TL;DR: In this paper, the theoretical modeling and practical design of millimeter wave reflectarrays using microstrip patch elements of variable size is discussed and a full-wave treatment of plane wave reflection from a uniform infinite array of microstrip patches is described and used to generate the required patch-design data and to calculate the radiation patterns of the reflectarray.
Abstract: This paper discusses the theoretical modeling and practical design of millimeter wave reflectarrays using microstrip patch elements of variable size. A full-wave treatment of plane wave reflection from a uniform infinite array of microstrip patches is described and used to generate the required patch-design data and to calculate the radiation patterns of the reflectarray. The critical parameters of millimeter wave reflectarray design, such as aperture efficiency, phase errors, losses, and bandwidth are also discussed. Several reflectarray feeding techniques are described, and measurements from four reflectarray design examples at 28 and 77 GHz are presented.
TL;DR: In this paper, the resonant frequencies and radiation Q-factors of the lowest order "magnetic-dipole" modes are derived on the basis of a first-order theory.
Abstract: Theoretical and experimental investigations on rectangular dielectric resonator antennas having a value of /spl epsiv//sub r/, in the range of 10 to 100 are reported. The resonant frequencies and radiation Q-factors of the lowest order "magnetic-dipole" modes are derived on the basis of a first-order theory. The accuracy of the model in predicting the resonant frequency and radiation Q-factor is verified by comparison with results of a rigorous theory and experiments. Various feeds for the antennas such as probe, microstrip slot, and microstrip line are described. Measured radiation patterns are shown and the effect of feed and mode degeneracy on the cross-polarisation levels is discussed.
TL;DR: In this paper, the results of a comprehensive investigation into the characteristics and optimization of inductors fabricated with the top-level metal of a submicron silicon VLSI process are presented.
Abstract: The results of a comprehensive investigation into the characteristics and optimization of inductors fabricated with the top-level metal of a submicron silicon VLSI process are presented. A computer program which extracts a physics-based model of microstrip components that is suitable for circuit (SPICE) simulation has been used to evaluate the effect of variations in metallization, layout geometry, and substrate parameters upon monolithic inductor performance. Three-dimensional (3-D) numerical simulations and experimental measurements of inductors were also used to benchmark the model accuracy. It is shown in this work that low inductor Q is primarily due to the restrictions imposed by the thin interconnect metallization available in most very large scale integration (VLSI) technologies, and that computer optimization of the inductor layout can be used to achieve a 50% improvement in component Q-factor over unoptimized designs.
TL;DR: Lee et al. as discussed by the authors used the Finite Difference Time Domain (FDTD) method to construct a probe-fed multilayer microstrip antenna. But their work focused on the design of the antenna.
Abstract: Probe-Fed Microstrip Antennas (K. Lee, et al.). Aperture-Coupled Multilayer Microstrip Antennas (K. Luk, et al.). Microstrip Arrays: Analysis, Design, and Applications (J. Huang & D. Pozar). Dual and Circularly Polarized Microstrip Antennas (P. Hall & J. Dahele). Computer-Aided Design of Rectangular Microstrip Antennas (D. Jackson, et al.). Multifunction Printed Antennas (J. James & G. Andrasic). Superconducting Microstrip Antennas (J. Williams, et al.). Active Microstrip Antennas (J. Navarro & K. Chang). Tapered Slot Antenna (R. Lee & R. Simons). Efficient Modeling of Microstrip Antennas Using the Finite-Difference Time-Domain Method (S. Chebolu, et al.). Analysis of Dielectric Resonator Antennas (K. Luk, et al.). References. Index.
TL;DR: In this paper, the U-slot patch on a foam substrate of about 0.08/spl lambda/thick was designed to attain 20-30% impedance as well as gain bandwidth.
Abstract: Experimental and simulation results are presented on the coaxially fed rectangular patch antenna with a U-shaped slot. Experimental results include impedance bandwidth, copolar- and crosspolar-pattern characteristics and gain measurements. Simulation results are obtained mainly through the development of a FDTD code. It is found that the U-slot patch on a foam substrate of about 0.08/spl lambda/ thick can be designed to attain 20-30% impedance as well as gain bandwidths without the need of parasitic patches on another layer or on the same layer. The far-field patterns have good copolar and crosspolar characteristics. By altering the patch width or feed position, the wideband characteristic can be changed into a dual-frequency characteristic. Simulation results are in good agreement with measurements.
