Sencer Koc

Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem

The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate---but fast---methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.

A Monolithic Phased Array Using 3-bit Distributed RF MEMS Phase Shifters

This paper presents a novel electronically scanning phased-array antenna with 128 switches monolithically implemented using RF microelectromechanical systems (MEMS) technology. The structure, which is designed at 15 GHz, consists of four linearly placed microstrip patch antennas, 3-bit distributed RF MEMS low-loss phase shifters, and a corporate feed network. MEMS switches and high-Q metal-air-metal capacitors are employed as loading elements in the phase shifter. The system is fabricated monolithically using an in-house surface micromachining process on a glass substrate and occupies an area of 6 cm times 5 cm. The measurement results show that the phase shifter can provide nearly 20deg/50deg/95deg phase shifts and their combinations at the expense of 1.5-dB average insertion loss at 15 GHz for eight combinations. It is also shown by measurements that the main beam can be steered to required directions by suitable settings of the RF MEMS phase shifters.

Calculation of acoustical scattering from a cluster of scatterers

The problem of determining the field scattered by a cluster of scatterers when they are insonified by a known acoustical field is addressed. The problem is formulated by using the T-matrix method and the resulting system of linear equations is solved by using the multilevel fast multipole algorithm (MLFMA) and the fast multipole method–fast Fourier transform (FMMFFT) method, and the efficiency of the two methods is compared. It was observed that, in general, the MLFMA performs better than the FMMFFT algorithm. However, when the scatterers are distributed uniformly on a rectangular grid, the FMMFFT algorithm performs as good as the MLFMA. The accuracy of the methods is evaluated by modeling a spherical scatterer as composed of many small spheres.

A succinct way to diagonalize the translation matrix in three dimensions

The fast multipole method is an effective way to expedite iterative solutions of integral equations for electrodynamic and elastodynamic problems. Iterative solvers, such as the conjugate gradient method, require matrix vector multiplies, and for dense matrices, these matrix-vector multiplies constitute the predominant computational cost as well as requiring a large memory. The fast multipole method is based on the translation of multipoles from one coordinate system to another, which is achieved by using translation matrices. However, the mere use of translation matrices does not reduce the computational cost nor the memory requirement for dynamic problems involving surface scatterers. For such problems, the crucial step in the fast multipole method is the diagonalization of the translation operators. The translation matrix for the three dimensional Helmholtz wave equation has been successfully diagonalized using an alternative and succinct method. The method reveals the relationship between the translation matrices and their representation of the translation group. A diagonalization is expected under a plane-wave basis for the representation since a plane-wave basis forms an irreducible representation for the translation group. Hence, the diagonalization of the translation matrices from the spherical harmonic representation can be viewed as a series of similarity transforms. The result can be used in the fast multipole method and the multilevel fast multipole method where multiple scattering involves interaction between multipoles.

Two alternative expressions for the spherical wave expansion of the time domain scalar free-space Green’s function and an application: Scattering by a soft sphere

The importance of expanding Green’s functions, particularly free-space Green’s functions, in terms of orthogonal wave functions is practically self-evident when frequency domain scattering problems are of interest. With the relatively recent and widespread interest in time domain scattering problems, similar expansions of Green’s functions are expected to be useful in the time domain. In this paper, two alternative expressions, expanded in terms of orthogonal spherical wave functions, for the free-space time domain scalar Green’s functions are presented. Although the two expressions are equivalent, one of them is seen to be more convenient for the calculation of the scattered field for a known equivalent source density, whereas the second expression is more suitable for setting up an integral equation for the equivalent source density. Such an integral equation may be setup, for example, by the application of a time domain equivalent of the T-matrix (extended boundary condition) method.

