An algorithm for direct identification of passive transfer matrices with positive real fractions via convex programming

Abstract

SUMMARYThe paper presents a new algorithm for the identification of a positive real rational transfer matrix of a multi-input-multi-output system from frequency domain data samples. It is based on the combination of least-squares pole identification by the Vector Fitting algorithm and residue identification based on frequency-independent passivity constraints by convex programming. Such an approach enables the identification of a priori guaranteed passive lumped models, so avoids the passivity check and subsequent (perturbative) passivity enforcement as required by most of the other available algorithms. As a case study, the algorithm is successfully applied to the macro-modeling of a twisted cable pair, and the results compared with a passive identification performed with an algorithm based on quadratic programming (QPpassive), highlighting the advantages of the proposed formulation.

Characteristic Impedance of Periodically Grounded Lossless Multiconductor Transmission Lines and Time-Domain Equivalent Representation

“…This is not compatible with the previously shown and discussed periodical frequency behavior of the characteristic impedance matrix. For this reason, the periodical behavior has to be extracted in terms of equivalent controlled generators, before identifying the remaining passive equivalent network [27]. Therefore, in the case of periodical grounding, the termination network will be an active network.…”

“…This means that, in the time domain, the equivalent circuit includes a more complex RLC load instead of just the resistive matrix R 0 . The RLC load can be easily computed with identification techniques [27]. This aspect will be investigated in future works.…”

Numerical validation of a procedure for direct identification of passive linear multiport with convex programming

“…General properties of the above formulation are fully analyzed in [8]. Here, we just mention the trade off between sub-optimality of the solutions, as compared to Positive Real Lemma based formulations, versus a significantly reduced computational cost.…”

“…Other schemes base on "a-priori" constraining passivity of the model during the identification process. A new procedure for identifying guaranteed passive models, originally named Positive Fraction Vector Fitting (PFVF), has been introduced in [7] (for the SISO case) and fully described (including generalization to MIMO systems) in [8], showing to work satisfactorily in practical cases of technical interest. Its formulation is briefly resumed in next section.…”

Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels

“…Such "local" problems, however, are only approximated and do not guarantee that the global optimum is found. Variants of the above schemes have been presented in [27]- [32]. A comprehensive comparison of main techniques is available in [33].…”