Vikram Jandhyala

Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory

This paper presents a method of calculating the elements of the generalized matrix representation of the macroscopic constitutive relations for a three-dimensional (3-D) array of non-magnetic inclusions with arbitrary shape. The derivation is based on the quasi-static Lorentz theory and the inclusions are represented by electric and magnetic dipole moments. The 6/spl times/6 constitutive relation matrix is expressed in terms of the interaction matrix and the polarizability matrix, which can be numerically calculated using the sum and the difference of opposing plane wave excitations. Numerical examples are given for split ring resonators and a chiral medium consisting of an array of helices to illustrate the usefulness of the formula and to verify the consistency constraint and reciprocity relations for a bianisotropic medium.

A combined steepest descent-fast multipole algorithm for the fast analysis of three-dimensional scattering by rough surfaces

The scattering of electromagnetic waves by random rough surfaces is a subject of great practical and intellectual interest. Applications include, but are not limited to, remote sensing, long-range communications, radio astronomy, medicine, and surface physics. Random surfaces also exhibit several interesting scattering and polarization characteristics, such as backscattering enhancement and the generation of localized modes. A host of numerical techniques exist for analyzing rough surfaces. However, it is only recently that the fast algorithms have been developed, enabling analysis of larger surfaces. An efficient algorithm of O(N) computational complexity is presented.

Analysis of a large number of vias and differential signaling in multilayered structures

A method is presented for full-wave modeling of vertical vias in multilayered circuits. The analysis of the interior problem is based upon the cylindrical wave expansion of the magnetic field Greens function. The multiple interaction among vertical vias is modeled by the Foldy-Lax scattering formula. Multilayered effects are included by using cascaded network of the single-layer components. The exterior problem of the via and the transmission line is analyzed using the method of moments approach. The exterior and interior problems are combined into a system of equations to facilitate the solution of a large number of vias. Using this approach, the scattering matrix of problems of several thousand vias can be calculated with moderate CPU and memory requirement. Numerical results have been obtained for different via configurations and for a large range of frequency. Also illustrated are results for common and differential mode in differential signaling with surrounding idle and shorting vias.

RFID: From Supply Chains to Sensor Nets

The next generation internet will be the internet of things (and not just of computing devices like PCs, PDAs); this is presumed to be enabled by integrating simple computing plus communications capabilities into common objects of everyday use. Radio-frequency identification (RFID) is a compelling technology for creation of such pervasive sensor networks due to its potential for ubiquitous, low-cost/low-maintenance use. However, the current drivers for RFID deployment emphasize supply chain management using passive tags, implying that RFID sensor nets require advances beyond the components and system designs aimed at supply chain applications. This work provides a glimpse of how this may be achieved.

Fast algorithm for the analysis of scattering by dielectric rough surfaces

A novel multilevel algorithm to analyze scattering from dielectric random rough surfaces is presented. This technique, termed the steepest-descent fast-multipole method, exploits the quasi-planar nature of dielectric rough surfaces to expedite the iterative solution of the pertinent integral equation. A combination of the fast-multipole method and Sommerfeld steepest-descent-path integral representations is used to efficiently compute electric and magnetic fields that are due to source distributions residing on the rough surface. The CPU time and memory requirements of the technique scale linearly with problem size, thereby permitting the rapid analysis of scattering by large dielectric surfaces and permitting Monte Carlo simulations with realistic computing resources. Numerical results are presented to demonstrate the efficacy of the steepest-decent fast-multipole method.

Efficient solution of EFIE via low-rank compression of multilevel predetermined interactions

This paper describes the predetermined interaction list oct-tree (PILOT) algorithm and its application in expediting the solution of full-wave electric field integral equation (EFIE)-based scattering problems for three-dimensional arbitrarily shaped conductors. PILOT combines features of the fast multipole method (FMM) and QR decomposition-based matrix compression techniques to optimize setup times, solve times, and memory requirements. The method is kernel independent and stable for electrically small structures unlike traditional FMM. The novel features of the algorithm, namely the mixed potential compression scheme and the hierarchical multilevel predetermined matrix structure are explained in detail. A complexity estimate is presented to demonstrate the scaling in time and memory requirements. Examples exhibiting the accuracy and the time and memory performances are also presented. Finally, a quantitative study is included to address the expected but gradual degradation of QR-based compression techniques for electrically large structures.

