Analytical approach for analysis of nonuniform lossy/lossless transmission lines and tapered microstrips

In this paper, distribution of voltage along a general nonuniform transmission line is expanded in an appropriate form, and by employing an approach similar to conventional and modified differential transfer matrix methods already proposed for optical structures, analytical expressions are obtained for voltage/current distributions and reflection/transmission coefficients. This method shows great accuracy in different test cases and has been found to be superior to the well-known analytical method of small reflections. Notwithstanding, the overall accuracy of proposed approach is further improved by introducing the technique of multiple divisions. In particular, lossy/lossless tapered microstrip lines are examined, and excellent results are obtained. In deriving the formulation, a rigorous approach is followed and no simplifying assumptions are made; however, thanks to the analytical nature of the proposed method, high computational resources are not needed, and the results can be obtained extremely fast. This feature makes it suitable for optimization and synthesis of nonuniform transmission lines.