Irregular Terms in the Impulse Response of a Multiconductor Lossy Transmission Line

Linear multiconductor transmission lines can be effectively represented in the time domain as a dynamic multiport through the describing input and transfer impulse responses. Unfortunately, these responses cannot be analytically evaluated for the most general case of lossy lines. In addition, they cannot even be evaluated numerically due to the presence of irregular terms such as Dirac pulses, functions that actually approximates Dirac pulses, and functions of the type 1/ptt. Nevertheless, all these irregular terms can be isolated from the regular ones. This paper proposes an analytical method to evaluate exactly the irregular terms. This method is based on the perturbation theory of the spectrum of symmetric matrices and can be easily and effectively applied to the most general case of frequencydependent lossy multiconductor lines. Once the irregular parts of the impulse responses are known, it is possible to evaluate accurately the regular ones through simple numerical methods, as shown through some examples.