Solving Low-Frequency EM-CKT Problems Using the PEEC Method

The partial element equivalent circuit (PEEC) formulation is an integral equation based approach for the solution of combined electromagnetic and circuit (EM-CKT) problems. In this paper, the low-frequency behavior of the PEEC matrix is investigated. Traditional EM solution methods, like the method of moments, suffer from singularity of the system matrix due to the decoupling of the charge and currents at low frequencies. Remedial techniques for this problem, like loop-star decomposition, require detection of loops and therefore present a complicated problem with nonlinear time scaling for practical geometries with holes and handles. Furthermore, for an adaptive mesh of an electrically large structure, the low-frequency problem may still occur at certain finely meshed regions. A widespread application of loop-star basis functions for the entire mesh is counterproductive to the matrix conditioning. Therefore, it is necessary to preidentify regions of low-frequency ill conditioning, which in itself represents a complex problem. In contrast, the charge and current basis functions are separated in the PEEC formulation and the system matrix is formulated accordingly. The incorporation of the resistive loss (R) for conductors and dielectric loss (G) for the surrounding medium leads to better system matrix conditioning throughout the entire frequency spectrum, and it also leads to a clean dc solution. We demonstrate that the system matrix is well behaved from a full-wave solution at high frequencies to a pure resistive circuit solution at dc, thereby enabling dc-to-daylight simulations. Finally, these techniques are applied to remedy the low-frequency conditioning of the electric field integral equation matrix

Design of Retrodirective Antenna Arrays for Short-Range Wireless Power Transmission

Application of retrodirective antenna arrays in wireless power transmission is proposed in this paper. The time reversal or phase conjugate theory and design considerations of the array factors are examined in GHz regime and meter range. The wireless power transmission efficiency is analyzed in the 2-D case with full-wave electromagnetic (EM) solution and validated by analytical array theory. The design factors of array size, array spacing, element size, and specific choice of the industrial, scientific and medical (ISM) band frequency are investigated to optimize the transmission focus. Design guidelines are provided for those factors and the impact of manufacturing variability is discussed. The proposed approach can also be extended to wireless power transfer with active retrodirective rectenna array and passive RFID systems.

Solving low frequency EM-CKT problems using the PEEC method

The partial element equivalent circuit (PEEC) formulation is an integral equation based approach for the solution of combined electromagnetic and circuit (EM-CKT) problems. Traditional EM solvers like the electric field integral equation (EFIE) method suffer from numerical problems at low-frequencies arising from the decoupling of the charge and current basis functions. In this paper, the low frequency behavior of the PEEC matrix is investigated. Techniques leading to an excellent condition number throughout the entire frequency spectrum are discussed. Finally, these schemes are applied to remedy the low-frequency conditioning of the EFIE method.

(S)PEEC: Time- and frequency-domain surface formulation for modeling conductors and dielectrics in combined circuit electromagnetic simulations

The partial element equivalent circuit (PEEC) formulation is an integral-equation-based approach for the solution of combined circuit and electromagnetic (EM) problems. In this paper, a surface-based PEEC formulation is presented to complement the existing volume-based method. With the rise in the operating frequencies and the increasing complexity of test structures on boards, packages, and chips, a surface-based formulation is more efficient for many problems in terms of the number of unknowns generated. The composite conductor dielectric modeling is based on the PMCHWT formulation which is transformed into a PEEC representation using equivalent magnetic and electric circuits connected by mutual coupling. Both time- and frequency-domain analyses are discussed, similar to a Spice-type circuit solver. The new formulation is compared with the volume-based PEEC approach in terms of accuracy and the number of unknowns generated