Features of an AMC such as dispersion diagram and reflection phase are discussed numerically and analytically, along with their experimental set up. Parametric study on polarization (TE and TM，substrate thickness and dielectric constant and unit cell size and spacing is carried out. Their design equations are included from different references.

1. HIS/AMC/RIS NUMERICAL AND ANALYTICAL ANALYSIS
Ntawangaheza Jean de Dieu(金利)
ntajado@mail.ustc.edu.cn
(PPT2 of PPT3)

2. OUTLINE
Dielectric-conductor interface & image theory
Maxwell equations & surface waves
Periodic structure& high impedance
surface(HIS/AMC)

3. 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)
𝝌 and p: Material Susceptibilities
polarization collectively.
 Taking into account the E/M polarization properties of
the material, dielectric constant is:
0
0
1
H=
1
E=
B H B
D E D




  
  
0 0 (1 )r       
0
r




0 
0 0
0
(1 ) E
1
(D p)
D E E p
E
   

     
 
 Generally speaking, all materials are in fact dispersive, however, over certain frequencies ,
𝜺 can be viewed as frequency independent
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

4. MODEL OF DIELECTRIC CONSTANT FOR
CONDUCTORS.
 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 𝝎 ≪ 𝜶(𝜶 =number of
collisions per unit time 𝐚𝐧𝐝 𝝉 = 𝟏 𝜶 𝐦𝐞𝐚𝐧𝐬 𝐭𝐢𝐦𝐞 𝐛𝐞𝐭𝐰𝐞𝐞𝐧 𝐜𝐨𝐥𝐥𝐢𝐬𝐢𝐨𝐧𝐬𝐰𝐡𝐢𝐜𝐡 𝐢𝐬 ≈
𝟏𝟎−𝟏𝟒
𝐨𝐫𝐝𝐞𝐫 𝐟𝐨𝐫 𝐠𝐨𝐨𝐝 𝐜𝐨𝐧𝐝𝐮𝐜𝐭𝐨𝐫𝐬. ), for copper 𝜶 = 𝟒. 𝟏 × 𝟏𝟎 𝟕
, assuming 𝝎 =
𝟎. 𝟏𝜶, 𝒘𝒆 𝒇𝒊𝒏𝒅 𝒇 ≤
𝟎.𝟏𝜶
𝟐𝝅
= 𝟔𝟓𝟑𝑮𝑯𝒛 ≫ 𝟎. 𝟑 − 𝟑𝟎𝟎𝑮𝑯𝒛 𝒎𝒊𝒄𝒓𝒐𝒘𝒂𝒗𝒆 𝒓𝒂𝒏𝒈𝒆 ,
 A wave propagating through a lossy media will set up conduction current
(Jcond=𝝈𝑬) along with polarization current(Jp=j𝝎D=j𝝎𝜺 𝒅 𝑬) such that :
2 2
0 2
0
( ) ,
p
p
Ne
j m
 
  
  
 

2 2
0
max
0
( ) p Ne
m
 
  
  
  
( )E jtot cond p d cJ J J j E      
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

5. MODEL OF DIELECTRIC CONSTANT FOR
CONDUCTORS(CONT.).
.
( )E jtot cond p d c
c d c d
J J J j E
j j j
  

    

    
    
 Though both quantities (𝜺 𝒅 𝒂𝒏𝒅 𝝈)may be complex and dispersive, over a
wide range of frequency 𝝈 is a large real number and 𝜺 𝒅 = 𝜺 𝟎 for a good
conductor( see previous slide).
0
0
1 1 tancr
c d
j j
j j
 
  






   
   
From Ampere’s law in a
lossy media
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

6. 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 E
n H H J
D D
B B

  
  
 
 
r
r
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

7. BOUNDARY CONDITIONS(BC)(PEC).
 For a good conductor the following boundary conditions are valid:
interface
( ) 0
( ) s
n E
n H J
 
 
r
r
 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 t
s gc sgc
it t
E E
E H
       ; (low<<𝜂)
Surface wave and out phase reflection
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

8. 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 M
n H
  
 
r
r
1 and Z »MPc sMPC high   ;
 In phase Reflection and high impedance surface, but imaginary!
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

9. 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 𝝅 shift(-1), the minimum antenna _PEC distance should be one 𝝀 𝟒 (too thick
and costly at UHF), still surface current are supported.
c/... ploss back sw d
rad acc loss
rad
acc
P p p
andP p p
p
forPEC
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

10. 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
Absorbe
r
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.