TL;DR: In this article, the theory and experiment of a new class of microstrip slow-wave open-loop resonator filters is presented, and two filter designs of this type are described in detail.
Abstract: This paper presents the theory and experiment of a new class of microstrip slow-wave open-loop resonator filters. A comprehensive treatment of capacitively loaded transmission line resonator is described, which leads to the invention of microstrip slow-wave open-loop resonator. The utilization of microstrip slow-wave open-loop resonators allows various filter configurations including those of elliptic or quasi-elliptic function response to be realized. The filters are not only compact size due to the slow-wave effect, but also have a wider upper stopband resulting from the dispersion effect. These attractive features make the microstrip slow-wave open-loop resonator filters promising for mobile communications, superconducting and other applications. Two filter designs of this type are described in detail. The experimental results are demonstrated and discussed.
TL;DR: In this article, a microstrip RF telemetry antenna is formed on or within the exterior surface of an implantable medical device housing that is formed either of a conductive metal or of a non-conductive dielectric material.
Abstract: A microstrip RF telemetry antenna is formed on or within the exterior surface of an implantable medical device housing that is formed either of a conductive metal or of a non-conductive dielectric material The microstrip antenna is formed of an electrically conductive radiator patch layer that is laminated upon an exterior facing side of a dielectric substrate layer of relatively constant thickness A conductive ground plane layer is formed on the opposite side of the dielectric substrate layer to extend parallel to and at least coextensively with the radiator patch layer The radiator patch layer is coupled to the transceiver circuitry within the implantable medical device housing by a feedthrough extending through the dielectric substrate layer, the ground plane layer and the implantable medical device housing side wall If the implantable medical device housing is conductive it may form the ground plane layer over which the dielectric substrate layer and the radiator patch layer are formed through deposition or other techniques If the implantable medical device housing is formed of a suitable non-conductive dielectric material, the ground plane layer is formed on an interior surface thereof and the radiator patch layer is formed on an exterior housing surface thereof, preferably by deposition techniques The ground plane layer may be recessed to form a cavity backed ground plane that receives the dielectric layer and radiator patch layer within the cavity The exterior surfaces of the radiator patch layer, the dielectric layer and any exposed surface of the ground plane layer may be electrically insulated by a radome layer
TL;DR: In this paper, a microstrip antenna on a micromachined 635-/spl mu/m thick substrate was used to synthesize a localized low dielectric-constant environment.
Abstract: Micromachining techniques using closely spaced holes have been used underneath a microstrip antenna on a high dielectric-constant substrate (/spl epsiv//sub r/=10.8) to synthesize a localized low dielectric-constant environment (/spl epsiv//sub r/=2.3). The measured radiation efficiency of a microstrip antenna on a micromachined 635-/spl mu/m thick /spl epsiv//sub r/=10.8 Duroid 6010 substrate increased from 48/spl plusmn/3% to 73/spl plusmn/3% at 12.8-13.0 GHz (including 3.3-cm feed line losses). We believe that this technique can be applied to millimeter-wave antennas (microstrip, dipoles, slots, etc.) on silicon and GaAs substrates to result in relatively wideband (3-6%) monolithic microwave integrated circuits (MMIC) active antenna modules for phased-arrays and collision-avoidance systems.
TL;DR: In this article, a triangular microstrip antenna with dual-frequency operation is presented, where the microstrip patch is shortcircuited using a shorting pin and fed by a single probe feed.
Abstract: This paper presents a novel design of triangular microstrip antenna with dual-frequency operation. In this design the microstrip patch is short-circuited using a shorting pin and fed by a single probe feed. By varying the shorting pin position in the microstrip patch, such a design can provide a large tunable frequency ratio of about 2.5-4.9 for the two operating frequencies. Experimental results for operating at frequencies of 464 and 2276 MHz are presented and discussed.
TL;DR: In this article, a novel uniplanar transition between microstrip lines and coplanar strips (CPS) was investigated in a velocity-matched distributed photodetector (VMDP).
