Home > All Issues > PIER
ISSN: 1070-4698

Vol. 100

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

2010-01-17 PIER Vol. 100, 397-415, 2010. doi:10.2528/PIER09121103

Homogeneous and Heterogeneous Breast Phantoms for Ultra-Wideband Microwave Imaging Applications

Joshua Chong Yue Lai, Cheong Boon Soh, Erry Gunawan, and Kay Soon Low

The paper discusses fabrication of homogenous and heterogeneous breast phantoms to simulate the dielectric properties of human breast over the microwave frequency range from 0.5 GHz to 13.5 GHz. The breast phantoms have stable mechanical configuration and dielectric properties suitable for microwave imaging experiments particularly ultra-wideband microwave imaging for breast cancer detection.

2010-01-15 PIER Vol. 100, 381-396, 2010. doi:10.2528/PIER09112401

The Anisotropic Cell Model in the Colloidal Plasmas

Qizheng Ye and Fei Lu

The anisotropic spherical Wigner-Seitz (WS) cell model --- introduced to describe colloidal plasmas --- is investigated using the linearized Poisson-Boltzmann (PB) equation. As an approximation, the surface potential of the spherical macroparicle expanded in terms of the monopole (q) and the dipole (p) is considered as an anisotropic boundary condition of the linear PB equation. Here, the "apparent" moments q and p are the moments 'seen' in the microion cloud, respectively. Based on a new physical concept, the momentneutrality, the potential around the macroparticle can be solvable analytically if the relationship between the actual moment and the "apparent" moment can be obtained according to the momentneutrality condition in addition to the usual electroneutrality. The calculated results of the potential show that there is an attractive region in the vicinity of macroparticle when the corresponding dipole part of the potential dominates over the monopole part, and there is an attractive region and a repulsive region at the same time, i.e., a potential well, when the corresponding dipole part of the potential just comes into play. It provides the possibility and the conditions of the appearance of periodic structure of the colloidal plasmas, although it is a result of a simple theoretical model.

2010-01-12 PIER Vol. 100, 351-379, 2010. doi:10.2528/PIER09102804

Exposure to 2.45 GHz Microwave Radiation Provokes Cerebral Changes in Induction of Hsp-90 α/β Heat Shock Protein in Rat.

T. Jorge-Mora, Marcos Alvarez Folgueiras, Jose Manuel Leiro-Vidal, F. J. Jorge-Barreiro, Francisco Ares-Pena, and Maria Elena Lopez-Martin

Physical agents such as non-ionizing continuous-wave 2.45 GHz radiation may cause damage that alters cellular homeostasis and may trigger activation of the genes that encode heat shock proteins (HSP). We used Enzyme-Linked ImmunoSorbent Assay (ELI-SA) and immunohistochemistry to analyze the changes in levels of HSP-90 and its distribution in the brain of Sprague-Dawley rats, ninety minutes and twenty-four hours after acute (30 min) continuous exposure to 2.45 GHz radiation in a the Gigahertz Transverse Electromagnetic (GTEM cell). In addition, we studied further indicators of neuronal insult: dark neurons, chromatin condensation and nucleus fragmentation, which were observed under optical conventional or fluorescence microscopy after DAPI staining. The cellular distribution of protein HSP-90 in the brain increased with each corresponding (0.034 ± 3.10-3, 0.069 ± 5.10-3, 0.27 ± 21.10-3 W/kg), in hypothalamic nuclei, limbic cortex and somatosensorial cortex after exposure to the radiation. At twenty-four hours post-irradiation, levels of HSP-90 protein remained high in all hypothalamic nuclei for all SARs, and in the parietal cortex, except the limbic system, HSP-90 levels were lower than in non-irradiated rats, almost half the levels in rats exposed to the highest power radiation. Non-apoptotic cellular nuclei and a some dark neurons were found ninety minutes and twenty-four hours after maximal SAR exposure. The results suggest that acute exposure to electromagnetic fields triggered an imbalance in anatomical HSP-90 levels but the anti-apoptotic mechanism is probably sufficient to compensate the non-ionizing stimulus. Further studies are required to determine the regional effects of chronic electromagnetic pollution on heat shock proteins and their involvement in neurological processes and neuronal damage.

