[SI-LIST] Re: Even mode, common mode, and mode conversion

• From: Steve Corey <steve@xxxxxxxxxxxxxx>
• To: si-list@xxxxxxxxxxxxx
• Date: Tue, 26 Feb 2002 10:21:22 -0800

```Chris -- you're right in that it's easier to work with systems whose
eigenvectors are orthogonal.  However, if the system is such that its
eigenvectors are not orthogonal, then you don't have any choice. Since
the eigenvectors are a property of the system, you can't choose whether
to generate orthogonal or non-orthogonal eigenvectors any more than you
can choose the eigenvalues.

"Analysis of Multiconductor Transmission Lines" by Clayton R. Paul
discusses various systems which do and do not necessarily have
orthogonal eigenvectors.  A good example of such a system is general
lossy microstrip.

The good news is that circuit designers don't have to worry about which
systems have orthogonal eigenvectors and which do not.  However, CAD
algorithm designers do.  This helps maintain job security...

-- Steve

Chris Cheng wrote:

> Steve,
>
> Agree. Its just easier to generate solutions with orthogonal
> eigenvectors.
>
> Chris
>
> -----Original Message-----
> From: Steve Corey [mailto:steve@xxxxxxxxxxxxxx]
> Sent: Tuesday, February 26, 2002 7:49 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Even mode, common mode, and mode conversion
>
>
>
> Actually, orthogonality of the eigenvectors is not necessary.  Linear
> independence is sufficient.
>
>    -- Steve
>
> -------------------------------------------
> Steven D. Corey, Ph.D.
> Time Domain Analysis Systems, Inc.
> "The Interconnect Modeling Company."
> http://www.tdasystems.com
>
> email: steve@xxxxxxxxxxxxxx
> phone: (503) 246-2272
> fax:   (503) 246-2282
> -------------------------------------------
>
>
> Chris Cheng wrote:
>
>
>>Classical definition of TEM mode propagation in an N
>>line coupled transmission line requires waveforms
>>to be propagating in N orthogonal eigen-vectors
>>(instead of individual waveforms at each port).
>>It just happen in a two line transmission line case
>>the vectors are [1,1] and [1,-1] ejwt and sometimes
>>people refer the pair as even and odd respectively.
>>
>>In current generic SI terms, it is sometimes
>>refered to a coupled N line transmission line system
>>where the victim is switching in the same direction
>>(even mode) as the aggressor or the opposite direction
>>(odd mode). Note, depends on the setup, sometimes the
>>waveform in the aggressor ports becomes meaningless
>>to simplify the analysis time.
>>
>>Chris
>>
>>-----Original Message-----
>>From: Doug Brooks [mailto:doug@xxxxxxxxxx]
>>Sent: Monday, February 25, 2002 9:31 AM
>>To: si-list@xxxxxxxxxxxxx
>>Subject: [SI-LIST] Even mode, common mode, and mode conversion
>>
>>
>>
>>Gurus,
>>
>>I've been following the thread on mode conversion and suspect I am not the
>>
>
>>only one with this question. Can someone explain, in layman's terms:
>>
>>The distinction between even mode and common mode?
>>        between odd mode and differential MODE (not to be confused with
>>differential traces)
>>
>>And does the existence of differential traces add any complications to
>>these distinctions?
>>
>>Thanks for bringing the dummies along with you!
>>
>>Doug Brooks
>>
>>
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>>
>>
>>
>
>

--
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com

email: steve@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax:   (503) 246-2282
-------------------------------------------

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```