Rohde & Schwarz 1145.1010.04/05/06, Operating Manual

Page: 138 / 813

Measured Quantities R&S
®
ZVA/ZVB/ZVT
1145.1084.12 3.28 E-1
The analyzer converts the measured S-parameters to determine the matched-circuit impedances.
Relation with S-parameters
It is possible to express the matched-circuit impedances Z
ii
in terms of the reflection S-parameters S
ii
and vice versa. The reflection parameters are calculated according to:
,
1
1
0
ii
ii
i ii
S
S
Z Z
−
+
=
where i numbers the analyzer/DUT port. The transmission parameters are calculated according to:
( )
, , 2
0 0
0 0
j i Z Z
S
Z Z
Z
j i
ij
j i
ij
≠ + −
⋅
⋅ =
The two sets of reflection S-parameters and input/output impedances provide equivalent descriptions of
the reflection in a linear n-port network. Another set of equivalent parameters is given by the matched-
circuit admittances, defined as the inverse of the impedances.
Examples:
•
Z
11
is the input impedance of a 2-port DUT that is terminated at its output with the reference
impedance Z
0
(matched -circuit impedance measured in a forward reflection measurement).
•
The extension of the impedances to more ports and mixed mode measurements is analogous to
S-parameters. Z
dd44
is the differential mode input impedance at port 4 of a DUT that is terminated
at its other ports with the reference impedance Z
0
. See More Impedances for detailed
information.
You can also read the converted impedances in a reflection coefficient measurement from the
Smith chart.
Z-Parameters
The Z-parameters describe the impedances of a DUT with open output ports (I = 0). The analyzer
provides the full set of open-circuit impedances including the transfer impedances (i.e. the complete
nxn Z-matrix for an n port DUT).
This means that Z-parameters can be used as an alternative to S-parameters (or Y-parameters) in
order to completely characterize a linear n-port network.
2-Port Open-Circuit Z-Parameters
In analogy to S-parameters, Z-parameters are expressed as Z
<out>< in>
, where <out> and <in> denote the
output and input port numbers of the DUT.
The open-circuit Z-parameters for a two-port are based on a circuit model that can be expressed with
two linear equations: