How to extract distributed circuit parameters from the scattering parameters of a transmission line

Distributed circuit parameters parameterize the transmission and reflection off a given transmission line in terms of a distributed resistance, inductance, capacitance, and conductance, which are per-unit-length, frequency-dependent quantities. While there are analytical models for extracting the distributed circuit parameters, these models are discontinuous as a function of frequency when the argument approaches a branch cut. Here, we develop a nonlinear least-square regression algorithm that accurately extracts the distributed circuit parameters. Compared to existing approaches and finite element models, our algorithm successfully extracts the distributed circuit parameters as a function of frequency, all while being less sensitive to these phase conditions. Such an algorithm is useful for understanding how to deembed transmission lines, and how to extract electrical properties of the materials used in a circuit.