Efficient Macromodeling Techniques of Distributed Networks Using Tabulated Data

Efficient macromodeling techniques used to model multi-port distributed systems using tabulated data are presented. First a method to macromodel large multiport systems characterized by noisy frequency domain data is shown. The proposed method is based on the vector fitting algorithm and uses an instrumental variable approach and QR decomposition to formulate the least squares equations. The instrumental variable method minimizes the biasing effect of the least squares solution caused by the noise of the data samples while QR decomposition decouples the least squares equations of multiport systems described by common set of poles. It is illustrated, that the proposed approach can increase the accuracy of the pole-residue estimates with less iteration when compared to the traditional QR decomposition vector fitting method. Second, a method to obtain delay rational macromodels of electrically long interconnects from tabulated frequency data, is presented. The proposed algorithm first extracts multiple propagation delays and splits the data into single delay regions using a time-frequency decomposition transform. Then, the attenuation losses of each region is approximated using the Loewner Matrix approach. The resulting macromodel is a combination of delay rational approximations. Numerical examples are presented to illustrate efficiency of the proposed method compared to traditional Loewner where the delays are not extracted beforehand.