high impedance surface_his_ris_amc_nurmerical_analytical_analysis

HIS/AMC/RIS NUMERICAL AND ANALYTICAL ANALYSIS

Ntawangaheza Jean de Dieu(金利 )[email protected]

(PPT2 of PPT3)

mailto:[email protected]

OUTLINE

Dielectric-conductor interface & image theory

Maxwell equations & surface waves

Periodic structure& high impedance surface(HIS/AMC)

CONSTITUTIVE RELATIONS

Over the course of this presentation only non magnetic ( ) dielectric materials will be considered. Since up to date, though magnetic materials are used in antenna design, but they significantly reduce its efficiency. Thus the constitutive relations(CR) are:

(CR)

and p: Material Susceptibilities polarization collectively.

.

Taking into account the E/M polarization properties of the material, dielectric constant is:

00

1 H=

1 E=

B H B

D E D

0 0 (1 )r

0r

0

0 0

0

(1 )E1 (D p)

D E E p

E

Generally speaking, all materials are in fact dispersive, however, over certain frequencies , can be viewed as frequency independent

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

MODEL OF DIELECTRIC CONSTANT FORCONDUCTORS.

According to simple model( Drude model ), the conductivity properties of a material is a complex function of frequency, which achieves max value at the low frequency limit(DC)

.

DC conductivity value holds for all frequencies such that (number of collisions per unit time , for copper , assuming

A wave propagating through a lossy media will set up conduction current (Jcond=) along with polarization current(Jp=jD=j) such that :

2 20 2

0

( ) , pp

Nej m

2 20

max0

( ) p Nem

( ) E jtot cond p d cJ J J j E


MODEL OF DIELECTRIC CONSTANT FORCONDUCTORS(CONT.).

.

( ) E j

tot cond p d c

c d c d

J J J j E

j j j

Though both quantities ()may be complex and dispersive, over a wide range of frequency is a large real number and for a good conductor( see previous slide).

0

0

1 1 tancr

c d

j j

j j

A good conductor has a complex

effective relative dielectric.

From Ampere’s law in a lossy media


BOUNDARY CONDITIONS.

The tangential components of the E fields are continuous across the interface, while the difference of the tangential components of the H fields are equal to surface current density.

The difference of the normal components of the D are equal to the surface charge density.

Boundary conditions for the E and H across material interfaces are as follows:

.

interface

1 2

1 2

1 2

1 2

( ) 0( ) (0)

(0)0

s

n n s

n n

n E En H H JD DB B


BOUNDARY CONDITIONS(BC)(PEC).

For a good conductor the following boundary conditions are valid:

interface

( ) 0( ) s

n En H J

The physical significance is that, not only the tangential components of the E is zero also there is a propagating surface current on the interface.

If we define reflection coefficient and surface impedance as:

and Z 1 Z 0rt ts gc sgc

it t

E EE H

(low<<)

Surface wave and out phase reflectionRef . Sophocles J. orfanidis,” EM waves and antennas, February 2004

BOUNDARY CONDITIONS(BC) (PMC)

In EM problems there is an imaginary conductor which is used to simplify calculations and its known as perfect magnetic conductor(PMC)

PMC satisfies the boundary conditions which are exactly the opposite of its counterpart(PEC) , that is:

( )( ) 0

sn E Mn H

1 and Z »MPc sMPC high

In phase Reflection and high impedance surface, but imaginary!


NEGATIVE EFFECTS OF BC(PEC) AND IMAGE THEORY

In radio communication when an antenna is placed above a PEC ground plane, the latter will act as mirror between the actual antenna and its image.

Due to shift(-1), the minimum antenna _PEC distance should be one (too thick and costly at UHF), still surface current are supported.

c/... ploss back sw d

rad acc loss

rad

acc

P p pandP p p

pforPEC

p

Antenna element

PEC

Antenna image

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004, Mustafa K. Tahel Al-Nuaimi low profile dipole antenna design using SSRs artificial GND,IEEE conference 2010, Joseph J. Carr, practical antenna handbook 5th,Mc Graw Hill,2012

PERSPECTIVE SOLUTIONS TO THE BC/PEC

An intuitive way to improve the antenna efficiency while reducing both cost and size, is to use a magnetic conductor (MC) instead of PEC, unfortunately it is a mathematical abstraction.

