Model Order Reduction Based On Dynamic Relative Gain Array And Interpolation Process

During the circuit design and manufacturing process,the circuit-level simulation is an indispensable step to reduce product waste due to design defects.As the circuit scale is increasing,how to reduce the computation complexity and the simulation time becomes a major problem.Model order reduction(MOR)is an important approach to improve the simulation efficiency by using a smaller system to approximate the original complex system.The input-output characteristics,stability and passivity of original systems should be maintained after reduction.At the same time,the error between the reduced system and the original system should be as small as possible.In this paper,two new MOR methods are proposed to improve the disadvantages of traditional Krylov subspace method.The computational efficiency of traditional MOR methods may degrade sharply for multi-input multi-output(MIMO)systems especially when the number of ports of MIMO system is very large.The MOR method based on dynamic relative gain array(DRGA)is proposed to solve this problem by decoupling the original system to several multi-input single-output(MISO)subsystems.We choose the dominant inputs and ignore the weak interactions.Then we reduce the subsystems by Krylov subspace method.The DRGA method is based on the state feedback predictive control,and both the steady state information and the dynamic information are considered in the process of loop pairing.Therefore,more accurate reduced systems can be obtained by this method compared to the method based on traditional relative gain array(RGA).Experimental results on RLC networks show that the proposed DRGA based MOR method has higher accuracy compared with the passive reduced-order interconnect macromodeling(PRIMA)method,the decentralized model order reduction(De MOR)method,and the balance truncation reduction(BTR)method.On the other hand,the traditional Arnoldi process cannot guarantee the passivity of the reduced systems.The passivity-preserving MOR method based on Caratheodory-Toeplitz interpolation process is proposed in this paper.In this method,we construct Toeplitz matrix using the moments of the original system,and transfer the Toeplitz matrix to Pick matrix.Then we obtain a series of interpolation points from the Pick matrix,and construct the projection matrices with these interpolation points.Finally passive reduction can be easily achieved using existing Arnoldi-based reduction method.The MOR method based on Caratheodory-Toeplitz interpolation process can lead to models capable of preserving stability and passivity.The proposed method is suitable for reduction of passive circuit models such as on-chip power grids.The advantage of the proposed method is demonstrated by comparisons with the existing MOR approaches.