RRAC(01)10
Information on frequency selective surfaces
History of FSS
The frequency selective surfaces (FSS) are periodic structures in either one, two
dimensions (i.e. singly or doubly periodic structures) which, as the name suggests,
perform a filter operation. Thus, depending on their physical construction, material and
geometry, they are divided into low-pass, high-pass, band-pass and band-stop filters.
Figure 1.1
As can be seen in Figure 1.1 the FSS can be cascaded to form a triply-periodic structure
which is commonly known as a photonic crystal.
The FSS were intensively studied since the early 1960s 12 although in 1919 Marconi
patented such periodic structures3. From 1969 until the end of 2000, 214 papers were
published containing the keyword "frequency selective surface" (INSPEC Catalogue
search 12/1/2001). Early work concentrated on the use of FSS in Cassegainian
subreflectors in parabolic dish antennas. FSS are now employed in radomes (terrestrial
and airborne), missiles and electromagnetic shielding applications.
The analysis of FSS started with mode matching techniques which were first applied in
waveguide problems. The mode matching method led to the approximate method of
equivalent circuit analysis which gave a lot of insight into the behaviour of FSS since it
was partly based on the transmission line principles. The modelling capability however
was limited by the inability of the Mode Matching Method to model any FSS geometry
and the inaccuracy the equivalent circuit method. With the advent of computers more
accurate numerical techniques were developed for the analysis of FSS such as the method
of moments (with entire or subdomain basis functions) the finite difference method and
the finite element method.
Experiment is necessary to verify the performance of a practical FSS structures, confirm
the accuracy of theoretical/numerical models and provide results for FSS structures
which are not amenable to simulation. The early experiments using bolometers have now
been replaced with Network Analysers that provide the capability of obtaining not only
power but amplitude and phase measurements of the scattered fields from FSS structures
provided an accurate calibration is performed.
Optical transparent or opaque Windows at 2.45 GHz–
research and applications
To the best of our knowledge, there are three reports on optically transparent conductor
FSS and FSS windows
1. A journal paper4 authored by Prof. Parker and his research team at Kent University,
UK, detailing the effect of conductivity on the performance of optically transparent
conductor FSS situated on opaque dielectric substrates. Circular patch (band-stop
FSS) and slot rings (band-pass FSS) were employed as FSS elements on a square
array. They were fabricated using 20/ Indium Tin Oxide (ITO) and 4-8/ Thinfilm Silver (Ag). The bandstop/bandpass regions were above 10 GHz. Test at normal
and angular (45°) plane wave incidence were made for both transverse magnetic
(TM) and transverse electric (TE) polarisations. By comparing the performance of
these transparent conductor FSS with copper FSS it was concluded that it is feasible
to construct optically transparent FSS provided the conductivity of the conductor is
below 4-8/.
2. A conference paper by the Kajima Technical Research Institute, Japan5. The
employed silver paint (95% Ag). The silver paint was deposited directly on glass. The
group designed two band-stop FSS structures. The first has a band stop frequency
centered at 1.95GHz and employed tripoles as FSS elements. The second FSS has
two band-stop frequencies, at 1.9GHz and 2.4GHz and consisted of 'hybrid' elements
(tripoles within triangular shaped elements).
3. Nippon product page6 on the World Wide Web (WWW). The company design a
shield film for windows that can shield the desired frequency. Either 2.45GHz for
wireless local area network (LAN) applications or 1.9GHz for Personal Hand-Phone
System (PHS) applications. They also claim that their product does not disturb mobile
phone communication bands at 900 MHz and television frequency bands.
The authors tested a variety of opaque materials. The choice of material was influenced
by two factors: (a) the conductivity of material which significantly affects FSS
performance and (b) the width of the material which affects both the resistance of the
FSS element and the optical transparency. Silver paint was the chosen material which
allowed FSS elements of width diameters of 0.5mm to be used with a resulting
attenuation of 35dB or more. Wedged guide horn antennas were used in the tests. The
glass size was 60cm60cm. Test conditions allowed for angles of incidence was 0 and
60 to the normal for both polarisations (vertical and horizontal). Antenna distance was
60cm and 200cm. The results in the paper are for the tripole structure and for normal
incidence. They cover a range of 1-3GHz and. The bandstop frequency is at 1.9GHz and
the frequency region over which transmission falls below 30dB has a width of 35MHz.
The conclusions drawn from the above work:
(1) Transparent conductors can be employed provided that the conductivity is less than 48/ and the dimensions of the element width and thickness are such that the
resistance of the strips is low (the latter is true for non-transparent conductors too).
(2) Silver paint FSS glass have a lower cost of production than other types of shielding
glass and much higher conductivity than transparent conductor materials. The
disadvantage is that the silver paint is opaque but it is compensated by the fact that
the width of the elements can be made very small owing to the paint’s high
conductivity.
None of the above publications shows the effect of cross-polarisation or a systematic
design methodology. The effect of environment is not examined. The effect of window
frames is not examined either. However it indicated in the Kajima paper that the problem
of gaps between frames and window glass can be covered using the silver paint.
In the Kajima paper there is no report on the behaviour of the resonance as the angle of
incidence increases nor does the paper show the frequency at which the onset of higher
order harmonics occurs. The effect of cascading FSS windows has not been examined.
Applications of transparent or opaque conductor FSS Windows:
1. 1.Selective shielding of the electromagnetic interference from high power microwave
heating machines adjacent to wireless communication base-stations.
2. Selective shielding of frequencies of communication in sensitive areas (military
installations, airport, police etc.)
3. Protection from harmful electromagnetic radiation especially in the 2-3GHz band7in
domestic environment, schools, hospitals etc. arising externally (wireless
communication base stations) or internally (microwave ovens).
4. Control of radiation at unlicensed frequency bands (eg. Bluetooth applications,
2.45GHz).
5. Picocellular wireless communications in office environments such as the Personal
Handy-phone System in offices where to improve efficiency each room needs to
prevent leakage of radio waves into and of the room. This implies that windows, floor
and ceiling need to be shielded. Kajima Research Institute is developing such a film
to be applied to buildings.
6. Isolation of unwanted radiation. FSS windows can be incorporate in trains prevent
mobile phone frequencies; around base station antennas to filter out unwanted
radiation.
Note: that in the above applications one wishes to prevent certain frequency bands of
electromagnetic radiation to be transmitted whereas others are required to pass
(frequencies related to emergency services for example). Hence the use of a broadband
shielding material is not an option.
Design by example
Example 1 (the example was presented by G. Gregorwich8 at the 1999 Aerospace
Conference).
Problem:Design an FSS structures that can transmit data across the 2.2 to 2.4 GHz
frequency range (in S-Band) and reject data across the 5.4 to 5.9 GHz frequency range (in
C-Band).
Step 1: Choose a suitable element or combination of elements. The choice depends on the
desired characteristics and the designers experience. The latter is accumulated via
experiments or numerical simulations. Available information also dictates the choice of
elements. In this example it was decided that a combination of a square grid and a
Jerusalem cross is used. The square grid acts as a high-pass filter and the cross as a band
stop filter. One could have chosen a square patch but the choice of the cross allows the
designer to employ more tuning parameters. Thus, maximisation of the bandpass
transmissivity and choice of bandstop frequency can be achieved simultaneously.
w
g
P
D
L
h
a
Let T be the thickness of the metal of the Jerusalem cross.
Step 2: Decide on the procedure (experimental or theoretical) to be followed to assess the
performance of the FSS structure. Let us, following Gregorwich, use the equivalent
circuit theory to model the FSS. This analysis assumes that
T  a, T  W  P, h  P   , g  D  
The equivalent circuit of the Jerusalem cross is a series LC circuit
L
Z0=1
Z0=1
C
L 
C 
 2P 
ln 