Yet another method that is widely used is employ an absorbing material , to cancel out antenna’s back-radiation. Although, antenna is shielded from other circuit but efficiency is remarkably reduced.

MC

Absorber

Forward radiation

backward radiation

Ref . Mustafa K. Tahel Al-Nuaimi low profile dipole antenna design using SSRs artificial GND,IEEE conference 2010, Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 2011,Faruk Erkmen et al. UWB magneto-dielectric GND for low profile antenna applications, IEEE antennas and magazine, August 2008.

MAXWELL’S EQUATIONS(MEs)

They dictate all classical EM phenomena, however they do not indicate how E and H fields interact with the medium of propagation.

E and H fields are created by either accelerated external charges( ) or changing electrical current ), while their interaction with the medium is explained via the so called constitutive relations(CR).

.

0

ext

ext

BEt

DH Jt

DB

Away from the sources ( =0) , source free

regions of space.

B HD E

1

1

H B

E E

Only valid for a linear, isotropic homogeneous no dispersive E/M media at low frequencies.

CR


MAXWELL’S EQUATIONS(CONT.)

The faraday’s and ampere’s law can be expanded and yield the following equations(single frequency( is assumed otherwise Fourier trans. Should be utilized )

source free regions, with an EM wave propagating in X direction and there is only one spatial variation of , and constant in y direction.

0

0

0

yzx

x zy

y xz

EE j Hy zE E j Hz xE E j Hx y

Faraday’s law expansion

0

0

0

yzx

x zy

y xz

HH j Ey zH H j Ez xH H j Ex y

Ampere’s law expansion

𝜀2

𝜀1

𝑝 𝑙𝑎𝑛𝑒 𝑧=0=𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006

SURFACE WAVES

Also known as Zenneck waves or surface currents, are EM waves that propagate along the interface between two dissimilar propagation medium and vanish in the transverse direction.

They are also called Plasmon surfaces at optical frequency range. Two special cases merit attention: TM(Hz=0) and TE(Ez=0). Therefore our equations become(recall also ):

1 0y

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006

TM AND TE SURFACE WAVES MODES EQUATIONS

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006; Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201

TM AND TE SURFACE WAVES EXISTENCE CONDITIONS

With the previous equations in hand, we are now ready to derive the properties of surface waves, we are going to solve a wave equation that decay expantially away from a dielectric interface with decaying constant in positive and negative Z direction, respectively.

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006

TM AND TE SURFACE WAVES EXISTENCE CONDITIONS

Which leads to the following system of equations:

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006;

PHYSICAL INTERPRETATION

1 2

1 2

21

1 2

2

1 2

kc

c

c

If medium one and two have positive permittivity, the considered waves don’t decay transversely away from the surface.

However, if permittivity of medium one or two is negative or cplx, wave can decay exp. Thus surface wave exists on conductors surface.

0

1 1 tancr j j

Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006;

PHYSICAL INTERPRETATION(CONT.)

2

2

2

2

2

1

11

1

kc

c

c

If medium one is air and second is metal, previous constant become:

0

1 1 tancr j j

0

0

02

2

1 (1 )22

(1 j)1 2

kc

jj c c

c

0

1 2, =j

Penetration coef.

Skin depth

1 1t zs

t y

E E j jZH H

Dissipated energystorage energy

IMPEDANCE SURFACE(TM)

0

0

0

yzx

x zy

y xz

HH j Ey zH H j Ez xH H j Ex y

Recall that for a TM( p mode) SW mode only has Ex, Ez and Hy are non zero field components.

