Identification of Lossy Y-Type Two-Port Circuit Models under Measurement Uncertainties: Closed-Form Solution and Statistical-Perturbative Characterization

The present paper treats a black-box estimation of the three independent parameters of a reciprocal lossy two-port network whose terminals are supposed to be accessible to an impedance measurement device. The discussed estimation method is based on the availability of a number of data pairs made of external load admittances paired to equivalent external admittances affected by measurement errors. The proposed method is framed as a squared-estimation-error minimization problem that leads to a system of three nonlinear equations in the three unknown parameters. A key observation is, however, that a core subsystem of two equations may be turned exactly to a linear form and hence may be solved in closed form. The purely real-valued case is treated first since it serves to clarify the optimization problem at hand and the structure of its solution. In the purely real-valued case, a statistical analysis is carried out as well, which affords the evaluation of the effects of the measurement errors. The results of the statistical analysis afford quantifying the dependence of the estimation errors from the number of samples and from the variance of the measurement errors. Subsequently, the full complex-valued case is treated. Results of numerical simulations complement and illustrate the theoretical findings. The obtained numerical results confirm the statistical analysis and that the proposed external identification method is effective.