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# Transient Analysis of Uniform Lossless Multiple Parallel Transmission Lines

IP.com Disclosure Number: IPCOM000074813D
Original Publication Date: 1971-Jun-01
Included in the Prior Art Database: 2005-Feb-23
Document File: 2 page(s) / 57K

IBM

## Related People

Narayanasamy, R: AUTHOR

## Abstract

An equivalent circuit for the uniform lossless multiple-parallel transmission line in a homogeneous medium, shown in Fig. 1, has been derived from the partial differential equations which describe the coupled transmission lines. The block circuit diagram is shown in Fig. 2 and the equivalent network in Fig. 3. The network which realizes the impedance matrix (Zo) shown in Figs. 2, 3 is drawn in Fig. 4. The equivalent circuit consists of 2n voltage sources and n(n+1) resistors, where n is the number of coupled transmission lines. The voltage vectors E(f) and E(b), whose components are the voltage sources shown in Fig. 3 can be expressed in terms of the terminal voltage vectors e(o,t- tau) at x=o and e(l,t-tau) at x=l by the following equations, where tau is the delay in the lines.

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Transient Analysis of Uniform Lossless Multiple Parallel Transmission Lines

An equivalent circuit for the uniform lossless multiple-parallel transmission line in a homogeneous medium, shown in Fig. 1, has been derived from the partial differential equations which describe the coupled transmission lines. The block circuit diagram is shown in Fig. 2 and the equivalent network in Fig. 3. The network which realizes the impedance matrix (Zo) shown in Figs. 2, 3 is drawn in Fig. 4. The equivalent circuit consists of 2n voltage sources and n(n+1) resistors, where n is the number of coupled transmission lines. The voltage vectors E(f) and E(b), whose components are the voltage sources shown in Fig. 3 can be expressed in terms of the terminal voltage vectors e(o,t- tau) at x=o and e(l,t-tau) at x=l by the following equations, where tau is the delay in the lines. E(f) (o,t-tau) = [2e(o,t-tau) - E(b) (l,t- tau)] E(B) (l t-tau) = [2e(l,t-tau) - E (o,t-2tau)].

Based on this equivalent circuit concept and the above equations, a computer subprogram has been written to model the coupled transmission lines. This subprogram can be used with any general transient analysis programs. This tool is useful in analyzing and designing electronic packages such as modules, cards and boards used in a digital computer, and directional couplers.

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