PIER B | PIER Journals

2012-08-02

PIER B

Vol. 42, 425-453, 2012

doi:10.2528/PIERB12050903

download: 235

Correlations of Deflection Angles of a Laser Beam in a Hot Turbulent Jet of Air: Theoretical Determination and Experimental Measurement of the Structure Coefficient of Refractive Index Fluctuations

Jean Bilong II , Elisabeth Ngo Nyobe , Jacques Hona and Elkana Pemha

Using the geometrical optics approximation, a theoretical prediction of the deflection angle correlation of a laser beam propagating in a hot turbulent jet is found as a functional form of the turbulent spectrum of the refractive index fluctuations. By applying the modified Von Karman model and Tatarskii model, the structure coefficient of the refractive index and the deflection angle correlation of the laser beam are then computed by means of a numerical procedure. Experiments to measure the structure coefficient are performed. A good agreement between the experimental results obtained and the theoretical predictions demonstrates the validity of the theoretical approach.

CORRELATIONS OF DEFLECTION ANGLES OF A LASER BEAM IN A HOT TURBULENT JET OF AIR: THEORETICAL DETERMINATION AND EXPERIMENTAL MEASUREMENT OF THE STRUCTURE COEFFICIENT OF REFRACTIVE INDEX FLUCTUATIONS

2012-07-26

PIER B

Vol. 42, 405-424, 2012

doi:10.2528/PIERB12052507

download: 191

Nonsynchronous Noncommensurate Impedance Transformers

Vitaliy Zhurbenko and Kseniya Kim

Nonsynchronous noncommensurate impedance transformers consist of a combination of two types of transmission lines: transmission lines with a characteristic impedance equal to the impedance of the source, and transmission lines with a characteristic impedance equal to the load. The practical advantage of such transformers is that they can be constructed using sections of transmission lines with a limited variety of characteristic impedances. These transformers also provide comparatively compact size in applications where a wide transformation ratio is required. This paper presents the data which allows to estimate the achievable total electrical length and in-band reflection coefficient for transformers consisting of up to twelve transmission line sections in the range of transformation ratios r=1.5 to 10 and bandwidth ratios χ=2 to 20. This data is obtained using wave transmission matrix approach and experimentally verified by synthesizing a 12-section nonsynchronous noncommensurate impedance transformer. The measured characteristics of the transformer are compared to the characteristics of the conventional tapered line transformer.

2012-07-25

PIER B

Vol. 42, 381-403, 2012

doi:10.2528/PIERB12050308

download: 174

Microwave Contrast Imaging of Breast Tissue from Local Velocity Estimation

Jean-François Deprez , Mantalena Sarafianou , Maciek Klemm , Ian J. Craddock and Penny J. Probert-Smith

This paper proposes a new method to display microwave images of breast tissue, based on estimation of local microwave velocity from time of flight measurements. Its computational demands are low compared with tomography. It has two major components: 1) the estimation of the travel time of microwaves across the tissue between a set of antennae using a wavelet decomposition, and 2) the estimation of the microwave velocity field from the set of travel times using a low dimensional set of radial basis functions to model local velocity. The technique is evaluated in 2-D on clinical MR-based numerical breast phantoms incorporated in Finite-Difference Time-Domain simulations. The basis functions, used with a regularisation scheme to improve numerical stability, reduce the dimensionality of the inverse problem for computational efficiency and also to improve the robustness to error in velocity estimation. The results support previously published findings that the wavelet transform is suitable for robust measurement of time of flight even in clinically significant simulations, and shows that the velocity contrast images can be constructed so different regions of breast tissue type can be distinguished. In particular, the presence of a tumour is clearly detected, demonstrating the potential of this approach for breast screening. Keywords: Biomedical signal processing; Microwave imaging; Image reconstruction.