2010-01-11 PIER Vol. 100, 327-349, 2010. doi:10.2528/PIER09112904

Investigation into Time- and Frequency-Domain EMI-Induced Noise in Bistable Multivibrator

Han-Chang Tsai

Electromagnetic interference (EMI) has a negative effect upon the performance of circuit communication systems. The present study considers the case of EMI induced in a conducting wire, and derives equations to establish the effect of the EMI on a bistable multivibrator. The validity of the equations is verified experimentally. The results indicate that the degree of influence of the EMI on the bistable oscillator depends on the interference power, the interference frequency, the induced power, the output resistance of the circuit, and the parasitic capacitance. Moreover, it is shown that the harmonic noise increases with an increasing interference amplitude and frequency. The theoretical results are found to be in good agreement with the experimental data.

2010-01-11 PIER Vol. 100, 309-325, 2010. doi:10.2528/PIER09120108

Sensitivity Analysis of 3-D Composite Structures through Linear Embedding via Green's Operators

Vito Lancellotti, Bastiaan P. de Hon, and Antonius G. Tijhuis

We propose a methodology --- based on linear embedding via Green's operators (LEGO) and the eigencurrent expansion method (EEM) --- for solving electromagnetic problems involving large 3-D structures comprised of ND ≥ 1 bodies. In particular, we address the circumstance when the electromagnetic properties or the shape of one body differ from those of the others. In real-life structures such a situation may be either the result of a thoughtful design process or the unwanted outcome of fabrication tolerances. In order to assess the sensitivity of physical observables to localized deviations from the "ideal" structure, we follow a deterministic approach, i.e., we allow for a finite number of different realizations of one of the bodies. Then, for each realization we formulate the problem with LEGO and we employ the EEM to determine the contribution of the ND - 1 "fixed" bodies. Since the latter has to be computed only once, the overall procedure is indeed efficient. As an example of application, we investigate the sensitivity of a 2-layer array of split-ring resonators with respect to the shape and the offset of one element in the array.

2010-01-11 PIER Vol. 100, 299-308, 2010. doi:10.2528/PIER09112701

A High Band Isolation and Wide Stopband Diplexer Using Dual-Mode Stepped-Impedance Resonators

Chun-Yueh Huang, Min-Hang Weng, Chang-Sin Ye, and Yong-Xiang Xu

In this paper, a high performance diplexer is designed and fabricated for Global Positioning System (GPS) and wireless local area network (WLAN) applications simultaneously. The diplexer mainly comprises two dual-mode ring bandpass filters (BPFs), operated at 1.575 GHz and 2.4 GHz, respectively. By using the stepped-impedance resonator (SIR) in the BPFs, the size reduction and wide stopband from 2.8 GHz to 6 GHz are obtained. Moreover, several transmission zeros are located at the passband edges, thus improving the passband selectivity. Due to impedance matching between two BPFs, a high isolation greater than 40 dB between two channels is obtained. The diplexer is investigated numerically and experimentally. The simulated and measured results have a good agreement with the proposed design concept.

2010-01-11 PIER Vol. 100, 285-298, 2010. doi:10.2528/PIER09112002

Cloaking a Perfectly Conducting Sphere with Rotationally Uniaxial Nihility Media in Monostatic Radar System

Xiangxiang Cheng, Hongsheng Chen, Xian-Min Zhang, Baile Zhang, and Bae-Ian Wu

In this paper, the backscattering properties of a perfect electric conducting sphere coated with layered anisotropic media whose constitutive parameters are close to nihility are investigated. We show that the backscattering is more sensitive to the radial constitutive parameters than to the tangential ones. Compared with isotropic case, the anisotropic media with small axial parameters have the potential to yield more reduction of backscattering magnitude on coated perfectly conducting spheres.

2010-01-06 PIER Vol. 100, 265-284, 2010. doi:10.2528/PIER09120302

Analysis of Vital Signs Monitoring Using an IR-UWB Radar

Antonio Lazaro, David Girbau, and Ramon Villarino

Ultra-Wide Band (UWB) technology is a new, useful and safe technology in the field of wireless body networks. This paper focuses on the feasibility of estimating vital signs --- specifically breathing rate and heartbeat frequency --- from the spectrum of recorded waveforms, using an impulse-radio (IR) UWB radar. To this end, an analytical model is developed to perform and interpret the spectral analysis. Both the harmonics and the intermodulation between respiration and heart signals are addressed. Simulations have been performed to demonstrate how they affect the detection of vital signs and also to analyze the influence of the pulse waveform. A filter to cancel out breathing harmonics is also proposed to improve heart rate detection. The results of the experiments are presented under different scenarios which demonstrate the accuracy of the proposed technique for determining respiration and heartbeat rates. It has been shown that an IR-UWB radar can meet the requirements of typical biomedical applications such as non-invasive heart and respiration rate monitoring.

