The Unified-FFT Algorithm for Fast Electromagnetic Analysis of Planar Integrated Circuits Printed on Layered Media Inside a Rectangular Enclosure

Abstract

The unified fast Fourier transform (UFFT) methodology is proposed for fast method of moments analysis of dense integrated circuits embedded in layered media inside perfectly electric conducting or perfectly magnetic conducting enclosures of rectangular cross section. The pre-corrected fast Fourier transform (FFT) method is modified to handle the dyadic Green's function (DGF) of shielded layered media through factorization of the DGF into four convolution/correlation terms enabling fast matrix solve operations (MSOs). Calculation of the impedance matrix elements in the form of an infinite series of waveguide modes is cast into the form of a 2-D discrete Fourier transform allowing for fast FFT-accelerated matrix fill operations (MFOs). Fast FFT-enhanced MSOs and MFOs used in conjunction form the UFFT method. The computational complexity and memory requirements for the proposed UFFT solver scale as and , respectively, where is the number of unknowns in the discrete approximation of the governing integral equation. New criteria specific to shielded circuits for the projection of the current expansion functions on a uniform FFT grid are developed. The accuracy and efficiency of the solver is demonstrated through its application to multiple examples of full-wave analysis of large planar circuits. Index Terms-Computer-aided design (CAD), CAD algorithms and techniques, fast algorithms, numerical analysis, RF integrated circuit (RFIC) modeling.

THE UNIFED-FFT GRID TOTALIZING ALGORITHM FOR FAST O(N LOG N) METHOD OF MOMENTS ELECTROMAGNETIC ANALYSIS WITH ACCURACY TO MACHINE PRECISION (Invited Paper)

“…In addition to those in [5], there is further noteworthy work. FFTs have been used to increase parallelization of MLFMA with the MLFMA-FFT method [11], and a similar application to GPU clusters [12].…”

“…A brief review of relevant and/or similar work can be found in [5]. In addition to those in [5], there is further noteworthy work.…”

“…The method is capable of providing the O(N log N ) MoM solution which is accurate to machine precision with respect to the traditional O(N 3 ) MoM solver, Sonnet [3], with its associated demonstrably high accuracy [4]. The latter takes advantage of the rectangular waveguide Green's function allowing for an efficient way of computing the impedance matrix elements with machine precision [5]. The novelty of the proposed algorithm is in generalization of the previously known CG-FFT methodology [6][7][8] to the structures situated in a rectangular enclosure, which is further combined with an FFT-enhanced MFO accurate to machine precision for the circuit discretization.…”

“…The MoM interactions are decomposed into four 2D convolution/correlation terms accounting for the walls of the rectangular enclosure and allowing for the use of FFT for their O(N log N ) evaluation. Analogous formulations have been previously developed only for the FFT-based fast algorithms involving pre-corrections [5,9]. Such formulations introduce additional error compared to the direct MoM solution making accurate resolution of weak but important interactions inaccurate.…”

“…Such formulations introduce additional error compared to the direct MoM solution making accurate resolution of weak but important interactions inaccurate. Unlike the prior pre-correction based algorithms, including the original version of the UFFT [5] henceforth referred to as UFFT-Precorrected (UFFT-P), the proposed method makes further improvement by eliminating the need for pre-correction due to MoM discretization on the uniform grid. Thus, no additional approximations versus the direct MoM solution (i.e., Sonnet, from which accuracy is only significantly limited by meshing) are made to the circuit geometry or to the dense system of equations solution.…”