Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

8/17/2019 Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

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Tutorial

on

Saptarshi Ghosh

Thesis Supervisor: Dr. Kumar Vaibhav SrivastavaDepartment of Electrical Engineering

Indian Institute of Technology, Kanpur, India


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Presentation Outline

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Introduction to Metamaterials

Overview of Metamaterial Absorbers

Modeling of Metamaterial Absorber Structure 1

PEC-PMC modes

Floquet Modes

Modeling of Other Metamaterial Absorber Structures

Conclusion


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Introduction to Metamaterials

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Overview of Metamaterial

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Artificial composite materials consisting of structural units smaller thanthe wavelength (λ ) of the incident radiation.

Conventional material with atoms

Unit-cell driven metamaterial (size < λ /4)

Controllable electromagnetic properties(ε, µ, n,…) at desired frequency.


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Historical Overview

1968: Veselago [1] predicted the existence of LHM.

1996: Realization of negative permittivity practically [2] by Pendry.

1999: Experimental verification of negative permeability [3] by Pendry. 2000: First Experimental Demonstration of LHM [4] by Smith.

2001: First realization of Negative Refractive Index [5] by Shelby.

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[1] V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of µ and ε,” Sov.

Phys. Uspekhi, Vol. 10, No. 4, pp. 509-514, 1968.

[2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic

microstructure,” Phys. Rev. Lett., Vol. 76, No. 25, pp. 4773-4776, June 1996.[3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced

nonlinear phenomena,” IEEE Trans. Micr. Theory. Tech., Vol. 47, No. 11, pp. 2075-2084, Nov. 1999.

[4] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with

simultaneously negative permeability and permittivity,” Phys. Rev. Lett., Vol. 84, No. 18, pp. 4184-4187, 2000.

[5] R. A.Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,”

Science, Vol. 292, pp. 77-79, April 2001.


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Metamaterial Absorbers

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[6] P.Saville, “Review of Radar Absorbing Materials,” Defense R & D Canada-Atlantic, Jan. 2005.

Salisbury Screen

Conventional Absorbers [6]

Pyramidal Absorber

~λ

Wide bandwidth above 90%

absorption bandwidth

Disadvantage :

large thickness and fragile

Single-band absorber


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Metamaterial Absorber [7]

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Structure is ultra-thin (λλλλ0 /35) compared to conventional absorbers.

Effective electromagnetic constitutive parameters (ε eff and µeff ) have

been tailored using unit cell design.

Absorbers can be made scalable- from microwave, terahertz,infrared, optical frequency range.

Structures can be easily fabricated using PCB technology.

First experimentally realized by Landy et. al. in 2008 [12].

[7] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,”Phys. Rev. Lett., vol. 100, pp. 207402, May 2008.

a1 = 4.2 mm, a2 = 12 mm, W = 4 mm,

G = 0.6 mm, t = 0.6 mm, L = 1.7 mm,

H = 11.8 mmFR4 substrate thickness = 0.72 mm

Copper thickness = 0.017 mm


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Metamaterial Absorber

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When the reflected power (|S11|2) and transmitted power (|S21|

2) have

been minimized simultaneously, absorptivity (A) will be maximum.

2

21

2

11 ||||1 S S A −−=

|S11|2 = 0.01%

|S21|2 ~ 0.9%

A = 1-|S11|2-|S21|2 = 96%

At 11.65 GHz,

Simulated Absorptivity

What is the reason behind the absorptivity?


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Metamaterial Absorber [8]

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When the reflected power (|S11|2) and transmitted power (|S21|

2)

have been minimized simultaneously, absorptivity (A) will be

maximum.

The design is made such a way that the input impedance is

matched exactly with the free space impedance.

Input impedance can be matched with free space impedance by

controlling the effective material parameters.

[8] D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from

inhomogeneous metamaterials,” Phys. Rev. E 71, pp. 036617, 2005.

2

21

2

11 ||||1 S S A −−=

ε ε

µ µ η

ε

µ η

ε ε

µ µ ω

′′+′

′′+′===

j

j Z

eff

eff

eff

eff

00

0

0)(

( )( ) 221

2

11

2

21

2

110

11)(

S S S S Z

−−−+=η ω

µ ε ′=′

ε ′′=′′

at absorption

frequency


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Effective Material Parameters [9]

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[9] C. L. Holloway, E. F. Keuster, and A. Dienstfrey, “Characterizing metasurfaces /metafilms: the connection

between surface susceptibilities and effective material properties,” IEEE Antennas Wireless Propag. Lett., Vol.10, pp. 1507-1511, 2011.

µ ε ′≈′ µ ε ′′≈′′

++

−−+=

2111

2111

0 1

121

S S

S S

d k

jeff ε

+−

−++=

2111

2111

0 1

121

S S

S S

d k

jeff µ

Re(εeff ): 1.04; Re(µeff ): -1.12 Im(εeff ): 11.06; Im( µeff ): 8.86

At

11.65 GHz


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Metamaterial Absorber Structure 1

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We are first going to design a single-band metamaterial absorber.

Metamaterial absorber structures are periodic structures Since metamaterial absorber structures are resonant structures, there must be

some equivalent capacitances (C) and inductances (L).

Inductance can be realized by any metallic patch

Capacitance can be realized by any gap between two metallic patches

depending on the direction of E-field.

