Compact Modeling of Interconnect Circuits over Wide Frequency Band by Adaptive Complex-Valued Sampling Method

Abstract

In this article, we propose a new model order-reduction method for compact modeling of interconnect circuits over wide frequency band using a novel complex-valued adaptive sampling and error estimation scheme. We address the outstanding error control problems in the existing sampling-based reduction framework over a frequency band. Our new method, WBMOR , explicitly and efficiently computes the exact residual errors to guide the sampling process. We show by sampling along the imaginary axis and performing a new complex-valued reduction that the reduced model will match exactly with the original model at the sample points. Additionally, we show in theory that the proposed method can achieve the error bound over a given frequency range. In practice, the new algorithm can help designers choose the best order of the reduced model for the given frequency range and error bound via the adaptive sampling scheme. In addition, WBMOR can perform wideband accurate reductions of interconnect circuits for analog and RF applications where model accuracy needs to be maintained over a wide frequency range. We compare several sampling schemes such as Monte Carlo, logarithmic, recently proposed resampling, and ARMS methods. Experimental results on a number of RLC circuits show that WBMOR is much more efficient than all the other sampling methods, including the recently proposed resampling and ARMS schemes with the same reduction orders. Compared with the traditional real-valued sampling methods, the complex-valued sampling method is more accurate for the same computational cost.