  w 
P
 2P 

ln 
  g 
4D
1 

Z  jX  j  L 

C 

At resonance
 r LC  1 or f r 
1
2 LC
Thus, at resonance,
 2P   2P 

 ln 
 w   g 
 r  2 PD ln 
The power transmitted though the FSS is
T
2
 1 R 
2
4X 2
1 4X 2
Thus to optimised the power transmission in the passband X must be as large as possible
which implies that L and 1/(C) must be as large as possible. But the L-C values must
satisfy the resonance condition. So a compromise must be reached.
Step3: Based on FSS theory, numerical/analytical models and experiments derive rules of
thumb to assist in the design of the FSS structure. The guidelines (generic and specific) to
the Jerusalem cross structure are as follows:
 Bandwidth of stopband increases as W and D increase (specific).
 Bandwidth of stopband increase by reducing h and g (specific).
 The passband approaches the stopband by increasing a and/or reducing g (specific).
 To avoid grating lobes keep the period less than 0.5 (generic).
 More multigrid FSS, the effects of dielectric separation can be canceled out by
spacing the FSS grids /4 apart (generic).
 To avoid coupling phenomena the FSS grids must be placed at least /2 from the
transmitting/receiving antenna (in the specific example it was a phased array antenna
(specific/generic).
 By stacking identical layers of FSS the stopband and the bandstop attenuation
increase.
 If the FSS grid is placed inside a dielectric then the resonance frequency becomes
lower.
Step 4: Test and modify. From the rules a structure of suitable geometrical dimensions is
constructed and tested. Since the equivalent circuit is true for normal incidence, angular
incidence experiments must be carried. If there is attenuation in the passband region then
the square grid can be modified or eliminated. Furthermore, if the equivalent circuit
cannot take the dielectric substrate into account, the FSS must be redesigned to allow for
the effect of the substrate. Novel approaches can be followed to improve further the FSS
performance. For example if the bandwidth needs to increase one may stack two
Jerusalem FSSs with different geometrical parameters.
L1
L2
Z0=1
Z0=1
C1
Z0=1
C2
l
Example 2 (the example was published by M.A.A. El-Morsy9, E.A. Parker and R.J.
Langley)
Transmitted power
The above work relies on analysis. Ideally one wishes to apply synthesis, based on a
desired transmission response, to obtain the desired parameters of FSS. Assume that the
following FSS response is required. This response can be recognised as the that of a
network with reactance admittance given by
0
1 e

2
e


 12
Y
jH  2   22
2


At 1 is a zero corresponding to a transmission resonance, at 2 is a pole corresponding
to a reflection resonance and H is a scale factor. The above equation can be expanded in
partial fractions as follows:
Y 
A


B
   22
2
where A and B are coefficients to be determined.
The equivalent circuit described by the above equation is
L2
L0
C2
A and B can be expressed in terms of H. Furthermore,
1 
1
C2 L0  L2 1 / 2
2 
H
1
C2 L2 1 / 2
L0 L2
L0  L2
and
Y
jC 2
1

jL0 1   2 L2 C 2
By specifying one more condition, say the transmitted power at e, the values of L0, L2
and C2 can be uniquely determined. Once a suitable element has been identified, a set of
non-linear equations, involving the circuit component values and the dimensions of the
element, are solved to obtain the exact element geometry. In general L and C are
expressed in terms of the FSS period, widths of the various conductor strips, gap
distances between the conductors angle of incidence and wavelength.
L  L( P, w, h,  , )
C  C ( P, w, h,  , )
Example 3 (the example was published by M.A.A. El-Morsy, E.A. Parker and R.J.
Langley)
Transmitted
power
We know that the response below can be obtained from the accompanied FSS element.
0
1
2
e