1

1

xjk zx

jkx zz

E Ae

E Be

1

0

0 1

xjk zx

kx zyy

x

E AeH j AeH

j Ez

01y xH j E

1

0 01

x xs

yx

E E jZH j E

TM mode is supported by a Positive (inductive) surface

TM solution

Ref . See previous slide

SURFACE IMPEDANCE(TE)

0

0

0

yzx

x zy

y xz

EE j Hy zE E j Hz xE E j Hx y

Note that only Hx, Hz and Ey component are non zero quantities in TE(S mode, perpendicular ) mode :E is perpendicular to the plane of incidence. TE solution

0

0

yx

x yjkx z

y

Ej H

H j EzE Ae

0ys

x

EZ j

H

TE mode is supported by a surface with capacitive reactance(negative impedance)

Ref . See previous slide

PERIODIC STRUCTURES

Materials are periodic at atomic scale, and this may lead to what is known as crystals with band gap.

Periodic structures can be made at macroscopic scale, and still have the band gap behavior. Periodicity should be much smaller than

Generation 2D example

Pure translation(a) Pure rotation (b)Combination of(a) and (b)

Unit cell can be any shape.

Square, triangle. hexagonal…

Ref . http://emlab.utep.edu/ee5390em21.htm

HIGH IMPEDANCE SURFACE（ HIS/AMC） The properties of MC/HIS/RIS are desirable in low profile antenna design, especially in

nowadays very limited space devices.

It turns out that its behavior can be emulated using periodic structures, where a lossless FSS layer supported by a medium is(not) shorted to GND via vias(Mushroom like structure).

Structure forms a parallel LC circuit, C is due to capacitance between adjacent metal pad while L originates from the loop current upper FSS and GND through vias.

At resonance, the structure yields a very high impedance, therefore it is called high impedance surface HIS or artificial magnetic conductor(AMC).

Ref . Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201, Fan yang ,”Electromagnetic Band gap structures in antenna engineering, Cambridge university press,2009,

HIGH IMPEDANCE SURFACE(HIS)

The AMC properties can be split into two parts reflection phase and band gap(where both TM and TE waves are not supported).

Band gap is determined using the so called dispersion diagram, that is how dispersive a medium is(k vs frequency), number of modes that a structure can support.

Structure symmetry simplifies the required calculation time using the so called irreducible Brillouin zone.

It has been shown that the structure reflected in phase rather than out of phase, in the range

Ref . Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201, Fan yang ,”Electromagnetic Band gap structures in antenna engineering, Cambridge university press,2009, R.C Hansen effect of a high impedance screen on a dipole antenna IEEE antennas and wireless propagtion,2002

HIGH IMPEDANCE SURFACE(HIS)/DISPERSION DIAGRAM

Analytically, dispersion diagram of HIS structure can be derived by solving the wave equations:

22 202

2 2 20

(k ) E 0

jkx zy

yx y

x

E Ae

Ek

zk k

For TM mode we find:

00

2 20

2 2 2 20 0

2 20

0 00 0

2

20

(Z )

( )

1

1

TM

s TM

TM

TM

TMTM

TMTM

jZ jZ

k k Z

Zk

Zkc

For TE mode we find:

0

2021

s

TETE

Z j

kc Z

Ref .; John A polo, Jr, Electromagnetic surface waves A modern perspective, Elservier 2013;Stefan Alexander MAIer Plasmonics fundamental and applications,Springer 2007 J M Pitarke Theory of surface plasmons and surface plasmon polaritons Institute of physics publishing, october 2006;

DISPERSION DIAGRAM OF HIS

Since unit size and periodicity are much smaller compared to the , the structure can be described using the so called effective medium, and lumped element can be used for equivalent circuit.

For TM mode we find:

2

20

1 TMTM

Zkc

For TE mode we find:

20

202

1

1TE

LC

kc Z

21sj LZLC

2

20

2

020

1

1 0

sj LZ

2

20

2

020

1

1 0

sj LZ

TM modes are supported below resonance, while TE modes appear above resonance

A band gap exist around resonance, where TM end and TE starts.

