Rodolfo E. Diaz

Design methodology for Sievenpiper high-impedance surfaces: an artificial magnetic conductor for positive gain electrically small antennas

The Sievenpiper high-impedance surface is a periodic structure characterized by a substrate filled with an array of vertical vias, capped by a capacitive frequency selective surface (FSS). It functions as the ideal antenna groundplane for wireless applications because it simultaneously enhances the gain of the antenna as it suppresses the surface waves associated with it (thus reducing the undesired back-lobe and the reactive coupling to nearby circuits). These two properties are known to occur approximately over the frequency bandwidth where the phase of the reflection coefficient of the surface changes from +90/spl deg/ to -90/spl deg/. Since this behavior takes place at frequencies where the unit cell of the structure is small compared to the wavelength, it can be modeled in terms of a layered homogeneous material where each layer has an anisotropic magneto-dielectric tensor. These tensors, readily derived using an effective medium model, can be designed to obtain independent control of the bandwidths of gain increase and surface wave suppression. Based on a transverse resonance model of the effective medium material model, it is shown that Sievenpiper high-impedance surfaces exist that can suppress TE surface waves alone or TM surface waves alone, or both TE and TM surface waves at the same time. Maximum TM surface wave suppression bandwidth is obtained when the distance between the vias in the via array is as close as possible to /spl lambda//2. Maximum TE bandwidth is obtained when the conductors of the capacitive FSS offer maximum blockage to the normal magnetic field of the wave. A reduction of the transverse resonance solution to nearly closed form is used to obtain a simple picture of the design space available when the desired operating frequency is fixed.

Effective medium theories for artificial materials composed of multiple sizes of spherical inclusions in a host continuum

This paper presents the application of nonempirical effective medium theories to describe composite mixtures of spherical inclusions within a host continuum. It is shown that the most common effective medium theories collapse into Bruggemans (1935) asymmetric formula when they are implemented in an iterative scheme to extend their validity to higher volume fractions. Comparisons of DC and 4-GHz data show that of all the formulas Bruggemans asymmetric formula corresponds best with experiment for large differences between the complex permittivities of the host and inclusion materials. Permeability values are also formulated and compared with experiment and a simple scheme is considered to extend the effective medium theories herein to a description of the diamagnetic effect of induced current in metal spherical inclusions.

An analytic continuation method for the analysis and design of dispersive materials

All materials, by nature, possess a frequency-dependent permittivity. This dispersion can be expressed in the form of the Kramers-Kronig relations by invoking the analytic consequences of causality in the upper half of the complex frequency plane. However, the Hilbert transform pair character of these relations makes them useful only when half of the answer is already known. In order to derive a more general form useful for both synthesis and analysis of arbitrary materials, it is necessary to analytically continue the permittivity function into the lower half plane. Requiring that the dielectric polarization be expressible in terms of equations of motion, in addition to obeying causality, conservation of energy and the second law of thermodynamics is sufficient to obtain the desired expression as a sum of special complex functions. In the appropriate limits, this sum reduces to the Debye relaxation and Lorentz resonance models of dielectrics, but it also contains phenomena not expressible in terms of those classical models. In particular, the classic problem of the existence of optical transparency in water is resolved.

A Compact and Low-Cost MEMS Loudspeaker for Digital Hearing Aids

A microelectromechanical-systems (MEMS)-based electromagnetically actuated loudspeaker to reduce form factor, cost, and power consumption, and increase energy efficiency in hearing-aid applications is presented. The MEMS loudspeaker has multilayer copper coils, an NiFe soft magnet on a thin polyimide diaphragm, and an NdFeB permanent magnet on the perimeter. The coil impedance is measured at 1.5 Omega, and the resonant frequency of the diaphragm is located far from the audio frequency range. The device is driven by a power-scalable, 0.25-mum complementary metal-oxide semiconductor class-D SigmaDelta amplifier stage. The class-D amplifier is formed by a differential H-bridge driven by a single bit, pulse-density-modulated SigmaDelta bitstream at a 1.2-MHz clock rate. The fabricated MEMS loudspeaker generates more than 0.8-mum displacement, equivalent to 106-dB sound pressure level (SPL), with 0.13-mW power consumption. Driven by the SigmaDelta class-D amplifier, the MEMS loudspeaker achieves measured 65-dB total harmonic distortion (THD) with a measurement uncertainty of less than 10%. Energy-efficient and cost-effective advanced hearing aids would benefit from further miniaturization via MEMS technology. The results from this study appear very promising for developing a compact, mass-producible, low-power loudspeaker with sufficient sound generation for hearing-aid applications.