Transmitted
power
It is therefore natural to suppose that by cascading to two such grids of different
geometrical sizes one can obtain more transmission resonances (see below). As a matter
of fact El-Morsy found that provided the conductors are not closely spaced this cascaded
structure is equivalent to a gridded double square.
0
1
2
e
3 4

It can be concluded from this example that a stack of FSS (as shown below) can be
employed to obtain the desired transmission response.
Z0
L1
C1
Z0
=1
L2
C2
Z0
=1
L3
C3
Z0
=1
l
This can also be achieved by a combination of elements.
L4
Z0
C4 =1
Factors Influencing the FSS performance and design
The performance and behaviour of the FSS filters depends on the following factors:
(1) The conductivity of the FSS conductor.
(2) The geometry of the FSS element (shape, with of conductive striplines, proximity of
conductive striplines, thickness of conductor)
(3) The permittivity of the FSS substrates.
(4) The period of the FSS array.
(5) The number of FSS arrays when these are employed in a cascade.
(6) The electrical distance between the FSS arrays in cascade configurations.
(7) The choice of element types in hybrid FSS configuration.
(8) The finite number of periods (for what number of periods does the FSS cease to
behave as periodic structure?)
(9) Metallic frames surrounding the FSS window.
In this investigation the following restrictions exists:
(1) The window must remain optically transparent. Thus the conductors must be either
transparent or opaque and very thin.
(2) The substrate must be transparent – preferably glass.
(3) At the bandstop frequency the attenuation must be at least -35dB (relative to the
passband power transmission).
(4) Cross-polarisation must also be below the –35dB limit.
(5) The FSS must withstand a power of 100W.
(6) The bandstop frequency must remain constant irrespective of the angle of wave
incidence and wave polarisation.
The influence of some of the above factors can be quantified theoretically leading to
generic rules. For the rest of the factors, their influence must be determined
numerically/experimentally leading, in some cases, to specific (to the element) rules of
thumb.
Let us therefore determined these generic (theoretically) and specific rules
(experimentally) for bandstop and bandpass filters.
Fundamental Theory of Spatially Periodic Structures
Two types of problems, involving spatially periodic structures, exists:
1. Scattering problems
2. Eigenvalue ( or dispersion) problems
In the first type of problem, the scattered field due to an incident plane wave on a singly
or a doubly periodic open structure is examined. In the eigenvalue problems (where there
are no sources of electromagnetic waves) the dispersion curves of the periodic structure,
(ie. the plots of the Floquet constant(s) versus frequency) are obtained.
Assuming that a periodic structure has an infinite number of periods, Floquet’s theorem
applies. The theorem states that:
“For a given mode of propagation at a given steady-state frequency the fields (electric or
magnetic) at one cross-section differ from those a period away only by a complex
constant.”
Considering a singly periodic structure, it is assumed to be infinite and uniform in the ydirection. Therefore, for modelling purposes, it is assumed to be two dimensional, From
Floquet’s theorem, the field F (E or H) satisfies the following equation,
F ( x, y, z  Dz )  F ( x, y, z )e  z Dz
(1)
Where z is the Floquet constant. Consequently, the field in the periodic structure can be
described as,
F ( x, y, z)  F p ( x, y, z)e  z z
(2)
where Fp denotes the periodic part of the field. Since Fp can be represented by a Fourier
series, F is written as,
F ( x, y , z ) 

G
n  
n
( x, y )e ( z  j 2n / Dz ) z
(3)
Each of the terms of the series (in Eq. 3) is called as spatial harmonic. For the scattering
problems, provided the incident plane wave is not attenuated or amplified in the direction
of the periodicity (i.e. there is no loss or gain in region 1 of Fig.1), .
 z  j z
where z is a real value variable.
(4)
Figure 1. An open 2D singly periodic structure. The unit cells are shown with a dashed line. The structure
k zinc
k1
Incident plane
wave
kxinc
Region 1
 1 , 1
x1
1
Unit cell
Region 2
x2
x3
x3  
2
 2 , 2
Dz
x3
Region 3
x3  
Figure 1
is assumed to be infinite and uniform along the y-direction. The unit cell of the structure is truncated along
the x-direction by two horizontal boundaries, x1 and x2..
Therefore, each harmonic has a propagation constant, in the direction of periodicity,
given by,
 zn   z 
2n
Dz
(5)
In addition, in the direction of the periodicity, the Floquet constant is equal to the
propagation constant of the incident plane wave. Let us prove this by considering a 2D
singly-periodic structure (Fig.1). The incident plane wave is assumed to be of the form,
F inc  Aince jkx x e  jkz
inc
inc
z
(6)
The plane wave is a periodic function along the z-direction, of any period, and when it
interacts with a periodic structure of period D z it produces a scattered field F sc which is
periodic with period D z also. The scattered field in regions 1 and 3 of Fig 1 is represented
by a superposition of propagating and evanescent spatial harmonics, Fig.2, which are
plane waves for the 2D singly periodic structures and TE/TM waves for the 3D doubly
periodic structures. Thus the total field in regions 1 and 3 of Fig. 1, is,
in the upper region, 1,
F
up
F
inc
sc  jkzup z
p
F e
A e
inc
jkxincx
e
 jkzincz


