- 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)
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.