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 > ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu