Analytical Techniques in Electromagnetics is designed for researchers, scientists, and engineers seeking analytical solutions to electromagnetic (EM) problems. The techniques presented provide exact solutions that can be used to validate the accuracy of approximate solutions, offer better insight into actual physical processes, and can be utilized in finding precise quantities of interest over a wide range of parameter values.
Beginning with a review of basic EMs, the text:
- Describes the use of the separation of variables technique in Laplace, heat, and wave equations, covering rectangular, cylindrical, and spherical coordinate systems
- Explains the series expansion method, providing the solution of Poisson's equation in a cube and in a cylinder, and scattering by cylinders and spheres, as examples
- Addresses the conformal transformation technique, offering a visual display of conformal mapping and a brief introduction to the Schwarz–Christoffel transformation
- Employs worked-out problems to demonstrate various applications of Fourier sine and cosine, two-sided Fourier, Laplace, Hankel, and Mellin transform techniques
- Discusses perturbation techniques, supplying examples of perturbed results degenerating to their unperturbed versions as the perturbation parameters tend to zero
Analytical Techniques in Electromagnetics maintains a balanced view of techniques for solving EM problems, refusing to overemphasize the importance of analytical methods at the expense of numerical techniques. Carefully selected topics give readers an appreciation of the kinds of EM problems that can be solved exactly.
Review of Electromagnetics
Power and Energy
Vector and Scalar Potentials
Time Harmonic Fields
Classification of EM Problems
Separation of Variables
Conditions for Complete Separability
Series Expansion Method
Generalized Fourier Series
Poisson's Equation in a Cube
Poisson's Equation in a Cylinder
Strip Transmission Line
Scattering by a Conducting Cylinder
Scattering by a Dielectric Sphere
Functions of a Complex Variable
Derivative of a Complex Function
Complex Electric Potential
Coplanar Strips at Fixed Potentials
Evaluation of Capacitance per Unit Length
The Schwarz–Christoffel Transformation
Strip Lines and Microstrip Lines
Strip with Finite Ground Plane
Strip Line with Elliptical Center Conductor
The Fourier Transform
The Fourier Sine and Cosine Transforms
The Hankel Transform
The Mellin Transform
The Underlying Technique
"... a very good set of analytical methodologies useful for solving electromagnetic problems. It could be used as a textbook for a separate, elective, senior-level course for students in electrical engineering departments. ... This book fills the gap in the current educational infrastructure."
—Marian K. Kazimierczuk, Wright State University, Dayton, Ohio, USA
"This text lays out in lavish detail classical analytic methods for solving second order partial differential equations in cartesian, cylindrical, and spherical geometries. Its singular strength is showing many of the steps in derivations, rather than just a few highlights."
—John D. Sahr, Electrical Engineering Department, University of Washington, Seattle, USA
"Overall, I appreciate the authors’ intent for the book, and their carefully selected analysis techniques and specific example problems. The mathematical techniques for solving the partial differential equations are straightforward and present a set of analysis methods that can be used to solve a wide variety of problems. The example solutions are rigorous and easy to follow given the foundations in chapter 2 and 3. I could see this book as a course textbook in beginning graduate courses on electromagnetics or as a desktop reference."
—Michael A. Saville, PhD, PE, Wright State University, Dayton, Ohio, USA
"... an essential textbook for anyone working with computations in electromagnetics. ... The book is very well written with a logical organization of the material into six chapters. The approach is pedagogical and there are detailed illustrations, in fact, around 100 of them. Applications of methods are illustrated with a variety of problems. Key references are provided at the end of each chapter. Each chapter is ended with a group of problems for exercise. The book provides a strong theoretical foundation for senior undergraduate students or graduate students and practicing engineers in analytical techniques in electromagnetics."
—Rajeev Thottappillil, KTH Royal Institute of Technology, Sweden
"As computer software for electromagnetic problems becomes ubiquitous, analytical solutions of these problems become indispensable for the validation and verification process. This book addresses the classical methods of solution by separation of variables. The book serves as a perfect introduction to the solution of the partial differential equation in the classical coordinate systems. To further widen the solution methods, the conformal mappings and perturbation methods are introduced. The generalized Fourier method is employed without too much mathematical artillery. Indeed, the focus is on the applications of the method. The text is comprehensive, and numerous examples illustrate the line of thought, which makes the text easy to follow."
—Gerhard Kristensson, Department of Electrical and Information Technology, Lund University, Sweden