2010-01-05 PIER Vol. 100, 245-263, 2010. doi:10.2528/PIER09112204

Application of the Improved Matrix Type FDTD Method for Active Antenna Analysis

Shao-Qiu Xiao, Zhenghai Shao, and Bing-Zhong Wang

An improved finite-difference time-domain (FDTD) method has been extended to analyze the antennas with complicated lumped/active networks in this paper. The improved FDTD method is based on a novel integral transform and the matrix theory. Combing the novel integral transform with Kirchhoff's circuit laws, the hybrid networks comprised of high order linear and nonlinear elements with arbitrary connection can be modeled by a stable matrix equation. An effective model is built for the linear lumped networks including the internal independent sources. A wire antenna loaded with wideband match network and a two-element active patch antenna loaded with Gunn diodes are analyzed by the developed techniques. The analysis results indicate that the improved matrix-type FDTD method is not only stable and accurate, but also time-saving in simulating the complicated hybrid networks.

2010-01-04 PIER Vol. 100, 235-243, 2010. doi:10.2528/PIER09120401

Novel Miniaturized Bandpass Filters Using Spiral-Shaped Resonators and Window Feed Structures

Gaole Dai and Mingyao Xia

In this paper, we present a new class of miniaturized microstrip bandpass filters with low-insertion loss, sharp-rejection and narrow-band performance. The proposed filters are composed of two spiral-shaped resonators and rectangle window feed structures. Both back-to-back and interdigital combinations of the resonators are adopted to obtain the miniaturized filter size. Compared to the traditional square loop bandpass filter, the sizes are reduced by 82% and 80%. It is also found that there is a pair of transmission zeros located on each side of the passbands, resulting in high selectivity. To validate the proposed idea, two demonstration filters with back-to-back and interdigital spiral-shaped resonators are implemented. The measured results exhibit good agreement with the full-wave simulation results.

2010-01-04 PIER Vol. 100, 219-234, 2010. doi:10.2528/PIER09111201

Three-Dimensional Nonlinear Inversion of Electrical Capacitance Tomography Data Using a Complete Sensor Model

Robert Banasiak, Radoslaw Wajman, Dominik Sankowski, and Manuchehr Soleimani

Electrical Capacitance Tomography (ECT) is a non-invasive and non-destructive imaging technique that uses electrical capacitance measurements at the periphery of an object to generate map of dielectric permittivity of the object. This visualization method is a relatively mature industrial process tomography technique, especially in 2D imaging mode. Volumetric ECT is a new method that poses major computational challenges in image reconstruction and new challenges in sensor design. This paper shows a nonlinear image reconstruction method for 3D ECT based on a validated forward model. The method is based on the finite element approximation for the complete sensor model and the solution of the inverse problem with nonlinear iterative reconstruction. The nonlinear algorithm has been tested against some complicated experimental test cases, and it has been demonstrated that by using an improved forward model and nonlinear inversion method, very complex shaped samples can be reconstructed. The reconstruction of very complex geometry with objects in the shape of letters H, A, L and T is extremely promising for the applications of 3D ECT.

2010-01-04 PIER Vol. 100, 201-218, 2010. doi:10.2528/PIER09110512

Log Periodic Fractal Koch Antenna for UHF Band Applications

Mohd Nazri A Karim, Mohamad Kamal Abd Rahim, Huda Abdul Majid, Osman Ayop, Maisarah Abu, and Farid Zubir

In this paper, the design of Log Periodic Fractal Koch Antennas (LPFKA) is proposed for Ultra High Frequency (UHF) band applications. The procedure to design the LPFKA with three different numbers of iterations in order to reduce the antenna size is discussed. The Computer Simulation Technology (CST) software has been used to analyze the performances of the designed antennas such as return loss, radiation patterns, current distribution and gain. The antennas have been fabricated using FR4 laminate board with wet etching technique. Using fractal Koch technique, the size of the antenna can be reduced up to 27% when the series iteration is applied to the antennas without degrading the overall performances. Both simulated and measured results are compared, analyzed and presented in this paper.

