Narrow Bandpass Filter using Symmetrical Left-Handed Transmission Line Zeroth-Order Resonators

giantsneckspiffyΗλεκτρονική - Συσκευές

13 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

115 εμφανίσεις

Narrow Bandpass Filter using Symmetrical
Left-Handed Transmission Line Zeroth-Order
Resonators
Godavarthi.Naga Satish
#1
,Kumar Vaibhav.Srivastava
#2
,Animesh Biswas
#3
and Danielle Kettle
4
#
Department of Electrical Engineering,Indian Institute of Technology Kanpur
Uttar Pradesh,India - 208016
E-mail:
1
nagasatishonnet@gmail.com,
2
kvs@iitk.ac.in,
3
abiswas@iitk.ac.in

School of Electrical and Electronics Engineering,The University of Manchester
Manchester,U.K
E-mail:
4
danielle.kettle@manchester.ac.uk
Abstract—A bandpass filter using symmetrical Left-Handed
(LH) transmission line (TL) Zeroth-Order Resonators (ZOR) is
proposed.The symmetrical LH TL is first characterized by the
dispersion characteristics of the unit cell and its left handedness is
verified by the transmission characteristics of 15 cells cascaded
LH TL.A symmetrical LH TL open circuited on both sides,
acting as a ZOR with shunt resonance,is used as a resonating
element in the microstrip end coupled resonator bandpass filter.
The open circuited ZOR is characterized by susceptance slope
parameter,and bandpass filter is designed using microstrip series
gaps as the admittance inverters.Size independent resonance
property of the ZOR combined with homogeneity condition of
the LH TL unit cell is utilized in the size reduction of bandpass
filter.The full wave simulated transmission characteristics of
the designed bandpass filter are experimentally verified.They
show that size of the filter is greatly reduced (approximately
64%) when compared to a conventional half wavelength coupled
bandpass filter.
I.I
NTRODUCTION
Over the past decade,artificially constructed electromag-
netic metamaterials,also known as left-handed (LH) materials
have generated great attention from the scientific and engi-
neering communities owing to their intriguing electromagnetic
characteristics not found in known naturally occurring materi-
als [1]-[3].Two configurations were proposed for the physical
realization of LH material using the microwave transmission
lines (TLs),i.e.the non-resonant,and resonant configurations.
The planar implementation of LH TLs consist of series ca-
pacitor and shunt inductor with unavoidable parasitic series
inductor and shunt capacitor forming a composite right/left
handed (CRLH) structure.Various novel LH devices have
been developed based on this structure,because of its easier
integration into printed circuits,advantages of size reduction,
lower loss and wide bandwidth [2].
In this paper,a detailed design procedure is presented
to synthesize compact bandpass filter that is based on the
zeroth-order resonance of LH TL.The traditional microstrip
LH TL with series interdigital capacitor and short circuited
shunt stub with via connecting to ground plane is slightly
modified to obtain a symmetrical structure of the unit cell.The
symmetrical configuration of LH TL in unbalanced mode is
characterized by the dispersion diagram and the transmission
characteristics are validated by simulation and experiments.
Open circuited zeroth-order resonators are designed to verify
the size independent resonant property of the LHTL.The open
circuited zeroth order resonator giving shunt type resonant
frequency is characterized by susceptance slope parameter
for designing the bandpass filter.The coupled half wave-
