mismatch loss (dB)
1.0	0	infinite	0 %	0
1.1	0.048	26.44	0.23 %	0.010
1.2	0.091	20.83	0.83 %	0.036
1.5	0.200	13.98	4.0 %	0.177
2	0.333	9.54	11.1 %	0.512
3	0.500	6.02	25 %	1.249
5	0.667	3.52	44.4 %	2.553
10	0.818	1.74	66.9 %	4.81

You can also compute any row with the VSWR, return loss and mismatch loss calculator.

Worked example: VSWR of 2

Take a load with a measured VSWR of 2 on a line.

1. Reflection coefficient: |G| = (2 - 1) / (2 + 1) = 1/3 = 0.333.
2. Return loss: -20 log10(0.333) = 9.54 dB.
3. Reflected power fraction: |G|^2 = 0.111, so 11.1 %.
4. Power reaching the load: 1 - 0.111 = 0.889, so 88.9 %.
5. Mismatch loss: -10 log10(0.889) = 0.512 dB.

If 100 mW is incident on this load, 11.1 mW is reflected and 88.9 mW is absorbed. The reflected part is not always wasted heat. It returns to the source, and what happens to it depends on the source. A source that is itself mismatched can reflect it again, and the two reflections can add or cancel depending on the line length between them. That is why a mismatch seen at one point can look different at another point in a system.

What VSWR cannot tell you

VSWR gives only the size of the mismatch, not its phase. Two loads with the same |G| have the same VSWR, yet one may be inductive and the other capacitive. A load of 100 ohm and a load of 25 ohm on a 50 ohm line both give |G| = 0.333, and both give a VSWR of 2. VSWR cannot separate them.

To find out which way a match must be corrected, you need the phase. The S11 phase supplies it, and so does a Smith chart, which plots the complex G directly. For a first pass, the VSWR number says how much to worry. For the design of a matching network, it is not enough.

In plain words · for students and beginners

VSWR in plain words

The echo picture

Shout toward a far wall and you hear an echo. A smooth, hard wall sends most of your voice back. A soft curtain sends back very little. A radio signal on a cable behaves in a similar way. When the cable meets something that does not suit it, part of the signal bounces back like an echo. The rest goes on into the load.

VSWR is a score for how strong that echo is. A score of 1 means no echo. A higher score means a stronger echo. Return loss says the same thing in decibels, and mismatch loss tells you how much signal you lose because of the echo.

The picture breaks down in one place. A sound echo comes back later and is simply a copy. A radio echo travels on the same cable as the main signal, so the two overlap and add up. At some points along the cable they push together and the voltage is high. At other points they pull against each other and it is low. That up-and-down pattern is the "standing wave", and VSWR is the high value divided by the low value.

The same example in simple steps

Say you measure a VSWR of 2 and send in 100 mW.

1. Subtract 1 from the VSWR and add 1 to it: 2 - 1 = 1, and 2 + 1 = 3.
2. Divide: 1 / 3 = 0.333. This is the reflection coefficient. It tells you how big the echo is, compared with the signal sent.
3. Square it: 0.333 x 0.333 = 0.111. Power follows the square, so 11.1 % of the power comes back.
4. The rest, 88.9 %, gets into the load. In numbers: 11.1 mW comes back and 88.9 mW goes in.
5. In decibels, the loss is 0.512 dB. That is small, about a tenth of a decibel for each tenth of reflected power at this level.

Mistakes beginners make

• Thinking VSWR 2 is terrible. It loses only 0.512 dB, and many systems accept it. What counts as good enough depends on the job.
• Mixing up return loss and insertion loss. Return loss measures what bounces back. Insertion loss measures what a part takes out of the signal as it passes through. A big return loss is good, because the echo is weak.
• Forgetting the sign. A VNA often shows S11 as a negative dB number. Return loss is the same value without the minus sign.
• Expecting VSWR to show the fix. The number gives size only. To know whether to add inductance or capacitance, look at the S11 phase or a Smith chart.

Remember

• VSWR is 1 for a perfect match, and it only goes up as the echo grows.
• SWR and VSWR are the same number, and |G| = (VSWR - 1) / (VSWR + 1).
• VSWR 1.5 reflects 4 % of the power, and VSWR 2 reflects 11.1 %. They lose 0.177 dB and 0.512 dB.

Related pages on RF View

• VSWR, Return Loss and Mismatch Loss Calculator
• Return Loss vs Insertion Loss: What Each Number Tells You