An impedance is the complex ratio between a voltage and a current. The analyzer provides two independent sets of impedance parameters:
Converted impedances (each impedance parameter is obtained from a single S-parameter)
Z-parameters (complete description of the n-port DUT)
The converted impedance parameters describe the input impedances of a DUT with fully matched outputs. In the figures below the indices i and j number the analyzer/DUT ports, Z0i is the reference impedance at the DUT port i.
The analyzer converts a single measured S-parameter to determine the corresponding converted impedance. As a result, converted Z-parameters cannot completely describe general n-port DUTs:
A reflection parameter Zii completely describes a one-port DUT. For n-port DUTs (n>1) the reflection parameters Zii describe the input impedances at ports i (i = 1 to n) under the condition that each of the other ports is terminated with its reference impedance (matched-circuit parameters).
A two-port transmission parameter Zij (i ≠ j) can describe a pure serial impedance between the two ports.
The converted impedances Zii are calculated from the reflection S-parameters Sii according to:
The transmission parameters are calculated according to:
The converted admittances are defined as the inverse of the impedances.
Examples:
Z11 is the input impedance of a 2-port DUT that is terminated at its output with the reference impedance Z0 (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. Zdd44 is the differential mode input impedance at port 4 of a DUT that is terminated at its other ports with the reference impedance Z0. See More Impedances for detailed information.
You can also read the converted impedances in a reflection
coefficient measurement from the Smith
chart.
The Z-parameters describe the impedances of a DUT with open output ports (I = 0). The analyzer provides the full set of Z-parameters 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.
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 Z-parameters for a two-port are based on a circuit model that can be expressed with two linear equations:
The four 2-port open-circuit Z-parameters can be interpreted as follows:
Z11 is the input impedance, defined as the ratio of the voltage V1 to the current I1, measured at port 1 (forward measurement with open output, I2 = 0).
Z21 is the forward transfer impedance, defined as the ratio of the voltage V2 to the current I1 (forward measurement with open output, I2 = 0).
Z12 is the reverse transfer impedance, defined as the ratio of the voltage V1 to the current I2 (reverse measurement with open input, I1 = 0).
Z22 is the output impedance, defined as the ratio of the voltage V2 to the current I2, measured at port 2 (reverse measurement with open input, I1 = 0).
Z-parameters can be easily extended to describe circuits with more than two ports or several modes of propagation; see section More Z-Parameters.
