This dissertation describes the approach to reconstruct the S-matrices of a multiport network from a set of one-port measurements. By properly using auxiliary circuits and
the type-II PRM, the S-matrix of a multiport network can be properly reconstructed.
Based on the considerations of reduction of the number of one-port measurements, the
accuracy of the reconstructed results and the solvability, discussion about the selection
and criteria of the auxiliary circuit is also given. By properly selecting the auxiliary
circuit, the S-matrices of three-port reciprocal and nonreciprocal DUTs and two-port
active DUT can be reconstructed from ten one-port and five one-port measurements
respectively and experimentally demonstrated. The reconstructed results are shown in
close agreement with the directly measured results.
As described in Section 2.1, the number of one-port measurements to reconstruct
the S-matrix of a two-port DUT is four or five. The rising curve of the number of
measurements in terms of the number of DUT ports over two ports is related to that of
type-II PRM being approximated to be 3n−2. Therefore, the number of one-port
measurements for an n-port DUT involved in this study is about 4 3× n−2 to 5 3× n−2. As
for the number of connections, a multiport VNA for three-port measurements needs six
connections including three for calibration using an E-cal kit and three for measurement.
Each experiment given in this study, however, needs thirty-five connections including
72
three for calibration and thirty-two for one-port measurements.
The developed results given in this study imply that extra efforts are required to
determine the S-matrix of an n-port DUT from one-port measurements. These efforts
include the hardware/software integration and the consideration of the imperfection of
cable-flex repeatability or switches in one-port measurements. For the hardware and
software, one needs to integrate one-port VNA, auxiliary circuit, switches, cables and a
PC with reconstruction algorithm. Short phase stable cables connecting the auxiliary
circuit and the DUT can mitigate ripples occurring in the reconstructed results. As for
the imperfection of switches, the mismatch and loss can be regarded as parts of the
auxiliary circuit or the terminations and de-embedded. However, considering Fig. 4.1,
the switch imperfect isolation will make the measured data to relate all the components
involved. This then renders the one-port measurement equation to be very complicated.
Although these issues have to be considered to improve the practicability of the
developed approach, the presented results provide an approach to extend the application
of a one-port VNA in the determination of the S-matrix of an n-port DUT.
73 Substituting (7) into the first two equations in (A.1) gives
0 1 12 2 21 Dividing (A.3) by (A.2) gives
1 0 0 1 12 2 0 0 2 21 According to (8) and (9), if the auxiliary circuit is reciprocal, then
1= 12 31= 21 13 = 2
N a a a a N (A.5)
1= − 32 = − 23 = 2
D a a D . (A.6) By substituting (A.5) and (A.6) into (A.4), one can prove
1 0 0 1 12 2 0 0 2 21
74
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