Transient Simulation of Coupled Transmission Lines based on Piecewise Exponential Approximation of Voltage and Current Distributions

An approach for the transient simulation of coupled transmission lines is described. By treating the line voltage/current distributions as state variables, the Telegrapher equation is transformed into an ordinary differential equation. This allows the use of Backward Differentiation Formulae to discretize the time derivatives, yielding a time domain companion model of the transmission line together with the formulae for calculating its local truncation error. As the distributions get more complicated with time, a novel technique to approximate these spatial voltage/current distributions in the form of multidimensional piecewise exponential function is thus proposed. This technique enables the line to be dynamically bisected until the approximation error is a small percentage of the computed local truncation error. Hence, this approach complies with the accuracy control of a standard circuit simulator.