Lossy transmission line simulation based on closed-form triangle impulse responses

• Published in: IEEE transactions on computer-aided design of integrated circuits and systems Vol. 22; no. 6; pp. 748 - 755
• Main Authors: Tingdong Zhou, Dvorak, S.L., Prince, J.L.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-06-2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Circuit simulation; Closed-form solution; Computer simulation; Convolution; Couplings; Distributed parameter circuits; Exact solutions; Fourier transforms; Frequency domain analysis; Impulses; Inverse; Mathematical analysis; Propagation losses; Time domain analysis; Transmission lines; Triangles
• ISSN: 0278-0070; 1937-4151
• DOI: 10.1109/TCAD.2003.811445

Analytical frequency-domain expressions for single and coupled transmission lines with triangular input waveforms are first developed. The inverse Fourier transform is then used to obtain an expression for the time-domain triangle impulse responses for frequency-independent transmission line parameters. The integral associated with the inverse Fourier transform is solved analytically using a differential-equation-based technique. Closed-form expressions for the triangle impulse responses are given in the form of incomplete Lipschitz-Hankel integrals (ILHI) of the first kind. The ILHI can be efficiently calculated using existing algorithms. Combining these closed-form expressions for the triangle impulse responses with a time-domain convolution method using a triangle impulse as a basis function, provides an accurate and efficient simulation method for very lossy transmission lines embedded within linear and nonlinear circuits.