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Delay Line Approach for Analyzing Lossy Transmission Lines

IP.com Disclosure Number: IPCOM000087007D
Original Publication Date: 1976-Nov-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 3 page(s) / 36K

Publishing Venue

IBM

Related People

Gruodis, AJ: AUTHOR [+4]

Abstract

The delay line approach based on the method of characteristics for simulating lossless transmission lines in a computer-aided circuit analysis program, as described by C. Ho, "Theory and Computer-Aided Analysis of Lossless Transmission Lines", IBM Journal of Research and Development, Vol. 17, May 1973, p. 249, is a fast and efficient technique when compared with the conventional method of replacing the distributed transmission line by lumped LC sections.

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Delay Line Approach for Analyzing Lossy Transmission Lines

The delay line approach based on the method of characteristics for simulating lossless transmission lines in a computer-aided circuit analysis program, as described by C. Ho, "Theory and Computer-Aided Analysis of Lossless Transmission Lines", IBM Journal of Research and Development, Vol. 17, May 1973, p. 249, is a fast and efficient technique when compared with the conventional method of replacing the distributed transmission line by lumped LC sections.

When lumped LC element sections are used, the number of LC sections has to be chosen such that the delay due to each of the sections is small compared with the rise-time of the pulses. This may result in a large number of LC sections and, hence, require large amount of storage and computer time.

In the delay-line approach, however, the transmission line is substituted internally in the program by a pair of voltage sources. This decouples the line from the rest of the circuit which is one form of "tearing" the original network into smaller pieces. The voltage and current "waves" entering the transmission line are computed and stored.

After an appropriate amount of delay time has elapsed, the waves emerge from the opposite end of the line and then interact with the rest of the network. The computer time required is only to calculate the voltage entering the lines and to do the interpolation for the voltage coming out of the lines. Furthermore, the storage required is dynamically dependent on the time step chosen by the integration routine of the computer program, and is therefore somewhat optimized.

To include the effect of DC losses in simulating the transmission line, the generalized delay line approach of replacing the transmission line by a pair of voltage sources is used to obtain the same advantage of the lossless case. However, once the waves have entered the lines, they are attenuated due to the resistive losses as well as delayed due to the capacitive and inductive effects. Thus, the transmission line can be conceptually partitioned into a small section, as shown in Fig. 1, where the lossless section of the line with a delay of t(o) is in series with a resistor R.

The incoming voltage V(1)(t) is first delayed by the amount t(o) to become V(2)(t). The voltage V(2)(t) sees the resistor R and the characteristic impedance for the next section Z(o), and is therefore split into two components. The transmitted wave V(3)(t) is determined as follows: V(3)(t) over V(2)(t) =...