Abstract: We report our recent investigation of a novel uniplanar transition between microstrip lines and coplanar strips (CPS) which is to be utilized in our velocity-matched distributed photodetector (VMDP). Both FDTD simulations and X-band experiments show broadband, low return loss performance of this newly proposed structure, with a measured 3 dB insertion loss bandwidth of 68 percent for the case of a balanced back-to-back microstrip-to-CPS transition.
TL;DR: In this article, the first comprehensive investigation of synthesized dielectric materials which possess distinctive stopbands for microstrip lines was performed using FDTD, and four types of these photonic band-gap (PBG) structures have been simulated with FDTD.
Abstract: We report the first comprehensive investigation of synthesized dielectric materials which possess distinctive stopbands for microstrip lines. Four types of these photonic band-gap (PBG) structures have been simulated using FDTD. Experiment with a honeycomb-lattice PBG line shows excellent agreement between theoretical prediction and measurement.
TL;DR: In this paper, thin-film microstrip lines (TFMSLs) fabricated on low-resistivity Si with polymerized cyclotene as the dielectric between signal and ground conductor are reported.
Abstract: We report on thin-film microstrip lines (TFMSLs) fabricated on low-resistivity Si with polymerized cyclotene as the dielectric between signal and ground conductor, all on top of the wafer Electro-optic high-frequency characterization of the TFMSLs reveals negligible modal dispersion up to the highest frequencies of 10 THz In spite of the high substrate conductivity, the attenuation is low (⩽1 dB/mm at 100 GHz) Over the full frequency range, it is dominated by conductor losses and not by absorption in the dielectric With these dispersion and attenuation properties, TFMSLs are an attractive alternative to coplanar waveguides, with the additional advantage of immunity against substrate absorption and radiation losses
TL;DR: In this article, the authors presented a feasibility study on optically transparent patch antennas with microstrip line and probe feeds, which operate at 2.3 GHz and 19.5 GHz respectively.
Abstract: The paper presents a feasibility study on optically transparent patch antennas with microstrip line and probe feeds. The two antennas operate at 2.3 GHz and 19.5 GHz respectively. They are constructed from a thin sheet of clear polyester with an AgHT-8 optically transparent conductive coating. The experimental results show good radiation patterns and input impedance match. The antennas have potential applications in mobile wireless communications.
TL;DR: In this article, a single-feed, reduced-size dual-frequency rectangular microstrip antenna with a cross slot of equal length is presented, where the frequency ratio is mainly determined by the aspect ratio of the rectangular patch, and the reduction in the two operating frequencies is achieved by cutting a cross-slot in the microstrip patch.
Abstract: A new design of single-feed, reduced-size dual-frequency rectangular microstrip antenna with a cross slot of equal length is presented. The frequency ratio of the two operating frequencies is mainly determined by the aspect ratio of the rectangular patch, and the reduction in the two operating frequencies is achieved by cutting a cross slot in the microstrip patch. Details of the experimental results for such a design are presented and discussed.
TL;DR: In this paper, a triangular microstrip antenna with a shorting pin can significantly reduce the antenna size at a given operating frequency, and the experimental results of such a triangulation antenna are presented.
Abstract: Loading a triangular microstrip antenna with a shorting pin can significantly reduce the antenna size at a given operating frequency. Experimental results of such a triangular microstrip antenna are presented. Variations of the resonant frequency of the triangular microstrip patch with different shorting-pin positions are given, and comparisons of the compact and conventional triangular microstrip antennas are also presented and discussed.
TL;DR: In this paper, a compendium of data for computing the characteristic impedance of transmission lines based on physical dimensions is presented, covering both conventional structures and unusual geometries, including coaxial, eccentric and elliptic coaxial.
Abstract: A compendium of data for computing the characteristic impedance of transmission lines based on physical dimensions. Covers both conventional structures and unusual geometries, including coaxial, eccentric and elliptic coaxial, twin-wire, wire-above-ground, microstrip and derivatives, stripline, slabline and trough line. Also details numerous configurations of coupled lines.
TL;DR: In this paper, the mixedpotential integral-equation (MPIE) method is developed in the spatial domain for multilayered media, which is useful for efficient computation for interacting microstrip elements, which may be located at any substrate layer and separated by an arbitrarily large distance.