R e
n  
 jkx nx
n
j
e
2n
z
Dx
e  jkz
up
z
(7)
in the lower region, 3,
F
low

low
F psc e  jk z z


 Tm e
jk x mx
j
e
2m
low
Dz  jk z z
(8)
e
n  
where e  jkz z , e  jkz z are the Floquet’s complex phase terms in the upper and lower
regions, respectively. Within region 2, the field is expressed as,
up
low
F  Fp ( x, z )e z
(9)
Figure 2
From the continuity of the tangential field at the interface 1 ( x  x1 ) ,
2n 
 
j
z
up
 jk xxnx1
 Ainc e jk zincx1  e  jk zincz  
Rn e
e Dz  e  jk z z  F p ( x1 , z ) e z



n





(10)
At points a period apart, the periodic terms inside the square brackets are constant and
therefore independent of z. There is an infinite number of such points and thus the only
condition that satisfies Eq 10 for every such point is,
  jk zinc  jk zup
(11)
Any other condition will violate the requirement that the square bracketed terms are
constant. Similarly, at 2 ,
2m 
 
j
z
low
jk
m
x
  Tm e x 2 e Dz  e  jk z z  F p ( x 2 , z ) e z
m 





(12)
Again, at points a period apart, the periodic terms inside the square brackets are constant
and therefore independent of z and consequently (using Eq. 11),
jk zlow    jk zinc
(13)
Since the harmonics are solutions of Maxwell’s equations and hence of the wave
equation, they must satisfy the dispersion relation, i.e.
k xn

k 02  r  r  k 2zn


 j k 2zn  k 02  r  r


for
k 02  r  r  k 2zn
for
k 02  r  r  k 2zn
(14)
where
k zn  k zinc 
2n
Dz
(15)
It can therefore be concluded that:
 An infinite sum of scattered waves, called harmonics, which are in the form of plane
waves are scattered (transmitted and reflected) from a periodic structure when a plane
wave is incident on the structure.
 These harmonics are either propagating or evanescent depending on which inequality
holds. The latter depends on the frequency, permittivity and permeability of the
homogeneous medium in which the harmonic propagates and the period of the
periodic structure.
The work can be extended to doubly periodic FSS structures in three dimensions (Fig.3).
Figure 3
From the time harmonic Maxwell’s equations the vector wave equation is obtained,
1
    F  k o2 qF  0
p
(16)
where, k 02   2  0  0 , p   r , q   r for F=E and p   r , q   r for F=H.
The field in a linear periodic structure obeys Floquet’s theorem, which states that the
field between associated periodic boundaries differs only by a complex constant,
Fx  Dx , y, z   Fx, y, z e  jkx
inc
Fx, y  D y , z   Fx, y, z e
Dx
 jk inc
y Dy
(17)
(18)
inc
where k inc
x , k y are the propagation constants of the incident plane wave along the axes of
periodicity,
k inc
x  k o pq sin  cos 
(19)
k inc
y  k o pq sin  sin 
(20)
Along the non-periodic boundaries the field is expressed as sum of TE and TM waves.
These waves completely represent the tangential field.
On the plane wave incident side (upper boundary in Fig. 3) the total tangential field is the
summation of the incident and the reflected field,
Ftup  Ftinc  Ft ref  Ainc eF00 
  Amrefn  eFm n  Bmrefn  hFm n


m   n  
(21)
and on the lower boundary the total tangential field is equal to the transmitted field,
Ftlow  Fttran 
  A

tran
Φ eFmn  Bmn
Φ hFmn 

tran
mn
(22)
m   n  
where superscripts ‘ref’, ‘tran’, over wave amplitudes A,B, denote reflected and
transmitted wave amplitudes respectively and subscript ‘t’ under the field F denotes the
tangential component of the field. F is the function of the TE/TM wave from the field F,
superscripts ‘e’ and ‘h’ denote TE and TM polarisation respectively, subscripts ‘m’, ‘n’
denote the harmonic order.
For E t
 eEm n 
 k yn i  k xm j  R 
 hEm n 
for Ht
k tm n D x D y
mn
 k xm i  k yn j  R 
k tm n D x D y
mn
for TE
for TM
(23)
(24)
 eHm n 
 k xm i  k yn j  R 
 hHm n 
k tm n D x D y
for TE
mn
 k yn i  k xm j  R 
k tm n D x D y
mn
(25)
(26)
for TM
Dx, Dy are the periods in the x and y directions respectively,
k xm  k inc
x 
2m
Dx
(27)
k yn  k inc
y 
2n
Dy
(28)
k 2tmn  k 2xm  k 2yn
(29)
k 2zmn  k o2 pq  k 2tmn
(30)
R mn  exp(  jk xm x) exp(  jk yn y) exp(  jk zmn z)
(31)
The dispersion relation Eq. 14 still holds but one should now incorporate the propagation
constant along the second axis of periodicity.
Let us now consider non-orthogonal axes of periodicity. Fig.3 shows a doubly periodic
structure with non-orthogonal axes of periodicity. One of the axes, u-axes, coincides with
x-axis and the other, v-axis, is at angle n-900 w.r.t. the y-axis. The position vector of any
point, in a plane, is the same whether the x-y or u-v coordinate system is used.
Consequently, from Fig. 3,
y  u sin 
(32)
x  u  v cos 
(33)
u  x  y cot 
(34)
The incident plane wave can be written as,
F inc  Ae  jk x x e
inc
 jk inc
y y
e
 jk inc
zy z
 Ae  jk u u e  jk v v e
inc
inc
 jk inc
zy z
(35)
where (using Eqs. 4.55, 4.56),
inc
k inc
u  kx
(36)
k uinc  k xinc cos   k yinc sin 
(37)
From Floquet’s theorem (modification 1),
F(u, v, z)  Fp (u , v, z)e  jk u u e  jk v
inc
inc
v
(38)
The scattered field Fsc can be represented by a double summation of the form,
F sc (u, v, z ) 


