Impedance Perturbation Theory for Coupled Uniform Transmission Lines

Taking the impedance mismatch of transmission lines as a small quantity, a novel impedance perturbation theory based on the lumped transmission line model is established for both the single-ended and coupled transmission lines. The propagation constant, S-parameters, and T-parameters can be directly constructed from an impedance perturbation factor. As an application example, a detailed perturbation analysis is carried out for differential striplines, which provides insights in the S-parameter features and the splitting in the modal propagation constants. The corresponding numerical simulation indicates that the perturbation model captures and explains the most important features of the exact S-parameters. As another application example, the perturbation model is employed in the through-reflection-line deembedding formulas to evaluate the measurement accuracy and sensitivity. The trends obtained by this analysis is later confirmed by experimental results.