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# Propagation Over Multiple Parallel Transmission Lines Via Modes

IP.com Disclosure Number: IPCOM000100311D
Original Publication Date: 1990-Apr-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 6 page(s) / 194K

IBM

## Related People

Nguyen, TH: AUTHOR [+2]

## Abstract

Disclosed is a method of propagating signals over a system of multiple parallel transmission lines via orthogonal modes. Transmission line currents and voltages are first decomposed into orthogonal modes and then propagated through a system of multiple parallel transmission lines. Orthogonal modes can be recombined to get back transmission line currents and voltages.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 28% of the total text.

Propagation Over Multiple Parallel Transmission Lines Via Modes

Disclosed is a method of propagating signals over a
system of multiple parallel transmission lines via orthogonal modes.
Transmission line currents and voltages are first decomposed into
orthogonal modes and then propagated through a system of multiple
parallel transmission lines. Orthogonal modes can be recombined to
get back transmission line currents and voltages.

Background Electromagnetic waves propagating over two
conductors and ground have two orthogonal modes known as the even
mode and the odd mode.  In general, n conductors and ground have n
orthogonal modes.  Because of its orthogonal properties, each mode
propagates independent of all other modes.  The resolution of line
voltages into orthogonal modes is analogous to the concept of
resolving a pulse wave form into its orthogonal Fourier components.
Just as the Fourier components can be studied separately because they
are orthogonal, and hence independent of each other, so the
orthogonal modes of transmission lines can be studied separately
because they are independent of each other.

For n parallel trip conductors and ground as shown in Fig. 1,
modes have been difficult to calculate and complicated to interpret.

Principal Features The multiple transmission lines system
considered here has cylindrical geometries (Fig. 2) with 2n identical
parallel conductors symmetrically arranged in a circle in a
homogenous medium.

The circular cross-section results in a unique symmetrical
pattern in the capacitance matrix, thereby permitting a simpler
decomposition of line voltages into orthogonal modes.

All information that can be transmitted through m conductors
and ground can also be transmitted through the same m conductors and
ground via modes.  The extra requirements are an encoder at the
beginnings and a decoder at the ends of the lines to translate bit
patterns into modes.

The implied advantage of propagating information via orthogonal
modes instead of via bits is that there is no cross-talk between
modes as there is between non-modal propagation.

Modal Decomposition The following method was used to obtain
orthogonal modes for the above structure.  Each mode is a particular
linear combination of all line voltages, and vice versa each line
voltage is a superposition of all modes.

In matrix notation, (V)=(T)x(U) or (U)=(T)-1x(V)

(Image Omitted)

v1(x,t)
v2(x,t)
where (V) =       .   is the matrix representing all
line voltages
.
.
vn(x,t)
u1(x,t)
u2(x,t)
...