Simulation of lossy multiconductor transmission lines using backward Euler integration

This paper presents a fixed time-step backward Euler integration algorithm for the time-domain analysis of linear circuits containing multiconductor lossy transmission lines. The new method requires the frequency derivatives of the circuit equations at a frequency point on the positive real axis that is related to the integration time step. The transient response is obtained efficiently from a single inversion of the circuit matrix. Although it is not as accurate as trapezoidal integration, the backward Euler integration is stable and gives smooth low-pass approximations for the actual response. In this paper, it is also shown that in case of impulse function excitation, the backward Euler results are equivalent to the shifted moments of the impulse response with an appropriate scaling of the frequency-dependent variables of the circuit. Numerical examples are presented for verification of the proposed method.