Abstract: Microstrip elements of arbitrary shape are modeled in multilayered media. The Green's function for the multilayered structure is developed in a form useful for efficient computation for interacting microstrip elements, which may be located at any substrate layer and separated by an arbitrarily large distance. This result is of significant value to a variety of applications in wave propagation besides those discussed in this paper. The mixed-potential integral-equation (MPIE) method is developed in the spatial domain. Examples for regularly/arbitrarily shaped geometries in single and multilayered media are presented. These involve the optimization of an open-end microstrip, a radial-stub microstrip, a five-section overlay-gap-coupled filter, and a circular-patch proximity-coupled microstrip antenna. Very good agreement with measurement and other published data is observed.
TL;DR: In this paper, the design of microstrip leaky-wave antennas for single and dual-beam applications is described, where the antennas are excited by open-ended CPW lines which both present a good coupling efficiency and high potentiality for the insertion of active circuits.
Abstract: The paper describes the design of microstrip leaky-wave antennas for single and dual-beam applications. Dispersion curves for the first higher order mode are given by analytical expressions with the help of a simple cavity model. From knowledge of the propagation characteristics, the radiation patterns of the leaky-wave antennas are easily computed. The antennas are excited by open-ended CPW lines which both present a good coupling efficiency and high potentiality for the insertion of active circuits. Several C-band applications on various substrates are presented, showing the usefulness and the easy design of microstrip leaky-wave antennas for the realisation of steerable dual-beam patterns.
TL;DR: In this article, two Ka-band, half-meter diameter, circularly polarized microstrip reflectarrays with variable element rotation angles have been developed, and one has identical square patches with variable-length phase delay lines.
Abstract: Two Ka-band, half-meter diameter, circularly polarized microstrip reflectarrays have been developed. One has identical square patches with variable-length phase delay lines. The other uses identical square patches and delay lines with variable element rotation angles. Although both antennas demonstrated excellent efficiencies, adequate bandwidths, and low average sidelobe and cross-pol levels, the one with variable rotation angles achieved superior overall performance. It is believed that these are electrically the largest microstrip reflectarrays (6924 elements with 42 dB gain) ever developed. It is also the first time that circular polarization has been actually demonstrated using microstrip patch elements. It is known that, if a circularly polarized antenna element is rotated from its original position by /spl psi/ degrees, the phase of the element will be either advanced or delayed by the same /spl psi/ degrees. Hence, the technique of rotating circularly polarized elements to achieve the required phases for a conventional array to scan its beam has been previously demonstrated. This technique was also demonstrated for a spiraphase reflectarray where physically large spiral elements with discrete and limited switchable phase states were used to scan the beam. Here small and low-profile printed microstrip elements are used in a reflectarray with continuous variable angular rotations to achieve far-field phase coherence. It has been previously proposed that a controllable miniature or micro-machined motor can be placed under each patch element of a reflectarray to scan the beam to wide angular directions. By doing so, the high-cost/high-loss phase shifters, T/R modules, and beamformer are no longer needed in a beam scanning antenna.
TL;DR: In this article, a dielectric substrate (14d) is provided on the dielectrics substrate of the MMICs to form a microstrip line thereon, and a strip conductor is provided to form the microstrip lines thereon.
Abstract: A microwave circuit package (10) includes a metallic base plate (3) on which are mounted a plurality of monolithic microwave integrated circuits (MMICs) (11,12,13) and a spacer (15), made of a dielectric material, separating the MMICs (11,12,13) from each other, and the MMICs (11,12,13) and spacer (15) are sealed in the package (10). The provision of the spacer (15) substantially reduces the volume of the interior space of the package (10). A dielectric substrate (14) having generally the same height as substrates of the MMICs (11,12) may also be mounted on the metallic base plate (3), and a strip conductor (14d) may be provided on the dielectric substrate (14) so as to form a microstrip line thereon.
TL;DR: In this paper, a new configuration of dielectric resonator antenna is proposed to achieve dual-band operation or wider bandwidth, which consists of two rectangular dielectrics displaced near two edges of a single slot in the ground plane of a microstrip line.
