1. Modeling Multiple Printed Antennas Embedded in Stratified Uniaxial Anisotropic Dielectrics Ph.D. Candidate: Benjamin D. Braaten Electrical and Computer Engineering North Dakota State University February 6 th, 2009

2. Topics  Introduction  The printed antenna.  Properties and applications.  Proposed research  Derivation of the new spectral domain immittance functions.  Solving the new spectral domain immittance functions.  Numerical results and measurements.  Future work.  Conclusion. North Dakota State University

3. Introduction  In 1953 Deschamps formally introduced the microstrip antenna [1].  Many uses:  Radar  Cellular comm.  Satellite comm.  Wireless networks  Wireless sensors  Biomedical devices  RFID … North Dakota State University [1] G. A. Deschamps, “Microstrip Microwave Antennas,” 3 rd USAF Symposium on Antennas, 1953.

4. Introduction  Disadvantages:  Many designs have a narrow bandwidth  Radiate into a half space  Poor endfire radiation  Poor isolation between the feed an radiating elements  Possible surface waves (power loss) North Dakota State University  Advantages:  Low profile  Lightweight  Low cost  Able to achieve UWB (in some cases)  Dual frequency capabilities  Simple to fabricate

5. Introduction North Dakota State University  Region between plates act like the region between a transmission line and a ground plane with both ends open.  Results in a standing wave.  Fringing fields are responsible for radiation.

6. Introduction North Dakota State University  Properties of interest include:  Input impedance  Current distribution  Radiation patterns  Bandwidth  Feed techniques  Mutual coupling with other elements  Conducting patch layout  … etc.

7. Introduction Many different types of layouts exist: North Dakota State University [3] H. Wang, X. B. Huang and D. G. Fang, “A single layer wideband U-slot microstrip patch antenna array,” IEEE Antennas and Wireless Propagation Letters, vol. 7, 2008, pp. 9-12. [3] [2] Anthony Lai and Tatsou Itoh, “Composite Right/Left Handed Transmission Line Metamaterials,” IEEE Magazine, September 2004. [2]

8. Proposed Research Consider: North Dakota State University

9. Proposed Research North Dakota State University RESEARCH QUESTIONS: What is the input impedance of a driven element in the layered anisotropic structure in the presence of other conducting patches defined on arbitrary anisotropic layers in the same structure? and  What is the mutual impedance between a driven element in the layered anisotropic structure and other conducting patches defined on arbitrary anisotropic layers in the same structure?

10. Proposed Research North Dakota State University The previous two questions are very significant 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 paramters of a frequnecy selective surface between anisotropic dielectric layers for incidnet 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.

11. The new spectral domain immittance functions North Dakota State University Start with the following Hertz vector potentials: and Electric Hertz potential Magnetic Hertz potential

12. 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.

13. Numerical results and measurements North Dakota State University The TEM, TM and TE modes [9] http://www.ibiblio.org/kuphaldt/electricCircuits/AC/02407.png [9] TEM mode TM and TE modes

14. 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:

15. The new spectral domain immittance functions North Dakota State University and

16. 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:

17. The new spectral domain immittance functions North Dakota State University This results in the following simplified expressions: where and

18. The new spectral domain immittance functions North Dakota State University Similarly for and

19. The new spectral domain immittance functions North Dakota State University Single layer problem

20. The new spectral domain immittance functions North Dakota State University Single layer problem Now use these expressions to enforce the boundary conditions:

21. The new spectral domain immittance functions North Dakota State University Single layer problem After extensive factoring and manipulation, the following spectral domain immittance functions are derived: and and where (typical expression – spectral expression – spectraldomain Green’s function)

22. The new spectral domain immittance functions North Dakota State University Double (d 3 = 0) and Triple layer problems

23. 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

24. 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.

25. Numerical results and measurements North Dakota State University The problem chosen to validate newly derived spectral domain immittance functions was the printed dipole.

26. Numerical results and measurements North Dakota State University The first step was to validate the numerical results with experimental measurements.  Radius a = 0.4 mm  Length L = 60 mm  FR-4: ε r = 4.35  Printed strip W = 4a

27. Numerical results and measurements North Dakota State University Picture of measured monopole.

28. Numerical results and measurements North Dakota State University This resulted in the following measured resonant frequencies:(Epsilam-10: and, Rogers 5880: )

29. Numerical results and measurements North Dakota State University Single layer results

30. Numerical results and measurements North Dakota State University Single layer results L = 15 mm W = 0.5 mm d 1 = 1.58 mm Notice the y- component has the most effect on the resonant frequency (TM 0 mode).

31. Numerical results and measurements North Dakota State University Single layer results The TEM, TM and TE mode reminder [9] http://www.ibiblio.org/kuphaldt/electricCircuits/AC/02407.png [9] TM and TE modes A quick illustration of the TM 0 mode.

32. Numerical results and measurements North Dakota State University Single layer results

33. Numerical results and measurements North Dakota State University Single layer results

34. Numerical results and measurements North Dakota State University Single layer results L = 15 mm W = 0.5 mm f = 500 MHz d 1 = 1.58 mm Notice:TM 0 has the most effect (i.e. y-compontent of the permittivity

35. Numerical results and measurements North Dakota State University Double layer results

36. Numerical results and measurements North Dakota State University Double layer results L = 15 mm W = 0.5 mm d 1 = 1.58 mm d 2 = 1.58 mm ε 1 = 2.55 Notice: ε x 2 affects the resonant frequency the most.

37. Numerical results and measurements North Dakota State University Double layer results The field lines:

38. Numerical results and measurements North Dakota State University Double layer results L = 15 mm W =0.5 mm d 1 = 1.58 mm ε 1 = 2.55 region 2: anisotropic

39. Numerical results and measurements North Dakota State University Double layer results L = 15 mm W = 0.5 mm f = 500 MHz d 1 = 1.58 mm d 2 = 1.58 mm ε 1 = 3.25.

40. Numerical results and measurements North Dakota State University Double layer results (Single layer results)

41. Numerical results and measurements North Dakota State University Double layer results L = 15 mm W = 0.5 mm f = 500 MHz d 1 = 1.58 mm d 2 = 1.58 mm ε 1 = 3.25.

42. Numerical results and measurements North Dakota State University Double layer results

43. Numerical results and measurements North Dakota State University Triple layer results L = 15 mm W = 0.5 mm f = 500 MHz d 1 = 1.58 mm d 2 = 1.58 mm d 3 = 1.58 mm ε 1 = ε 2 = 3.25.

44. Numerical results and measurements North Dakota State University Triple layer results (Double layer results)

45. Conclusion North Dakota State University  New spectral domain immittance functions have been derived.  The new spectral domain immittance functions have been validated with measurements, published literature and commercial software.  One, two and three layer problems have been investigated.

46. Conclusion North Dakota State University  The following has been shown:  The permittivity in the direction of the optical axis below the printed dipole has the most impact on the resonant frequency.  The layer thickness values eventually have little effect on the resonant frequency.  The permittivity in the direction of the optical axis above printed dipoles has little or no effect on the mutual coupling.  The permittivity in the direction orthogonal to the optical axis in the layers above the dipoles can be used to control the mutual coupling.

47. Conclusion North Dakota State University  Future work  Investigate coupling between rectangular microstrip antennas in layered anisotropic diel.  Investigate coupling between UWB antennas in layered anisotropic diel.  Investigate how anisotropic materials could be used to control coupling between RFID tags  IC based antennas  Metamaterial based designs  Mathematical aspects  poles  surface wave modes  convergence

48. Questions North Dakota State University Thank you for listening