The University of Mississippi Center of Applied Electromagnetic Systems Research (CAESR) Design and Analysis of Reconfigurable Frequency Selective Surfaces using FDTD Khaled ElMahgoub, Fan Yang and Atef Z. Elsherbeni Center of Applied Electromagnetic System Research (CAESR), Department of Electrical Engineering, University of Mississippi, USA
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 2
The University of Mississippi Introduction What is an FSS? Periodic structure that exhibit total reflection or transmission for certain frequency range. In what application such structures are used? Electromagnetic (EM) filters, radomes, absorbers, artificial electromagnetic band gap materials, and many other applications. What is a reconfigurable FSS (RFSS)? It is an FSS which has a frequency response that can be shifted or altered altogether while in operation. 3
4 The University of Mississippi Different Techniques for RFSS How can the response of the FSS be alerted or shifted during operation? This can be accomplished by mainly three techniques as follows: 1. By changing the electromagnetic properties of the FSS screen or substrate. 2. By altering the geometry of the structure. 3. By introducing elements into the FSS screen that vary the current flow between metallic patches. (1) (2) (3) (1) G. Y. Li, Y. C. Chan, T. S. Mok, and J. C. Vardaxoglou, Analysis of frequency selective surfaces on biased ferrite substrate, in IEEE AP-S Dig., vol. 3, Jun. 1995, pp. 1636 1639. (2) J. M. Zendejas,, J. P. Gianvittorio,, Y. Rahmat-Samii, and J. W. Judy, Magnetic MEMS Reconfigurable Frequency-Selective Surfaces, J. of Microelctromechanical Systems, Vol. 15, No. 3, Jun 2006, pp. 613-623. (3) S. M. Amjadi and M. Soleimani, Design of Band-Pass Waveguide Filter Using Frequency Selective Surfaces Loaded with Surface Mount Capacitors Based On Split-Field Update FDTD Method, Progress In Electromagnetics Research B, Vol. 3, 271 281, 2008.
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 5
The University of Mississippi Periodic Boundary Conditions (PBC) Various implementations of PBCs have been developed such that only one unit cell needs to be analyzed instead of the entire structure. Floquet Theory: Extended in y- direction Extended in x- direction y y Exy (, = 0, z) = Exy (, = P, z) e. Unit A y jk P With plane wave Excitation 6
The University of Mississippi Field Transformation Method Split Field Method Previous PBC for FDTD Multi-spatial Grid Method PBC for FDTD Sine-Cosine Method Direct Field Method Constant Horizontal wavenumber Method Field transformation methods are used to eliminate the need for time-advanced data. Direct field methods, work directly with Maxwell s equations and there is no need for any field transformation 7 Analytical reflection coefficient of infinite dielectric slab
8 The University of Mississippi Constant Horizontal Wave Number Approach Electric field in frequency domain can be written as: jkxpx Ex ( = 0, yz, ) = Ex ( = Px, yz, ) e. Frequency domain to time domain Px Ex ( = 0, yzt,, ) = Ex ( = Px, yzt,, + sin θ ) C Fix k x in FDTD simulation instead of the angle θ. k x = k 0 sinθ Frequency domain to time domain jkxpx Ex ( = 0, yzt,,) = Ex ( = P, yzt,,) e. x
The University of Mississippi Skewed Grid Approach Using the same constant horizontal wavenumber method one can easily simulate periodic structure with skewed grid (x = 0, y = 0) (x = P x, y = P y ) 9
10 The University of Mississippi Constant Horizontal Wavenumber for Skewed Grid (x = P x, y = P y ) (x = 0, y = 0) For i -(S x / x ) > 0 n+ 1 n+ 1 S jk S jk P x x y y E i n + k = E i x k e e x y x (, 1, ) (,1, ). x So to update E x at the boundary y = 0 For i + (S x / x ) n x H n + 1/2 1/2 ( i,0, k n jkxs jk x ypy z ) = H + z ( i +, y, ). x n k e e S x For i + (S x / x ) > n x S x n+ 1/2 n+ 1/2 jkx( Sx P ) jk yp x y z (,0, ) = z ( + x, y, ). H i k H i x n n k e e To update E x at the boundary y = P y For i -(S x / x ) 0 n+ 1 n+ 1 S jk ( S P ) jk P x x x y y (, 1, ) ( x + = +,1, ). x y x x E i n k E i n k e e x
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 11
12 Reflection coefficients magnitude The University of Mississippi 1 0.8 0.6 0.4 0.2 Motivation Skew angle of 90 o and 63.43 o Skewed Method α = 90 Skewed Method α = 63.43 Axial Method α = 90 Axial Method α = 63.43 0 0 2 4 6 8 10 12 14 16 Frequency [GHz] Reflection coefficient for dipole FSS normal incident TE z plane wave with skew angle of 90 o and 63.43 o. Normal Incidence (k x = 0 m -1 ) Skew angle of 90 o Skew angle of 63.43 o
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 13
14 The University of Mississippi The New Reconfigurable FSS This RFSS has two control parameters which increase the degree of freedom of the reconfigurability. The first control parameter is the diode which has two states, ON or OFF ( qvd / kt ) Id = I 0 e 1, Diode Current Equation. The second control parameter is the movements of different rows of the FSS
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 15
16 Reflection coefficients magnitudes Reflection coefficients magnitudes 0.8 0.6 0.4 0.2 The University of Mississippi 1 α = 90 α = 75.06 α = 68.19 Diode OFF 0 2 4 6 8 10 12 14 15 Frequency [GHz] 1 0.8 0.6 0.4 0.2 α =90 α =68.19 Diode OFF 0 2 4 6 8 10 12 14 15 Frequency [GHz] Numerical Results Normal incident (k x = k y = 0 m -1 ) with different skew angles Oblique incident (k x = 20 m -1, k y = 0 m -1 ) with different skew angles Reflection coefficients magnitudes Reflection coefficients magnitudes 1 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 α = 90 α = 75.06 α = 68.19 Diode ON 0 2 4 6 8 10 12 14 15 Frequency [GHz] 1 α =90 α =68.19 Diode ON 0 2 4 6 8 10 12 14 15 Frequency [GHz]
The University of Mississippi Case No. Diode State Numerical Data Different simulation cases Skew Angle Incident k x (m -1 ) Position of Reflection Coefficient Peak 1 OFF 90 o Normal k x = 0 13.36 GHz 2 ON 90 o Normal k x = 0 7.53 GHz 3 OFF 75. 06 o Normal k x = 0 13.92 GHz 4 ON 75. 06 o Normal k x = 0 7.69 GHz 5 OFF 68.19 o Normal k x = 0 14.37 GHz 6 ON 68.19 o Normal k x = 0 7.83 GHz 7 OFF 90 o Oblique k x = 20 13.27 GHz 8 ON 90 o Oblique k x = 20 7.54 GHz 9 OFF 68.19 o Oblique k x = 20 14.32 GHz 10 ON 68.19 o Oblique k x = 20 7.84 GHz 17
The University of Mississippi Outlines Introduction Analysis of Skewed Grid Periodic Structures Motivation The New Reconfigurable FSS Numerical Results Conclusion 18
The University of Mississippi Conclusion A new RFSS design was introduced. The reconfigurability of the design is based on two techniques: Controlling a diode state Controlling a mechanical movement to change the skew angle of the FSS grid. The design was simulated using FDTD/PBC algorithm (fullwave EM simulator), while taking into account the actual model of the diode and different skew angles. The simulations were efficient in both memory usage and computational time. 19
The University of Mississippi Center of Applied Electromagnetic Systems Research (CAESR) Thank you for Listening Any Questions?? 20