Mutual Coupling Between Broadside Printed Dipoles Embedded in Stratified Anisotropic Dielectrics Benjamin D. Braaten* Robert M. Nelson David A. Rogers North Dakota State University Topics Problem Definition Spectral domain immittance functions Results Discussion Conclusion North Dakota State University Problem Definition Consider: North Dakota State University Interests The previous problem is of interest in many fields. Microstrip antenna arrays [4]. Frequency Selective Structures (FSS) [5] Radio Frequency Identification (RFID) [6] IC based antennas Radar [4] David M. Pozar and Daniel H. Schaubert, Microstrip Antennas: The analysis and Design of Microstrip Antennas and Arrays, IEEE Press, Piscataway, NJ, [5] A.L.P.S. Campos an A.G. d'Assuncao, Scattering parameters of a frequency selective surface between anisotropic dielectric layers for incident co-polarized plane waves, IEEE Antennas and Propagation Society International Symposium, 2001, Vol. 4, July 8-13, 2001, p [6] K. Finkenzeller, RFID Handbook:Fundamentals and Applications in Contactless Smart Cards and Identification, John Wiley and Sons, West Sussex, England, 2003. The new spectral domain immittance functions North Dakota State University Start with the following Hertz vector potentials: and Electric Hertz potential Magnetic Hertz potential The new spectral domain immittance functions North Dakota State University Next, only the y-direction of the Hertz vector potential is needed. and This is because the optical axis is in the y- direction and this component satisfies the higher order TE and TM tangential boundary conditions. The new spectral domain immittance functions North Dakota State University Now define the following expression for the magnetic and electric field: where the Hertzian vector potentials are solutions to the following wave equations: The new spectral domain immittance functions North Dakota State University and The new spectral domain immittance functions North Dakota State University To simplify evaluating the previous expressions, we define the following Fourier transform: This results in the following relations: The new spectral domain immittance functions North Dakota State University This results in the following simplified expressions: where and The new spectral domain immittance functions North Dakota State University Similarly for and The new spectral domain immittance functions North Dakota State University Double layer problem The new spectral domain immittance functions North Dakota State University Double (and Triple) layer problems After extensive factoring and manipulation, the following spectral domain immittance functions are derived: and and The new spectral domain immittance functions North Dakota State University An example of a spectral domain immittance function: Solving the new expressions North Dakota State University The spectral domain moment method was used to solve for the unknown current. PWS functions were used as expansion and basis functions. A delta source was used to drive the problem. Dipole Results North Dakota State University Consider: Dipole Results North Dakota State University A single anisotropicsubstrate (d 1 = 1.58 mm): Dipole Results North Dakota State University A single anisotropiccover (d 1 = 1.58 mm d 2 = 1.58 mm): d 2 = 1.58 mm): Dipole Results North Dakota State University Separated by a single anisotropic layer (d 1 = 1.58 mm d 2 = 1.58 mm): d 2 = 1.58 mm): Conclusion North Dakota State University New multi-conductor spectral domain immittance functions have been summarized. Broadside printed dipoles on a single anisotropic substrate have been investigated. It is shown that the permittivity in the y-direction (direction of the optical axis) has the largest impact on the mutual coupling. Broadside printed dipole with a single anisotropic superstrate have been investigated. It is shown that the mutual coupling is unaffected by the permittivity in the y-direction (direction of the optical axis). Conclusion North Dakota State University Broadside printed dipoles separated by a single anisotropic superstrate have been investigated. It is shown that both components of the permittivity affect the mutual coupling. Questions Thank you for listening North Dakota State University