Measuring Radio Antenna VSWR
Posted: Sun Dec 31, 2017 9:31 am
In an earlier article, I described how to measure transmitter power output using an in-line directional wattmeter. That same wattmeter can also measure the voltage-standing-wave-ratio or VSWR on the transmission line. The VSWR can be deduced by the measuring the forward power Pfwd and reverse power Prev, then calculating VSWR according to the relationship:
VSWR = [1 + (Prev/Pfwd)0.5] / [1 - (Prev/Pfwd)0.5]
The value (Prev/Pfwd)0.5 is also known as the reflection coefficient, Psi or ψ. This simplifies the VSWR calculation to
VSWR = (1 + ψ) / (1 - ψ)
For example, if we measure forward power at 22-Watts and reverse power at 2-watts, we have a reflection coefficient of
ψ = (2/22)0.5 = 0.30
The VSWR is then
VSWR = (1+0.30)/(1−0.3)
VSWR = 1.3 / 0.7
VSWR = 1.85
A further consideration is the distance between the antenna and the wattmeter and the effect of any loss in the transmission line. In a typical small boat installation there is a length of coaxial transmission line from the antenna, and that is the point in the circuit the wattmeter will be inserted. On a small boat the transmission line is likely to be RG-58C/U and be 15-feet long. We must consider the effect of attenuation in that transmission line on the measurement of the antenna VSWR.
First we must calculate the loss in the transmission line. As mentioned previously, RG-58C/U will have a characteristic attenuation of 6.2 dB in 100-feet. Thus in 15-feet the attenuation will proportionally be 0.945 dB.
In our test set up, the wattmeter is placed 15-feet away from the antenna. If we measured 22-Watts at the wattmeter location, that power will be attenuated by 0.945 dB by the time it reaches the antenna. We must calculate the actual power at the antenna as being 0.945 dB lower. Again we use the relationship
dB = 10 log10 (P2/P1)
and insert the known values, -0.945 dB and P1 = 22 watts. Solving we get
P2 = 17.7 Watts
This is the actual power that reached the antenna, only 17.7-Watts, due to transmission line loss in the 15-feet of RG-58C/U. This value is our actual Pfwd for the VSWR calculation.
At the antenna some portion of this 17.7-Watts will be reflected back toward the transmitter. The reflected power will also be attenuated in the transmission line by 0.945 dB. We know that after attenuation, there was 2-Watts of power at the wattmeter, but we need to know how much reverse power was at the antenna, which will be 0.945 dB greater. Again we use the relationship of two powers and the known ratio between them in dB to find the actual reverse power at the antenna, in this case 2.49-Watts.
Now we can calculate the actual VSWR at the antenna, using
Pfwd = 17.7-Watts
Prev = 2.49-Watts
First we find the reflection coefficient, ψ
ψ = (2.49/17.7)0.5 = 0.375
Then we compute the VSWR
VSWR = (1+0.375)/(1−0.375)
VSWR = 1.375 / 0.625
VSWR = 2.2
Now we have an accurate measurement of the VSWR of the antenna at its feed point. The actual VSWR at the antenna is 2.2, quite a bit higher than the measured VSWR of 1.85 at a point 15-feet away on the transmission line. Note that any transmission line loss will always tend to make the antenna VSWR appear better (lower) that the actual VSWR at the antenna.
A further compounding of this calculation is to adjust the transmission line attenuation to include an allowance for the influence of a high VSWR on the transmission line. For all practical transmission lines, the presence of any standing waves on the transmission line (that is a VSWR greater than 1) causes the attenuation in the transmission line to increase. In the analysis above, we have ignored that effect.
VSWR = [1 + (Prev/Pfwd)0.5] / [1 - (Prev/Pfwd)0.5]
The value (Prev/Pfwd)0.5 is also known as the reflection coefficient, Psi or ψ. This simplifies the VSWR calculation to
VSWR = (1 + ψ) / (1 - ψ)
For example, if we measure forward power at 22-Watts and reverse power at 2-watts, we have a reflection coefficient of
ψ = (2/22)0.5 = 0.30
The VSWR is then
VSWR = (1+0.30)/(1−0.3)
VSWR = 1.3 / 0.7
VSWR = 1.85
A further consideration is the distance between the antenna and the wattmeter and the effect of any loss in the transmission line. In a typical small boat installation there is a length of coaxial transmission line from the antenna, and that is the point in the circuit the wattmeter will be inserted. On a small boat the transmission line is likely to be RG-58C/U and be 15-feet long. We must consider the effect of attenuation in that transmission line on the measurement of the antenna VSWR.
First we must calculate the loss in the transmission line. As mentioned previously, RG-58C/U will have a characteristic attenuation of 6.2 dB in 100-feet. Thus in 15-feet the attenuation will proportionally be 0.945 dB.
In our test set up, the wattmeter is placed 15-feet away from the antenna. If we measured 22-Watts at the wattmeter location, that power will be attenuated by 0.945 dB by the time it reaches the antenna. We must calculate the actual power at the antenna as being 0.945 dB lower. Again we use the relationship
dB = 10 log10 (P2/P1)
and insert the known values, -0.945 dB and P1 = 22 watts. Solving we get
P2 = 17.7 Watts
This is the actual power that reached the antenna, only 17.7-Watts, due to transmission line loss in the 15-feet of RG-58C/U. This value is our actual Pfwd for the VSWR calculation.
At the antenna some portion of this 17.7-Watts will be reflected back toward the transmitter. The reflected power will also be attenuated in the transmission line by 0.945 dB. We know that after attenuation, there was 2-Watts of power at the wattmeter, but we need to know how much reverse power was at the antenna, which will be 0.945 dB greater. Again we use the relationship of two powers and the known ratio between them in dB to find the actual reverse power at the antenna, in this case 2.49-Watts.
Now we can calculate the actual VSWR at the antenna, using
Pfwd = 17.7-Watts
Prev = 2.49-Watts
First we find the reflection coefficient, ψ
ψ = (2.49/17.7)0.5 = 0.375
Then we compute the VSWR
VSWR = (1+0.375)/(1−0.375)
VSWR = 1.375 / 0.625
VSWR = 2.2
Now we have an accurate measurement of the VSWR of the antenna at its feed point. The actual VSWR at the antenna is 2.2, quite a bit higher than the measured VSWR of 1.85 at a point 15-feet away on the transmission line. Note that any transmission line loss will always tend to make the antenna VSWR appear better (lower) that the actual VSWR at the antenna.
A further compounding of this calculation is to adjust the transmission line attenuation to include an allowance for the influence of a high VSWR on the transmission line. For all practical transmission lines, the presence of any standing waves on the transmission line (that is a VSWR greater than 1) causes the attenuation in the transmission line to increase. In the analysis above, we have ignored that effect.