A monolithic phased array using 3-bit DMTL RF MEMS phase shifters

This paper presents a phased array system designed at 15 GHz employing 3-bit distributed MEMS transmission line (DMTL) type phase shifters which are monolithically integrated with the feed network of the system and the radiating elements on the same substrate. The phase shifter can give 0deg-360deg phase shift with 45deg steps at 15 GHz which is used to obtain various combinations of progressive phase shift in the excitation of radiating elements. The phased array is composed of four linearly placed microstrip patch antennas. In order to monolithically integrate the patch antennas and phase shifters, tapered lines with low return loss from microstrip to coplanar waveguide (CPW) have been designed. The design of the phased array system and its components is given. Since the DC biasing schema of a MEMS system is also an important issue in terms of the RF losses, the paper also addresses the effect of the bias lines on the loss characteristics of the phase shifters. Moreover, the process steps, which are used in the fabrication of the phased array, are also summarized

A Reconfigurable RF MEMS Triple Stub Impedance Matching Network

This paper presents a reconfigurable triple stub impedance matching network using RF MEMS technology centered at 10GHz. The device is capable of covering impedances on the whole Smith Chart. The device structure consists of three variable length stubs which are designed as distributed MEMS transmission lines and two lambdag/8 length CPW transmission lines connecting the stubs. The variable length stubs are implemented with 12 MEMS switches over CPW lines and CPW lines connecting the switches. lambdag/8 spacing between the stubs is selected to obtain a uniform distribution of the impedance points on the Smith Chart. Initial measurement results of the fabricated structure show a good agreement with the simulation results

Dual-frequency reconfigurable slot dipole array with a CPW-based feed network using RF MEMS technology for X- and ka-band applications

In recent years there is a growing interest to combine various wireless applications in a single system for miniaturization purposes. A reconfigurable MEMS antenna that can operate in multi- frequencies is an appropriate way of reducing system volume. The monolithic integration of tunable MEMS components with antennas can also reduce parasitic effects, the losses, and packaging costs. Moreover an array of these types of antennas can offer solutions for the systems requiring high antenna gains. This paper presents a 4-element linear array of dual-frequency slot dipole antennas whose resonant frequencies are controlled via MEMS switches placed on the slots. The corporate feed network of the array is realized with coplanar wave transmission (CPW) lines. A CPW-based feed network has advantages over a microstrip feeding network, such as low radiation losses, less dispersion, easier in combining active devices for active array implementation, and the possibility of connecting shunt lumped without the need of via holes through the substrate. The CPW-based feed network in this paper includes properly designed T-junctions, chamfered corners, and dual-frequency impedance transformers in order to match the input impedance at the resonant frequency of the antennas. The proposed array structure, reconfigurable slot dipole antenna, and the details about the dual-frequency impedance transformer are presented in the following sections.

Reconfigurable reflectarray using RF MEMS technology

This paper presents the design of a reconfigurable microstrip slot-coupled patch reflectarray using RF MEMS switches. The reflectarray is designed on two back-to-back bonded glass substrates front side of which contains the microstrip patch antenna elements and the backside contains the phase shifting elements. The phase shifting elements consist of microstrip lines the lengths of which are adjusted with MEMS switches resulting with adjustable phase characteristics of each antenna element. A transmission line based model is used to model the unit element of the array which is used to obtain a phase design curve and the design is verified with HFSS. The 4 × 1 array is then designed at 26 GHz to verify the phase design curve and according to the HFSS simulations, the main beam of the array is rotated by 14° by reconfiguring the length of the microstrip transmission lines with RF MEMS switches.

RF MEMS adjustable impedance matching network and adjustable power divider

MEMS applications are gaining wide acceptance in microwave applications. In this paper we present two novel applications of MEMS on well known RF devices: triple stub matching and power divider. Particularly for phased array antennas, controllable components are vital. We have developed a triple stub matching circuit. The stub lengths are electrically adjustable and therefore impedance matching is achieved for any impedance depending on changing conditions such as frequency of operation. This triple stub matching circuit is utilized in the design of an adjustable power divider.