MICROWAVE CONTRAST IMAGING OF BREAST TISSUE FROM LOCAL VELOCITY ESTIMATION

2012-07-25

PIER B

Vol. 42, 363-380, 2012

doi:10.2528/PIERB12042711

download: 201

A Multi-Objective Memetic Optimization Approach to the Circular Antenna Array Design Problem

Abhronil Sengupta , Tathagata Chakraborti , Amit Konar and Atulya K. Nagar

The paper describes a novel approach to the design of non-uniform planar circular antenna arrays for achieving maximal side lobe level suppression and directivity. The current excitation amplitudes and phase perturbations of the array elements are determined using an Adaptive Memetic algorithm resulting from a synergy of Differential Evolution (DE) and Learning Automata that is able to significantly outperform existing state-of-the-art approaches to the design problem. However, existing literature considers the design problem as a single-objective optimization task that is formulated as a linear sum of all the performance metrics. Due to the conflicting nature of the various design objectives, improvements in a certain design measure causes deterioration of the other measures. Following this observation, the single-objective design problem is reformulated as a constrained multi-objective optimization task. The proposed memetic algorithm is extended to the multi-objective framework to generate a set of nondominated solutions from which the best compromise solution is selected employing a fuzzy membership based approach. An instantiation of the design problem clearly depicts that the multi-objective approach provides simultaneous side lobe level suppression and directivity maximization in comparison to the single-objective scenario.

A MULTI-OBJECTIVE MEMETIC OPTIMIZATION APPROACH TO THE CIRCULAR ANTENNA ARRAY DESIGN PROBLEM

2012-07-24

PIER B

Vol. 42, 335-362, 2012

doi:10.2528/PIERB12062009

download: 187

Comprehensive Solution to Scattering by Bianisotropic Objects of Arbitrary Shape

Chong Mei , Moamer Hasanovic , Jay Kyoon Lee and Ercument Arvas

This paper presents a method of moments (MoM) solution for the problems of electromagnetic scattering by inhomogeneous three-dimensional bianisotropic scatterers of any shape. The electromagnetic response of bianisotropy has been described by the constitutive relations of the most general form composed of four 3 x 3 matrices or tensors. The volume equivalence principle is used to obtain a set of mixed potential formulations for a proper description of the original scattering problem. Here, the total fields are separated into the incident fields and the scattered fields. The scattered fields are related to the electric and magnetic potentials which are excited by electric and magnetic bound charges and polarization currents. The body of the scatterer is meshed through the use of tetrahedral cells with face-based functions used to expand unknown quantities. At last, the Galerkin test method is applied to create a method of moments (MoM) matrix from which the numerical solution is obtained. Implemented in a MATLAB program, the numerical formulation is evaluated and verified for various types of scatterers. The results are compared with those of previous work, and a good agreement is observed. Finally, a scattering from a two-layered dispersive chiroferrite sphere is presented as the most general example.

COMPREHENSIVE SOLUTION TO SCATTERING BY BIANISOTROPIC OBJECTS OF ARBITRARY SHAPE

2012-07-24

PIER B

Vol. 42, 311-333, 2012

doi:10.2528/PIERB12061210

download: 237

Experimental Performance Comparison of Six-Port and Conventional Zero-IF/Low-IF Receivers for Software Defined Radio

Cristina de la Morena-Álvarez-Palencia and Mateo Burgos-Garcia

This paper presents an experimental performance comparison among three RF architectures that are very suitable for Software Defined Radio (SDR) implementation: zero-IF, low-IF, and six-port network. A six-port receiver and a dual zero-IF/low-IF receiver have been developed for this purpose. Six-port receiver is a very promising and flexible RF architecture for the low-cost implementation of integrated microwave and millimeter-wave systems. Competitive advantages such as ultra-broadband behavior, low-cost, reconfigurability, and low power consumption, point to the six-port architecture as a good candidate to implement a SDR. However, two issues on broadband six-port receivers require intensive research: dynamic range extension, and miniaturization. In this paper, two solutions are proposed to solve these problems: the use of biased detector diodes for dynamic range extension, and the use of low temperature co-fired ceramic (LTCC) technology for six-port reduction. The measurement results indicate that the six-port receiver shows high potential benefits and advantages compared to conventional zero-IF and low-IF receivers. In addition, the capability of the six-port architecture to operate as both zero-IF and low-IF receivers has been experimentally demonstrated for the first time.