2009-12-17 PIER Vol. 100, 189-200, 2010. doi:10.2528/PIER09112607

A Dual-Polarized Wide-Band Patch Antenna for Indoor Mobile Communication Applications

Mustafa Secmen and Altunkan Hizal

This paper proposes the configuration of a novel dual-polarized wide-band patch antenna system suitable for indoor mobile communication applications. This configuration consists of two compact patch antennas, which have different feed structures from classical patch antenna configuration. These antennas, which are separated by a thin absorber to have a good isolation, are fed independently to obtain dual polarization. The antenna structure is designed, simulated, manufactured and measured. The operation bandwidth spans 1900-2700 MHz covering Bluetooth, Wireless Local Area Networks (WLAN) and Universal Mobile Telecommunications System (UMTS) bands. The simulations show good agreement with the measurement results that the antennas have return losses higher 15 dB, and the coupling between two antennas is below -20 dB within the operation band.

2009-12-16 PIER Vol. 100, 175-187, 2010. doi:10.2528/PIER09111501

Modified Two-Element Yagi-Uda Antenna with Tunable Beams

Bao-Hua Sun, Shi-Gang Zhou, Yun-Fei Wei, and Qi-Zhong Liu

A modified two-element Yagi-Uda antenna with tunable beams in the H-plane (including four significant beams: forward, backward, omni-directional, and bi-directional beams) is presented. These tunable beams are achieved by simply adjusting the short-circuit position of the transmission line connected to the parasitic element. The principle of operation is investigated by examining the current relations between the driven and parasitic elements. Measured results of a fabricated prototype are presented and discussed.

2009-12-16 PIER Vol. 100, 153-173, 2010. doi:10.2528/PIER09073002

Design of the Compact Parallel-Coupled Lines Wideband Bandpass Filters Using Image Parameter Method

Chang-Sin Ye, Yan-Kuin Su, Min-Hang Weng, Cheng-Yuan Hung, and Ru-Yuan Yang

In this paper, the design of compact and high performance parallel coupled line wideband bandpass filter using image parameter method are proposed. The filter mainly comprising one-stage parallel coupled line and two open stubs are designed and implemented on commercial RT/Duroid 5880 substrate. The equivalent circuit of the proposed structure is initially derived by using the image parameter method. It is found that, the normalized bandwidth (NBW) of image impedance for the one-stage parallel coupled line has a relation to the electromagnetic (EM) simulated bandwidth. To further improve the selectivity, two open stubs are connected near the input/output (I/O) ports. The design procedures and their limitations are discussed in detail. The proposed filters are fabricated, measured and showing good characteristics of 87% fractional bandwidth as well as good insertion/return loss, flat group delay varies between 0.3-1.5 ns. High passband selectivity and wide stopband from 8-14 GHz are obseved. The measured results are also having a good agreement with the simulated results.

2009-12-16 PIER Vol. 100, 129-152, 2010. doi:10.2528/PIER09091705

Critical Analysis of Microwave Specular Scattering Response on Roughness Parameter and Moisture Content for Bare Periodic Rough Surfaces and its Retrieval

Gunjan Mittal and Dharmendra Singh

The main aim of this paper is to accentuate the sensitivity of correlation length 'l' as an important roughness parameter in quantifying the moisture content of bare soil surfaces with specular scattering. For this purpose, an indigenously designed bistatic scatterometer has been used to generate co-polarized specular data at X-band (10 GHz) with incidence angle varied from 30°-- 70°in steps of 10 degrees. The moisture and roughness conditions of the bare soil surface were changed under controlled conditions. Twenty seven experimental fields specified on the ground of different roughness and moisture conditions have been analyzed. Higher level of moisture content with larger correlation lengths was found to be more suitable for observing the effect of increasing rms height on specular scattering. Kirchhoff approach (KA) considered under the stationary phase approximation (SPA) has been used as an inversion algorithm with the application of genetic algorithm for the retrieval of soil parameters. A good agreement was observed between the experimental and retrieved values of soil moisture content (mν) and roughness parameters (s and l).