11. 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( 𝝆 𝒆𝒙𝒕 ) or changing
electrical current (𝑱 𝒆𝒙𝒕), while their interaction with the medium is explained via the so
called constitutive relations(CR).
.
0
ext
ext
B
E
t
D
H J
t
D
B


  


  

 
 
B H
D E


 
 
1
1
H B
E E


 
 
Only valid for a linear, isotropic
homogeneous no dispersive
E/M media at low frequencies.
CR
Ref . Sophocles J. orfanidis,” EM waves and antennas, February 2004

12. MAXWELL’S EQUATIONS(CONT.)
 The faraday’s and ampere’s law can be expanded and yield the following
equations(single frequency(𝝎 = 𝟐𝝅𝒇 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 𝜺(𝒛), and constant in y direction.
0
0
0
yz
x
x z
y
y x
z
EE
j H
y z
E E
j H
z x
E E
j H
x y




 
 
  
  

   
  



Faraday’s law expansion
0
0
0
yz
x
x z
y
y x
z
HH
j E
y z
H H
j E
z x
H H
j E
x y




  
 
  
    

    
  



Ampere’s law expansion
𝜀2
𝜀1
𝑝𝑙𝑎𝑛𝑒 𝑧 = 0 = 𝑖𝑛𝑡𝑒𝑟𝑓𝑎𝑐𝑒
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

13. 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

14. 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

15. 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 𝜶 𝒂𝒏𝒅 𝜸 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

16. 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;

17. PHYSICAL INTERPRETATION
1 2
1 2
2
1
1 2
2
1 2
k
c
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;

18. PHYSICAL INTERPRETATION(CONT.)
2
2
2
2
2
1
1
1
1
k
c
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
k
c
j
j c c
c

   

  



 



  
 


   
;
0
1 2
, =
j
 
  


1 1t z
s
t y
E E j j
Z
H H   

    
storage energy

19. IMPEDANCE SURFACE(TM)
0
0
0
yz
x
x z
y
y x
z
HH
j E
y z
H H
j E
z x
H H
j E
x y



 
  
 
  
    

    
  



 Recall that for a TM( p mode) SW mode only has Ex, Ez and Hy are
non zero field components.
1
1
xjk z
x
jkx z
z
E Ae
E Be


 
 
 


1
0
0 1
xjk z
x
kx z
yy
x
E Ae
H j AeH
j E
z




 
 
 

 



0
1y xH j E


  
1
0 0
1
x x
s
y
x
E E j
Z
H j E

 

   

TM mode is supported by a Positive (inductive) surface
Ref . See previous slide

20. SURFACE IMPEDANCE(TE)
0
0
0
yz
x
x z
y
y x
z
EE
j H
y z
E E
j H
z x
E E
j H
x 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.
0
0
y
x
x y
jkx z
y
E
j H
H j Ez
E Ae 
 


 
  
 
0y
s
x
E
Z j
H


   
 TE mode is supported by a surface with capacitive
reactance(negative impedance)
Ref . See previous slide

21. 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
𝝀, 𝐢𝐧 𝐚𝐧𝐭𝐞𝐧𝐧𝐚 𝐞𝐧𝐠𝐢𝐧𝐞𝐞𝐫𝐢𝐧𝐠 𝟐𝐃 𝐢𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐠𝐫𝐞𝐚𝐭 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭.
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

22. 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,

23. 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 ±𝟒𝟓, ±𝟗𝟎 𝒂𝒏𝒅 𝟗𝟎 ± 𝟒𝟓.
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

24. HIGH IMPEDANCE SURFACE(HIS)/DISPERSION DIAGRAM
 Analytically, dispersion diagram of HIS structure can be derived by solving
the wave equations:
2
2 2
02
2 2 2
0
(k ) E 0
jkx z
y
y
x y
x
E Ae
E
k
z
k k




 


  

  
For TM mode we find:
0
0
2 2
0
2 2 2 2
0 0
2 2
0
0 0
0 0
2
2
0
(Z )
( )
1
1
TM
s TM
TM
TM
TM
TM
TM
TM
j
Z jZ
k k Z
Z
k
Z
k
c