length resonators of conventional microstrip bandpass filter
are replaced by the open circuited zeroth-order resonators.
The size independent property of zeroth-order resonance and
the homogeneity condition of LH materials(unit cell period,
p  guide wavelength) are utilized in the realization of
compact bandpass filter.Finally,full wave simulated and
experimental transmission characteristics of the bandpass filter
are presented.
II.LEFT-HANDED TRANSMISSION LINE
ZEROTH-ORDER RESONATOR
A.Left-Handed Unit cell Characterization
The microstrip layout of symmetric LH TL unit cell is
shown in Fig.1(a).Dispersion diagram of the unit cell is
obtained by applying periodic network analysis [5] and by
extracting S-parameters at the input and output terminal planes
of the unit cell.The full wave EM simulated dispersion
diagram of the unit cell is shown in Fig.1(b).
B.Open Circuited Zeroth-Order Resonator and its Charac-
terization
In an open circuited/short circuited LH TL,the zeroth-order
resonance occurs at frequencies corresponding to β=0 [4].In
[3],it is shown that in an unbalanced LH TL,the zeroth-order
resonance of an open circuited and short circuited LH TL
occurs at the shunt and series resonance frequencies of the unit
cell,respectively.From the dispersion characteristics shown in
Fig.1(b),the frequency points where β=0 can be identified
as 4.3 GHz and 5.1 GHz which corresponds to the shunt and
series type resonance frequencies of the unit cell shown in Fig.
106German Microwave Conference 2010
(a)
(b)
Fig.1.(a) Unit cell layout of microstrip symmetrical LH transmission line
on a RT Duroid 6010 dielectric substrate with ε
r
= 10.2,thickness = 1.27
mm,tanδ = 0.0023 and 1oz thick copper on both sides.Stub width = 0.5
mm and via diameter = 0.3mm.All dimensions indicated in the geometry are
in millimeters.(b) Simulated dispersion characteristics(p is the period of unit
cell).
1(a).Using the equivalent circuit parameters extraction method
described in [3],the shunt and series resonance frequencies of
the unit cell shown in Fig.1(a) can be obtained as 4.3 GHz and
5.1 GHz respectively,which are indicated as f
sh
and f
se
in
Fig.1(b).The susceptance B,shown in Fig.2,is obtained by
calculating input admittance of single unit cell open circuited
zeroth-order resonator using full wave EM simulation.Zero
value of susceptance at 4.3 GHz further confirms the shunt
type resonance of open circuited zeroth-order resonator.Such
type of resonator can be more generally characterized by the
susceptance slope parameter b,which is widely used in the
design of bandpass filters.The susceptance slope parameter of
a shunt type resonator with resonance frequency f
o
is defined
Fig.2.Input susceptance of open circuited LH TL unit cell.
(a)
(b)
Fig.3.(a) Equivalent circuit model of n
th
order bandpass filter with zeroth-
order resonators and admittance inverters,(b) Geometry of 3 pole bandpass
filter with zeroth-order resonators.
as [6].
b =
f
o
2
dB(f)
df
￿
￿
￿
￿
f=f
o
(1)
Using (1) the susceptance slope parameter of the open cir-
cuited zeroth-order resonator at 4.3 GHz is obtained as 0.0242
mhos.
III.D
ESIGN OF
B
ANDPASS
F
ILTER
The schematic of bandpass filter shown in Fig.3(a) is
designed using the traditional inverter transformation and the
open circuited zeroth-order resonators as resonating elements.
The design equations of the bandpass filter are given as [6]
J
01
=
￿
G
0
bFBW
g
0
g
1
,J
n,n+1
=
￿
G
n+1
bFBW
g
n
g
n+1
(2)
and J
i,i+1
=
bFBW

