IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 51, NO. 4, APRIL 2003 739 Efficient Analysis of Input Impedance and Mutual Coupling of Microstrip Antennas Mounted on Large Coated Cylinders V. B. Ertürk, Member, IEEE, and R. G. Rojas, Fellow, IEEE Abstract—An efficient and accurate hybrid method, based on the combination of the method of moments (MoM) with a special Green’s function in the space domain is presented to analyze an- tennas and array elements conformal to electrically large mate- rial coated circular cylinders. The efficiency and accuracy of the method depend strongly on the computation of the Green’s func- tion, which is the kernel of the integral equation that is solved via MoM for the unknown equivalent currents representing only the antenna elements. Three types of space-domain Green’s function representations are used, each accurate and computationally effi- cient in a given region of space. Consequently, a computationally optimized analysis tool for conformal microstrip antennas is ob- tained. Input impedance of various microstrip antennas and mu- tual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hy- brid method. Index Terms—Coated cylinders, Green’s function, input impedance, method of moments, mutual coupling. I. INTRODUCTION T HERE have been major advances in the area of computer- aided design (CAD) technology directed toward the de- velopment of efficient and accurate numerical methods for the design and analysis of microstrip antennas and arrays. Although there are many practical applications that require the use of an- tennas that conform to their supporting surfaces, most work on microstrip elements has been for planar structures. There are some techniques that can be used for the analysis of con- formal arrays; however, they are usually restricted to small ar- rays mounted on electrically small cylinders. This necessitates the development of efficient analytical and numerical tools for this class of antennas conformal to electrically large, cylindri- cally shaped substrates. Several techniques to design/analyze cylindrical microstrip antennas and arrays have been reported for a number of appli- cations [1]–[10]. Among them, cavity-model analysis [2], [3] and generalized transmission-line model (GTLM) theory [8], [9] are fairly simple and accurate models but not suitable for many structures, in particular, if the thickness of the substrate is not very thin [10]. On the other hand, full-wave solutions [4]–[7] are more accurate and applicable to many structures. The Manuscript received February 25, 2001; revised July 19, 2001. V. B. Ertürk is with the Department of Electrical and Electronics Engineering, Bilkent University, TR-06533 Bilkent, Ankara, Turkey. R. G. Rojas is with the Department of Electrical Engineering, ElectroScience Laboratory, The Ohio State University, Columbus, OH 43212-1191 USA. Digital Object Identifier 10.1109/TAP.2003.811060 full-wave analysis of microstrip antennas and arrays on coated circular cylinders has been mainly performed using a method of moments (MoM)/Green’s function technique in the spectral domain where the traditional eigenfunction series representa- tion of the Green’s function is used as the kernel of the inte- gral equation [4]–[6]. However, due to the computational com- plexity of the solution, which involves a series summation in terms of Bessel and Hankel functions and a Fourier integral, most of the numerical results have been given for microstrip antennas mounted on circular cylinders with electrically small radii. Furthermore, the spectral-domain representation of the Green’s function has serious convergence problems for electri- cally large separations between source and observation points on electrically large cylinders. This makes the analysis of mu- tual coupling between microstrip antennas intractable, in partic- ular, at high frequencies. Carefully chosen basis functions for the expansion of the patch surface currents can alleviate this problem only to an extent. A few asymptotic representations for the dyadic Green’s function of impedance and dielectric coated circular conducting cylinders have been presented to overcome this difficulty [11]–[15]. However, an asymptotic Green’s func- tion must be accurate for arbitrary source and observation loca- tions if it is to be used in an MoM-based solution. As shown here, more than one asymptotic Green’s function representa- tion may be required for an efficient and accurate analysis of microstrip antennas/arrays mounted on electrically large mate- rial-coated circular cylinders. Purely numerical techniques such as the finite-element as well as the finite-difference time-domain [16] techniques are becoming popular and have also been used for the analysis of conformal antennas. Although purely numer- ical techniques can handle arbitrary geometries, they are not ef- ficient when the structures become electrically large. In this paper, we present a highly efficient and accurate hybrid method to design/analyze microstrip antennas and arrays con- formal to electrically large material coated circular cylinders. This hybrid method is based on the combination of the MoM with a special Green’s function in the space domain. To obtain a high degree of accuracy, three different space-domain represen- tations are used for this special Green’s function, each chosen on the basis of its computational efficiency and the region where it remains accurate. Consequently, a computationally optimized design/analysis tool for conformal microstrip antennas and ar- rays is obtained. In Section II, development of the integral equa- tion and expressions for three different space-domain represen- tations are given along with the MoM solution. In Section III, numerical results involving the mutual impedance between two 0018-926X/03$17.00 © 2003 IEEE