Closed-form representations for triangle impulse responsesassociated with single and coupled lossy transmission lines

摘要

A fast simulation method was proposed for single and coupledtransmission lines that are connected to linear and non-linear circuitelements by Z. Chen et al. (1999) [1]. In that method, the time-domainvoltages and currents at the ends of the lines are approximated by aseries of triangular expansion functions. A time-stepping procedure canthen be employed for the circuit simulation provided that the triangleimpulse responses for the lines are known. In [1], a triangle impulseresponse database for the lossy transmission lines is employed. Othersimulation tools are used to calculate the required lossy transmissionline triangle impulse responses numerically. The numerical results forthe triangle impulse responses are then used with a convolutionalgorithm to carry out the circuit simulation. In our work, analyticfrequency-domain expressions for single and coupled transmission lineswith triangular input waveforms are first developed. The inverse Laplacetransform is then used to obtain an expression for the time-domaintriangle impulse responses. The integral associated with inverse Laplacetransform is solved analytically using a differential-equation-basedtechnique. Closed-form expressions for the triangle impulse responsesare given in the form of incomplete Lipschitz-Hankel integrals (ILHI's)of the first kind. The ILHIs can be efficiently calculated usingalgorithms developed by S.L. Dvorak and E.F. Kuester (1990). Combiningthese closed-form expressions for the triangle impulse responses withthe method proposed in [1], provides an accurate and efficientsimulation method for transmission lines embedded within linear andnon-linear circuits