EXPERIMENTAL PERFORMANCE COMPARISON OF SIX-PORT AND CONVENTIONAL ZERO-IF/LOW-IF RECEIVERS FOR SOFTWARE DEFINED RADIO

2012-07-24

PIER B

Vol. 42, 291-309, 2012

doi:10.2528/PIERB12052406

download: 218

CSRRs for Efficient Reduction of the Electromagnetic Interferences and Mutual Coupling in Microstrip Circuits

Xiaoke Han , Habiba Hafdallah-Ouslimani , Tao Zhang and Alain C. Priou

This paper proposes an efficient microstrip isolator filter which suppresses the surface and lateral waves (SW and LW) in planar antenna arrays. The structure consists in a double or triple row of periodic and flipped array of subwavelength Complementary Split Ring Resonators (CSRRs). The array of CSRRs is etched on a dielectric substrate backed by a metallic ground plane. These structures can both block the electromagnetic (EM) energy in one direction and guide it along the other transverse direction. In particular, the flipped array of CSRRs presents wider bandgap characteristic (stopband ≥20%) than periodic array of CSRRs (~16%) and conventional array of SRRs (≥12%). Then, the metamaterial filter is inserted between two 6.1 GHz probe-fed patch antenna elements separated by a distance of 0.8 λ₀. Excellent agreements between the simulated and the experimental results are obtained. In fact, a significant reduction of the EM mutual coupling is achieved, more than 24 dB, over a wide frequency bandwidth. Moreover, the proposed CSRR structures are compact, low complex and, as printed antennas, are very easy to manufacture. They have numerous applications in MIMO systems and directive phased arrays.

CSRRS FOR EFFICIENT REDUCTION OF THE ELECTROMAGNETIC INTERFERENCES AND MUTUAL COUPLING IN MICROSTRIP CIRCUITS

2012-07-18

PIER B

Vol. 42, 263-289, 2012

doi:10.2528/PIERB12051001

download: 210

A Synthesis Method for Time-Domain Passive Filters Compensating for Waveform Distortion

Ushio Sangawa

A novel synthesis method for a class of time-domain passive filters that compensates for waveform distortion caused by frequency dependencies of the transmission properties of signal propagation paths, is formulated. The method is based on the linear response theory and mathematical properties of scattering matrices for passive circuits. This paper focuses on the formulation and theoretical consistency of the method. The causal transfer functions for the filters can be extracted by "regularizing" the inverse of a transfer function of the path. To fulfill the necessary restrictions imposed on the causal functions, regularization is realized by multiplying the function of linear phase filters comprising a sufficient number of resonators by the inverse. The filter circuits are easily derived from the regularized transfer functions through numerical optimization techniques and the coupling matrix synthesis method to determine transmission poles and extract each lumped element value, respectively. The method is then applied to practically designing a filter that compensates for the frequency dependencies of a two-port radio propagation path having a pair of wideband antennas. In addition, applications of the filter and the scope of further developments of this technology are discussed.

A SYNTHESIS METHOD FOR TIME-DOMAIN PASSIVE FILTERS COMPENSATING FOR WAVEFORM DISTORTION

2012-07-17

PIER B

Vol. 42, 245-262, 2012

doi:10.2528/PIERB12051804

download: 178

Space-Time Adaptive Processing Based on Weighted Regularized Sparse Recovery

Zhaocheng Yang , Xiang Li and Hongqiang Wang

In this paper, novel space-time adaptive processing algorithms based on sparse recovery (SR-STAP) that utilize weighted l₁-norm penalty are proposed to further enforce the sparsity and approximate the original l₀-norm. Because the amplitudes of the clutter components from different snapshots are random variables, we design the corresponding weights according to two different ways, i.e., the Capon's spectrum using limited snapshots and the Fourier spectrum using the current snapshot. Moreover, we apply the weighted idea to both the direct data domain (D3) SR-STAP and SR-STAP using multiple snapshots from adjacent target-free range bins. Simulation results illustrate that our proposed algorithms outperform the existing SR-STAP and D3SR-STAP algorithms.

