Hi Lenny,
Yes, this may happen if you have more than two ports. You need to check that
the largest eigenvalue of the matrix (S*S') doesn't exceed 1 (S' is a Hermitian
conjugate of S). Because for passive S-parameters Hermitian matrix U - S*S'
must be non-negative (U is unity matrix).
Reducing the norm of a single matrix component or setting it to zero may reduce
the amount of reflected or transmitter power coming to/from a particular port,
but for a multiport system we need to watch for a global passivity that
considers multiple inter-reflections, in presence of an arbitrary passive load
conditions.
Example: S below is an original matrix with maximal eigenvalue of S*S' equal
1.0. Sx is obtained from S by zeroing out the components with indices (2,3) and
(3,2). The maximal eigenvalue Sx*Sx' is 1.005390823157963 > 1:
S =
0.647702905880147 + 0.117081243704661i 0.229759559503444 +
0.534609362251502i 0.001650528801219 + 0.199828011536207i
0.229759559503444 + 0.534609362251502i 0.547447911840171 -
0.248798055988079i 0.024336911579367 + 0.009811227990395i
0.001650528801219 + 0.199828011536207i 0.024336911579367 +
0.009811227990395i 0.003538416914948 - 0.702120459562955i
Sx =
0.647702905880147 + 0.117081243704661i 0.229759559503444 +
0.534609362251502i 0.001650528801219 + 0.199828011536207i
0.229759559503444 + 0.534609362251502i 0.547447911840171 -
0.248798055988079i 0.000000000000000 + 0.000000000000000i
0.001650528801219 + 0.199828011536207i 0.000000000000000 +
0.000000000000000i 0.003538416914948 - 0.702120459562955i
Vladimir
Msg: #2 in digest
Date: Tue, 26 May 2020 19:28:24 +0000 (UTC)
From: "L R" <dmarc-noreply@xxxxxxxxxxxxx> (Redacted sender "lrayzman" for
Subject: [SI-LIST] Passivity of matrix with muted terms
Hi si-listers,
If I were to take a lossy (as in passive) and reciprocal s-parameter matrix and
"mute" pairs of certain cross-coupling (off-diagonal) terms, by zeroing the
term out for all frequencies, my understanding (or more like intuition) tells
me that the new matrix should become more passive than the original matrix.
However from what I saw computing passivity for a matrix with muted terms
apparently doesn't necessarily yield "passive" eigenvalues. Perhaps there is a
constraint on which terms can be modified in such a matter. I am confident I am
not clear on some important detail of the math behind this and would appreciate
a pointer to an explanation.
Best,
Lenny
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