International Journal of Electrical and Computer Engineering (IJECE)
Vol.x, No.x, Month 201x, pp. xx~xx
ISSN: 2088-8708
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Highly-Selective and Compact Bandpass Filters Using
Microstrip – Coaxial Resonator
Trong-Hieu Le*,**, Le-Cuong Nguyen*, Xiao-Wei Zhu**
* Faculty of Electronics and Telecommunications, Electric Power University, Hanoi, Vietnam
** State Key Laboratory of Millimeter Waves, School of Information and Engineering, Southeast University, P. R. China
Article Info
ABSTRACT (10 PT)
Article history:
This paper presents two compact high performance second-order bandpass
filters using high quality factor Q hybrid microstrip - coaxial resonator. In
design, the hybrid resonator of proposed filters is composed of a microstrip
line and a short-circuit coaxial line, which utilizes great use of space in the
shielding box. Additionally, the unloaded quality factor of the proposed
resonator Q = 455, shows a high value in comparison to the conventional
microstrip resonator. Furthermore, by employing source-load coupling and
mixed electromagnetic coupling scheme, two adjustable transmission zeros
separate on each of side of passband are generated to enhance the selectivity
and the out-of-band rejection simultaneously. To verify this attractive design
concept, two second-order bandpass filters show the advantages such as
small in size, high Q-factor and good rejection level as well as easy to
integrate with other printed circuits, are designed, fabricated, and tested. The
measured results are in good agreement with theory and simulations.
Received Jun 12, 201x
Revised Aug 20, 201x
Accepted Aug 26, 201x
Keyword:
Bandpass filter
Hybrid resonator
Unloaded Q-factor
Transmission zeros,
Highly selective
Copyright © 201x Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Trong-Hieu Le,
Faculty of Electronics and Telecommunications,
Electric Power University,
235 Hoang Quoc Viet Street, Hanoi, Vietnam.
Email: hieult@epu.edu.vn
1.
INTRODUCTION
Miniaturized highly selective microwave bandpass filers (BPFs) are highly desirable in modern
wireless communication systems, especially in satellite and mobile communications systems. To obtain the
requirements, various structures of BPFs with new features based on microstrip coupled resonator; cavity
resonator; coaxial line resonator, have been presented in recent work [1]-[5].
In [1], a miniaturized microstrip cross-coupled resonator filter is presented. The filter has high
selectivity but the measured result was not good as simulated. In [3] and [4], a dual-band filter design
methodology based on dual-capacitively-loaded (DCL) cavity resonators and dual-mode coaxial bandpass
filter are fabricated, both of them also have high Q-factor but with the drawback of a relatively large
structure. On the other hand, Adnan et al. in [5] utilized degenerate modes of a square loop resonator with
capacitively loaded open-loop arms in the design of a very compact dual- mode microstrip filter, however the
low insertion loss target is not achieved.
In this letter, two high performance second-order BPFs using hybrid resonator with high quality
factor, are constructed and carried out experimentally. The hybrid resonator is composed of a microstrip line
and a short-circuit coaxial line. In practical, with maximum the space utilization of the structure, the
proposed filter configuration enable significantly miniaturized design with an improvement unloaded Qfactor in the resonator. Moreover, the location of upper and lower transmission zeros which are created based
on source-load coupling and mixed electromagnetic (EM) coupling, can be adjusted to improve the filters
selectivity and the out-of-band rejection. Good agreement was obtained between the simulated and
experimental results.
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2.
FILTER DESIGN METHOD
In this section, we propose a new hybrid resonator that are shaped by microstrip and short-circuit
coaxial line. Not requiring the metallic walls inside the cavity, the proposed filter maximizes the space
utilization, thus achieving an optimal Q-factor for a given volume. In this way, the proposed filter
configuration enables low insertion loss and compact design with an improvement in the resonator unloaded
Q compared to the conventional microstrip filters.
2.1 Hybrid resonator
The schematic structure of the proposed second-order filter is sketched in Figure 1. The hybrid
resonator is composed of two section of transmission line, microstrip line on the substrate and the coaxial
line. The bottom part of the filter is formed from printed circuit whose layout is illustrated in Figure 1(a). The
radius and the length of each of the copper rod is r and h, respectively, as shown in Figure 1(b). Two copper
rods are short-circuited on the top of metallic housing. The center to center distance between two copper rods
is d, which mainly determines internal coupling between the resonators. The gap s1 between the low
impedance lines offers electric coupling and the short circuit coaxial lines (copper rods) provide the magnetic
coupling, respectively, both of them can be tunable. The electric and magnetic coupling can be separately
controlled by adjusting the gap s1 and the distance d of the copper rods. The mixed EM coupling strength [6]
can be defined as (1). Owing to the canceling effect of mixed EM coupling, a finite transmission zero can be
obtain in the high side of stopband.
f odd  f even
2
k mixed 
2
(1)
f odd  f even
2
2
(a)
d
h
(b)
Figure 1. Configuration of the proposed symmetric filter: (a) Top view, (b) Side view.
Where f odd and f even are the two resonance frequency of the odd-mode and even-mode,
respectively.
Let us consider as an example a cavity size is 16 x 34 x h (mm), with h is the height of the copper
rods as well as the shielding case. The other dimensions regarding the microstrip resonator are as follows: L1
= 10.1 mm, L2 = 4.32 mm, L3 = 8.7 mm, L4 = 4.3 mm, W1 = 1.53 mm, W2 = 0.68 mm, W3 = 0.2 mm, and d
= 10.1 mm. Figure 2 shows the simulated unloaded Q of a hybrid resonator with different copper rods sizes
which are determined by h and r, respectively, while the other parameters are kept constant. When a hybrid
resonator is loaded by two copper rods of different sizes (Figure 2), it is observed that the unloaded Q
changed from 515 to 622 individually versus the size of the copper rods. As mention above, the proposed
hybrid resonator has a unique feature, which is that the resonant modes have different equivalent resonant
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space due to the boundary condition, which can be considered as virtual inside walls. Therefore, the stored
energy of each mode is also different from the others, resulting in different unloaded Q values. The optimum
unloaded Q is achieved when h and r has a proper value, around 10 mm and 1.5 mm, respectively, in this
simulation. The simulation is conducted with the electromagnetic (EM) full-wave simulator ANSYS HFSS
(in Eigenmode).
Figure 2. Unloaded Q of the proposed hybrid resonator with different h and r.
It is worth mentioning that the unloaded Q of the proposed hybrid resonator filter is larger much
more comparison with a conventional microstrip resonator filter (Qu < 200). Moreover, since the proposed
resonator eliminates the need of inside metallic walls, the space utilization can be further improved and the
volume of implemented filters based on this resonator, especially the base-station filters/diplexers, will be
significantly miniaturized, thus reducing the equipment weight. Additionally, the smaller surface area
resulting from the removal of the inside metallic walls also contributes to the improvement of the unloaded
Q. Therefore, the proposed resonator demonstrates superior behavior of the performance and is very
attractive for designing low insertion loss and miniaturized filters for wireless communication systems.
2.2 Synthesis of the coupling matrix and coupling coefficient
In this investigation, a second-order Chebyshev-response bandpass filter is designed with 15-dB
equal-ripple return loss. A ( N  2)  ( N  2) normalized coupling matrix of the second-order filter is given
by
 0
M
S1
M 
 0

