Restoration of passivity in S-parameter data of microwave measurements

Circuit modeling of networks described by tabulated S-parameters has generated immense interest during the recent years. The tabulated data may be obtained either from measurements or full-wave EM simulations. However, one of the major difficulties with such type of data is that, the data can be non-passive in the frequency bandwidth of interest, due to the measurement errors or the numerical errors associated with the full-wave simulator. This causes significant difficulty while interfacing such a data with circuit simulators. To overcome this difficulty, this paper presents an efficient algorithm for restoring the passivity of the S-parameter data, prior to its circuit modeling. Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.