Design and Analysis of Reconfigurable Frequency Selective ...inside.mines.edu/~aelsherb/assets/Reconfigurable...and J. W. Judy, “Magnetic MEMS Reconfigurable Frequency-Selective

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Frequency Selective Surfaces using FDTD

Center of Applied Electromagnetic System Research (CAESR) , Department of

Electrical Engineering, University of Mississippi, USA

Khaled ElMahgoub, Fan Yang and Atef Z. Elsherbeni

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

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Introduction

What is a reconfigurable FSS (RFSS)?

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It is an FSS which has a frequency response that can be shifted or altered altogether while in operation.

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.

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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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.

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

(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.

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Various implementations of PBCs have been developed such that only one unit cell needs to be analyzed instead of the entire structure.

Floquet Theory:

With plane wave

Excitation

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Unit A

Extended in x- direction

Exte

nded

in y

- dire

ctio

n

( , 0, ) ( , , ) .y yjk PyE x y z E x y P z e= = = ×

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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7 Analytical reflection coefficient of

infinite dielectric slab

PBC for FDTD

Field Transformation Method

Split Field Method

Multi-spatial Grid Method

Direct Field Method

Sine-Cosine 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

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Electric field in frequency domain can be written as: ( 0, , ) ( , , ) .x xjk PxE x y z E x P y z e= = = ×

Fix kx in FDTD simulation instead of the angle θ. kx = k0 sinθ

( 0, , , ) ( , , , ) .x xjk PxE x y z t E x P y z t e= = = ×8

( 0, , , ) ( , , , sin )xxPE x y z t E x P y z tC

θ= = = +

Frequency domain to time domain

Frequency domain to time domain

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Using the same constant horizontal wavenumber method one can easily simulate periodic structure with skewed grid

(x = Px, y = Py)

(x = 0, y = 0)

9 ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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(x = Px, y = Py)

(x = 0, y = 0)

Constant Horizontal Wavenumber for Skewed Grid

So to update Ex at the boundary y = 0

For i + (Sx /∆x ) ≤ nx

1/ 2 1/ 2( ,0, ) ( , , ) .y yx x jk Pjk Sn nz z yxSxH i k H i n k e e+ +

∆= + × ×

For i + (Sx /∆x ) > nx

( )1/ 2 1/ 2( , 0, ) ( , , ) .y yx x x jk Pjk S Pn nz z x yxS

xH i k H i n n k e e−+ +

∆= + − × ×

To update Ex at the boundary y = Py

For i -(Sx /∆x ) ≤ 0 ( )1 1( , 1, ) ( ,1, ) .y yx x x jk Pjk S Pn nx y x x x

SxE i n k E i n k e e

−− −+ +

∆+ = + − × ×For i -(Sx /∆x ) > 0 1 1( , 1, ) ( ,1, ) .y yx x jk Pjk Sn nx y x x

SxE i n k E i k e e

−−+ +

∆+ = − × ×

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Motivation

Reflection coefficient for dipole FSS normal incident TEz plane wave with skew angle of 90o and 63.43o.

Skew angle of 90o and 63.43o

0 2 4 6 8 10 12 14 160

0.2

0.4

0.6

0.8

1

Frequency [GHz]

Ref

lect

ion

coef

ficie

nts

mag

nitu

de

Skewed Method α = 90°Skewed Method α = 63.43° Axial Method α = 90°Axial Method α = 63.43°

Normal Incidence (kx = 0 m-1)

Skew angle of 90o

Skew angle

of 63.43o

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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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

The second control parameter is the movements of different rows of the FSS

( )0

/ 1 ,d dqV kTI I e = −

Diode Current Equation.

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

The University of Mississippi Department of Electrical Engineering C

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Numerical Results

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

Normal incident (kx = ky = 0 m-1) with different skew angles

2 4 6 8 10 12 14 150

0.2

0.4

0.6

0.8

1

Frequency [GHz]

Ref

lect

ion

coef

ficie

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nitu

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α = 90°α = 75.06°α = 68.19°

Diode OFF 2 4 6 8 10 12 14 15

0

0.2

0.4

0.6

0.8

1

Frequency [GHz]

Ref

lect

ion

coef

ficie

nts

mag

nitu

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α = 90°α = 75.06°α = 68.19°

Diode ON

2 4 6 8 10 12 14 150

0.2

0.4

0.6

0.8

1

Frequency [GHz]R

efle

ctio

n co

effic

ient

s m

agni

tude

s

α =90°α =68.19°

2 4 6 8 10 12 14 150

0.2

0.4

0.6

0.8

1

Frequency [GHz]

Ref

lect

ion

coef

ficie

nts

mag

nitu

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α =90°α =68.19°

Oblique incident (kx = 20 m-1, ky = 0 m-1) with different skew angles

Diode OFF Diode ON

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Numerical Data

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

Case No. Diode State

Skew Angle Incident kx (m-1) Position of Reflection Coefficient Peak

1 OFF 90o Normal kx = 0 13.36 GHz 2 ON 90o Normal kx = 0 7.53 GHz 3 OFF 75. 06o Normal kx = 0 13.92 GHz 4 ON 75. 06o Normal kx = 0 7.69 GHz 5 OFF 68.19o Normal kx = 0 14.37 GHz 6 ON 68.19o Normal kx = 0 7.83 GHz 7 OFF 90o Oblique kx = 20 13.27 GHz 8 ON 90o Oblique kx = 20 7.54 GHz 9 OFF 68.19o Oblique kx = 20 14.32 GHz

10 ON 68.19o Oblique kx = 20 7.84 GHz

Different simulation cases

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Outlines Introduction Analysis of Skewed Grid Periodic Structures

Motivation

The New Reconfigurable FSS

Numerical Results Conclusion

ACES Conference 2011 © Khaled ElMahgoub 31 March 2011

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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 (full-wave 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.

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Thank you for Listening

Any Questions??

Design and Analysis of Reconfigurable Frequency Selective Surfaces using FDTD OutlinesIntroductionSlide Number 4OutlinesPeriodic Boundary Conditions (PBC)Previous PBC for FDTDConstant Horizontal Wave Number ApproachSkewed Grid ApproachConstant Horizontal Wavenumber for Skewed GridOutlinesMotivationOutlinesThe New Reconfigurable FSSOutlinesNumerical ResultsNumerical DataOutlinesConclusionThank you for Listening��Any Questions??