In this paper, the Baum-Liu-Tesche (BLT) equation is extended from the frequency domain into the time domain, so as to permit an analysis of a transmission line with nonlinear loads at each end of the line. To do this, we use both the voltage and current BLT equations in the time domain, together with the nonlinear v-i relationships for the termination loads, to formulate a nonlinear BLT equation for the unknown reflection coefficients at each end of the line. This equation is solved by a time-marching procedure, and its solution provides transient reflection coefficients at the nonlinear terminations. Once the reflection coefficients are determined, the load voltages and currents can be computed from the transient BLT equations. This computational procedure is illustrated with several examples.

https://derric1.people.uic.edu/Website_MURI_RF/Publications_Canta/Papers/Nonlinear%20BLT.pdf

On the Analysis of a Transmission Line With Nonlinear Terminations Using the Time-Dependent BLT Equation

Two approaches, one based on the circuit concept and the other based on field theory, are used to model the crosstalk between two microstrip lines of finite length and arbitrary orientation. In the circuit-concept modeling, a set of equations for the line voltages and currents has been derived from a modified telegrapher's equation. A four-port network expression is resultantly obtained by solving the equations, thus the crosstalk can be predicted by applying terminal conditions to the network expression. On the other hand, the extended finite-difference time-domain (FDTD) method has been used to model the terminal resistors and the feeding resistive voltage source in the crosstalk analysis. Several physical models have been fabricated and experiments performed. The calculated results are compared to measurements. In our experiment, for microstrip lines of finite length and arbitrary orientation, there are short line-sections or vias at each of the four ports, which should be incorporated into the crosstalk analysis. This effect has been investigated numerically and experimentally.

Analysis of crosstalk between finite-length microstrip lines: FDTD approach and circuit-concept modeling

In this paper, an unconditionally stable finite-difference time-domain algorithm is presented for analysis of lossy nonuniform multiconductor transmission line (MTL). The results of the proposed algorithm are confirmed by those of the Leap-Frog algorithm. The unconditionally stable algorithm alone cannot decrease the time consumption, especially when the MTL is excited by modulated signals. The complex phasor transformation approach is used to separate the modulating signal from the carrier signal when an MTL is excited by a modulated signal. A new set of equations is generated using this approach. The new equations are based on the modulating signal, and the carrier signal is eliminated in these equations. The derived equations are solved by Leap-Frog algorithm, and the results confirm the accuracy of these equations. Finally, the proposed equations are solved by the unconditionally stable algorithm at several temporal step sizes. The results indicate that this method has much lower CPU time compared with the conventional method and also has a very good accuracy.

Efficient Method for Time-Domain Analysis of Lossy Nonuniform Multiconductor Transmission Line Driven by a Modulated Signal Using FDTD Technique

The aim of this work is the development and validation of compact SPICE models suitable to analyze the conducted and radiated immunity of shielded cables. The reference structures are coaxial cables, and shielded cables with two parallel wires (i.e., twinax cable). The conducted and radiated immunity of the shielded cables are evaluated considering as source a known injected current on the cable shield, and the coupling with an external plane wave electromagnetic field, respectively. The circuit models are validated by comparing the results with those obtained by other approaches. The developed models are then used to quantify the main grounding practices of shielded cables.

SPICE-like models for the analysis of the conducted and radiated immunity of shielded cables

In this paper, a finite-difference time-domain (FDTD) analysis of the transmission line equations for a general circuit simulator is presented. A two-port circuit representation is derived for integrating a dispersive transmission line network within a circuit/system simulator. The circuit model consists of resistive elements and dependent current sources, which are updated at every time step by the FDTD algorithm. The frequency dependence of the conductors' parameters is taken care of by a recursive integration that employs the Vector Fitting algorithm. The application of this model is presented for several examples, such as nonuniform transmission lines, plane wave excitation of the line, and determination of overvoltages induced by a nearby lightning stroke.

Finite-difference analysis of dispersive transmission lines within a circuit simulator

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.

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

A method of moments procedure to obtain the capacitance matrix for a cable harness is presented. The geometry consists of multiple, parallel, insulated wires, possibly above a ground plane. The method uses Fourier harmonic expansion functions for the total charge and Galerkin testing functions. The capacitance matrix is obtained by the relationship of free charge to potential. Computed and experimental results are presented and compared to exact analytical solutions when possible. >

Capacitance calculations for cable harnesses using the method of moments

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

Capacitance calculations for cable harnesses using the method of moments