VSWR Measurement

jimh
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VSWR Measurement

This series of articles will look at the topic of VSWR Measurement in four sections:
• Calculating VSWR from forward and reflected power readings with a directional wattmeter
• Transmission line loss in various type coaxial cables
• Effect of directivity in the directional wattmeter on VSWR measurement accuracy
• Effect of high VSWR on line loss.

Calculating VSWR from Forward and Reflected Power Readings
with a Directional Wattmeter

The voltage standing wave ratio or VWSR (sometimes written as just SWR) is a measurement made on a radio-frequency or RF transmission line, and usually made on coaxial cable transmission lines. The VSWR is an indicator of how well the transmission line impedance and the antenna feed point impedance are matched. Ideally, the impedance of the antenna feed point should be the same as the transmission line impedance, and this will result in a VSWR of 1:1.

If the transmission line is terminated into an impedance that is not matched to the transmission line's impedance, not all of the power will be delivered to the antenna. Some power will be reflected back toward the transmitter.

The VSWR can be measured by a reflectometer or a directional wattmeter. These devices measure the forward voltage or power and the reflected voltage or power. A directional wattmeter generally has a fixed scale, calibrated in watts, and VSWR is determined by the ratio of forward and reflected power, often by consulting a chart. Or the VSWR can be calculated from the two power measurements. (See below.)

A reflectometer generally has an adjustable meter scale; the meter is set to full-scale for the forward power measurement, the reflectometer is then switch to the reflected power direction, and the VSWR is read from a calibrated scale on the meter.

The placement of the measuring device in the transmission line will affect the reading obtained for VSWR due to loss in the transmission line. For the most accurate measurement of the antenna VSWR, the measuring device should be placed at the antenna end of the transmission line. In this way, loss in the transmission line will not affect the measurement. However, to place the measuring device at the antenna is often difficult due to the usually elevated position of the antenna, and VSWR measurements are often made at the transmitter end of the transmission line. When measured in this manner, any loss in the transmission line affects the VSWR that will be measured. I will demonstrate with an example.

Let us assume the transmission line between antenna and transmitter is long and there is loss in the transmission line. For use in VHF Marine Band radios, the transmission line is often RG-58/U. This cable has a loss characteristic at 150-MHz of about 7-dB in 100-feet. Let us assume a particular installation as 43 feet of RG-58/U cable. The cable loss is proportional to length, so the 42-foot cable has a loss of -3 dB.

If the directional wattmeter at the transmitter shows a forward power of 20-Watts, with the -3 dB loss in the cable, only 10-Watts will reach the antenna. Let us assume there is actually no antenna connected, so all of the power is reflected back to the transmitter, that is, all 10-Watts. This is a VSWR of infinity--the worst possible situation. This reflected power now returns on the lossy transmission line, and it is attenuated by -3 dB, so only 5-watts arrives at the transmitter. The directional wattmeter shows a reflected power of 5-Watts.

The VSWR is calculated from forward and reflected power according to

VSWR = (1 + (Pref/Pfwd)0.5) / (1 - (Pref/Pfwd)0.5)
(See the following article for the derivation of the formula for the technical reader.)

For Pfwd = 20 and Pref = 5, the VSWR = 3

Here we have a situation in which a transmission line loss of 3 dB turns an actual VSWR of infinity into a VSWR of 3-to-1.

Shorter lengths of RG-58/U transmission line will have less loss. For example, many antennas are delivered with 15-feet of RG-58/U transmission line attached to the antenna. The line loss for 15-feet of RG-58/U will be -1.1 dB or a factor of 0.92. Using a 20-Watt forward power as in the example above, 18.4-Watts is delivered to the antenna end of the transmission line. Again assuming no antenna is connected, all the power is reflected back. The 18.4 watts is attenuated by -1.1 dB, so 16.6-Watts arrives at the transmitter end.

The directional wattmeter reads Pfwd = 20 and Pref = 16.6, and the VSWR is then 11.2-to-1.

jimh
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Re: VSWR Measurement

ASIDE: Derivation of the formula used above.

