Array Solutions AIM4170 - Page 31

Antenna Analyzer AIM4170 page 31
The reflection coefficient also has an associated phase angle, Theta, between the incident
voltage from the transmitter and the reflected voltage. The real and imaginary parts of
Rho can be related to its magnitude and phase angle with the following equations:
Real_part_of_Rho = rho
a
= Magnitude_of_rho * COS(Theta)
Imaginary_part_of_Rho = rho
b =
Magnitude_of_rho * SIN(Theta)
Rho = rho
a
+ j rho
b
Standing Wave Ratio (SWR):
SWR is the ratio of the Maximum Voltage to the Minimum Voltage along a transmission
line. On a perfectly matched line, the maximum is equal to the minimum since there is
no variation in the voltage along the line and the SWR is 1.0. In the real world, SWR is
somewhere between 1.0 and infinity. The special case of infinity means all the power
from the transmitter is reflected back by the antenna. This would the case for a short
circuit or an open circuit at the antenna when using a lossless transmission line.
If the transmission line has no loss, the SWR is the same at all points along the line. That
is, the SWR at the transmitter is the same as it is at the antenna. As the transmission line
loss increases, the effect is to make the SWR measured at the transmitter appear to go
down since less power is received back from the antenna. This power gets lost along the
transmission line, so it does not arrive at the SWR meter and the meter responds more to
the outgoing power from the transmitter. The meter thinks the antenna is a better match
than it really is because there seems to be less reflected power.
The SWR only depends on the magnitude of the reflection coefficient, Rho:
SWR = [ 1 + magnitude(Rho)] / [ 1 – magnitude(Rho)]
This shows that when the magnitude of Rho = 0 (that is, the transmission line and the
antenna are a perfect match), the SWR is [1+0]/[1-0] = 1 (this is the ideal case).
When the mismatch is very large and the magnitude of Rho is nearly 1, the term in the
denominator approaches zero and the SWR approaches infinity.
Since only the magnitude of Rho appears in this equation, SWR is not a complex number
(it’s a real number).