Abstract: To achieve dual-band operation or wider bandwidth, a new configuration of dielectric resonator antenna is proposed. This structure consists of two rectangular dielectric resonators displaced near two edges of a single slot in the ground plane of a microstrip line. The measured impedance and radiation patterns for two cases are presented. The results for typical examples indicate that an impedance bandwidth twice that of a single element or dual-frequency operation at two separate bands can be achieved.
TL;DR: In this article, a millimeter waveguide for a resonator is presented, where a cavity is formed in substrates with grounding conductive layers on surfaces of the cavity, a probe extending from a microstrip line on a top surface of the substrates.
Abstract: A millimeter waveguide is disclosed which includes: a first single crystal substrate having a groove therein; a conductor film on a surface of said groove and a surface of said first single crystal substrate connected to said surface of said groove; a second single crystal substrate covering said conductor film; and a microstrip line on a surface of said second single crystal substrate, exposed to a cavity in said groove. A protruding portion may be formed on a bottom surface of the groove. The microstrip line including foundation (nickel chromium) and conductive (gold) layers may be formed on a surface of the groove. A protruding portion may be formed on the second single crystal substrate, wherein the height of this protruding portion is less than the depth of the groove. A millimeter waveguide for a resonator is also disclosed wherein a cavity is formed in substrates with grounding conductive layers on surfaces of the cavity, a probe extending from a microstrip line on a top surface of the substrates. Similar millimeter waveguide is also disclosed wherein the probe is replaced by magnetic field coupling structure. A circuit apparatus is also disclosed which comprises the millimeter waveguide apparatus mentioned above mentioned and an active circuit fixed on the millimeter waveguide apparatus.
TL;DR: In this paper, the resonant frequencies of a microstrip-ring resonator capacitively coupled to a feed line were accurately analyzed using a transmission-line model, making use of ABCD and Y-admittance matrices.
Abstract: The resonant frequencies of a microstrip-ring resonator capacitively coupled to a feed line are accurately analyzed using a transmission-line model. By making use of ABCD- and Y-admittance matrices, a compact closed-form expression for the input impedance of the ring alone is analytically derived and shows that the ring ran be equivalently viewed as a frequency-dependent capacitor. The coupling gap is then modeled by an equivalent L-network comprising a parallel and a series gap capacitance obtained by modifying Garg and Bahl's closed-form expressions for an end-to-end microstrip gap. By simplifying the parallel and series combinations of the overall equivalent circuit, the total input impedance looking from the feed line to the gap is analytically derived to predict the resonant frequencies. To verify the analysis, the resonant frequencies of the capacitively coupled ring resonator have been accurately measured, with the experimental results showing very good agreement with the theoretical predictions.
TL;DR: In this paper, a simple model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconding transmission line and a microstrip resonator and the specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves.
Abstract: The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
TL;DR: In this article, a waveguide-to-microstrip transition package is proposed for processing electromagnetic wave signals, which includes an iris (48) formed from a metallized pattern on the opposite side of the substrate from the probe.
Abstract: A waveguide-to-microstrip transition package (30) for processing electromagnetic wave signals includes a waveguide (32) for directing the signals to the input of the waveguide (32). A substrate (34) overlaps the input of the waveguide (32) to form a hermetic seal. A metallized probe (36) conducts the signals to a microstrip line (40) and is patterned upon the substrate (34). The transition (30) also includes an iris (48) formed from a metallized pattern on the opposite side of the substrate (34) from the probe (36). The special design of the probe (36), the structure of the iris (48) and the wave guide cavity (46) above the probe (36) allow impedance matching and efficient signal transfer from waveguide (32) to microstrip line (40) or from microstrip line (40) to waveguide (32).
TL;DR: In this paper, a multi-layer circuit structure including a plurality of substrate layers is considered, and at least one planar transmission line, including microstrip, stripline, or coplanar line, is disposed on the plurality of the substrate layers.
Abstract: A multi-layer circuit structure including a plurality of substrate layers. At least one planar transmission line, including microstrip, stripline, or coplanar line, disposed on the plurality of substrate layers. A via transmission line connected to that at least one planar transmission line and extending through the plurality of substrate layers. The via transmission lines having the same topology as the at least one planar transmission line for providing wide frequency band transition between the via transmission lines and the at least one planar transmission line.