  C m ne  jkumu e  jkvnv
(38)
m   n  
k um  k inc
u 
2m
Du
(39)
inc
k vn  k vn

2n
Dv
(40)
Let us make the following definition (modification 2),
Dx  Du
(41)
D y  Dv sin 
(42)
From the above equations we obtain,
F sc (u, v, z ) 


  C m ne  jk x x e
m   n  
where (modification 3)
 jk y y
(43)
k x  k inc
x 
k y  k yinc 
2m
Dx
2n 2m

cot 
Dy
Dx
(44)
(44)
The TE/TM waves can still used to represent the incident and the scattered fields
provided kxm, kyn are replaced by kx, ky respectively and Dx, Dy are defined by Eqs. 4142.
Effect of lossy conductive material
Compared with copper which might be considered as a material of infinite conductivity,
the silver paint and the transparent conductor have much lower conductivities resulting in
a finite resistance value along the conducting elements. Let this loss be represented by a
resistance in series with the conductor inductance. It is shown below how by varying this
resistance value the transmitted power through an FSS varies. Two types of FSS are
considered: (a) a series LC resonant circuit and (b) a parallel LC resonant circuit.
Lossy FSS - parallel-LC (L=C=1) with loss R in series with L
1
Z0
0.9
0.8
L
increasing R
R
normalised transmitted power
Z0
0.7
0.6
0.5
0.4
0.3
0.2
C
0.1
0
0
0.5
1
1.5
angular frequency
2
2.5
3
Lossy FSS - series-LC (L=C=1) with loss R in series with L
1
0.9
R
C
L
0.8
normalised transmitted power
Z0
Z0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
angular frequency
2
2.5
3
The effect of resistance is indicated in the experimental graphs where the same FSS
pattern is made from copper and silver paint.
Copper square loops
0
-5
Transmittance (dBm)
-10
-15
-20
-25
-30
-35
1
2
3
4
5
6
7
Frequency(Hz)
8
9
10
11
12
9
x 10
Silver square loops
0
-5
Transmittance (dBm)
-10
-15
-20
-25
-30
-35
1
2
3
4
5
6
7
Frequency(Hz)
8
9
10
11
12
9
x 10
Experimental Results
The aim of the experiments is to determine the best band-stop FSS element type. Wu
produced in his book the following table. It is our aim to verify this table as other
researchers (like those of the Kajima Institute) did not choose the square elements that
suppose to have the best performance.
Element shape and perfromance based on free-standing single screen performance.
Ratings: best = 1, second best = 2 etc.
Type of Element
Loaded dipole
Jerusalem cross
Rings
Tripole
Cross dipole
Square loop
Dipole
Angular
insensitivity
1
2
1
3
3
1
4
CrossPolarisation
2
3
2
3
3
1
1
Larger
Bandwidth
1
2
1
3
3
1
4
Small band
separation
1
2
1
2
3
1
1
Circular Rings:
Close packing in a triangular lattice of rings provides insensitivity of the resonance
frequency to the angle of incidence and the plane of incidence. This was demonstrated by
Parker and Hamdy 10. It was also observed that close packed rings give wider reflection
bandwidth (defined as the range between the frequencies at which the reflection
coefficient fall to -0.5dB. It was noted that for closed packed rings in free space designs
(rings in air or on very thin substrates of low refractive index) to a good approximation
the resonant wavelength (near the centre of the reflection band) is equal to the ring
circumference.
The transmission characteristic of ring FSS can be modified by using concentric rings
(instead of single rings). Parker, Hamdy and Langley11 observed that concentric rings
produce two reflection resonances. The lower one is insensitive to the angle of incidence
and polarisation plane as with single rings but the upper resonance is much more
sensitive as in the case of arrays of single rings that are not close packed. A correlation
was made to the fact that in concentric rings the outer rings are closely packed whereas
the inner ones are not. Note that the experiments were performed using square lattice
FSS.
It was noted that although the upper resonant band may not be particularly useful due to
its sensitivity, its presence was modifying the shape of the transmission close to the lower
resonance leading to a transmission coefficient that rose more rapidly with frequency
than it did in the case of closed packed rings. Applications of concentric rings are
dichroic mirrors in dual-band Cassegrain antenna systems.
Cahill and Parker12 measured the cross-polarisation of concentric rings and Jerusalem
Crosses for frequency regions at which the copolar loss was 0.5dB or less. The incidence
angle was 45 Both reflection and transmission cross-polarisation measurements were
made. They found that the cross-polarisation of the concentric rings was less than –30dB
for both the reflection and transmission measurements.The cross-polarisation levels of
the Jerusalem Crosses for the reflection measurements were approximately the same as
for the rings for the reflection measurements. For the transmission measurements though
values as much as –26dB were observed.
Circular Ring FSS
1. Effect of calibration at angle
5
Structure C 2*4mm Glass 15deg Blue: Calibration Red:No Calibration
Transmitance dB
0
-5
-10
-15
-20
-25
0.4
0.6
0.8
1
1.2
Frequency Hz
1.4
1.6
1.8
9
x 10
Structure C 2*4mm Glass 30deg Blue: Calibration Red: No calibration
5
Transmitance dB
0
-5
-10
-15
-20
0.4
0.6
0.8
1
1.2
Frequency Hz
1.4
1.6
1.8
9
x 10
Structure C, 2*4mm Glass 45deg Blue: Calibration Red: No calibration
5
