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# Characterization and Simulation of Coupled Dispersive Transmission Lines

IP.com Disclosure Number: IPCOM000052359D
Original Publication Date: 1981-Jun-01
Included in the Prior Art Database: 2005-Feb-11
Document File: 3 page(s) / 93K

IBM

## Related People

Chang, CS: AUTHOR [+2]

## Abstract

Coupled, dispersive transmission lines with frequency-dependent characteristics can be simulated by a model in the time domain. Two such coupled lines are represented in the figure. Several modes of propagation are induced by the input voltage configuration. For ideal lines, with line parameters that are frequency-independent, the propagation constant Gamma is: Gamma/2/ = [j Omega L][j Omega C] =[P] Lambda/2/(Gamma) [P]/-1/ (1) where Lambda/2/ is a diagonal matrix representing the eigen values of the (j Omega L][j Omega C] matrix product. The square root of these eigen values divided by j Omega is the delay for the different modes as determined by [P] (the eigen vector matrix).

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Characterization and Simulation of Coupled Dispersive Transmission Lines

Coupled, dispersive transmission lines with frequency-dependent characteristics can be simulated by a model in the time domain. Two such coupled lines are represented in the figure. Several modes of propagation are induced by the input voltage configuration. For ideal lines, with line parameters that are frequency-independent, the propagation constant Gamma is: Gamma/2/ = [j Omega L][j Omega C] =[P] Lambda/2/(Gamma) [P]/-1/
(1) where Lambda/2/ is a diagonal matrix representing the eigen values of the (j Omega L][j Omega C] matrix product. The square root of these eigen values divided by j Omega is the delay for the different modes as determined by [P] (the eigen vector matrix).

For lossy coupled lines, [j Omega L] is replaced by [Z] Xi [R + j omega L ]and (j Omega C ]is replaced by Y ]Xi G j Omega C , so that: Gamma/2/ = [Z][Y] = [P] Lambda/1/(Gamma)[P]/-1/ (2)

The square root of the eigen values, which are now complex, represents the propagation constant for each mode. The real part is the attenuation constant (Alpha), and the imaginary part is the phase constant (Beta See Original pp.101- 103.

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