## Standing Wave Ratio (SWR)

The Standing Wave Ratio (SWR) is the parameter that is easiest for most hams to measure, as meters are very common, both built into many newer radios or as a shack accessory. It is a convenient indicator of how well the transmitter load matches the output impedance for which the transmitter was designed, and it often is the first indicator of a broken wire or other fault with the antenna or the feedline. But, contrary to what some hams may believe, it does not give any indication of how well the antenna actually works.

But first, let’s back up and make sure we understand the term.

### Standing Waves

When the load impedance on a transmission line does not match the characteristic impedance, some of the arriving power is reflected back down the feedline. The phase and magnitude of this reflected wave, along with the incoming wave, set up standing waves of voltage and current along the line.

At some points, the voltages will be in phase, but the currents are out of phase, resulting in higher voltage and lower current at that point. Since impedance is the ratio of voltage to current, these points have a higher impedance than the characteristic impedance of the line. At other points, the currents are in phase but the voltages are out of phase, resulting in a low impedance. At most points, the two waves are not exactly in phase, there may be partial cancellation and reinforcement, and we need to do our calculations using complex numbers.

The ratio of the maximum voltage to the minimum voltage is known as the Voltage Standing Wave Ratio (VSWR). The ratio of the maximum current to the minimum current is known as the Current Standing Wave Ratio (ISWR). These numbers will be identical, so the term SWR is generally used.

Note that we can still talk about SWR even when the line is too short to contain both a minimum and maximum point. If we know the impedance at a given point, we can calculate the SWR, even if the line length is effectively zero.

Note also that the ratio is always that of the maximum value to the minimum value, so it will always be greater than one. This is generally specified in the form ” 1.7 : 1 “, although simply “1.7” conveys the same information.

However, in the internet era someone mistakenly though this would be look better written ” 1 : 1.7 ” instead. Please don’t use this style: it marks you as being ignorant about antennas, and I certainly don’t want anyone who reads this site to fall into that category. Always express SWR as a ratio of some number to one, or simply as a single number.

### Properties of SWR

There are a number of important properties of SWR that we regularly use in antenna work:

Except for line losses, SWR is constant along a feedline, determined by the characteristic impedance of the line and the termination impedance. With practical lines, the loss causes the SWR to decrease slightly along the line from the load to the transmitter. (This loss causes the characteristic impedance of the feedline to have a small capacitive reactance component, although we often ignore it for convenience.)

The SWR is given by the ratio of the load impedance to the characteristic impedance of the line (or the reciprical, if the result is less than 1.0). If the load is reactive, this calculation must be done using complex numbers. For example, a 100 + j0 ohm termination on 50 ohm coax gives an SWR of 100 / 50 = 2.0 : 1. A 25 + j0 ohm load will give the same SWR: 50 / 25 = 2.0 : 1. (The number is always greater than or equal to one.) A load impedance of 50 + j35 ohms also gives the same result, but it is more difficult for most of us to do complex arithmetic in our heads.

Note that the SWR is a function of the impedance of the transmission line. SWR meters are calibrated for a particular load impedance, and using, for example, a 50 ohm meter in 75 ohm coax won’t give you the proper result for the 75 ohm line: it will tell you what it would be if a short section of 50 ohm coax was inserted at that point. And while the SWR remains relatively constant along a single line, it isn’t constant when the line changes impedance.

While the SWR is relatively constant along the feedline (decreasing slightly due to the line losses), the impedance will vary along the line unless it is perfectly terminated (that is, the SWR is 1.0 : 1). This is an important concept for impedance matching. For example, if the SWR on a 50 ohm coax is 3 : 1, then at some point along the feedline the impedance will be 3 * 50 = 150 ohms, and at some point it will be 50 / 3 = 33 ohms. (These points will be 1/4 wavelength apart.) Perhaps more importantly, at any point in between the impedance will have a resistive component between these two values, with a reactance (inductive or capacitive) to maintain the constant SWR. This means, for a 50 ohm feedline, we could find a length of coax that gives R = 50 ohms with some reactance, then insert a reactance of opposite sign in series to cancel it and have a 50 ohm match. (More commonly, we would choose a point with a conductance of 0.02 Siemens, and add a shunt component to get a match, often using a coaxial T connector.)

If you are adjusting the length of an antenna for minimum SWR at a desired frequency, measuring at the transmitter is just as good as measuring at the antenna, or anywhere else along the line. While the SWR might dip to a slightly different value, the frequency of the minimum will remain the same regardless of where it is measured.

## Misconceptions about SWR

There probably are more misconceptions and simply false statements about SWR than any other aspect of ham radio that I have encountered. And they often are stated quite vigorously. You need to understand the underlying source of the errors in thought and understanding that produce them, so you are not lead astray.

Perhaps the most common comes from thinking of impedance as a scalar, rather than a complex number. For example, say that the complex load impedance on a 50 ohm feedline is 30 + j40 ohms. The magnitude of impedance is 50 ohms, so some will claim that the SWR is 1 : 1, but in fact the SWR is 3 : 1. (Variants on this theme may use just R, or R + X, as the scalar value, but those also give the wrong answer.)

A side effect of this error in thinking often appears as a reference to the wrong type of SWR. That phrase often implies that the speaker is calculating SWR based on the magnitude of impedance, in which case a load impedance of 0 – j50 (a pure capacitive reactance) would give an SWR of 1 : 1 (while in reality the SWR is infinite). The problem is that the magnitude of impedance is calculated relative to 0 + j0, while SWR is calculated relative to the characteristic impedance of the line (50 + j0 in this case, if we are ignoring the detail of the slight capacitive reactance due to line loss.)

Note that there the phrase “wrong type of SWR” may sometimes be used to refer to SWR that is low due to a long length of lossy feedline, when measured at the transmitter end, and the actual SWR at the antenna feedpoint is much higher. The result is that, if the SWR at the transmitter end is used to calculate the line losses, the losses will appear lower than they actually are. This might be better described as “low SWR for the wrong reason”.

Also, you can’t determine the “power lost due to SWR” based simply on the SWR. Yes, you can find various tables that give such numbers, but those who use, promote, or provide them clearly have no idea how feedlines and matching actually work. If you see such a table or calculator that can’t handle a 100 : 1 SWR with less than 1% of loss (as can be the case with a very short piece of low loss coax), or ignores that fact that, in some cases, operating a line at high SWR can REDUCE THE LOSSES (at least over a short segment), then don’t rely on that source.