Homer Hot Measurement and Tuning System - S-TEAM Lab

Reflection coefficient modulus
M
M
max
min
M u
M u
The formulas assume M > u. For M < u, M min = 0.
Reflection coefficient phase angle
where
max
min
180
u
M
is phase angle uncertainty in degrees. The formula derivation assumes M >> u. Clearly, given a value of u, the phase
angle uncertainty grows when the reflection coefficient magnitude decreases. For M < u, phase angle loses meaning
at all.
Return loss R
R
R
max
min
20log(
M
20log(
M
min
max
)
)
Voltage standing wave ratio V
V
V
max
min
(1 M
(1 M
max
min
) /(1
M
) /(1
M
max
min
)
)
Effective directivity and test port (source) match
Two independent quantities usually characterize heterodyne network analyzers. These are
Effective directivity E D (critical for the measurement of small reflection coefficients)
Effective test port (source) match E S (affecting primarily the measurement of high reflection coefficients)
In the six-port reflectometer, effective directivity can be linked with the uncertainty circle radius u as
E D
20logu
Effective test port match cannot practically be defined.
See also Deembedded Reflection Coefficient Accuracy Considerations.
Measurement Uncertainty Example
An example of return loss uncertainty considerations is depicted in Figure 3. If, for instance, the uncertainty radius is
u = 0.02 (E D = 34 dB) and the measured return loss is 20 dB (i.e. M = 0.1), then the true value lies somewhere
between R min = 18.42 dB and R max = 21.94 dB.
If you wish to be sure that the true return loss is greater than 20 dB, the measured value must be so that R min is at
least 20 dB. The intersection of 20-dB horizontal graticule with the lower blue line (green circle) then shows that the
measured return loss must be at least 22 dB.
Mathematically, R min = 20 dB corresponds to M max = 0.1. Because, as stated above, M max = M + u, the measured
reflection coefficient magnitude must not exceed the value M x = M max – u = 0.1 – 0.02 = 0.08, hence the measured
return loss must be at least R x = -20 log(M x ) = -20 log(0.08) = 21.94 dB, which is approximately the 22 dB obtained
from the graph.
User's Handbook Homer Hot Measurement and Tuning System Introduction 7