2009-12-16 PIER Vol. 100, 119-128, 2010. doi:10.2528/PIER09111606

Subspace-Based Optimization Method for Reconstructing Perfectly Electric Conductors

Xiuzhu Ye, Xudong Chen, Yu Zhong, and Krishna Agarwal

Reconstruction of perfectly electric conductors (PEC) with transverse magnetic (TM) illumination by a subspace-based optimization method (SOM) is presented. Apart from the information that the unknown object is PEC, no other prior information such as the number of the objects, the approximate locations or the centers is needed. The whole domain is discretized into segments of current lines. Scatterers of arbitrary number and arbitrary shapes are represented by a binary vector, and the descent method is used to solve the discrete optimization problem. Several numerical simulations are chosen to validate the proposed method. In particular, a combination of a line type object and a rectangular shape object is successfully reconstructed. The subspace-based optimization method for PEC scatterers is found to be more complex than its counterpart for dielectric scatterers.

2009-12-15 PIER Vol. 100, 105-117, 2010. doi:10.2528/PIER09102903

Design Optimization of a Bow-Tie Antenna for 2.45 GHz RFID Readers Using a Hybrid Bso-Nm Algorithm

Korany Mahmoud

Recently the Bacterial foraging optimization algorithm (BFA) has attracted a lot of attention as a high-performance optimizer. This paper presents a hybrid approach involving Bacterial Swarm Optimization (BSO) and Nelder-Mead (NM) algorithm. The proposed algorithm is used to design a bow-tie antenna for 2.45 GHz Radio Frequency Identification (RFID) readers. The antenna is analyzed completely using Method of Moments (MoM), then the MoM code is coupled with the BSO-NM algorithm to optimize the antenna. The simulated antenna and the optimization algorithm programs were implemented using MATLAB version 7.4. To verify the validity of numerical simulations, the results are compared with those obtained using Feko Software Suite 5.3.

2009-12-15 PIER Vol. 100, 83-103, 2010. doi:10.2528/PIER09111611

Optimum Design of Lumped Filters Incorporating Impedance Matching by the Method of Least Squares

Homayoon Oraizi and Mehdi Esfahlan

The method of least squares (MLS) is used to develop an algorithm for the optimum design of any type of filter under any design specifications for the realization of lowpass, bandpass, highpass and bandstop characteristics. The proposed filter design method can be used for any general filter network topology, which provides high flexibility for the selection of circuit configurations suitable for any desired application. The MLS filter design procedure also incorporates source and load impedance matching, which eventually leads to the simplicity of circuits. The proposed method of filter design may be used for lowpass prototype filters or directly for bandpass, highpass or bandpass filters. Several examples of MLS filter designs are given, which compare very well with the classical methods and indicate the advantages of the proposed method of filter design. The MLS filter design may realize any frequency response characteristics, such as spurious response elimination, multiband filter realization and enhancement of some desired behaviors.

2009-12-14 PIER Vol. 100, 69-82, 2010. doi:10.2528/PIER09112201

A Wideband Wide-Strip Dipole Antenna for Circularly Polarized Wave Operations

Li-Pin Chi, Sheau-Shong Bor, Sheng-Ming Deng, Ching-Long Tsai, Peng-Hao Juan, and Kuo-Wei Liu

A thin dipole antenna is a well-known antenna with linearly polarized wave operation. In this work, a wide-strip dipole antenna is proposed for circularly polarized wave operations. To obtain circularly polarized (CP) wave operations, there are two conditions to be satisfied. One is that the antenna must have two degenerated orthogonal modes with different resonant frequencies. The other is that the phase difference of two orthogonal modes is 90 degrees. To match the first condition, the slab width W is tuned to generate current distributions directed in two different directions. In addition, the second condition is matched by asymmetric feeding point by adjusting the overlapped square width C. The parametric study is completed by the Ansoft HFSS simulator. Simulated results reveal that the CP wave is mainly influenced by the slab width W. The influences of the parameters C and d on the performances of the proposed antenna are also investigated in this paper. Taking -8 dB as reference, there are two working bands for this proposed antenna and the measured center frequencies are 0.66 GHz and 2.04 GHz, respectively, and the corresponding bandwidths are 0.27 GHz (40%) and 1.78 GHz (87%), respectively. In addition, the measured center frequencies and bandwidths of the axial ratio are 1.94 GHz and 0.53 GHz (27%), respectively.