g
i
g
i+1
(i = 1,2,...n) (3)
where FBW is the fractional bandwidth,g
0
,g
1
,..g
n+1
are
element values of n
th
order low-pass filter prototype and
107
(a)
(b)
(c)
Fig.4.(a) Measured and simulated transmission characteristics of 15 cells
cascaded LH TL,(b) Measured and simulated unwrapped transmission phase
characteristics,(c) Fabricated 15 cells cascaded LH TL on the same substrate
of unit cell in Fig.1(a).
J
i,i+1
is the value of admittance inverters.G
0
and G
n+1
are
the admittances at input and output ports respectively.In mi-
crostrip technology the admittance inverters are implemented
by series gap capacitance [7],and the negative lengths of the
TLs are absorbed into the adjacent microstrip lines of zeroth-
order resonator.Prototype bandpass filter,with schematic
shown in Fig.3(a),is implemented here using microstrip line
technology whose layout is shown in Fig.3(b).
IV.S
IMULATIONS AND
E
XPERIMENTS
The simulated and measured transmission characteristics of
15 cells cascaded LH TL is shown in Fig.4(a).The dispersion
characteristics obtained by unwrapping the transmission phase
[3] of 15 cells cascaded LH TL and the fabricated structure are
shown in Fig.4(b) and (c) respectively.Two cells and three
cells zeroth-order resonators are designed and their simulated
and experimental transmission characteristics are shown in
Fig.5.It can be seen that there is almost no change in zeroth-
order resonance frequency at 4.3 GHz thus confirming the size
independent resonance of zeroth-order resonator.
A three pole microstrip bandpass filter is designed on the
same substrate of unit cell shown in Fig.1(a).The pass band
ripple is 1 dB,the center frequency is 4.3 GHz and FBW
is 3%.The zeroth-order resonator,replacing the conventional
microstrip half wavelength resonators,is characterized by their
center frequency of 4.3 GHz.The admittance inverter of slope
parameter 0.0242 is realized with series gap capacitance.The
element values of low-pass filter prototype are obtained as
g
0
= g
4
= 1,g
1
= g
3
= 2.0236,g
2
= 0.9941.The capacitance
values of admittance inverters are realized by interpolating the
capacitance vs series gap curve of the microstrip line.The
designed geometrical parameters of the bandpass filter,shown
in Fig.3(b),are optimized for practically realizable vales by
an EM simulator as follows:X
01
= X
34
= 0.1 mm,X
12
=
X
23
= 1.00 mm,w
1
= w
4
= 0.2 mm,w
2
= w
3
= 0.4 mm.
The photograph of the fabricated filter is shown in Fig.6(a).
The simulated and experimental transmission characteristics
of the proposed bandpass filter are shown in Fig.6(b).It can
be seen that the measured transmission characteristics deviate
a little from the predicted simulations.These are attributed to
the substrate parameters tolerances and fabrication tolerances.
The period of LH TL unit cell is 4.8 mm which is 0.18
times the guide wavelength of conventional 50Ω microstrip
line thus ensuring homogeneity condition of LH TL.In the
case of a conventional microstrip bandpass filter with half
wavelength resonators [6],the filter size will be three times
the half wavelength for three pole bandpass filter.At the center
frequency of 4.3 GHz,with a guide wavelength of 26.4 mm
for the same substrate,the total length of the conventional
filter would be approximately 39 mm.The total length of the
bandpass filter with zeroth-order resonators shown in Fig.5(a)
is 13.8 mm,there by achieving approximately 64% reduction
in size when compared with the half wavelength resonators
implementation.The insertion loss of the proposed filter can be
improved further by using some more optimization.However,
its higher insertion loss can be tolerated while considering its
significant size reduction.
V.C
ONCLUSION
The synthesis of microstrip bandpass filter using LH TLs is
studied.The symmetric LH TL unit cell is characterized,and
the shunt type zeroth-order resonance frequency of the open
circuited LH TL is identified from the dispersion characteris-
tics of the unit cell.The size independent resonance and shunt
type resonance frequency are confirmed by both simulation
and experiment of different lengths of open circuited LH
TL.A three pole bandpass filter is designed,fabricated and
measured.It is shown that the size reduction of 64% is
108
Fig.5.Measured and simulated resonance characteristics of open circuited
zeroth-order resonator.
(a)
(b)
Fig.6.(a) Photograph of the fabricated 3 pole bandpass filter with zeroth-
order resonators,(b) Measured and Simulated S-parameters of the proposed
bandpass filter.
achieved when compared to the conventional filter working
in the same frequency band and substrate.
R
EFERENCES
[1] V.G.Veselago,“The electrodynamics of substances with simultaneously
negative values of ε and μ,” Sov.Phys.Uspekhi,vol.10,no.4,pp.509-
514,Jan.1968.
[2] A.Lai,C.Caloz,and T.Itoh,“Composite right/left-handed transmission
line metamaterials,” IEEE Microw.Mag.,vol.5,no.3,pp.34-50,Sep.
2004.
[3] C.Caloz and T.Itoh,Electromagnetic Metamaterials:Transmission Line
Theory and Microwave Applications.New Jersey:Wiley & Sons,2004.
[4] A.Sananda,C.Caloz,and T.Itoh,“Novel zero-order resonance in
composite right/left-handed transmission line resonators,” in Proc.Asia
Pacific Microwave Conf.,Nov.2003,pp.1588-1592.
[5] R.E.Collin,Foundations for Microwave Engineering.Second Edition,
McGraw-Hill,1992.
[6] G.L.Matthaei,L.Young,and E.M.T.Jones,Microwave Filters,
Impedance-Matching Networks,and Coupling Structures.Artech House,
Norwood,MA,1980.
[7] K.C.Gupta,R.Garg,I.Bahl,and P.Bhartia,Microstrip Lines and
Slotlines.Second Edition,Artech House,Boston,1996.
109