International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 2278 – 0882
Volume 4, Issue 7, July 2015
MULTILAYERED BUTTERWORTH THIRD ORDER LOW
PASSFILTERBASED ONSPIRAL HEXAGON RING RESONATOR
Anish kumar Gupta1, Bimal Garg2
1
Departmentof Electronics, Madhav Institute of Technology and Science, Gwalior, India
Departmentof Electronics, Madhav Institute of Technology and Science, Gwalior, India
2
ABSTACT
Filters play significant roles in many microwave
applications. Emerging applications such as wireless
communications, satellite communication continue to
challenge RF filters with ever more stringent
requirements—higher performance, least size, lighter
weight, and lower cost. A high performance ,small size
third order multilayered microstriplow pass filter is
designed and fabricated in the Middle layer and periodic
pattern of Spiral hexagon ring resonatorsare etched on
the top layer of the Metamaterial structure. The
proposed filter is designed with cut-off frequency of
1.5GHz.Computer simulation technique(CST) is used to
simulate the filter. Resonator is a sub-wavelength
resonator, having size much smaller than the
conventional Microstrip resonator; thereby extensive
size miniaturization is possible.Main objective of this
paper is to offer a unique RF/microwave microstrip filter
based on the Spiral hexagon resonator structures.
Proposed filter has small size and better performance
both in pass and stop band ,also simulated and measured
results are compared , measured results follows the
simulated result.
Keywords- Kuroda’s identities,Low pass filter,
maximally flat micro -strip filter, Metamaterial,
Richard’s
transformation,spiral
hexagon
ring
resonators.
I. INTRODUCTION
In the late 1960s, Russian physicist Victor Vaselago
pondered whether two key electromagnetic properties
could ever be negative. In conventional materials,
permeability and permittivity are always positive,but he
proposed that if both permeability and permittivity
werenegative,so too would the refractive index of that
medium [1],[2].One result was the prediction that a light
ray entering a transparent material with negative
refractive index would bend the ‗wrong‘ way relative To
the surface normal. The reason behind this change lies in
the group and phase velocities of a wave. Refractive
index is a ratio of phase velocities. So, the phase velocity
of a light wave has to turn negative when the wave
encounters a medium with a negative refractive index,
while its group velocity can remain positive.No real
world bulk materials have negative permeability or
permittivity.Negative permittivity can be encountered
naturally under certain circumstances[3]. Ametal below
the plasma frequency – the point at which it becomes
transparent to light – show the effect and it comes from
free electrons in the metal that act to screen out external
electromagnetic radiation.The plasma frequency depends
on the density of carriers and their effective mass. In a
wire lattice, the geometry controls both parameters – by
making the wires thinner, it is possible to increase the
effective mass of the charge carrier which, in turn,
reduces the effective plasma frequency. In principle, it is
possible to achieve negative permittivity using wire
meshes or gratings all the way from the low radio
frequency to the optical region of the spectrum[4].Prof.
Pendry's team proposed a structure for negative
permeability [5]. The split ring resonator – which, as the
name suggests, is an almost complete circle of metal –
behaves like the inductive-capacitance (LC) resonator of
an electrical filter circuit [6-8]. When the resonator sits
in a magnetic field those changes with time, charge
builds up across the gap in the ring. At low frequencies,
the currents that oscillate within the resonator stay in
phase with the driving field. But at higher frequencies,
the currents start to lag, generating an out of phase
response – which produces the effect of negative
permeability at those higher frequencies.Hence the
Metamaterial is defined as ―an artificial or man-made
material which gains its properties such as negative
permittivity and negative permeability both from its
structure rather than directly from its composition‖
[9].The microwave Metamaterials are fabricated with
printed circuit Boards(PCB) by making different metal
architectures on PCB. The refractive index is defined as
n = √εrμr. Where εrand μrare Relative permittivity and
permeability of the material respectively.Fig.1 illustrates
all possible properties of isotropic and lossless materials
in the ε –μ domain [10].The first quadrant (ε > 0 and μ >
0) represents right-handed materials (RHM), which
supports the forward propagating waves.The third
quadrant (ε < 0 and μ < 0) is the well-known left-handed
materials (LHM), which was proposed by Veselago in
1968, supports backward propagating waves.
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763
International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 2278 – 0882
Volume 4, Issue 7, July 2015
Microwave filter is a device which offers different
impedances for different frequency range of a signal. A
low pass filter offers low impedance forlow frequencies
and high impedances for high frequency, hence it passes
low frequency band up to certain frequency called cut
off frequency and block all higher spectrum
Fig.1 All possible properties of isotropic materials in the ε –μ
domain
II.
FILTER DESIGNING
The proposed Butterworth low pass filter is designed
andsimulated using CST software with dielectric
constant of 4.3 with cut off frequency of 1.5GHz [11].