Transmitance dB
0
-5
-10
-15
-20
-25
0.4
0.6
0.8
1
1.2
Frequency Hz
1.4
1.6
1.8
9
x 10
Structure C, 2*4mm 60deg Blue: Calibration Red: No calibration
5
Transmitance dB
0
-5
-10
-15
-20
-25
0.4
0.6
0.8
1
1.2
Frequency Hz
1.4
1.6
1.8
9
x 10
2. Comparison of Antennae
10
Structure B 2*4mm Glass Tx:0.5m Rx:1,7m
Blue: Antennae1 Red: Antennae2 Green: Antennae3
5
0
Transmitance dB
-5
-10
-15
-20
-25
-30
-35
-40
0
5
10
Frequency Hz
15
9
x 10
Structure B 2*4mm Glass Tx:1,7m Rx:1,7m
Blue:Antennae 1 Red:Antennae2 Green:Antennae3
20
Transmitance dB
10
0
-10
-20
-30
-40
0
5
10
Frequency Hz
15
9
x 10
Structure B 2*4mm Glass Tx:0.5m Rx:0.5m
5 Blue: Antennae 1 Green: Antennae 3 Red: Antennae 2
0
Transmitance dB
-5
-10
-15
-20
-25
-30
-35
0
5
10
15
Frequency Hz
9
x 10
Free-Space Cross-Polarization
Blue: Antennae 1 Red: Antennae2 Green: Antennae3
5
0
-5
Transmitance dB
-10
-15
-20
-25
-30
-35
-40
-45
0
2
4
6
8
10
Frequency Hz
12
14
16
18
9
x 10
3. Antennae 1 at Different Distances for Transmitter and
Receiver.
For the following measurements Structure B has been used between two 4mm
glass sheets.
Tx:0.5m
10
Rx: Blue:0.5m Gree:0.8m Red:1.1m
5
Transmitance dB
0
-5
-10
-15
-20
-25
0
5
10
Frequency Hz
Tx:0.5m
Rx: Blue:1.4m
15
9
x 10
Green: 1.7m Red:2m
10
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
0
5
10
Frequency Hz
15
9
x 10
Rx:0.5m
Tx:Blue:0.5m Green:0.8m Red:1.1m
5
Transmitance dB
0
-5
-10
-15
-20
-25
0
5
10
Frequency Hz
Rx: 0.5m
10
Tx: Blue: 1.1m Green: 1.4m
15
9
x 10
Red: 1.7m
5
Transmitance dB
0
-5
-10
-15
-20
-25
0
5
10
Frequency Hz
15
9
x 10
4. Single Layer Squares on one 4mm Glass Sheet
Blue:0deg Green: 15deg Red: 30deg
6
4
0
-2
-4
-6
-8
-10
-12
1
0
2
3
10
9
8
7
6
5
4
Frequency Hz
9
x 10
Blue:0deg Green: 45deg Red:60deg
6
4
2
0
Transmitance dB
Transmitance dB
2
-2
-4
-6
-8
-10
-12
-14
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
5. Double Layer Squares with Glass in between and 4mm sheets
on the outer sides.
Glass in Between: Blue:4mm Red:6mm Green:8m Yellow:10mm, 0deg
10
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
-35
0
10
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
Glass in Between: Blue:4mm Red:12mm Green:14mm Yellow:16mm, 0deg
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
-35
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
Glass in Between: Blue:4mm Red: 18mm Green:20mm 0deg
5
0
Transmitance dB
-5
-10
-15
-20
-25
-30
-35
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
6. Double-Layer Squares with Glass in Between at 45° for Vertical
and Horizontal Polarisation.
Blue: 4mm Vert. Green:4mm Horiz. Red:6mm Vert. Yellow:6mm Horiz.
10
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
-35
3
2
1
0
10
9
8
7
6
5
4
Frequency Hz
9
x 10
Blue:8mm Vert. Green:8mm Horiz. Red: 10mm Vert. Yellow:10mm Horiz.
5
0
Transmitance dB
-5
-10
-15
-20
-25
-30
-35
-40
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
Blue:12mm Vert. Green: 12mm Horiz. Red: 14mm Vert. Yello:14mm Horiz.
10
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
-35
10
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
Double-Layer Squares Blue:16v Red:18v Green:16h Yellow:18v 45deg
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
-35
0
1
2
3
4
5
6
Frequency Hz
7
8
9
10
9
x 10
7. Super-dense Structure Using Ring Elements
Comparisson of the two types of rings used to produce the S-D Structure
Blue: Rings used in Structure D Red: Rings used in Structure B
15
10
Transmitance dB
5
0
-5
-10
-15
-20
-25
-30
0
2
Blue: 0deg
10
4
6
Red:15deg
8
10
Frequency Hz
12
14
16
18
9
x 10
S-D between 2mm Glass Sheets
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
0
5
10
Frequency Hz
15
9
x 10
BLue:0deg Green:30deg
Red:45deg S-D between 2mm Glass Sheets
10
5
Transmitance dB
0
-5
-10
-15
-20
-25
-30
0
5
10
Frequency Hz
15
9
x 10
Super-Dense Blue: 2mm Red: 4mm 45 deg
5
-5
-10
-15
-20
-25
15
10
5
0
Frequency Hz
9
x 10
Super-Dense Sandwitched Between: Blue: 2mm Sheets Red: 4mm Sheets 0deg
10
5
0
Transmitance dB
Transmitance dB
0
-5
-10
-15
-20
-25
-30
0
5
10
Frequency Hz
15
9
x 10
Square Ring FSS
P
Structure
P (mm)
g
(/4)(mm)
w (mm)
g
A-S
15.3
11.4
B-S
15.3
11.4
C-S
15.3
0.99
1
1
1
w
Structure A-S and B-S are identical to each other where as C-S has been made to fit
exactly inside B-S. The conductivity was checked for both A-S and B-S using a
multimeter. B-S showed to have slightly better conductivity, therefore was used
instead of A-S where appropriate.
Antenna Distances
Transmission
Tx
Rx
1.77m
0.87m
Network
Analyser
Reflection
Rx
1.77m
1.77m
Tx
Copper film
Tx
Transmitter
Rx
Receiver
Results
The difference of putting four clips instead of one to reduce the air gaps between the
structures
10
One clip
Four clips
5
0
Att
enu
atio
-5
n,
(dB
)
-10
-15
-20
-25
0
2
4
6
Frequency, (GHz)
8
10
12
x 10
9
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
B-S
TE
0
Test100
The graphs above show the difference of reducing the air gaps between the structures. At first only one
clip was being used at the top of the stand to hold the structure in place, to carry out the experiment for zero
angle of incidence. It was then realised that by placing four clips around the stand to hold the structure in
place improves the attenuation and gives a more accurate resonant frequency.
