Fast and Efficient Analysis of Transmission Lines With Arbitrary Nonuniformities of Sub-Wavelength Scale

Abstract

The Telegrapher's equations for a general nonuniform transmission line (NUTL) is analytically solved when the nonuniformities are of sub-wavelength scale. The proposed solution is based on an approximation of the chronological ordering operator for the Telegrapher's equations in an arbitrary NUTL. The proposed approximation is quite accurate when the transmission line has sub-wavelength nonuniformities. The scale of transmission line nonuniformity is assessed by using the concept of minimum resolvable length of nonuniformity (MRLN), which is based on the physically intuitive idea that electromagnetic waves are not affected by spectrally mild nonuniformities. The MRLN is inferred by using the spatial Fourier transform of the characteristics impedance of the NUTL. The proposed formulation is verified by using the measured scattering parameters of three different NUTLs.

A Two-Step Perturbation Technique for Nonuniform Single and Differential Lines

“…in which the sources are left out and unperturbed quantities are replaced by first order perturbations. Integrals similar to (22) and (23) will appear in the final solution, but instead of the e ±2jk0z exponentials, e ±2jkoz , e ±2jkez , e ±2j(ko−ke)z and e ±2j(ko+ke)z exponentials will now appear. Following (24) it turned out that for the unperturbed value of the p.u.l.…”

“…All calculations were performed on a computer with an Intel(R) Core(TM) Quad CPU Q9650 and 8 GB of installed memory (RAM). For the perturbation technique, the computational cost is attributed to the calculation of the integrals (22), (23) and (24) given in Appendix ??. For the reference technique, the computational complexity scales with the number of sections one uses, and hence, it is less efficient than the newly proposed method.…”

“…[21]. In [22] an improved averaging technique for single lines with subwavelength nonuniformities is presented. Finally, [23] presents an equivalent source technique for single lines solving the pertinent integral equation in an iterative way and presenting examples using two iterations.…”