A Galerkin analysis of microstrip circuits of arbitrary plauar geomehy enclosed in a rectangular conducting box is described. The technique entails a time-harmonic electromagnetic analysis evaluating all fields and surface currents. This analysis is suitable for the accurate verification of microstrip designs prior to fabrication. A computer program implementing the analysis has been written in Pascaf on a persomd compnter. Agreement with measurements of severaf microstrip strnctores suggests a high degree of accuracy.

This paper describes and rigorously validates single-and multiple-layer models of microstrip conductor loss appropriate for high-accuracy application in electromagnetic analysis software. The models are validated by comparison with measurement and by comparison with converged results. It is shown that in some cases an extremely small cell size is needed in order to achieve convergence. Several effects that make a significant contribution to loss and are not modeled by the classic square root of frequency loss model are investigated including dispersion and current on the side of transmission lines. Finally, the counterintuitive result that there is an optimum metal thickness for minimum planar conductor loss is explored.

A “double delay” de‐embedding algorithm appropriate for electromagnetic analyses is described. This algorithm uses only two standards, a through and a double length through. By evaluating these standards, a special class of port discontinuities may be characterized and removed from the data calculated for a complete structure. Unlike related physical de‐embedding algorithms, both the characteristic impedance and the velocity of propagation of the through lines are determined. The technique described here is difficult to implement in a physical de‐embedding. The de‐embedding theory also provides a new definition of characteristic impedance, “equivalent TEM impedance,” for inhomogeneous media, such as microstrip. This new impedance exhibits a nonmonotonic dispersion which has been measured experimentally but is not seen using previous impedance definitions.

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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.