SPACE-TIME ADAPTIVE PROCESSING BASED ON WEIGHTED REGULARIZED SPARSE RECOVERY

2012-07-16

PIER B

Vol. 42, 225-243, 2012

doi:10.2528/PIERB12060404

download: 245

Least Squares Filtering Algorithm for Reactive Near Field Probe Correction

Mohammed Anisse Moutaouekkil , Abdelhak Ziyyat , Mohammed Serhir and Dominique Picard

The probe correction technique applied to reactive near field characterization is based on a deconvolution process. However, the classical deconvolution based on an inverse Fourier transform has a restrictive limitation. It is based on the use of noiseless measurement data. Consequently, measurement noise makes the result obtained by the classical deconvolution based technique inefficient and requires an extremely low noise measurement facility. In this paper, a method to improve the probe correction stability when using corrupted measurement data is presented. The proposed constrained least squares filtering algorithm (CLSF) uses an inverse filtering approach that takes into account the statistical characteristics of the measurement noise. Computations data with electromagnetic software of two different structures validate this method and illustrate its reliability.

LEAST SQUARES FILTERING ALGORITHM FOR REACTIVE NEAR FIELD PROBE CORRECTION

2012-07-15

PIER B

Vol. 42, 207-224, 2012

doi:10.2528/PIERB12052508

download: 210

Low Cost 60 GHz New Thin Pyralux Membrane Antennas Fed by Substrate Integrated Waveguide

Tristan Sarrazin , Hamsakutty Vettikalladi , Olivier Lafond , Mohamed Himdi and Nathalie Rolland

A low cost technology based on FR4 and thin flexible Pyralux substrate to develop membrane antennas/array with high efficiency and wide bandwidth for high speed V-band communication systems is proposed in this paper. A new low cost thin Pyralux substrate with a thickness of 75 μm, relative permittivity of εr = 2.4 and tanδ = 0.002 is used. First we developed the known classical aperture coupled antennas based on FR4 and pyralux substrate to validate this technology. The simulated and measured antenna radiation parameters for a single patch, 1x4 array of patches using aperture coupled technology give good results in terms of S11 bandwidth, gain and radiation pattern. But the back radiation is found to be high due to some radiation from the slot and the feeding microstrip line. Measurements of the antennas show approximately 9.7% and 10.8% impedance bandwidth (S11= -10 dB) with a maximum gain of 7.6 dBi and 12.4 dBi around 60 GHz, respectively. In order to reduce the back radiation, we developed slot coupled antennas with substrate integrated waveguide (SIW) technology. Measurements show a 10 % and 7.5 % impedance bandwidth with a maximum antenna gain of 7.9 dBi and 12.7 dBi around 60 GHz for SIW single patch and 1 x 4 array antenna, respectively. The efficiency in this case is found to be very good due to very low back radiation. The measured results are in good agreement with the numerical simulations. The new thin substrate used for making the antenna helps easy integration with millimeter wave components and circuits.

LOW COST 60 GHZ NEW THIN PYRALUX MEMBRANE ANTENNAS FED BY SUBSTRATE INTEGRATED WAVEGUIDE

2012-07-12

PIER B

Vol. 42, 181-205, 2012

doi:10.2528/PIERB12060109

download: 229

Fd2td Analysis of Electromagnetic Field Propagation in Multipole Debye Media with and Without Convolution

Mauro Feliziani , Silvano Cruciani , Valerio De Santis and Francesearomana Maradei

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD²TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD²TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD²TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD²TD method. A comparative analysis of several FD²TD methods in terms of stability, dispersion, computational time and memory is carried out.

FD2TD ANALYSIS OF ELECTROMAGNETIC FIELD PROPAGATION IN MULTIPOLE DEBYE MEDIA WITH AND WITHOUT CONVOLUTION

2012-07-12

PIER B

Vol. 42, 163-180, 2012

doi:10.2528/PIERB12052704

download: 241

Scattering of a Radially Oriented Hertz Dipole Field by a Perfect Electromagnetic Conductor (PEMC) Sphere

Abdul Ghaffar , Nasir Mehmood , Muhammad Shoaib , Muhammad Yasin Naz , Ahsan Illahi and Qaisar Naqvi

PEMC medium is a special type of metamaterial which generalizes the pre-existing concepts of perfect electric conductor (PEC) and perfect magnetic conductor (PMC). PEMC medium is described by a special parameter named as admittance and denoted as M. This admittance parameter acts as a base in order to extract the nature of medium as PEC or PMC. Electromagnetic fields scattered by a PEMC sphere are investigated theoretically. A Hertz dipole as a source of excitation is considered. Co-polarized as well as cross-polarized component of the scattered fields are taken into consideration. A general solution of fields scattered by the PEMC sphere has been sought.