Ref. Ref. Daniel Frederic” High impedance EM surfaces, UCLA PhD dissertation 1999; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009

HIS REFLECTION PHASE

Another important property of the AMC/RIS/HIS is reflection phase, unlike their counterparts PEC and MC GND, its reflection phase varies with frequency.

It resonates at zero degree(PMC), however the frequency range of can be considered as in phase reflection bandwidth.

Transmission line is used for general reflection behavior study( oblique), for both TM and TE polarization, where the FSS and spacing layer are both assigned different impedance (Zg and Zd)which are connected in parallel.

g ds

g d

Z ZZ

Z Z

0

0

0

0

coscos

Z coscos

TM s

s

TE s

s

ZZ

Z

Ref.; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009

REFLECTION PHASE TE AND TM

For a plane wave striking a an EBG surface with anArbitrary angle, two polarizations have to be distinguished(TM and TE).

,TM0

TEdZ j h

2

( ,0)( , )

cosgTE

g

ZZ

( , ) ( ,0)TMg gZ Z

( ,0)gg

jZC

0(1 ) 2log( )r

ga aC

g

0

0

0

0

coscos

Z coscos

TM s

s

TE s

s

ZZ

Z

g ds

g d

Z ZZ

Z Z

Both TM and TE reflection phase depends on incident angle, which is similar for normal incident.FSS impedance depends on the geometry of the unit cell.The equations presented herein, can be used to analytically analyze the EBG structure characteristics such surface wave bandgap and in phase reflection.

Ref.; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009

AMC/HIS SIMULATION(NUMERICAL)

Though analytical method provides physical insight into the functioning of the AMC, it lacks accuracy and it might be a timing consuming design process.

Numerical methods are widely used to overcome the above drawbacks.

Since the unity cell size and periodicity are much smaller than effective medium is applied for analysis, where lumped elements are used to describe its equivalent circuit.

C and L are due to fringing fields and current loop, respectively and are derived using conformal mapping and solenoid alike method.

21sj LZLC

11 2( ) cosh ( )

L hW gW

gC

Ref. Ref. Daniel Frederic” High impedance EM surfaces, UCLA PhD dissertation 1999; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009, , Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002


Inductance depends on permeability and thickness of the substrate, while the capacitance depends on permittivity and the geometrical form of an unit cell.

Both BWs( surface wave band gap and in phase reflection BW) depend on the electromagnetic and physical dimensions( and/or form) of the structure, the thicker the structure(the higher ) the wider the BW is achievable.

For a fixed h and the higher the C, the narrower the BW and the lower the fr.

21sj LZLC

11 2( ) cosh ( )

L hW gW

gC

01LC

0

1gap

LBWC

90 00

2 ,rhBW h

Ref. Daniel Frederic” High impedance EM surfaces, UCLA PhD dissertation 1999; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009, , Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002; Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201

AMC/HIS SIMULATION EXAMPLE

AMC design steps(procedures)

(a) Determine the structure geometry by plotting as a function of the structure dimensions.

(b) With the structure chosen dimensions go back and calculate the corresponding C and L

(c) Calculate other structure parameters such as BW, …(d) Use 3D EM simulation software to optimize the structure.

Ref. Ref. Daniel Frederic” High impedance EM surfaces, UCLA PhD dissertation 1999; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009, , Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002; Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 2011

AMC/HIS/RIS SIMULATION(NUMERICAL)

(a) Initial unit cell dimensions prediction by plotting as a function of the structure dimensions.

01LC

fr as function of structure width and gap( h and fixed)

For fixed h and the smaller the gap, the lower the fr(higher C).

Unit cell can be miniaturized by using tightly spaced unit cell, albeit BW suffers.

Different unit cell dimensions can be used to achieve similar fr, final decision depends on cost, and fabrication complexity

0

1gap

LBWC

Ref, Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002;


(a) Initial unit cell dimensions prediction by plotting as a function of the structure dimensions.

01LC

fr as function of structure width and ( h and g fixed)

For fixed h and gthe smaller the , the higher the fr ( decreased C)

Unit cell can be miniaturized by using high substrate.

