Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction From Noisy Frequency Responses

Abstract

The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise. We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise. We denote the resulting algorithm as vector fitting with adding and skimming (VF-AS). A thorough validation of the VF-AS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VF-AS algorithm to measured scattering responses of interconnect structures and networks typical of high-speed digital systems.

Macromodeling of Multiport Systems Using a Fast Implementation of the Vector Fitting Method

“…This iteration is known to have good convergence properties if the signal-to-noise ratios are sufficiently high. However, it was shown in [9] that the convergence may stall or diverge if the data samples are contaminated with simulation or measurement noise. An efficient solution to this problem is presented in [4], where the high frequency asymptotic constraint on is removed.…”

“…Once these coefficients of are computed, the common poles of the transfer function are found by solving an eigenvalue problem (9), and the corresponding residues of the macromodel can easily be calculated as in [1].…”

Experimental characterization of the distribution of resonance widths in chaotic reverberation chambers

“…Two different post-processing methods have been applied to the four measured S-parameters, namely the Vector Fitting Algorithm [6] and the harmonic inversion method [7]. The first method consists of a rational approximation of these parameters in the frequency domain, the poles being common to the four S-parameters.…”

Efficient linear macromodeling via least-squares response approximation

“…2) The convergence of VF will be seriously affected by even a small spectral noise (disturbance), e.g, when SNR=30dB [12], which always happens in practical measurement. In the proposed algorithm, the noise in the measured response signal is automatically suppressed during the digital filter operation.…”