Image parameter method and insertion loss method are
two methods of filters designing. First method consists
of a cascade of simpler two port filter sections to provide
the desired cutoff frequencies and attenuation
characteristics but specification of a particular frequency
response over the complete operating range is not
specified. Insertion loss method on the other hand uses
network synthesis techniques to design filters with a
completely specified frequency response.In order to
design a simple maximally flat low pass filter, there are
mainly two steps. In first step, selection of appropriate
low pass filter prototypes which are normalized in terms
of impedance and frequency
are done and then
impedance scaling and frequency scaling are used to get
the desired result [12]. Frequency scaling is used to
change the cut-off frequency of a low pass filter
prototype from unity to ωc.Generally source impedance
is 50 ohms for microstrip filters. In second step, the
scaled electronic lumped –element components are
replaced with distributed circuit elements for
implementation at microwave frequencies. Lumped
elements are replaced with distributed circuit by using
Microstrip linetheory, Richard‘s transformation and
Kuroda‘s identities [13],[14]. The lumped-element filter
designs work well at low frequencies, but at higher RF
frequency there are mainly two problems. First, lumpedelement inductors and capacitors are not available for
higher frequency range values. Second, at microwave
frequencies the distances between filter components is
not negligible. Richards‘ transformation is used to
convert lumped elements to transmission line sections,
the series inductors to the equivalent series stubs, and the
shunt capacitors to the equivalent shunt stubs.Kuroda‘s
identities are then used to physically separate filter
elements by using transmission line sections, since
additional transmission line sections do not affect the
filter characteristics. Kuroda‘s identities are useful to
transform the series stub into shunt stubs.Microstrip line
theory is used to convert filter‘s segments into
Microstrip stubs [15]. Finally proposed low pass filter is
designed and simulated at resonant frequency 1.5 GHz.
The simple microstrip low pass filter is fabricated for
comparison.
(A) Design specifications for the filter under
consideration are
Relative Dielectric Constant, єr = 4.3
Cut-off frequency, fc = 1.5GHz
Height of substrate, h = 1.6 mm
Zo= 50 Ω
In the insertion loss method a filter response is defined
by its insertion loss, or power loss ratio, PLR. For
maximally flat low pass filter it is specified by
Where N is the order of the filter and ωc is the cutoff
frequency. And insertion loss in dB is given by
IL = 10 log PLR.
General Ladder circuit for low-pass filter prototypes and
their element definitions having N elements (order of the
filter) are illustrate in fig.2.
Fig.2Low pass prototype network with five components.
In order to design a low pass filter , Element values for
Butterworth low pass prototype filters with 3dB ripple is
given in table 1.
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764
International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 2278 – 0882
Volume 4, Issue 7, July 2015
N
g1
g2
g3
g4
g5
g6
1
2.0000
1.0
2
1.4142
1.4142
1.0
3
1.0000
2.0000
1.0000
1.0
4
0.7654
1.8478
1.8478
0.7654
1.0
5
0.6180
1.6180
2.0000
1.6180
0.6180
Impedance(ohm)
Length(mm)
Width(mm)
50
13.45
2.85
25
12.77
8.00
100
14.23
0.61
Table 2 Dimensions for a microstrip low pass filters
1.0000
Table 1 Element Values for Maximally Flat Low-Pass Filter
Prototypes with 3 dB ripple (g0 = 1, ω c = 1, N = 1 to 5)
The dimensional view of Spiral hexagon resonator is
shown in fig. 4.
For proposed 3rd order lowpass filter, the low pass
prototype element values are taken from table 1 as
g1=1.0000,g2 = 2.0000,g3 = 1.000,g4=1.0
The selected lumped element values for maximally flat
low pass filter are further converted to distributed
elements by using Richard‘s transformation and
Kuroda‘s identities. The impedance of each section is
given in fig.3.
Fig.4 Spiral
c=2.5mm)
Fig.3 Low pass filter showing required impedance values
The parameters of the microstrip filter are calculated
from the formulas proposed below:
For w/h <=1
…………………… (1)
hexagon
resonator
(a=4.5mm,
b=3.5mm,
The proposed Microstrip low pass filter is designed in
Middle layer as shown in fig. 5(a) and hardware is
fabricated on PCB as shown in fig. 5(b).
For w/h>=1
.. (2)
With
……………… . (3)
The w/h ratio to determinate Microstrip line impedance:
For w/h<2
Fig. 5(a) Middle layer of proposed microstrip low pass filter
…………………………………… (4)
With
… (5)
For w/h>2
………………………………………..... (6)
With
………………………………………... (7)
Fig. 5(b)Fabricated Middle layer view of proposed low pass
filter
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765
International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 2278 – 0882
Volume 4, Issue 7, July 2015
Spiral hexagon resonator is designed on Top layer using
CST software as shown in fig.6(a) and hardware is in
fig. 6(b).
Fig. 7(a) Photograph of fabricated proposed low pass filter
(Bottom view)
Fig. 6(a) Top layer of proposed microstrip low pass filter with
Spiral Hexagon resonators
The simulated S11 and S21 results of the Butterworth
microstrip low pass filter with resonator areshown in
Fig. 8 (a) and 8(b). The combined,simulated S11 and
S21 result is shown in fig. 8(c).
Fig. 6(b) Fabricated Top layer of proposed microstrip low pass
filter with Spiral Hexagon resonators
III.
