[SI-LIST] Re: Even/Odd mode general case
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: "'Doug Brooks'" <dbrooks9@xxxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Thu, 9 Feb 2012 12:13:14 -0800
Doug,
Good questions - it looks like there is no common classification and there
are reasons for that.
In general, there is N propagating TEM or quasi-TEM modes in N-conductor
transmission line with reference conductor (N+1 conductors line) [1],[2].
Modes are pure TEM (only transverse components of electric and magnetic
field) in idealized case of lossless conductor and homogeneous lossless
dielectric in cross-section. Modes are quasi-TEM (have predominantly
transverse and small longitudinal components of electric and magnetic field)
in all cases with lossy conductors and lossy or inhomogeneous dielectrics.
There is also infinite number of high-order modes. They are evanescent up to
a cutoff frequency and propagate above that frequency. The cut-off
frequencies depend on the geometry of the cross-section and may be
relatively low in case of shielded traces.
Any mode can be classified either as even or odd mode in case if there is
symmetry in the cross-section (symmetric 2-conductor strip or microstrip
line for instance). In case if there is no symmetry modes are usually called
pi-mode (quasi-even) and c-mode (quasi-odd). Note, that things may become
complicated even in 2-conductor case. For instance, with increase of
frequency c mode may become pi mode and the other way around [3] to remove
the modal degeneration possible in case of symmetric line.
Typically, after analysis modes are sorted using propagation constant, slow
down factor or effective dielectric constant and simply called mode 1, 2,
3,... Integral of current at each conductor (or conductor voltage in case
of electrically small cross-section) can be used to annotate modes at lower
frequencies using current sign for instance. Even mode with positive
currents on both conductors of 2-conductor line can be marked as ++ and odd
mode with currents with opposite signs becomes +- mode. This notation can be
extended to the number of modes more than 2 as shown in [4]. Modes in
3-conductor line can be called +-+, +0- (zero total current on the middle
conductor), and +++. Unfortunately, this is suitable only at relatively low
frequencies - at higher frequencies mode +-+ may become +0- and the other
way around, depending on the dispersion of each mode.
References:
1. C. Paul, Analysis of Multiconductor Transmission Lines
2. F. Olyslager, Electromagnetic Waveguides and Transmission Lines
3. A. B. Yakovlev, G. W. Hanson, Mode-Transformation and Mode-Continuation
Regimes on Waveguiding Structures, IEEE Trans. On MTT, v. 48, No. 1, 2000,
p. 67-75.
4. G. G. Gentili, M. Salazar-Palma, The Definition and Computation of Modal
Characteristic Impedance in Quasi-TEM Coupled Transmission Lines, IEEE
Trans. On MTT, v.43, No.2, 1995, p. 338-343.
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
3030 S Torrey Pines Dr. Las Vegas, NV 89146, USA
Office +1-702-876-2882
Cell +1-206-409-2368
Skype: shlepnev
www.simberian.com
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Doug Brooks
Sent: Wednesday, February 08, 2012 6:42 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Even/Odd mode general case
Even mode and odd mode describe the types of current that can occur on a
PAIR of (differential) traces. What is the more general description if there
are more than two traces coupled together? How many modes can exist in a
general case, and how do we denote them?
Thanks
Check out our resources at http://www.ultracad.com
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