

VSWR and the Decibel 
The Decibel
The decibel (dB) is one of the most useful parameters in radio communications. It allows one to simply add all of the losses and gains together in order to calculate how much power is actually leaving the antenna and to calculate the effective radiated power.
The decibel itself is a ratio, it has no unit and is meaningless unless you state the value or unit that it is related to.
Transmitter output power can be quoted in decibel watts (dBW). This value is calculated from the equation 10 log_{10} P, where P is the power in watts.
Coaxial cable loss is normally quoted as dB loss per 10m or 100m. If a particular cable has a loss of 3dB per 100m and you require a 20m run of cable, the loss on your cable will be 3 x (20/100) = 0.6dB. Note however that all coax cable losses vary with frequency and tend to increase as the frequency increases.
Antenna gains are usually quoted as either dBd  decibel gain relative to a dipole antenna or dBi  decibel gain relative to a theoretical omidirectional antenna.
The effective radiated power can therefore be calculated by taking power output of the transmitter in dBW, subtracting all of the losses due to coax, VSWR, filters etc. and then adding the antenna gain.
To convert back into watts, use 10^{(d/10) }(or ten to the power d over ten), where d is the power in dBW.
Power in watts Power in dBW 0.001 0.01 0.1 0.5 1 2 5 10 20 25 50 100 200 400 1000 1500 30 20 10 3 0 3 7 10 13 14 17 20 23 26 30 31.75
VSWR
VSWR or Voltage Standing Wave Ratio (SWR for short), is a subject often discussed in amateur radio circles. It is therefore surprising how many radio hams misunderstand the meaning of the value shown on an SWR meter.
An SWR of 1:1 is the ideal that can never be achieved. This value would indicate 100% efficiency in a transmitter, transmission line and antenna system, with no reflected signal whatsoever.
An SWR of 1:infinity is the very worst case, with 100% of the transmitted signal being reflected back towards the transmitter.
The VSWR ratio is given by Z_{1}/Z_{2} or Z_{2}/Z_{1}, whichever is greater. Z_{1} and Z_{2} being the two impedances at the interface. i.e. the impedance of the coax cable and that of the filter or antenna etc.
What is an acceptable VSWR?
Most modern transceivers detect a poor VSWR and reduce the output power in order to keep the reverse power down to a safe level. A medium SWR of 1:1.5  1:3.0 will therefore do no harm to the transceiver, however the output power will be reduced.
Antenna tuning units (ATU's) do not remove or reduce a poor VSWR, they merely 'dump' the reverse power so the transmitter 'sees' a perfect transmission line and therefore increases the power to 100%. However, 100% of the signal will not leave the antenna as there is still a VSWR present on the coaxial cable and some of the signal is lost in the ATU. As you can see from the table below, a VSWR of 1:1.4 causes a loss of less than 0.15dB or 3%, this is likely to be less than the coax cable loss. Trying to reduce such an SWR still further will be expensive and pointless as the increase in effective radiated power will be totally undetectable by other stations. It should also be noted that a transmitter is seen as a bad load in reverse, the majority of reverse power will therefore be reflected at the coax / transmitter interface.Reverse power is given by the equation P_{r} = P x (S1)^{2} / (S+1)^{2}^{ }, where P_{r} is the reverse power, P is the transmitter power and S is the VSWR presented to the transmitter.
Below is a table showing the reverse power for a transmitter presented with different SWR's
VSWR presented to a transmitter Percentage power loss Percentage power transfer Decibel loss (dB) 1:1.0 1:1.1 1:1.2 1:1.3 1:1.4 1:1.5 1:1.6 1:1.7 1:1.8 1:1.9 1:2.0 1:2.2 1:2.4 1:2.6 1:2.8 1:3.0 1:3.5 1:4.0 1:5.0 1:7.0 1:10.0 1:20.0 1:50.0 1:infinity 0 0.23 0.83 1.70 2.78 4.00 5.33 6.72 8.16 9.63 11.1 14.1 17.0 19.8 22.4 25.0 30.9 36.0 44.4 56.3 67.0 81.9 92.3 100 100 99.8 99.2 98.3 97.2 96.0 94.5 93.7 91.8 90.4 88.9 85.9 83.0 80.2 77.6 75.0 69.1 64.0 55.6 43.7 33.0 18.1 7.7 0 0 0.01 0.04 0.08 0.12 0.18 0.25 0.28 0.37 0.44 0.51 0.66 0.81 0.96 1.10 1.25 1.61 1.94 2.55 3.60 4.81 7.42 11.1 infinity
Reducing VSWR
What can be done about a poor VSWR?
Firstly, check your coax cable, it's impedance will change with age. Avoid sharp bends at all cost as this will also change the impedance. Check your connectors. Use the recommended connectors and never tape coax together. The SWR of PL259 connectors increases quite dramatically over 100MHz. Therefore Ntype connectors should be used wherever possible. Finally, one should consider the distance between components on the coax cable! This is something that is rarely discussed in amateur radio literature.Consider what happens if you have a transmitter, a filter and an antenna connected by lengths of coax. The signal leaves the transmitter, travels along the coax cable and meets the filter. Filters normally have a VSWR of around 1:1.5, this means that 96% of the signal will proceed through and 4% will be reflected back. The antenna will probably have a VSWR of around 1:1.2. Therefore a further 1% will be reflected and 99% of the 96% will proceed. The coax will therefore contain 5% reverse power from the two components. These components, along with the transmitter will in turn reflect some of the reverse power forward again. Depending on the length of the coax between each of the components, this double reflected power may or may not be in phase with the main signal.
If the double reflected power is totally out of phase with the main signal, destructive interference will occur and the main signal will be reduced. If however, the double reflected power can be made to be in phase, the two signals will constructively interfere and will add to each other.
Radio signals propagate through coax cable at a speed 66% of that in a vacuum. Whilst the frequency remains unchanged, the wavelength reduces by 66% in order to compensate. Constructive interference will therefore occur at 0, n/3, 2n/3, n, 4n/3 etc. where n is the wavelength. Destructive interference will occur at n/6, 3n/6, 5n/6, 7n/6 etc. One should therefore aim to use lengths of coax that are multiples of n/3 or butt components together. If you use more than one band, a common multiple must be found. e.g. For the 6m, 2m and 70cm bands, coax lengths of 4.2m, 6.2m or 13.75m are good compromises and should help to reduce the VSWR.
The worst case when using the wrong length of coax is given by SWR_{1}xSWR_{2} for two components or SWR_{1}xSWR_{2}xSWR_{3} for three components. The best case when using the right length of coax is given by SWR_{1}+SWR_{2 } 1 for two components and SWR_{1}+SWR_{2}+SWR_{3 }2 for three components. Therefore if you have a filter with an SWR of 1:1.5 and an antenna of 1:1.2 the worst case will be 1:1.8 and the best case will be 1:1.7. If your VSWR is already below 1:1.4 you will not see any great difference.
HF operators need not worry, the wavelengths are too long to use this, just keep coax lengths as short as possible. It is not a good idea to add an extra 20m of coax as the increased loss will cancel out any benefits due to reduced VSWR.
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