Analytic Extension of Eigenvalues for Fast Frequency Sweep Analysis of RF Circuits

Highly efficient and accurate simulation of RF circuits is crucial for the design and optimization of novel devices in electronic gadgets and wireless communications. However, it is time-consuming to perform full-wave analysis using numerical methods such as the finite element method (FEM) and the moment method (MoM) over a broad frequency band because a large numerical system must be solved repeatedly at many frequencies. Therefore, fast frequency sweep techniques are needed to reduce computational costs and expedite the design process. In this paper, we present a fast analytic extension of eigenvalues (AEE) method to predict frequency responses of passive RF circuits over a wide frequency band with a sufficient accuracy. From full-wave solutions at only a few frequencies, the responses can be quickly computed within the entire frequency range of interest at a very low cost. Compared with existing mathematically based model order reduction (MOR) techniques which must be implemented in a specific numerical method, the proposed AEE can be incorporated with any full-wave solvers and readily adopted by designers using commercial software. Besides, the AEE generates equivalent circuits that provide direct physical insights for circuit designers. In this approach, the impedance- (Z-) parameters of a circuit are first extracted from full-wave solutions at a few sampling frequencies and then decomposed into eigenmodes by solving a standard eigenvalue problem. Lumped equivalent circuits are constructed to analytically extend the eigenvalues from the sampling frequencies to all other frequencies. Through numerical investigation, eigenvalues can be categorized into two types, either capacitively or inductively dominant at low frequencies, whose behaviors are mimicked by series or parallel LC topologies. As frequency increases, resonance or anti-resonance occurs and higher-order circuit models are required by connecting more LC blocks. Various loss models are also included to take into account frequency-dependent losses due to radiation, imperfect dielectrics, and conductor skin effect. In this work, the half-, first- and second-order circuit models are employed to approximate frequency variations of the eigenvalues requiring computation at only one, two, and four frequencies, respectively. An eigenvalue-eigenvector identity is utilized to calculate the frequency-dependent eigenvectors from eigenvalues of the submatrices. By eigen expansion, the Z-parameters and thus the responses of the circuit can finally be obtained. Numerical examples validate the accuracy by comparing the results with full-wave solutions. It is found that the first-order AEE is very accurate for RF circuits with their electrical sizes smaller than a half wavelength and the validity range for the second-order AEE reaches up to one wavelength. For larger circuits or higher frequencies, one can divide the whole circuit into several segments, apply AEE to each segment, and then cascade the parameters to obtain the characteristics of the entire circuit. With the proposed method, significant speedups can be achieved, which are demonstrated through many examples including highly complicated realistic RF filters.