Computational models of transmission lines with skin effects and dielectric loss

We present circuit models of a length of transmission line with skin effect and frequency-dependent dielectric loss, treating the ordinary RLGC line as a special case. The line is modeled as a characteristic two-port in which the characteristic impedance is approximated as the input impedance of a lumped circuit and the propagation function is approximated as the transfer function of a second lumped circuit plus an ideal delay. A unified approach based on frequency matching is presented to form the model. In the approximation, the skin effect is represented as the impedance of an RL ladder, and the complex dielectric parameter as the admittance of an RC ladder. A table of the rms error of the approximation is derived from which the complexity of the model can be found for a desired accuracy. The model is guaranteed to be stable, and since it consists entirely of lumped circuit elements and ideal delay lines and since the model parameters can be easily computed, it can be incorporated as a subcircuit model in a general circuit simulator, and the solution can be obtained by integrating the circuit equations in the usual manner. No FFT or convolution is required