Points to remember:

LC f

2

2

1

π ≈


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8 x 8 Array Front View of Unit Cell Side View

Perspective

View

a = 10 mm, w = 0.4 mm,

l = 6.5 mm, g = 0.2 mm

Copper thickness = 0.035 mm,FR4 thickness = 1 mm

(εr =4.25 & tanδ =0.02)

t


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HFSS →Insert the Design → Draw a 3-D rectangular box


3D box

Properties window

Project manager

Progress windowMessage manager


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Project Variables

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Project variables are applicable

to a particular project

Prefixed with “$” sign

Project variable is applied to all

the designs inside a project


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Design Variables

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Design variables are applicable

to a particular design

Independent from one design to

another design


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Square Metal Ground Plane

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Positional coordinates : 0,0,0

X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm

Assign material: copper

FR-4 Dielectric Substrate

Positional coordinates : 0,0,0

X-size: 10 mm; Y-size: 10 mm; Z-size: 0.035 mm



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Top Metallic Patch

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First draw a square box

Then, draw a middle line and add it to the square loop

Lastly, subtract a small gap from the middle line


Air Box

An air box needs to be provided for providing boundary condition

Assign material: vacuum


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PEC/PMC Boundary condition

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Opposite Current : PEC

PEC: Opposite CurrentSame Current : PMC

Same Current : PMC


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PEC/PMC Boundary condition

PEC boundary PMC boundary


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Assigning Wave ports

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Since back side is full metal plane, transmission (S 21) is zero

No need to put wave port 2 at the back

Deembedding is not necessary, as we are interested in magnitude of

reflection coefficient (|S 11|2

) only.


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Analysis

Solution Frequency: 6 GHz

Maximum delta S (∆S): 0.02

Frequency range: 2 GHz – 10 GHz

Sweep type : Fast/ Interpolating/ Discrete

Sweep type Solution time Comments

Fast 7 min 10 sec Quickest, but most inaccurate

Interpolating 10 min 12 sec Not the quickest, not the most accurate

Discrete ∼∼∼∼16 hours Slowest, but most accurate

It is the difference in

error between two

consecutive passes


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Since only 1 port, only 1 S-parameter is available

Reflection coefficient: S(1,1) in dB or in mag

Reflection coefficient : -24 dB at 6.07 GHz

Absorptivity: {1- (mag(S(1,1))2)}*100

Results


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Surface Current Distributions

Top surface Bottom surface

Current is flowing in circulating loop around the incident magnetic field


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What if the PEC/PMC boundary conditions will be interchanged ?

Some Common Questions

PEC boundary PMC boundary

Reflection dip will change to 7.42 GHz instead of 6.07 GHz

Reflection coefficient (S 11) will decrease to -9.03 dB instead of -24 dB


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Will this PEC/PMC boundary condition be valid if the structure is

complicated ?

Will this PEC/PMC boundary condition work when the current flow

will not be as simple as this ?How to measure the oblique incidence measurement ?

How to measure the reflectivity when the structure is rotated ?

Some Common Questions

Solution Use Floquet Ports


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Used exclusively with planar periodic structures

Example : Planar phased array, frequency selective surface (FSS)

Floquet Ports

The analysis of the infinite structure is then accomplished by analyzing a

single unit cell by providing periodic boundary conditions (PBC).

PBC

PBC

P B C P

B C

Periodic in x-y plane


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Master/ Slave Boundary Condition

Master 1

Master 2Slave 1

Slave 2

No change in reflection coefficient or reflection dip under normal

incidence even if there is reversal of master 2 and slave 2 directions


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Assigning Floquet ports

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No need to put floquet port 2 at the back

Deembedding is not necessary, as we are interested in magnitude of

reflection coefficient (|S 11|2) only.

We have to provide lattice vectors “a” and “b” to define theperiodicity in x- y plane

Periodic in x-direction

Periodic in y-direction


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Fast sweep is not available in lower versions of HFSS (upto HFSS 13)

Result remains almost same

Absorptivity: {1- (mag(S(1,1))2)}*100

Analysis and Results

Any Other advantage ?


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There is a phase delay between the Master and Slave boundary

The default value is zero

Assign some variables in place of scan angles

Angle variation


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When phi scan angle is varied from 0o to 90o, the incident wave is

polarized keeping the incident wave propagation direction constant

Since the structure is asymmetrical, reflection dip will change

Polarization Angle variation


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Floquet port has the extra advantage of modal decomposition

During assigning “floquet port”, the default number of modes is : 2

These number of modes and type of modes can be manually controlled

Oblique Incidence

TE mode TM mode


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Variation of theta scan angle (θ) from 0o to 90o

TE Polarization TM Polarization

When mode is TE (0,0) When mode is TM (0,0)


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Some Other Examples

C L f

2

1

2

1

×≈

π

Resonant frequency will decrease to 4 GHz whereas the early

presented structure has a reflection dip at 6 GHz

However, the structure is still asymmetrical w.r.t. field vector directions


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Some Other Examples (contd.)

Structure is symmetrical w.r.t.

incident field vector directions.

The structure exhibits reflection dip at close to 6 GHz

Small deviation in frequency from the initial proposed structure is due

to difference in gap (g) value

Structure is four-fold symmetrical

Structure is polarization-insensitive


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Conclusion

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A brief introduction about metamaterial and metamaterial absorber has been

discussed.

A single-band metamaterial absorber structure has been studied in detail.

Different boundary conditions and modes have been investigated to analyze the

structure.

Some other examples have also been discussed.


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Tutorial on Modeling of Metamaterial Structure in Ansys HFSS

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