A Two-Port Equivalent Model for a Transmission Line with Distributed Sources

Abstract

The theory of a transmission line with distributed sources is useful in the analysis of electromagnetic pulse coupling to shielded cables and in the analysis of system generated electromagnetic pulse. To facilitate computer simulations of cable surges induced by these nuclear environments, a new two port equivalent source model for a uniform, time invariant transmission line with independent distributed sources is presented. The equivalent source model is based on a newly recognized circuit synthesis of the boundary conditions imposed by the line's reflection coefficient and requires only the solution of the matched-load termination responses. This model greatly simplifies the algebra required by previously published techniques. The model is compact, requiring only six nodes for a mathematically precise simulation, and it should prove useful in the assessment of interface cable surge threats in electrical systems where large numbers of circuits need to be evaluated with some precision. As with earlier techniques, this model is valid in the frequency domain with linear load terminations and dispersive, lossy transmission line propagation parameters. The Fourier spectra of linear load responses are readily formulated for numerical inversion to the time domain. For the lossless line or the distortionless lossy line, a time domain source model is derived here for efficient, time-saving use with computer circuit analysis programs containing passive two port transmission line models. Loads in this case can be non-linear.