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

From: Steve Corey <steve@xxxxxxxxxxxxxx>
To: si-list@xxxxxxxxxxxxx
Date: Wed, 27 Feb 2002 08:22:31 -0800
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
>
> In a nutshell, odd and even modes, and any modes in general,
> are special voltage patterns that propagate undistorted down
> a pair of transmission lines. For example, in a pair of
> microstrip traces, if you send a +1 v on one line and a 0v
> signal on the other, the actual voltage on the two lines
> will change, as the signals move down the line. The 0v line
> will see a growing negative signal as the far end cross talk
> builds up and the +1v signal will drop and distort as it
> looses energy to the quiet line. This voltage pattern is not
> a mode. It is just a particular driven voltage pattern.
> There is nothing special about it.
>
> However, there are two special voltage patterns that you can
> impose on the lines which will not change as the signals
> propagate down the lines. If you put a +1v on each line, wrt
> the return plane below, there will be no voltage difference
> between the two signal lines and the voltage pattern will
> continue undistorted. The other voltage pattern is a +1v and
> a -1v applied to the two lines, wrt the return plane.
>
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Follow-Ups:
- [SI-LIST] Re: Even mode, common mode, and mode conversion
  - From: Mary
References:
- [SI-LIST] Re: Even mode, common mode, and mode conversion
  - From: Mary
[SI-LIST] Re: Even mode, common mode, and mode conversion

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