Ashok K. Agrawal

Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field

The time-domain transmission-line equations for uniform multiconductor transmission lines in a conductive, homogeneous medium excited by a transient, nonuniform electromagnetic (EM) field, are derived from Maxwells equations. Depending on how the line voltage is defined, two formulations are possible. One of these formulations is considerably more convenient to apply than the other. The assumptions made in the derivation of the transmission-line equations and the boundary conditions at the terminations are discussed. For numerical calculations, the transmission -line equations are represented by finite-difference techniques, and numerical examples are included.

Experimental Characterization of Multiconductor Transmission Lines in the Frequency Domain

Although a number of papers have been published on the experimental characterization of multiconductor transmission lines, they are limited to the time domain for lossless multiconductor lines in homogeneous media. This paper presents a method for the characterization of multiconductor transmission lines in inhomogeneous media. The experimental technique for the measurement of multiconductor line parameters is presented and the appropriate multiconductor line equations are solved to obtain these parameters. The experimental method involves only the short-and open-circuit impedance measurements for different configurations. The experimental results for a four-conductor line are found to be in good agreement with computed results and a low-frequency lumped model.

Experimental Characterization of Multiconductor Transmission Lines in Inhomogeneous Media Using Time-Domain Techniques

An effective method for the time-domain characterization of lossless multiconductor transmission lines with cross-sectionally inhomogeneous dielectrics is presented. Lines of this type are characterized by multiple propagation modes having different velocities. Time-domain reflectometry is used to obtain the characteristics impedance and the modal velocities of the line. A pulse or step-function response of the line is used to obtain the modal amplitudes which, in turn, determine the velocity matrix. The appropriate multiconductor transmission-line equations are solved to obtain the per-unit-length inductance and capacitance matrices in terms of the measured characteristic-impedance and velocity matrices. The method is concise and complete and identifies the propagation modes in a way that permits direct physical interpretation of the results. The time-domain experimental results for a four-conductor transmission line are presented and are found to be in good agreement with independent frequency-domain measurements.

Application of Modal Analysis to the Transient Response of Multiconductor Transmission Lines with Branches

An effective method for computing the time-domain response of lossless multiconductor transmission lines with branches in cross-sectionally inhomogeneous dielectric media is presented. Lines of this type are characterized by multiple propagation modes having different velocities. The theory of wave propagation on lossless multiconductor transmission lines with inhomogeneous dielectrics is used to obtain the modal amplitudes on the uniform sections of the line. The scattering matrix for the junction is used to compute the transmitted and reflected waves in the different branches at the junction. Each mode arriving at the junction excites multiple modes in all branches. The method described in this paper identifies all propagation modes in all branches of the line, and leads to the direct physical interpretation of the results. The method is general and can be applied to either partially or completely nondegenerate cases. Experimental results for a six-conductor transmission line with a single branch are found to be in good agreement with the results computed using the described method.

The Response of a Transmission Line Illuminated by Lightning-Induced Electromagnetic Fields

This paper presents the theory and procedures used to estimate the voltages and currents induced on long transmission lines by cloud-to-cloud lightning. A model for cloud-to-cloud lightning phenomena is presented, and the theory necessary to calculate the electromagnetic fields created by the lightning stroke is derived. The time-domain transmission-line equations in the presence of external electromagnetic fields are presented. A time-domain formulation is more convenient if, in the future, nonlinear effects are to be included. The results of sample calculations, using finite-difference techniques for the solution of the transmission-line equations, are presented.

Experimental Characterization of Partially Degenerate Three-Conductor Transmission Lines in the Time Domain

In a recent paper [1], a method for the time-domain characterization of lossless multiconductor transmission lines with cross sectionally inhomogeneous dielectrics was presented. This method is limited to lines with completely nondegenerate propagation; i.e., all the modes have distinct propagation velocities. In this paper, a method is presented for the characterization of lossless partially degenerate three-conductor lines, together with experimental data. The results are in good agreement with independent frequency-domain measurements.

Comments on " Further Experimental Verification of Frequency-Domain Multiconductor-Transmission-Line Characterization"

This correspondence alludes to two recent publications [1], [2] which developed techniques for frequency-domain characterization of multiconductor transmission lines. Theoretical aspects of [1], although quite general, had been verified only for a symmetrical three-conductor cable. The present paper considers unsymmetrical three-wire, four-wire, and five-wire multiconductor cables and shows that measured values of [2] do agree with the calculated parameters within the uncertainties of experimental factors, such as voltage and current-probe loading, etc. Excellent agreement of theoretical and experimental data permits simulation of fairly complex problems involving generalized multiconductor transmission lines.

Numerical Representation of Multiconductor Transmission-Line Equations by Integration along Characteristics

It is often necessary to obtain the solution of the transmission-line equations in the time domain, for example, for lines excited by transient, nonuniform electromagnetic fields (fields due to nuclear detonations). This paper presents the solution of the multiconductor transmission-line equations by representing them by integration along their characteristic directions. The multiconductor transmission-line equations are first decoupled to a set of n single-line equations and then the method of characteristics is applied to solve these equations. It is shown in this paper that the multiconductor transmission-line equations can always be decoupled into a set of n single-line equations. The transmission-line equations are stable along their characteristics in the presence of high air conductivity, whereas the finite-difference solutions become unstable.