Comparison at 0 and 45 Degrees for TE Polarization
10
0 Degrees
45 Degrees
5
0
Att
enu
atio -5
n,
(dB
)
-10
-15
-20
-25
0
2
4
6
Frequency, (GHz)
8
10
12
x 10
9
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
B-S
TE
0
45
Test102
It can be seen from the graph above that the resonant frequency stays the same when the angle changes, but
the attenuation at resonance decreases as the angle of incidence increases.
Comparison between single and double grid at normal incidence
10
Single Grid
Double Grid
5
0
Att
en
uat -5
ion
,
(dB
) -10
-15
-20
-25
0
2
4
6
Frequency, (GHz)
8
10
12
x 10
9
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
4|4|4
B-S
A-S&B-S
TE
0
Test103
This results show that with the double grid there is a greater bandwidth than with the single grid. It can
also be seen that that sharpness in the attenuation is almost identical for the structures.
The difference in angles between for the double grid
10
0 Degrees
45 Degrees
5
0
-5
Att
en -10
ua
tio
n, -15
(d
B) -20
-25
-30
-35
-40
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
A-S&B-S
TE
0
45
Test104
The above graph shows that the attenuation increases and the angle of incidence increases also the
bandwidth decreases.
A comparison between TE and TM polarization at 45 degrees
10
TE
TM
5
0
-5
Att
en -10
ua
tio
n, -15
(d
B) -20
-25
-30
-35
-40
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
A-S&B-S
TE
TM
45
Test105
It can be seen from this graph that TE and TM have the same transmission characteristics as expected.
Comparison between cross polarisation and TE for the double grid at normal
incidence
0
-5
-10
Attenuation, (dB)
-15
-20
-25
-30
-35
Cross Polarized
TE
-40
-45
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
A-S&B-S
CP
TE
0
Test106
It can be seen that the general characteristic of the waveform seems to be the same. The reason that the
cross polarization plot is above zero is due to the nature of the way it is calculated. It is calculated using
the following formula:
The reflection characteristics for cross polarised, TE and TM on a single grid
10
0
Attenuation, (dB)
-10
-20
-30
Cross Polarized
TM
TE
-40
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Reflection
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
Red
Blue Green
0.5 to 12G
4|4
B-S
CP TM
TE
0
Test107
The graph above shows that there is a considerable difference between TE and TM in terms of noise. The
TE waveform seems to be very noisy. Although around
4.5 GHz (resonance frequency) the structure seems to have good transmission. Also the trend of the cross
polarization seems to be the similar; again it seems to have good transmission around 4.5GHz. It may have
gone above zero attenuation due to the way it has been calculated.
Reflection characteristics of cross polarization, TE and TM on a double grid at normal incidence
10
0
Attenuation, (dB)
-10
-20
-30
Cross Polarized
TM
TE
-40
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Reflection
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
Red
Blue Green
0.5 to 12G
4|4|4
A-S&B-S
CP TM
TE
0
Test108
It can be seen from the graph above that again around the 4.5GHz region there is transmission, for both TE
and TM. The cross polarization plot is not very accurate and therefore in this case is difficult to analyse.
A comparison by increasing the width of the dielectric in between the structures
5
4mm Seperation
6mm Seperation
0
-5
Att
en
ua
tio
n, -10
(d
B)
-15
-20
-25
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Reflection
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
4|6|4
A-S&B-S
TM
0
Test109
Double Square Rings and Circular Rings
A comparison between TE and cross polarization for the concentric squares
10
Cross Polarized
TE
0
Attenuation, (dB)
-10
-20
-30
-40
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
* Cross
polarization
Transmission
Line Colour
RED
BLUE
Freq Range (Hz)
0.5G to 12G
Glass Arrangement
4|4|4
Structure
B-S&C-S
Polarization
CP*
TE
Angle of Incidence (degrees)
0
File Name
Test110
It can be seen from the graph above that the cross polarization effects are similar to that of the TE plot.
Comparison between 0 and 45 degrees for TE using concentric squares
5
0 Degrees
45 Degrees
0
-5
Attenuation, (dB)
-10
-15
-20
-25
-30
-35
-40
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
B-S&C-S
TE
0
45
Test111
From the graph above it can be seen that there is an increase in attenuation when the angle increases there
fore improving the structure.
A Comparison between the concentric squares and the double grid
5
A-S&B-S
B-S&C-S
0
Attenuation, (dB)
-5
-10
-15
-20
-25
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
A-S&B-S B-S&C-S
TE
0
Test112
This graph shows that there is not much difference between the two sets of structures. Although, there
seems to be a slight increase in bandwidth for the concentric squares.
Comparison of cross polarization for concentric squares at 0 and 45 degrees
10
0 Degrees
45 Degrees
0
Attenuation, (dB)
-10
-20
-30
-40
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4|4
A-S&B-S B-S&C-S
CP
0
45
Test113
The graph above shows that the bandstop seems to disappear at 45 for cross polarization.
Comparison between rings in a square lattice and triangular lattice at normal
