Clayton R. Paul

Frequency Response of Multiconductor Transmission Lines Illuminated by an Electromagnetic Field

A well-known result [1], [2] for the response of a two-wire transmission line illuminated by a nonuniform electromagnetic field is extended to multiconductor lines. A simple matrix equation for the currents induced in arbitrary termination networks is obtained. Air Development Center.

Decoupling the multiconductor transmission line equations

A comprehensive discussion is presented of the method of decoupling the multiconductor transmission line (MTL) equations by the method of transformation of the voltages and currents to mode voltages and currents in order to obtain their general solution. Various ways of defining and obtaining the transformations are shown which serve to connect the myriad of such definitions and also point out where inconsistencies in those definitions can result. Structures for which the decoupling is assured are also discussed. The MTL equations to be decoupled are in the frequency domain, and extensions to their applicability in the time-domain are shown.

Incorporation of terminal constraints in the FDTD analysis of transmission lines

A method of incorporating lumped terminal conditions into a finite-difference, time-domain (FDTD) analysis of multiconductor transmission lines is given. The method provides an exact solution of the transmission-line equations via the FDTD technique when the line discretization, /spl Delta/t, and the time discretization, /spl Delta/t, are chosen such that /spl Delta/t=/spl Delta/z/v where v is the phase velocity of propagation on the line. Examples are given to show that in the case of a multiconductor line in an inhomogeneous medium where the mode velocities are not identical, the method gives accurate results with a minimum of computational effort. >

Finite-difference, time-domain analysis of lossy transmission lines

An active and efficient method of including frequency-dependent conductor losses into the time-domain solution of the multiconductor transmission line equations is presented. It is shown that the usual A+B/spl radic/s representation of these frequency-dependent losses is not valid for some practical geometries. The reason for this the representation of the internal inductance the at lower frequencies. A computationally efficient method for improving this representation in the finite-difference time-domain (FDTD) solution method is given and is verified using the conventional time-domain to frequency-domain (TDFD) solution technique.

A SPICE model for multiconductor transmission lines excited by an incident electromagnetic field

This paper describes a SPICE model that may be used for predicting the time-domain or frequency-domain voltages and currents induced at the terminations of a multiconductor transmission line (MTL) by an incident electromagnetic held. Explicit results for the entries in the SPICE circuit model are obtained for an incident uniform plane wave that may represent sources such as radio and television transmitters, radars, lightning, etc. The result relies on the transformation of the MTL equations into uncoupled modal lines by similarity transformations. The entries in the similarity transformations are provided for lossless lines. The model is implemented using controlled sources to implement the modal transformations and delay lines to implement the modal lines. If the model is implemented as a SPICE subcircuit model, the time-domain form of the incident field can be implemented as a source external to that subcircuit model so that changes in the line responses due to changes In the incident field waveform can be simulated without changing the subcircuit model. In order to avoid negative line delays, the result is restricted to incident waves having components of the propagation vector in the positive direction along the line. This restriction can be removed by simply reversing the line. The paramount advantages of the model are that both time-domain and frequency-domain results can be easily obtained with the existing SPICE code, and nonlinear loads, such as transistors and digital devices, as well as dynamic loads, such as inductors and capacitors, may be easily incorporated using the existing elements in the SPICE code. Predicted results for MTLs using the method are compared to those of the time-domain to frequency-domain transformation and finite difference-time-domain (FDTD) methods. >

Computation of the Capacitance Matrix for Systems of Dielectric-Coated Cylindrical Conductors

The method of moments is applied to the computation of the charge distributions and capacitance matrix for electrostatic systems of bare and dielectric-coated cylindrical wires. Several choices of expansion functions are investigated in detail and compared. Harmonic series expansion functions are shown to be especially well suited to problems involving systems of closely-spaced dielectric-coated cylindrical wires.

Computation of the Transmission Line Inductance and Capacitance Matrices from the Generalized Capacitance Matrix

In a recent paper [1], a method for computing the per-unitlength generalized capacitance matrix of a system of dielectric-insulated wires was given. In this-paper, a method for computing the per-unitlength inductance and capacitance matrices used in multiconductor transmission-line models in terms of the elements of the generalized capacitance matrix is given. Certain approximate formulas for large wire separations are also given. Rome Air Development Center.

Prediction of Crosstalk Involving Twisted Pairs of Wires-Part I: A Transmission-Line Model for Twisted-Wire Pairs

A transmission line model for predicting electromagnetic coupling (crosstalk) involving twisted-wire pairs (TWP) is developed. The twisted pair is modeled as a cascade of loops consisting of uniform two-wire sections with abrupt interchanges of wire positions at the ends of each loop. Experimental results are obtained for the coupling between a single wire above ground and a twisted pair above ground. The experimental correlation with the model predictions indicates that the simulation model is typically accurate within 3 dB for frequencies such that the total line length is less than 1/ 10 of a wavelength. For higher frequencies, the model tracks the experimental results quite well although the prediction error is somewhat larger.

Effectiveness of multiple decoupling capacitors

The effectiveness of using the parallel combination of large-value and small-value capacitors to increase the frequency coverage of either one and overcome the effect of lead inductance is examined. Computed and experimental results are given that show this scheme is not significantly effective. The improvement at high frequencies is at most 6 dB over the use of only the large-value capacitance. >

Effect of an image plane on printed circuit board radiation

It is shown that the predominant radiation from a PCB (printed circuit board) with or without an attached cable is the result of common-mode current. For the PCB investigated here, the common-mode current was caused primarily by a source proportional to the signal voltage driving the traces and the cable as an asymmetric dipole antenna. Moreover, the PCB was an effective common-mode antenna even without the cable. The concept of partial inductance was used to calculate the inductance of the ground-return trace. The effect of placing an image plane beneath and close to a PCB was shown. The image plane dramatically reduced the radiated emissions from a PCB even though the plane was not electrically connected to the PCB. The image plane also dramatically reduced the emissions from a PCB with an attached cable when the image plane was correctly connected to the PCB.<<ETX>>