 

 


  
 


   
 
 
 
 
For TE mode we find:
0
2
0
2
1
s
TE
TE
Z j
k
c 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;

25. DISPERSION DIAGRAM OF HIS
 Since unit size and periodicity are much smaller compared to the 𝝀, 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
2
0
1 TM
TM
Z
k
c


 
For TE mode we find:
2
0
2
0
2
1
1
TE
LC
k
c Z



 
2
1
s
j L
Z
LC




2
2
0
2
02
0
1
1 0
s
j L
Z




 



 f p
2
2
0
2
02
0
1
1 0
s
j L
Z




 



 p f
 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

26. 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 ±𝟒𝟓, ±𝟗𝟎 𝒂𝒏𝒅 𝟗𝟎 ±
𝟒𝟓 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 d
s
g d
Z Z
Z
Z Z



0
0
0
0
cos
cos
Z cos
cos
TM s
s
TE s
s
Z
Z
Z
 
 
 
 

 


 

Ref.; Fan Yang and Yahya Rahmat, EBG structures in antenna engineering, Cambridge university press2009

27. REFLECTION PHASE TE AND TM
For a plane wave striking a an EBG surface with an
Arbitrary angle, two polarizations have to be distinguished(TM and
TE).
,TM
0
TE
dZ j h
2
( , 0)
( , )
cos
gTE
g
Z
Z

 


( , ) ( , 0)TM
g gZ Z  
( , 0)g
g
j
Z
C




0(1 ) 2
log( )r
g
a a
C
g
 
 


0
0
0
0
cos
cos
Z cos
cos
TM s
s
TE s
s
Z
Z
Z
 
 
 
 

 


 

g d
s
g d
Z Z
Z
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

28. 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 𝝀, 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.
2
1
s
j L
Z
LC




1
1 2( ) cosh ( )
L h
W g
W
g
C

 






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

29. AMC/HIS SIMULATION(NUMERICAL)
 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 𝝁) the wider the BW is achievable.
 For a fixed h and 𝝁 the higher the C, the narrower the BW and the lower the fr.
2
1
s
j L
Z
LC




1
1 2( ) cosh ( )
L h
W g
W
g
C

 






0
1
LC
 
0
1
gap
L
BW
C

 
 
V
90 0
0
2
,r h
BW 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

30. AMC/HIS SIMULATION EXAMPLE
 AMC design steps(procedures)
(a) Determine the structure geometry by plotting 𝝎 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, 𝝎 …
(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

31. AMC/HIS/RIS SIMULATION(NUMERICAL)
(a) Initial unit cell dimensions prediction by plotting 𝜔 as a function
of the structure dimensions.
0
1
LC
 
fr as function of structure width and gap( h and 𝜀 fixed)
 For fixed h and 𝜺, 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
1
gap
L
BW
C

 
 
V
Ref, Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002;

32. AMC/HIS SIMULATION(NUMERICAL)
(a) Initial unit cell dimensions prediction by plotting 𝜔 as a function of
the structure dimensions.
0
1
LC
 
fr as function of structure width and 𝜺( h and g fixed)
 For fixed h and g, the smaller the 𝜺, the
higher the fr ( decreased C)
 Unit cell can be miniaturized by using
high 𝜺 substrate.
Fixed g, W and 𝜀
L increases with increasing h,
while fr is decreasing.
1
,gap
L
BW L h
C


 
Ref, Dr R.B Waterhouse, microtrip patch antennas: A designer’s guide Springer science + Busness, 2002;

33. 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 0
1
LC
 1
,gap
L
BW L h
C


 

34. 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
0
1
LC
 
 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.
1
1 2( ) cosh ( )
L h
W g
W
g
C

 







35. 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.

36. 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.

37. 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 (𝜇 < 0 𝑎𝑛𝑑 𝜀 < 0) 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

38. 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.
 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 )

39. 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 velocity
iv. Dispersion (deviation from the light line)
2
0
2
0
;
nx
x
ny
y
d
d
d periodicity




p p
p p
Ref. http://emlab.utep.edu/ee5390em21.htm( 21 century EM lecture notes), Razav, Dispersion diagram using CST MWS
QuickGuide_2,

40. DISPERSION DIAGRAM REFLECTION PHASE SIMULATION

41. 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;