TL;DR: In this paper, a full-wave space-domain method is presented for the rigorous and fast investigation of printed circuit structures of arbitrary shape on uniaxial anisotropic layered substrates including three dimensional (3-D) metallizations.
Abstract: A full-wave space-domain method is presented for the rigorous and fast investigation of printed circuit structures of arbitrary shape on uniaxial anisotropic layered substrates including three dimensional (3-D) metallizations. The electromagnetic (EM) fields are described in terms of a mixed-potential-integral-equation (MPIE) formulation, Two different techniques-the matrix pencil (MP) technique and a cross-sectional eigenvalue (CSEV) approach-are employed to extract the S-parameters of the circuit under consideration. The usage of a triangular mesh allows the convenient modeling of arbitrarily shaped structures. Therefore, the main advantage of this method is its generality, which allows a large variety of printed circuit structures to be characterized. The flexibility of the method is demonstrated for the example of spiral inductors including air-bridges with finite-metallization thickness.
TL;DR: In this article, the authors used simulation software for modeling the properties of a 2-15 GHz liquid crystal microstrip phase shifter, which was designed at Thomson-CSF.
Abstract: Electromagnetic simulation software is used for modeling the properties of a 2–15 GHz liquid crystal microstrip phase shifter previously designed at Thomson-CSF. After experimental validation of the computed results, the software is applied to the modeling of a new 30–40 GHz multilayer microstrip phase shifter, where the active medium is a liquid crystal inserted between solid dielectric substrates. Measurements carried out at between 10 and 40 GHz on 4.35 cm long lines are in good agreement with theoretical predictions. A maximum experimental phase shift of 219.3° at 37 GHz (about 50°/ cm) was observed for a structure with a commercial liquid crystal (BDH-E44) and silica substrates.
TL;DR: In this article, a field-theoretical characterization of unbounded multiport microstrip passive circuits using an explicit network technique is presented, which is based on a method of moments (MoM) that makes use of the explicit representation of a generalized matrix of network parameters.
Abstract: This paper is concerned with a field-theoretical characterization of unbounded multiport microstrip passive circuits using an explicit network technique. The cornerstone of this efficient modeling framework is based on a method of moments (MoM) that makes use of the explicit representation of a generalized matrix of network parameters. To physically formulate the equivalent multiport network for a multiport circuit, a delta-gap voltage source backed by a vertical electric wall is conceptually introduced to terminate each port. In this way, the multiport microstrip circuit to be modeled is externally connected at an adequate location. The image principle is applied at the port to remove the electric wall and the open environment can effectively be simulated. With the unified impressed delta-gap source model and appropriate partition of the entire multiport circuit topology, a MoM procedure is developed and applied to extract the network parameters directly from the field-theoretical formulations. All possible physical phenomena such as radiation and leakage losses are incorporated in the algorithm. Two distinctive examples presented in this paper demonstrate the effectiveness of the proposed algorithm for handling multilayered multiport passive and antenna circuits. Convergence analysis is made for the filter example compared with experimental results, showing that the proposed algorithm is very stable and accurate. Theoretical and experimental results indicate that the implicit unbounded effects may be influential on electrical performance and should be considered in such a field-theoretical modeling and design tool as proposed in this paper.
TL;DR: In this article, a full-wave finite-element method (FEM) is formulated and applied in the analysis of practical electronic packaging circuits and interconnects, which is used to calculate S-parameters of unshielded microwave components such as patch antennas, filters, spiral inductors, bridges, bond wires and microstrip transitions through a via.
Abstract: A full-wave finite-element method (FEM) is formulated and applied in the analysis of practical electronic packaging circuits and interconnects. The method is used to calculate S-parameters of unshielded microwave components such as patch antennas, filters, spiral inductors, bridges, bond wires, and microstrip transitions through a via. Although only representative microwave passive circuits and interconnects are analyzed in this paper, the underlined formulation is applicable to structures of arbitrary geometrical complexities including microstrip and coplanar-waveguide transitions, multiple conducting vias and solder bumps, multiple striplines, and multilayer substrates. The accuracy of the finite-element formulation is extensively verified by calculating the respective S-parameters and comparing them with results obtained using the finite-difference time-domain (FDTD) method. Computational statistics for both methods are also discussed.