SCATTERING OF A RADIALLY ORIENTED HERTZ DIPOLE FIELD BY A PERFECT ELECTROMAGNETIC CONDUCTOR (PEMC) SPHERE

2012-07-02

PIER B

Vol. 42, 141-161, 2012

doi:10.2528/PIERB12042504

download: 221

Investigation of Cavity Reflex Antenna Using Circular Patch Type FSS Superstrate

Abhay Kotnala , Prateek Juyal , Ashok Mittal and Asok De

Cavity reflex antenna (CRA) employing a circular patch type FSS (Frequency Selective Surface) superstrate is investigated. Analysis in terms of gain, bandwidth (impedance and gain) and radiation pattern has been presented. The aim of this work was to study low profile CRA having very thin superstrate sizes. In this CRA a circular patch antenna is used as a feeding source. The circular patch type FSS possesses some unique properties favorable for thin superstrate sizes. In practice when the excitation source of the CRA is a probe-fed microstrip antenna with finite ground plane, substrate and superstrate, cross-polarization increases. In the presented design, the cross polar level has been reduced by choosing the optimum air gap and superstrate geometrical and electrical properties. A CRA with circular patch type FSS offers better performance both in terms of gain and impedance bandwidth for, thin superstrates (0.008) while giving a gain of 13 dBi and considerably reduced crosspolar level. The proposed antenna exhibit nearly equal E-plane and H-plane radiation pattern. Measurement results are provided to support the simulated results (by Ansoft HFSS). The circular patch type FSS is easy to fabricate and can be embedded into the host profile.

INVESTIGATION OF CAVITY REFLEX ANTENNA USING CIRCULAR PATCH TYPE FSS SUPERSTRATE

2012-07-02

PIER B

Vol. 42, 115-139, 2012

doi:10.2528/PIERB12041610

download: 214

Generalized Synthesis and Design of Symmetrical Multiple Passband Filters

Akhilesh Mohan , Surinder Singh and Animesh Biswas

In this paper, we present a new synthesis method for a generalized symmetric multiple band bandpass filter. By using frequency transformations on the low pass prototype, the poles and zeros of the single/dual band filtering function are obtained. These poles and zeros are combined and re-arranged to get the multiband filtering function. The coupling matrix is obtained from this multiband filtering function. A variety of filters are synthesized in order to validate the proposed theory. A triple band and quadruple band filters have been designed, fabricated and measured. The measured results have good agreement with the simulated results.

GENERALIZED SYNTHESIS AND DESIGN OF SYMMETRICAL MULTIPLE PASSBAND FILTERS

2012-07-02

PIER B

Vol. 42, 93-113, 2012

doi:10.2528/PIERB12052506

download: 237

Studies on the Dynamics of a System of Bilaterally Coupled Chaotic Gunn Oscillators

Bishnu Charan Sarkar , Chaitali Koley , Arun Kanti Guin and Suvra Sarkar

The dynamics of a system of two bilaterally coupled chaotically oscillating X-band Gunn oscillators (GOs) has been studied by numerical simulation and by hardware experiment. The effect of variation of the coupling strengths between two oscillators in two paths has been explored. The chaotic oscillations in two GOs have become synchronized in most of the cases when coupling factors (CFs) are around 20% or more. However, the transformation of chaotic states of the GOs to quasi-periodic ones has been observed for some values of CFs. A detailed numerical analysis on the instantaneous error parameters of the GO state variables is presented to identify different steady state dynamical conditions of the system. Experimental observations of the GO output frequency power spectra and the averaged product of the two GO outputs in the coupled mode confirm the occurrence of synchronization as well as quenching of chaotic oscillations for different values of CFs.

