Wideband reduced modeling of interconnect circuits by adaptive complex-valued sampling method

In this paper, we propose a new wideband model order reduction method for interconnect circuits by using a novel adaptive sampling and error estimation scheme. We try to address the outstanding error control problems in the existing sampling-based reduction framework. In the new method, called WBMOR, we explicitly compute the exact residual errors to guide the sampling process. We show that by sampling along the imaginary axis and performing a new complex-valued reduction, the reduced model will match exactly with the original model at the sample points. We show theoretically that the proposed method can achieve the error bound over a given frequency range. Practically the new algorithm can help designers choose the best order of the reduced model for the given frequency range and error bound via adaptive sampling scheme. As a result, it can perform wideband accurate reductions of interconnect circuits for analog and RF applications. We compare several sampling schemes such as linear, logarithmic, and recently proposed re-sampling methods. Experimental results on a number of RLC circuits show that WBMOR is much more accurate than all the other simple sampling methods and the recently proposed re-sampling scheme with the same reduction orders. Compared with the real-valued sampling methods, the complex-valued sampling method is more accurate for the same computational costs.