Brian J. Rautio

Shielded Dual-Mode Microstrip Resonator Measurement of Uniaxial Anisotropy

An improved technique to measure uniaxial anisotropy in planar substrates is described. This technique builds on previous work performed with stripline. The improved approach offers substantially larger bandwidth, lower error, and ease of measurement. An almost complete automation of the entire calibration and measurement extraction process is described. It is also demonstrated that the horizontal (parallel to substrate surface) dielectric constant is less than the vertical dielectric constant for glass fiber weave reinforced substrates for the purposes of microstrip and stripline design. This directly conflicts with bulk measurements of dielectric constant and is believed due to microstrip horizontal electric field concentrating in the substrate surface. This is supported by measurements of a homogeneously ceramic loaded substrate showing the expected relationship. Effects of electromagnetic analysis accuracy, metal roughness, metal thickness, and edge profile (due to etching) are found to be important.

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

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 Greens 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 O(NlogN) and O(N), respectively, where N 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.

High accuracy broadband measurement of anisotropic dielectric constant using a shielded planar dual mode resonator

We investigate a proposed shielded dual mode planar “RA” resonator used for measuring the uniaxial anisotropic dielectric constants of planar substrates. Prior microstrip RA resonators have been unshielded, which introduces error due to radiation, especially for thick substrates. A detailed error evaluation is performed and presented. The resonator is long, allowing evaluation of nearly 100 resonances. Each pair of resonances of the dual mode resonator is evaluated to determine two substrate dielectric constants, one for horizontal (parallel to the substrate surface) electric field and the other for vertical electric field. Broad band anisotropic dielectric constants extracted from resonator measurements from 0.2 to 10 GHz are presented.

Synthesis of Perfectly Causal Parameterized Compact Models for Planar Transmission Lines

Per-unit-length series impedance and shunt admittance are extracted from electromagnetic analysis of a transmission line at a few discrete frequencies. Compact models are synthesized from the per-unit-length extraction. The lumped models are then used to rapidly calculate characteristic impedance, effective dielectric constant, and RLGC parameters at all frequencies, including dispersion and loss. The resulting models are perfectly physically (i.e., speed of light) causal, a critical consideration for time-domain analysis. To demonstrate feasibility, the models are parameterized as a function of transmission linewidth. Total error is carefully quantified and is typically less than 1%. The process is demonstrated for several planar transmission lines. New concepts, ¿modal¿ and ¿environmental¿ sensitivity, are introduced and quantified.

The Unified-FFT Grid Totalizing Algorithm for Fast O(N logN) Method of Moments Electromagnetic Analysis with Accuracy to Machine Precision

(Invited Paper) Abstract—While considerable progress has been made in the realm of speed-enhanced electromagnetic (EM) solvers, these fast solvers generally achieve their results through methods that introduce additional error components by way of geometric type approximations, sparse-matrix type approximations, multilevel type decomposition of interactions, and assumptions regarding the stochastic nature of EM problems. This work introduces the O(N log N ) Unified-FFT grid totalizing (UFFT-GT) method, a derivative of method of moments (MoM), which achieves fast analysis with minimal to zero reduction in accuracy relative to direct MoM solution. The method uniquely combines FFT-enhanced Matrix Fill Operations (MFO) that are calculated to machine precision with FFT-enhanced Matrix Solve Operations (MSO) that are also calculated to machine precision, for an expedient solution that does not compromise accuracy.

Fast 3D planar electromagnetic analysis via Unified-FFT method

Microwave and mm-wave circuits today are larger, faster, and more integrated than ever. This trend continually increases the requirements and applications of electromagnetic simulation. To satisfy this demand, a Unified-FFT method is developed, implemented, and tested, with promising results. The Unified-FFT method combines the fast Matrix Solve Operations (MSO) of the FFT-enhanced Pre-Corrected FFT (PFFT) method with the fast Matrix Fill Operations (MFO) of the FFT-enhanced Sonnet V13. Together, these operations allow for high-accuracy simulation with reduced size constraints, and overall speed improved by more than an order of magnitude.

Simulation geometry rasterization for applications toward graphene interconnect characterization

In this work, we present a novel methodology for geometric rasterization of arbitrary 3D planar geometries, and apply it to perform electromagnetic simulation based calibration for accurate high-frequency measurements of Graphene conductivity. The conductivity measurements may find application in the area of high-frequency Graphene-based circuits, specifically that of interconnects. Preliminary experimental and simulation results are shown and discussed.

Broadband analysis and characterization of anisotropic dielectric temperature dependence

A broadband methodology for measurement of uniaxial dielectric anisotropy is described. Previous work is improved with reduced measurement error, enhanced automation, and additional material testing. Additionally, permittivity variation with temperature is explored.

GPU performance estimation of various matrix solve operations for application to 3D planar MoM

A method for estimating the suitability of GPUs for computational algorithms is presented. The method is used to estimate performance for several matrix solutions for planar method of moments simulation.

Novel high precision UFFT methodology for fast analysis of 3D Planar circuits embedded in shielded layered media

Unified-FFT (UFFT) is a novel 3D-Planar Method of Moments (MoM) solver of the Electric Field Integral Equation (EFIE). UFFT is the resultant algorithm of combining the FFT-enhanced Matrix Solve Operations (MSO) currently utilized in Sonnet Suites with FFT-enhanced Matrix Fill Operations (MFO). It has been shown, in conjunction with iterative MSO based on GMRES, to solve matrix vector products scaling with O(NlogN) operations and O(N) memory for planar, single-plane geometries (B. J. Rautio, V. I. Okhmatovski, J.K. Lee, IMS 2013). Previous UFFT implementations have achieved O(NlogN) scaling through acceleration of iterative matrix-vector products within GMRES by separating near and far interactions and calculating far interactions implicitly as in PFFT. In this work, the same uniform grid used with MFO is extended for use with MSO, negating the need to treat near and far interactions independently and allowing the entire matrix to be stored implicitly with no significant loss of precision. The resulting algorithm, UFFT-Grid Totalizing (UFFT-GT), achieves O(NlogN) operations and O(N) memory scaling with minimal loss in precision vs. full matrix inverse beyond numerical noise.