ANALYSIS AND DESIGN OF CONFORMAL ARRAY ANTENNAS Patrik Persson KTH Royal Institute of Technology Division of Electromagnetic Theory Stockholm 2001 P. Persson: Analysis and Design of Conformal Array Antennas ISBN 91-7283-231-2 Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan framlägges till offentlig granskning för avläggande av teknisk doktorsexamen i teoretisk elektroteknik, tisdagen den 29 januari 2002, kl. 13.15 i Kollegiesalen, Administrationsbyggnaden, KTH, Valhallavägen 79, Stockholm. Avhandlingen kommer att försvaras på engelska. Copyright 2001 Patrik Persson Printed in Sweden by Universitetsservice US AB, Stockholm December 2001 ii Abstract Abstract Today there is a great need for communication between people and even between things, using systems onboard e.g. aircraft, cars, ships and satellites. As a consequence, these communications needs require antennas mounted on or integrated in the surfaces of different vehicles or platforms, i.e. conformal antennas. In order to ensure proper operation of the communication systems it is important to be able to determine the characteristics of these antennas. This thesis is about the analysis and design of conformal antennas using high frequency asymptotic methods. Commonly used eigenfunction solutions or numerical methods such as FDTD, FEM or MoM are difficult to use for arbitrarily shaped electrically large surfaces. However, the high frequency approximation approach together with an accurate ray tracing procedure offers a convenient solution for these surfaces. The geodesics (ray paths) on the surfaces are key parameters in the analysis and they are discussed in detail. In the first part of the thesis singly and doubly curved perfectly electrical conducting (PEC) surfaces are studied, with respect to the mutual coupling among aperture type elements. A synthesis problem is also considered where the effect of the mutual coupling is taken into account. As expected, the mutual coupling must be included in the synthesis procedure to be able to realize the prescribed pattern, especially in the shaped main lobe. Furthermore, the polarization of the antenna elements is very important when considering antennas on generally shaped surfaces. For such antennas the polarization must most likely be controlled in some way for a proper function. For verification of the results two experimental antennas were built at Ericsson Microwave Systems AB, Mölndal, Sweden. The first antenna is a circular cylinder with an array of rectangular waveguide fed apertures and the second antenna is a doubly curved surface (paraboloid) with circular waveguide fed apertures. It is found that it is possible to obtain very accurate results with the asymptotic method when it is combined with the Method of Moments, i.e. a hybrid method is used. The agreement compared to measurements is good at levels as low as –80 dB in many cases. The second part of the thesis is about the development of a high frequency approximation for surface field calculations on a dielectric covered PEC circular cylinder. When using conformal antennas in practice they have to be covered with a radome for protection and with the method developed here this cover can be included in the analysis. The method is a combination of two different solutions, one valid in the non-paraxial region of the cylinder and the other is valid in the paraxial region. The method is verified against measurements and reference results obtained from a spectral domain moment method code. Keywords: Conformal antennas, conformal arrays, UTD, high frequency method, MoM, hybrid method, mutual coupling, singly curved surface, doubly curved surface, geodesics, dielectric covered circular cylinder, non-paraxial region, paraxial region, waveguide fed apertures, synthesis. iii P. Persson: Analysis and Design of Conformal Array Antennas iv Preface Preface The work of this thesis has been carried out mainly at the Division of Electromagnetic Theory (formerly the Department of Electromagnetic Theory) at the Royal Institute of Technology (KTH). I have spent almost 5 years at KTH (February 1997 to December 2001) working with conformal antennas and it has certainly been an interesting time. I have enjoyed (almost) every day of this part of my life. I will, in particular, remember my visit at the ElectroScience Laboratory, The Ohio State University, Columbus, Ohio during the period September 2000 to March 2001. Thank you Prof. Roberto G. Rojas for your support during this time. Thanks to Prof. Prabhakar H. Pathak as well (I am looking forward to the dinner...). During this period at KTH I have had the honor of working with Adj. Prof. Lars Josefsson, my supervisor. I would like to express my deepest gratitude to you for your excellent guidance and support on this work. Thank you for taking the initiative to build two experimental conformal antennas at Ericsson Microwave Systems AB (EMW), Mölndal, Sweden. I also owe you a great dept of gratitude for long spent hours reading my manuscripts. It has always been an interesting event reading your comments; how much red ink did you use this time? I also want to thank my colleagues at "TET" for the inspiring atmosphere. In particular Björn Thors for fruitful discussions and for your careful review of my work. In addition to calculated results, this thesis would not have been anything without the measured data obtained at EMW. Thank you Stefan Lindgren for doing the measurements on the circular cylinder (without the dielectric layer). Many thanks to Maria Lanne as well for your patience with the measurements on the doubly curved surface, but also on the circular cylinder (with the dielectric layer). Furthermore, it has been a pleasure to get to know you Dr. Zvonimir Sipus, University of Zagreb, Croatia. I wish to thank you for the calculated reference data and for interesting discussions. Finally, I wish to thank my wife for her patience and sacrifice. Jeanette, this is for you, I love you! Patrik Persson Stockholm December, 2001 v P. Persson: Analysis and Design of Conformal Array Antennas vi Table of contents Table of contents Abstract iii Preface v Table of contents vii List of papers ix Specification of my contributions to the included papers xi 1. Conformal antennas 1 1.1 Introduction 1 1.2 Definition of a conformal antenna 1 1.3 A historical review 1 1.4 Why a conformal antenna? 8 1.5 The challenges 9 1.6 Conformal arrays versus planar arrays 9 1.7 The future 10 2. Analyzing conformal array antennas – an overview 11 2.1 Introduction 11 2.2 Low frequency analysis 11 2.3 High frequency analysis 12 2.4 Final comments 15 3. Development of asymptotic methods 17 3.1 Introduction 17 3.2 Properties of the integrand 18 22− 3.3 Definition of kkz in the complex plane and the 19 determination of the path of integration 3.4 The Watson transformation 20 3.5 The Fock substitution 24 3.6 The polar transformation 26 3.7 The steepest descent representation 27 3.8 The paraxial region 29 4. General smooth convex surfaces 31 4.1 Introduction 31 4.2 Geodesics 31 4.3 The convex cylindrical surface 31 4.4 Generalization to an arbitrary convex surface 32 4.5 Final comments 33 vii P. Persson: Analysis and Design of Conformal Array Antennas 5. Poles and surface waves 35 5.1 Introduction 35 5.2 The dielectric covered PEC circular cylinder 35 5.3 The grounded dielectric slab, planar case 38 5.4 Discussion of the relation between the planar and 40 cylindrical cases 6. Summary of papers 43 6.1 Introduction 43 6.2 Summary of paper I 44 6.3 Summary of paper II 44 6.4 Summary of paper III 44 6.5 Summary of paper IV 45 6.6 Summary of paper V 45 6.7 Summary of paper VI 46 6.8 Summary of paper VII 46 7. References 47 Paper I Calculating the Mutual Coupling between Apertures on a 55 Convex Circular Cylinder Using a Hybrid UTD-MoM Method Paper II The Mutual Coupling between Apertures on Convex Cylinders 71 Paper III Conformal Array Synthesis Including Mutual Coupling 85 Paper IV Calculating Geodesics on Doubly Curved Surfaces: The case 95 of a General Paraboloid of Revolution Paper V Investigation of the Mutual Coupling between Apertures on 119 Doubly Curved Convex Surfaces: Theory and Measurements Paper VI A High Frequency Approximation for Mutual Coupling Calculations 139 between Apertures on a PEC Circular Cylinder Covered with a Dielectric Layer Valid in the Non-Paraxial Region: The Gzz and Gϕϕ cases Paper VII A High Frequency Approximation for Mutual Coupling Calculations 169 between Apertures on a PEC Circular Cylinder Covered with a Dielectric Layer Valid in the Paraxial Region: The Gzz case viii List of papers List of papers I. Patrik Persson and Lars Josefsson, ”Calculating the Mutual Coupling between Apertures on a Convex Circular Cylinder Using a Hybrid UTD-MoM Method”, IEEE Transactions on Antennas and Propagation, Vol. 49, No. 4, pp. 672-677, April 2001. II. Patrik Persson, ”The Mutual Coupling between Apertures on Convex Cylinders”, RVK 99, Karlskrona, Sweden, June 1999. III. Lars Josefsson and Patrik Persson, ”Conformal Array Synthesis Including Mutual Coupling”, Electronics Letters, Vol. 35, No. 8, pp. 625-627, 15th April 1999. IV. Patrik Persson and Lars Josefsson, ”Calculating Geodesics on Doubly Curved Surfaces: The case of a General Paraboloid of Revolution”, Technical report TRITA-TET 00-07, KTH, Stockholm, May 2000. V. Patrik Persson, Lars Josefsson and Maria Lanne, ”Investigation of the Mutual Coupling between Apertures on Doubly Curved Convex Surfaces: Theory and Measurements”, Submitted to IEEE Transactions on Antennas and Propagation. VI. Patrik Persson and Roberto G. Rojas, ”A High Frequency Approximation for Mutual Coupling Calculations between Apertures on a PEC Circular Cylinder Covered with a Dielectric Layer Valid in the Non-Paraxial Region: The Gzz and Gϕϕ cases”.