Chapter 1 17
Introduction and Measurement Theory
Cable Impedance and Structural Return Loss Measurement Theory
Method 3 (Z-average normalization). The mathematics for the Z-average
normalization as performed by the analyzer are shown below.
Equation 4
Z
0
= system impedance, 50 or 75 Ω
Equation 5
Equation 6
In Equation 4, ρ(ω) is the reflection coefficient from the analyzer measured at each
frequency and Z
in
(ω) is the impedance of the cable for that measured reflection
coefficient.
Step 1. The calculation of Z
cable
, described in Equation 5, is the Z-average impedance of the
cable over the number of frequency points (N). The default frequency range is
approximately 5 MHz to 200 MHz. This frequency range is chosen because
mismatch effects of the input connector are small. High quality connectors must be
used if the average impedance is calculated over a wider span. The frequency range
for this calculation can be modified by using the
Z Cutoff Freq. softkey in the
connector model menu to change the cable impedance cutoff frequency.
Equation 6 is the structural return loss for the cable. This calculation can be done by
the analyzer or an external computer.
Z
in
ω() Z
0
1 ρω()+()
1 ρω()–()
--------------------------
×=
Z
cable
Z
in
ω
n
()
n 1=
N
N
--------------------------------
=
ρ
SRL
ω()
Z
in
ω() Z
cable
–
Z
in
ω() Z
cable
+
-------------------------------------
=
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