RESULT AND DISCUSSION
A Multilayered Butterworth low pass filter with Spiral
hexagon resonator is designed and fabricated with a cut
off frequency of 1.5 GHz. Low pass filter is designed
and fabricated in Middle layer and resonators are on Top
layer with simple ground plane.
The photographs of fabricated filter are shown in fig. 7.
Fig. 8(a)Simulated S11 results of the proposed Microstrip low
pass filter with resonator
Fig. 7(b) Photograph of fabricated proposed low pass
filter(Top view)
Fig. 8(b) Simulated S21 results of the proposed Microstrip low
pass filter with resonator
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766
International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 2278 – 0882
Volume 4, Issue 7, July 2015
REFERENCES
Fig. 8(c) Combined, simulated S11 and S21 results of the
proposed Microstrip low pass filter with resonator
The simulated and measured S21 response of proposed
multilayered Butterworth low pass filter based on Spiral
Hexagon resonators is shown in fig. 9.
Fig. 9Simulated and measured S21 result of proposed filter
From figure 8(c), it is clear that the proposed filter has a
cut off frequency of 1.5 GHz. Figure 9. Illustrates the
perfect matching of the simulated and measured result
of the designed filter.it is also evident that filter has
negligible ripples in both pass band and stop band.
Hence designed filter is fulfilling all the proposed
requirements.
IV.
CONCLUSION
This work has presented a design and analysis of
Butterworth low pass filter by using repeated Spiral
resonator structures. Filter performance increased
significantly with reduced filter size. Filter has a sharp
cutoff frequency of 1.5 GHz. The reflection coefficient
of the proposed filter has been improved significantly
both in pass band and stop band.
[1]V. G. Veselago, ―The electrodynamics of substances with
simultaneously negative values of μ and ε,‖ Sov. Phys.
Uspekhi, vol. 10, no. 4, pp. 509 _ 514, 1968.
[2] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser,
and S. Schultz, "Composite medium with simultaneously
negative permeability and permittivity," Phys Rev Lett 84, pp.
4184_4187, 2000.
[3]Ali, Z. Hu, ―Negative permittivity metamaterial microstrip
binomial low pass filter with sharper cut-off and reduced
size,‖ 2008.
[4] Dr.Bimal Garg, ―Experimental Verification of Double
Negative Property of LHM with Significant Improvement in
Microstrip Transceiver Parameters in S Band,‖ Vol. 2, no.1,
2013.
[5]Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J.
Stewart,
―Magnetism from conductors and enhanced
nonlinear phenomena," IEEE Transactions on Microwave
Theory and Techniques., Vol. 47, no. 11, pp. 2075_2084, Nov
1999.
[6] Swati Jindal, Jigyasa Sharma, ―Review of Metamaterials in
Microstrip Technology for Filter Applications,‖ Vol.54, no.3,
Sep. 2012.
[7] J. D. Baena, J. J. Bonache, F. F. Martin, R. Marques, F.
Falcone, T. Lopetegi, M. A. G. Laso, J. Garcia-Garcia, I. Gil,
M. F. Portillo, M. Sorolla, ―Equivalent–Circuit Models for
Split Ring Resonators Coupled to Planar Transmission Lines,‖
IEEE Transaction on Microwave Theory and Techniques., vol.
53, no. 4, pp. 1451_1461, Apr. 2005.
[8] J. Bonache, M. Gil, I. Gil, J. Garcia-Garcia, F. Martin, ―On
the Electrical Characteristics of Complementary Metamaterial
Resonators,‖ IEEE Microwave and Wireless Components
Letters., vol. 16, no. 10, pp. 543-_545, 2006.
[9] Ricardo Marqués, Ferran Martín, Mario Sorolla,
―Metamaterials with Negative Parameters: Theory, Design and
Microwave Applications,‖ Wiley Series in Microwave and
Optical Engineering.
[10] G. V. Eleftheriades, K. G. Balmain, ―Negative Refraction
Metamaterials: Fundamental Principles and Applications,‖
New York, Wiley Interscience, 2005.
[11]Hanane Nasraoui , Ahmed Mouhsen , Jamal EL Aoufi,
―A New Design of a Band pass Filter at 2.45 GHz Based on
Microstrip Line Using the Property of the Double Negative
Metamaterials,‖ Vol. 4, Issue 4, Apr. 2014
[12] David Pozar, ―Microwave Engineering,‖ Third Edition,
John Wiley &Sons., p.405, 2005.
[13]Jia-Sheng Hong, M. J. Lancaster, ―Microstrip Filters for
RF/Microwave Applications,‖ John Wiley &Sons., 2001.
[14] Ahmed Hameed Reja, Syed Naseem Ahmad, Abdul
Kareem Kasim Abdul Raheem, MushtaqA. Alqaisy, ―Design
of Microwave Lowpass Filters Based on Metamaterial
Components,‖ NNGT Int. J. on Networking and
Communication. Vol. 1, Jul. 2014.
[15] Kai Chang, ―Encyclopedia of RF and Microwave
Engineering,‖ John Wiley & Sons, Inc.: Hoboken, NJ, USA,
2005.
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