Fixed g, W and L increases with increasing h, while fr is decreasing.

1 ,gapLBW L hC

Ref, Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002;

AMC/HIS SIMULATION/ REFLECTION PHASE

(a) Based on the previous plots, arbitrary Rogers RT5880 with h=9.51mm, w=10mm and g=1mm was chosen for application at ISM band 2.5GHz

01LC

1 ,gapLBW L hC

AMC/HIS REFLECTION PHASE PARAMETRIC STUDY

(a) Based on the previous plots, arbitrarily Rogers RT5880 with h=9.51mm, w=10mm and g=1mm was chosen for application at ISM band 2.5GHz

01LC

With a decrease in g, there is an increase in C and a decrease in fr.

Unit cell can be miniaturized with this method, albeit BW suffers.

11 2( ) cosh ( )

L hW gW

gC

AMC/HIS REFLECTION PHASE PARAMETRIC STUDY

With a decrease in W, there is a decrease in C and an increase in fr.

Resonance frequency may be increased by decreasing W.

By increasing h, the L increases which increases BW while reducing f.

Thicker substrate can be used for wideband EBG, with a material high cost.

AMC REFLECTION PHASE ANGLE AND POLARIZATION

In TE mode E is orthogonal to XZ plane and vias.

fr (zero phase ) slightly increases with angle of incidence while BW decreases.

In TM H is orthogonal to XZ plane(E is inclined)

fr slightly decreases with increasing angle of incidence and BW increases at 60.

Dual band behavior due to induced current E_vertical and via.

AMC/HIS MINIATURIZATION

Like other microwave circuits, AMC size reduction means reducing its resonate while keeping its physical size intact.

Increasing L, thus increasing BW simultaneously

Using metamaterial with () method known as negative impedance converter(NIC) or non foster circuit

Use of low loss magnetic material especially at UHF. Increasing C, but BW suffers significantly.

Double layer structure( introducing a parallel C) Capacitor and inductor loading such fractal and

meander line( for these 2 techniques only SW BG is increased)

Ref; Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201

AMC/HIS DISPERSION DIAGRAM

Shows how propagation constant (Bloch wave vector) changes with frequency( how many modes are supported by the structure).

The amplitude of the wave travelling through a periodic structure has the same periodicity and symmetry as the structure itself.

Bloch theorem

To save computational time only irreducible Brillouin zone( smallest volume of space within Brillouin zone that fully characterizes the field inside a periodic structure )

Ref: http://emlab.utep.edu/ee5390em21.htm( 21 century EM )

http://emlab.utep.edu/ee5390em21.htm


BAND/ DISPERSION DIAGRAM SIMULATION

Irreducible Brillouin zone has first to be determined, which depends on the structure geometry.

5 EM features that can be predicted from a band diagram i. Band gaps( no modes are supported in this frequency range).ii. Transmission/ reflection spectra iii. Phase velocity/ group velocityiv. Dispersion (deviation from the light line)

20

20

;

nxx

nyy

d

d

d periodicity

Ref. http://emlab.utep.edu/ee5390em21.htm( 21 century EM lecture notes), Razav, Dispersion diagram using CST MWS QuickGuide_2,



DISPERSION DIAGRAM REFLECTION PHASE SIMULATION

BAND GAP/ DISPERSION DIAGRAM EXPERIMENT SET UP

Two methods can be used to experimentally characterize surface wave band gap(SW BG).

i. A pair of Monopole and loop antennas to detect TM and TE surface waves, respectively(in TM mode E is normal to the surface and in TE H is normal to the surface)

ii. Due to the enhanced reflectivity in the band gap frequency range, suspended transmission line can be used.

Ref; Frank B. Gross,” Frontiers in antennas next generation design and engineering, Mc Graw Hill 201, Ref. Daniel Frederic” High impedance EM surfaces, UCLA PhD dissertation 1999;

high impedance surface_his_ris_amc_nurmerical_analytical_analysis

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