incidence
10
Triangular Lattice
Square Lattice
5
Attenuation, (dB)
0
-5
-10
-15
-20
0
2
4
6
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
8
10
Frequency, (GHz)
12
14
16
18
9
x 10
RED
0.5G to 18G
BLUE
0.5G to 12G
4|4
C
k
TM
0
Test114
The graph above shows that the triangular lattice has a higher attenuation, otherwise both graphs seem to be
the same.
Comparison between rings in a square lattice and triangular lattice at normal
incidence
5
Triangular Lattice
Square Lattice
0
Attenuation, (dB)
-5
-10
-15
-20
-25
0
2
4
6
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
8
10
Frequency, (GHz)
12
14
16
18
9
x 10
RED
0.5G to 18G
BLUE
0.5G to 12G
4|4
C
k
TM
0
45
Test115
This graphs confirms that the attenuation is more on a triangular lattice; this seems to be more evident at an
angle.
Comparison between superdense circles(S-D) and square lattice (k) circles at
normal incidence
10
Square Lattice
Superdense
5
0
Attenuation, (dB)
-5
-10
-15
-20
-25
-30
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
C
k
TM
0
Test116
Comparison between S-D circles at normal incidence for 0 and 45 degrees
10
0 Degrees
45 Degrees
5
0
Attenuation, (dB)
-5
-10
-15
-20
-25
-30
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
C
k
TM
0
45
Test117
Comparison between S-D and square lattice for cross polarization
10
0
Attenuation, (dB)
-10
-20
-30
-40
-50
Square Lattice Rings
Super-Dense
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
C
k
CP
0
Test118
With absorbers around the structure because the rings did not fill the glass
Comparison between S-D and square lattice for cross polarization at 45 degrees
20
Square Lattice Rings
Super-Dense
10
Attenuation, (dB)
0
-10
-20
-30
-40
-50
0
2
4
6
Frequency, (GHz)
8
10
12
9
x 10
Transmission
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
4|4
C
k
CP
45
Test119
With absorbers around the structure
Comparison between complementary antenna positions for reflection test
10
0
Att-10
en
ua
tio -20
n,
(d
B) -30
-40
-50
0
2
4
6
Frequency,
(GHz)
8
Tx = TE, Rx =
Tx
TM= TM, Rx =
TE
10
12
x 10
9
Reflection
Line Colour
Freq Range (Hz)
Glass Arrangement
Structure
Polarization
Angle of Incidence (degrees)
File Name
RED
BLUE
0.5G to 12G
Freespace
CP
Test120
A graph to show the ohmic losses
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
0
2
4
6
8
10
12
9
x 10
Reflection and Transmission
This graph above shows the ohmic losses of a double grid. Theoretically this line show be around zero. It
has been calculated by taking 1-R-T=0. Between ½ and 1G it can be seen that there is a lot of noise, this
could be due to the television frequency which is applied in this region.
FUTURE WORK
(1) The idea behind periodic structures:
The question is how band-stop periodic structures work. It is known that the element
geometry (circumference of the ring elements) is directly related to the resonance
frequency. Consider the dipoles. At half-wavelength a band-stop resonance occurs. But
we know that a current on a dipole generates an omni-directional radiation pattern. Why,
therefore, no transmitted field is observed (at the resonance frequency)? We will attempt
to answer this problem by using a random distribution of dipoles.
(2) Novel Band-Pass FSS filter
Transmitted Power
Uniform FSS
FSS with Gap
frequency
(3) Environmental effects
raindrop
REFERENCES
F. O’Nians and J. Matson ''Antenna feed
system utilizing polarisation independent frequency
selective intermediate reflector'', US Patent 3,231,892, January 1966.
2
B.A. Munk, ''Periodic Surface for Large Scan Angles'', US Patent 3,789,404, January
1974.
3
G. Marconi and C.S. Franklin, ''Reflector for use in wireless telegraphy and telephony'', US
Patent 1,301,473, April 1919.
4
E.A. Parker, C. Antonopoulos and N.E. Simpson, ''Microwave Band FSS in Optically
Transparent Conducting Layers: Performance of ring element arrays'', Microwave and
Optical Technology Letters, vol. 16, no. 2, October 1997, pp. 61-63.
5
J. Hirai and I. Yokota, ''Electro-magnetic shielding glass of frequency selective surfaces'',
Proceedings of the International Symposium on electromagnetic compatibility, 17-21
May 1999, pp. 314-316.
1
6
Nippon Paint world wide web address: www.nipponpaint.co.jp
American Conference of Government Industrial Hygienists (ACGIH), 2000 Threshold Limit Values and
Biological Exposure indices, www.acgih.org
8
W. Gregorwich, ''The design and development of frequency selective surfaces for phased
7
arrays'', AerospaceConference, 1999, Conference Proceedings IEEE, vol. 5, pp. 471-479.
9
M.A.A. El-Morsy9, E.A. Parker and R.J. Langley, ''Application of Foster network synthesis to
frequency selective design'', International Journal of Electronics, vol. 62, no. 2, 1987, pp.
193-198.
10
E.A. Parker and S.M.A. Hamdy, ''Rings as elements for frequency selective surfaces''.
Electronics Letters, vol. 17, no. 17, August 1991, pp. 612-614.
11
E.A. Parker, S.M.A. Hamdy and R.J. Langley, ''Arrays of concentric rings as frequency
selective surfaces'', Electronics Letters, vol. 17, no. 23,November 1981, pp. 880-881.
12
R. Cahill and E.A. Parker, ''Concentric ring and Jerusalem cross arrays as frequency
selective surfaces for a 45 incidence diplexer''. Electronics Letters, vol. 18, no. 17, April
1982, pp.313-314.