2009-12-13 PIER Vol. 100, 55-68, 2010. doi:10.2528/PIER09110103

Planar Transformers Excited by Square Waves

Eduard Montgomery Meira Costa

This paper presents an analysis of found results in experiments developed with transformers built with planar coils, when they are excited by square waves, in comparison with transformers built with planar coils inner ring coils. The transformer was built joining two planar coils one over the other. In this kind of transformer, similar responses as analysis of transformers built with planar coil inner ring coil are found, as well the results of resonance. Because the low self-inductances and parasitic capacitances obtained in these configurations, although the coils resistance is low, which generates low exponential drops on responses. The resonance is found in higher frequencies, but satisfying conditions of sum of responses in resonance.

2009-12-14 PIER Vol. 100, 37-54, 2010. doi:10.2528/PIER09111108

Hybrid Method of Obtaining Degrees of Freedom for Radial Airgap Length in SRM Under Normal and Faulty Conditions Based on Magnetostatic Model

Hossein Torkaman and Seyed Ebrahim Afjei

In this paper, a new hybrid method of obtaining the degrees of freedom for redial airgap length in Switched Reluctance Motor operation under normal and faulty conditions based on magnetiostatic analysis is presented. At the beginning, this method goes through the magnetic design of the motor utilizing three dimensional (3-D) Finite Element Method (FEM) in order to consider the end effects as well as axial fringing field effects. The motor parameters, such as torque, flux linkage, flux density versus rotor position are precisely obtained. Then, a Multi Layered Perceptron Neural Network is designed by considering the nonlinear behavior of the motor parameters obtained under different modes of operatin. Using this network and the obtained parameters from FEM, an Objective Function (OF) for torque ripple with the aim of having a minimum mean square error is estimated. In addition, an improved Genetic Algorithm (GA) for the minimization the OF is also presented to determine the motor's operational regions. Finally, the legal intervals for different modes of motor operation are addressed.

2009-12-10 PIER Vol. 100, 27-36, 2010. doi:10.2528/PIER09111610

Enhancement of Photonic Band Gap in a Disordered Quarter-Wave Dielectric Photonic Crystal

Chien-Jang Wu, Yu-Nian Rau, and Wei-Hsieh Han

The enhancement of the photonic band gap in visible region for a disordered one-dimensional dielectric-dielectric photonic crystal (DDPC) is theoretically investigated. The DDPC is made of alternating two high/low-index quarter-wave dielectric layers stacked periodically. A disordered DDPC is modeled by randomly changing the real thicknesses, or, the optical lengths, of the two dielectrics. In a single disorder case, where the disorder only appears in one of the two constituents, it is found the photonic band gap can be preferably enhanced for the disordered high-index layer. In the double disorder stack, in which both the constituent layers are disordered, the photonic band gap can, however, be significantly enlarged. In addition, numerical results illustrate that a flat band gap can be obtained by the use of disorder in the optical length.

2009-12-09 PIER Vol. 100, 13-26, 2010. doi:10.2528/PIER09091706

Microwave Measurements of Dielectric Constants by Exponential and Logarithmic Mixture Equations

Jyh Sheen, Zuo-Wen Hong, Che-Wei Su, and Heng-Chou Chen

This article reports on a study of the dielectric constants of ceramic dispersions in the polyethylene matrix at microwave frequency. The exponential and logarithmic mixture rules are studied in three ceramic powders of fillers with dielectric constants 10, 20, and 36, respectively. The experimental values of the dielectric constants of the mixtures are compared to those obtained by using different mixing laws. The mixing rules are also adopted to calculate the dielectric constants of pure ceramics from the measured dielectric constants of composites with various concentrations. The theories on errors of calculations are studied. The most adequate mixture equation for measuring the dielectric constants of pure ceramics is suggested.

2009-12-09 PIER Vol. 100, 1-12, 2010. doi:10.2528/PIER09112506

Equivalent Electrical Circuit for Designing MEMS-Controlled Reflectarray Phase Shifters

Farooq Ahmad Tahir, Herve Aubert, and Etienne Girard

This article presents an equivalent electrical circuit for designing Radio-Frequency MEMS-controlled planar phase shifter. This kind of phase shifters has recently been incorporated in reconfigurable reflectarrays. The proposed equivalent circuit depends on the number, the ON/OFF state and the locations of the switches inside the unit cell. Such equivalent circuit is used for determining, with a little computational effort, the two important design parameters i.e., the number and the locations of RF-MEMS switches in the phase shifter cell. These two design parameters then allow a designer to design a phase shifter cell having a linear distribution of a given number of phases over 360° phase range at a single desired frequency.