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

  • From: Steve Corey <steve@xxxxxxxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Thu, 28 Feb 2002 07:40:46 -0800

Mary -- thanks for bringing me back to the earlier question.  Because 
each mode has its own characteristic impedance, each has a different 
relationship between its voltage and current waves.  As a result, the 
responses to the even and odd modes do not add up to zero on the 
quiescent conductor, and this is where the crosstalk comes from. 
Because modal analysis takes all the coupling into account, it properly 
predicts crosstalk.  And of course, if there's negligible coupling, the 
modal impedances are effectively the same, and the modal 
responses essentially cancel out for zero crosstalk.

I also want to emphasize as a more general point that any set of 
inputs/responses, eigenmodes or not, have to propagate independently 
from one another, due to linearity. Otherwise the system is nonlinear 
and superposition does not hold, and all of our jobs just got a lot harder.

Finally, I was looking over my previous post (I suppose I should have 
done that before sending it out...) and I spotted a couple of errors 
which I would like to correct.  First, as I stated above, in the 
presence of coupling, each mode has its own unique characteristic 
impedance.  Second, if the dielectric is homogeneous -- even if it is 
lossy -- (as long as the conductors are lossless) then every mode shares 
the same propagation constant.  Inhomogeneity and/or lossy conductors 
cause splitting of the modal propagation constants.  Sorry if I created 
any confusion there.

   -- Steve

Mary wrote:

> Steve,
> 
> I agree that we should not complicate the discussion
> by referring to non-homogeneous media, non-TEM propagation
> or skin-effect losses. I also agree that the even and odd
> modes can be viewed as eigenvectors of the system.
> 
> Perhaps you or someone else would like to address the point
> that Mr. Haedge made. If a 1-volt excitation on trace 1 can
> be viewed as a superposition of a pure 0.5 volt even-mode
> excitation on both traces and a 1-volt odd-mode excitation
> between traces, and if both of these modes propagate
> independent of one another, the signal should reach
> its termination unattenuated. If crosstalk occurs, then
> don't we have to conclude that the modes do not propagate
> independently?
> 
> Mary
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Steve Corey
> Sent: Wednesday, February 27, 2002 10:23 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Even mode, common mode, and mode conversion
> 
> 
> 
> Mary -- you are correct in that the signals can be broken down according to
> an
> infinite number of orthogonal bases.  However, the significance of the even
> and
> odd modes is not that they are orthogonal.  Their significance is that they
> are
> the eigenvectors of the system (although they happen to be orthogonal in
> this
> case).  A non-degenerate system (i.e., all distinct eigenvalues) has only
> one
> eigenvector basis, so yes, they are special.  The modes do propagate
> independently, but so does any excitation, due to linearity and
> superposition.
> The significance is that the eigenvectors, applied as a similarity transform
> to
> the system matrix, diagonalize the matrix, which decouples all of its
> eigenvalues, which correspond to the modes of the network.  The equations
> are
> then easily viewed as the superposition of each mode propagating
> independently.  Transmission line theory and analysis has relied on this
> powerful tool for many years.
> 
> Any signal can be decomposed into a weighted combination of the different
> modes
> by doing an eigendecomposition.  Each mode can be analyzed independently
> using
> its characteristic propagation velocity and attenuation (which is the
> associated eigenvalue, or propagation constant).  Finally, the responses can
> be
> recombined, by inverting the eigendecomposition, into a final result.  It is
> this recombination (superposition) of modes, each often with its own
> propagation velocity, attenuation, and characteristic impedance, that causes
> the distortion to which Eric was referring.  Using some arbitrary set of
> orthogonal or non-orthogonal vectors to decompose and recombine the system
> will
> not result in each component propagating independently with a characteristic
> propagation constant and impedance, and will be of little analytical value.
> And note that if you actually excite the system with one of its eigenmodes,
> there is no need to decompose it before modal analysis or recombine it after
> modal analysis -- one of the system's instrinsic modes is propagating with
> its
> associated propagation constant -- without distortion, as Eric has pointed
> out.  This is what makes excitation using one of the eigenmodes different
> from
> using just any excitation vector, orthogonal or not.
> 
> You are correct in implying that in a lossless, homogeneous medium all modes
> propagate with the same velocity and impedance.  However, I think many
> designers on this list are operating in the presence of skin loss,
> dielectric
> loss, and/or inhomogeneous media, and if any of these factors is present,
> the
> modes will split.  So I think varying propagation velocities of different
> modes
> was a valid point for an earlier poster to bring up, and need not confuse
> the
> issue, even though it may lead to a more complicated analysis than the ideal
> lossess, homogeneous case.
> 
>   -- Steve
> 
> 
> 
> Mary wrote:
> 
> 
>>Don't confuse the issue by referring to what happens in an
>>inhomogeneous medium. I believe Mr. Haedge's point is valid.
>>After all, aren't there an infinite number of ways to divide
>>a signal on three conductors into two complete-orthogonal modes?
>>The even/odd mode description is convenient for many reasons.
>>However, I don't think there's anything magical about these
>>modes. They do not propagate down a transmission line
>>independent of one another. It's true that if you launch an
>>odd (or even) mode signal down a symmetric pair of traces you
>>will theoretically get an odd (or even) mode signal at the
>>termination. However, if you launch an odd and an even mode
>>signal at the same time, you no longer have the symmetry that
>>was responsible for the "single-mode" propagation.
>>
>>I don't believe it's proper to assume that the odd-mode
>>propagation and even-mode propagation can be analyzed
>>independently. Yet there is a tendency on this list to ignore
>>what happens to the even mode component when the "intentional"
>>signal is all odd mode.
>>
>>Mary
>>
>>-----Original Message-----
>>
>>Each propagates undistorted, but at different velocities?
>>
>>Timothy J. Christman
>>Test Engineer
>>Tel 651.582.3141  Fax 651.582.7599
>>timothy.christman@xxxxxxxxxxx
>>Guidant Corporation
>>4100 Hamline Ave. N.
>>St. Paul,  MN   55112  USA
>>www.guidant.com
>>
>>-----Original Message-----
>>From: David G Haedge [mailto:haedge@xxxxxxxxxxxx]
>>Sent: Tuesday, February 26, 2002 3:56 PM
>>To: si-list@xxxxxxxxxxxxx
>>Subject: [SI-LIST] Re: Even mode, common mode, and mode conversion
>>
>>Eric and all,
>>
>>My understanding of a transmission line that has  +1 volt signal on one
>>line and
>>0 volts on the other is actually the superposition of an even mode signal
>>of +0.5 volt / +0.5volt and an odd mode signal of +0.5volt/-0.5volt,
>>
> giving
> 
>>you
>>the +1volt/0volt signal on the line, in which case each mode should
>>propagate
>>undistorted.  Is this not what in fact is occurring in a line excited in
>>this nature?
>>
>>David Haedge
>>Raytheon
>>
>>
> 
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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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