Analytic framework for the modeling of effective media

Synthetic materials in which new electromagnetic properties are obtained from the combination of two or more materials have been of theoretical and practical interest for nearly a century. The ability to explain and predict the properties of these materials has traditionally relied on combining physicomathematical models of the effective environment seen by the various constituents of the mixture with some assumptions about the way these microscopic properties should translate into macroscopic homogeneous parameters. Thus, even in the simplest case of the binary mixture, with every new set of assumptions, a new effective medium theory (EMT) results, and, with each new theory, stronger claims of correctness and applicability are made. This issue of correctness becomes critical when the properties of one of the constituents is unknown a priori and the claim is made that by inverting a fit of experimental results to the EMT model those properties can be ascertained. For this inverse procedure to be possible,...

TM mode analysis of a Sievenpiper high-impedance reactive surface

Builds on the published work of King and Park [see IEEE Trans. Ant. Propag., vol AP-31, p. 471-6, 1983] in which they analyze TM modes on a Fakirs grounded bed-of-nails structure. Sievenpipers reactive surface is essentially a Fakirs structure with the addition of a capacitive FSS loading the ends of the rods. In this analysis, we show that an infinite number of TM modes can exist on this structure, and that the apparent TM mode cutoff, experimentally observed, is a manifestation of the two lowest order modes coalescing, and then being cut off. Furthermore, we show that this apparent TM mode cutoff can be adjusted independent of the +90/spl deg/ reflection phase frequency by controlling the density and diameter of the rods.

The effect of the 2-D Laplacian operator approximation on the performance of finite-difference time-domain schemes for Maxwell's equations

The behavior of the finite-difference time-domain method (FDTD) is investigated with respect to the approximation of the two-dimensional Laplacian, associated with the curl-curl operator. Our analysis begins from the observation that in a two-dimensional space the Yee algorithm approximates the Laplacian operator via a strongly anisotropic 5-point approximation. It is demonstrated that with the aid of a transversely extended-curl operator any 9-point Laplacian can be mapped onto FDTD update equations. Our analysis shows that the mapping of an isotropic Laplacian approximation results in an isotropic and less dispersive FDTD scheme. The properties of the extended curl are further explored and it is proved that a unity Courant number can be achieved without the resulting scheme suffering from grid decoupling. Additionally, the case of a 25-point isotropic Laplacian is examined and it is shown that the corresponding scheme is fourth order accurate in space and exhibits isotropy up to sixth order. Representative numerical simulations are performed that validate the theoretically derived results.

The Gilbert-Holland FDTD thin slot model revisited: an alternative expression for the in-cell capacitance

This paper proposes an alternative expression for the in-cell capacitance of a photoelectrical cell (PEC)-mounted slot, which is the conceptual cornerstone of the Gilbert-Holland subcell finite difference time domain (FDTD) model. By treating a slightly modified electrostatic problem, the extraneous charge singularity on the PEC edges touching the cell, which is characteristic of the originally proposed model, is removed. The latter offers better physical grounds for a new expression of the capacitance and the effective permittivity used in the update equations. High resolution standard FDTD simulation results are presented in support of the new expression.

A time-domain vector potential formulation for the solution of electromagnetic problems

Several techniques have been proposed for the solution of Maxwells equations, such as FDTD, which rely on discretization of Maxwells equations in time. These techniques are attractive because of their simplicity but are limited to dealing with structures with low dispersion characteristics. Other techniques such as condensed TLM offer superior characteristics in terms of dispersion but are more demanding in terms of computer resources. Attempts to use the vector potential formulation by discretization of the vector potential wave equation have also been made in the past. Although the scheme is attractive because of some of the advantages of the TLM technique, they have the shortcoming of the difficulties in implementing metal boundaries. In this paper a new technique for the solution of scattering problems based on discretization of Maxwells equations in vector potential form (VP) is presented. This new technique maintains the advantage of condensed node representation as in the vector potential formulation, but offers an easy way to treat metal boundaries.

Examination, Clarification, and Simplification of Stability and Dispersion Analysis for ADI-FDTD and CNSS-FDTD Schemes

We describe a rigorous analysis of unconditional stability for the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) and Crank-Nicholson split step (CNSS-FDTD) schemes avoiding use of the von Neumann spectral criterion. The proof is performed in the spectral domain, and uses skew-Hermitivity of matrix terms in the ADI and CNSS total amplification matrices. A bound for the total ADI amplification matrix is provided. While the CN and CNSS-FDTD amplification matrices are unitary, the bound on the ADI-FDTD depends on the Courant number. Importantly, we have found that the ADI-FDTD amplification matrix is not normal, i.e., the unit spectral radius alone cannot be used to prove the ADI-FDTD unconditional stability. The paper also shows that the ADI-FDTD and CNSS-FDTD schemes share the same dispersion equation by a similarity of their total amplification matrices, and the two schemes have identical numerical dispersion in the frame of plane waves.