Mutual Coupling Between Broadside Printed Dipoles Embedded in Stratified Anisotropic Dielectrics Benjamin D. Braaten* Robert M. Nelson David A. Rogers
Topics Problem Definition Spectral domain immittance functions Results Discussion Conclusion
Problem Definition Consider:
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, 1995. [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. 382-385. [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 Start with the following Hertz vector potentials: and Electric Hertz potential Magnetic Hertz potential
The new spectral domain immittance functions 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 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 and
The new spectral domain immittance functions To simplify evaluating the previous expressions, we define the following Fourier transform: This results in the following relations:
The new spectral domain immittance functions This results in the following simplified expressions: where and
The new spectral domain immittance functions Similarly for and
The new spectral domain immittance Double layer problem functions
The new spectral domain immittance functions Double (and Triple) layer problems After extensive factoring and manipulation, the following spectral domain immittance functions are derived: and
The new spectral domain immittance functions An example of a spectral domain immittance function:
Solving the new expressions 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 Consider:
Dipole Results A single anisotropic substrate (d1 = 1.58 mm):
Dipole Results A single anisotropic cover (d1 = 1.58 mm d2 = 1.58 mm):
Dipole Results Separated by a single anisotropic layer (d1 = 1.58 mm d2 = 1.58 mm):
Conclusion 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 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.
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