In transmission line theory and terminology, the ratio of reflected voltage to the forward voltage is called the reflection coefficient and is indicated by the Greek capital Gamma, thus

(1) Γ = Vref/Vfwd

VSWR can be calculated from the reflection coefficient as

(2) VSWR = (1 + Γ) / (1 - Γ)

If a directional wattmeter is used and forward and reflected power are measured, the power is actually proportional to the square of the voltage. In that instance, the square root of the power ratios can be used to express the reflection coefficient:

(3) Γ = (Pref/Pfwd)0.5

Substituting the forward and reflected power readings as in (3) into equation (2), the VSWR is calculated from forward and reflected power according to

(4) VSWR = (1 + (Pref/Pfwd)0.5) / (1 - (Pref/Pfwd)0.5)

jimh
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Re: VSWR Measurement

Transmission Line Loss in Various Type Coaxial Cables

Coaxial cable loss in deciBels per 100-feet by type for 150-MHz (the nominal VHF Marine Band) when a perfect match (VSWR=1) exists on the line:

`RG-58C/U = 6.2 to 7.1Belden RG-8X = 4.1 LMR-200 = 3.9LMR-240 = 3.0RG-213/U =  2.8LMR-400UF = 1.8Belden 9913F7 = 1.7Belden 9914 = 1.7LMR-400 = 1.5LMR-600 = 0.96`

Actual loss will vary with the brand of cable. Cable tends to deteriorate with age. A 25-year-old cable may no longer meet the original loss specifications. Cable damaged by sunlight or ingress of water will have higher loss. Cables that will be exposed to UV rays MUST have a Type-II Vinyl outer jacket. Loss increases when the VSWR increases (see below).

A general rule to follow is to have no more than 1 dB loss in the transmission. Using the values above for loss-per-100 feet, you can calculate the maximum length of each type cable that will have no more than 1 dB loss.

Coaxial cable length in feet for 1 dB loss at 150-MHz:

`RG-58C/U = 15-feetBelden RG-8X = 21LMR-200 = 25LMR-240 = 33RG-213/U = 36LMR-400UF = 55Belden 9913F7 = 59Belden 9914 = 59LMR-400 = 67LMR-600 = 100`

jimh
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Re: VSWR Measurement

Effect of Directivity in the Directional Wattmeter on VSWR Measurement Accuracy

In order to be a directional wattmeter the measuring device must be able to separately measured the forward and reverse waves on the transmission line, without interference from the wave that is not being measured. The ability of the measuring device to detect only the desired wave is its directivity which will be specified in deciBels. For a good quality directional wattmeter, the directivity will be 30 dB or greater.

The difference between forward power and reflected power in dB is known as return loss. When the return loss in a VSWR measurement becomes equal to the directivity of the measuring device, the accuracy of the measured return loss has an uncertainty of -6 to +6 dB.

For example, a true VSWR were 1.2-to-1 has a return loss of 20 dB. In order to accurately measure a value of VSWR in this range, the measuring device must have a directivity about ten time better, or 30 dB. A Bird Model 43 directional wattmeter is rated to have 30 dB directivity, and on that basis we can assume a Model 43 can reasonably accurately measure a VSWR of 1.2-to-1. Very inexpensive \$30 directional couplers are unlikely to have directivity that good, and measurements of VSWR lower than 1.4 to 1 (15 dB directivity) may not be particularly accurate.

jimh
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Re: VSWR Measurement

Effect of High VSWR on Line Loss

In making measurements with lossy transmission line and high VSWR values, the high VSWR on the transmission line increases the average voltage and current flowing in the transmission line, [*]which increases the loss in the transmission line from its matched impedance. As a result, in situations with a lossy transmission line, if the actual VSWR is very high, the loss in the transmission line increases, further causing the measured value of VSWR at the transmitter end of the line to be more affected by the now higher loss, resulting the VSWR measurement to be inaccurate, i.e., much lower than the actual VSWR at the antenna.