STUDIES ON THE DYNAMICS OF A SYSTEM OF BILATERALLY COUPLED CHAOTIC GUNN OSCILLATORS

2012-06-27

PIER B

Vol. 42, 75-91, 2012

doi:10.2528/PIERB12050905

download: 253

Multimode Behavior of a 42ghz, 200kw Gyrotron

Ashutosh Singh , B. Ravi Chandra and Pradip Kumar Jain

The multimode beam wave interaction behavior in a tapered, cylindrical cavity RF interaction structure of a 42 GHz gyrotron operating in the TE₀₃ mode has been investigated through nonlinear analysis and PIC simulation. A technique for producing the annular gyrating electron beam in PIC simulation code CST Particle Studio has been described. An energy transfer phenomenon from electron beam to RF has been demonstrated. The performance of cavity has been monitored to ensure the device operation in the desired mode and frequency. In the PIC simulation, the effect of beam velocity spread on the power output has been discussed. Using multimode behaviour, the effect of presence of nearby modes on the cavity performance has been observed. The simulation results have been compared with the results obtained from self-consistent single-mode analysis and time-dependent multimode analysis. It has been found that output power is well above the desired 200 kW level for the designed 42 GHz gyrotron operating in TE₀₃ mode.

MULTIMODE BEHAVIOR OF A 42GHZ, 200KW GYROTRON

2012-06-26

PIER B

Vol. 42, 45-74, 2012

doi:10.2528/PIERB12052001

download: 536

Challenges and Opportunities of Electric Machines for Renewable Energy (Invited Paper)

Kwok-Tong Chau , Wenlong Li and Christopher H. T. Lee

This paper gives an overview of various electric machines for application to renewable energy harvesting, and reveals the corresponding challenges and research opportunities. After introducing various renewable energies and electric machines, the concept of renewable energy machines is coined. Then, the existing machines, including the DC, induction and synchronous types, for renewable energy harvesting are challenged. Consequently, research opportunities of advanced machines, including the stator-permanent magnet (PM), direct-drive PM and magnetless types, are elaborated. Finally, both near-term and long-term renewable energy machines are identified especially the emerging stator-PM, vernier PM and stator doubly fed doubly salient types.

CHALLENGES AND OPPORTUNITIES OF ELECTRIC MACHINES FOR RENEWABLE ENERGY (Invited Paper)

2012-06-25

PIER B

Vol. 42, 23-44, 2012

doi:10.2528/PIERB12051019

download: 266

A Novel Wideband Circularly Polarized Antenna for Worldwide UHF Band RFID Reader Applications

Elias Mireles and Satish Kumar Sharma

This paper presents the novel design of a wideband circularly polarized (CP) Radio Frequency Identification (RFID) reader microstrip patch antenna for worldwide Ultra High Frequency (UHF) band which covers 840-960 MHz. The proposed antenna, which consists of a microstrip patch with truncated corners and a cross slot, is placed on a foam substrate (ε_r = 1.06) above a ground plane and is fed through vias through ground plane holes that extend from the quadrature 3 dB branch line hybrid coupler placed below the ground plane. This helps to separate feed network radiation, from the patch antenna and keeping the CP purity. The prototype antenna was fabricated with a total size of 225 x 250 x 12.8 mm³ which shows a measured impedance matching band of 840-1150 MHz (31.2%) as well as measured rotating linear based circularly polarized radiation patterns. The simulated and measured 3 dB Axial Ratio (AR) bandwidth is better than 23% from 840--1050 MHz meeting and exceeding the target worldwide RFID UHF band.

A NOVEL WIDEBAND CIRCULARLY POLARIZED ANTENNA FOR WORLDWIDE UHF BAND RFID READER APPLICATIONS

2012-06-25

PIER B

Vol. 42, 1-22, 2012

doi:10.2528/PIERB12051016

download: 183

Theoretical Examination of Electromagnetic Wave Tunneling through Cascaded ϵ- and μ-Negative Metamaterial Slabs

Chien-Hao Liu and Nader Behdad

In this paper, we examine the close relationship that exists between the phenomenon of electromagnetic (EM) wave tunneling through stacks of single-negative metamaterial slabs and classical microwave filter theory. In particular, we examine the propagation of EM waves through a generalized multi-layer structure composed of N ϵ-negative layers separated from each other by N-1 μ-negative layers, where N≥2 is a positive integer. We demonstrate that, if certain conditions are met, this multi-layer structure can act as a capacitively-coupled, coupled-resonator filter with an Nth-order bandpass response. Exploiting this relationship, we develop a generalized, analytical synthesis method that can be used to determine the physical parameters of this structure from its a priori known frequency response. We present several design examples in conjunction with numerical EM simulation results to demonstrate the validity of this analogy and examine the accuracy of the proposed synthesis procedure.