Hi Lenny,
Doing this you violate internal physics of a multiport.
Here is why "muting" does not work:
Passivity is condition of non-negative power transferred to multiport
(difference of power between incident (a) and reflected (b) waves) for ANY
possible incident vector:
Pin = sum(|ai|^2-|bi|^2) >=0 (1)
b = S*a
Can you increase bn in this equation and make the sum negative by just
zeroing out the off-diagonal terms in S-parameters?
The answer is yes, simply because of vector b is a superposition of columns
of S multiplied by elements of vector a:
b = sum(Si*ai) - here Si are vectors formed from columns of S and ai are
element of incident.
It is even simpler. For a 4 port system the reflected wave at the first
port:
b1 = S11*a1+S12*a2+S13*a3+S14*a4
If we zero out S14 and S41 in the S matrix for instance, we will have
b1' = S11*a1+S12*a2+S13*a3
|b1'| may be greater |b1| and condition (1) violated because of that -
simply because of the incident vector a is arbitrary and phase of each
S-parameter will matter too. Looks like you have got such example.
So, do not do it. See more on properties of S-matrices in our old DesignCon
2010 tutorial #2010_01 at
https://www.simberian.com/TechnicalPresentations.php The "theoretical" has
everything.
Now, if you want to produce 4-port S-parameters from a 4*N port multiport
for COM analysis for instance, the ports have to be properly terminated.
Something like shown in demo-video #2019_07 at
https://www.simberian.com/ScreenCasts.php?view=list or at Simbeor YouTube
channel https://youtu.be/j_1fzjaF9qM ;
Note that you can "mute" a port by eliminating whole row and column without
any consequences on the passivity - it does not violate the physics of
multiport.
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
www.simberian.com
Simbeor THz - Accurate, Productive and Cost-Effective Electromagnetic Signal
Integrity Software to Design Predictable Interconnects!
Simbeor SDK - The Industry-First Signal Integrity Analysis Automation Kit!
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of L R (Redacted sender "lrayzman" for DMARC)
Sent: Tuesday, May 26, 2020 12:28 PM
To: SI-LIST
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,б= my understanding (or more like
intuition) tells me that the new matrix should become more passive than the
original matrix.б= 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.б=I am confident I am not clear on some important detail of the math
behind this and would appreciate a pointer to an explanation.б=б=
Best,
Lenny
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