 0
M S1
0
M 11
M 12
M 12
M 22
0
M 2L
0 
0 

M 2L 

0 
(2)
Where M S 1 and M L1 denote input and output external couplings, respectively, and M 12 represents
inter-resonator coupling. M 11 and M 22 stand for the detuning of each resonator’s resonant frequency from
the center frequency of the filter’s frequency response. M 11  0 (or M 22  0 ) indicates that the first
resonator (or second resonator) is tuned to the center frequency of the filter response. The relationship
between a non-zero M 11 and the resonant frequency of the first resonator (f1) is given by
2

M 11 
 M 11 


f1  f 0  1  
 
(3)
2 

 2 


Where f0 is the center frequency and  is the fractional bandwidth. For a non-zero M 22 , we can
find the resonant frequency of the second resonator, f2, by replacing M 11 in (3) by M 22 .
Title of manuscript is short and clear, implies research results (First Author)
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Figure 3. General coupling topology of the implemented 2 nd-order filter.
Figure 3 produces general coupling topology of the proposed coupled hybrid resonators. In this
topology, each node represents a resonant mode; S and L denote the source and load nodes, respectively. This
investigated general topology contain not only the mixed EM coupling between resonator nodes, the input
and output coupling to resonator nodes, but also an additional coupling between the source and the load.
Figure 4 shows the extended general coupling reciprocal matrix for a second-order BPF with source–load
coupling [6], where the coupling coefficients kij are replaced by m(i,j) corresponding to resonant modes in the
coupled hybrid resonator, respectively.
 0
M
1S
M 
 0

 M LS
M S1
0
0
M 12
M 21
0
0
M L2
M SL 
0 

M 2L 

0 
Figure 4. General coupling matrix of the proposed filter.
The direct coupling coefficients between the source and the load can be computed in term of
scattering parameter S21
M SL  
1  1  S 21
2
(4)
S 21
The MSi and MLj, which denote the couplings between the source and load to each resonant mode,
can be extracted from external quality factors by
Qe,Si 
Qe , Li 
i  S11 i 
1

M Si2  FBW
4
i  S22 i 
1

M Li2  FBW
4
(5)
(6)
The calculated inter-stage coupling matrix according to the low-pass prototype is given in figure as
follows
0
1.0904
0

 1.0904
0
1.3805
M 

0
1.3805
0

0
1.0904
 0.0202
0.0202 

0

1.0904 

0

Figure 5. The extracted normal coupling matrix of the implemented filter.
2.3 Design example
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Let us consider as an example a bandpass filter has a fractional bandwidth FBW = 0.03 and a center
frequency of f0 = 2.6 GHz is designed with 0.9 dB in-band insertion loss.
By carried out mixed EM coupling an extra transmission zero can be generated in the high side of
passband. Here, s is fixed as 0.1 mm. Figure 7 shows the impacts of L and d on the locations of the
transmission zero TZ2 and passband bandwidth. As can be seen, with the decrease of the length L from 4 to
1.1 mm, the location of the TZ2 will be move far away from the passband. However, the increase of the
distance d will make passband bandwidth smaller as discuss on previous section. So a compromised choice
of L, s1 and d would be made. Consequently, a sharper fall-off at both lower and upper passband edge can be
achieved. Furthermore, we can obtain a new filter with improved out-of-band rejection performance by
adjusting the mixed EM coupling strength.
Figure 7. Simulated transmission coefficient S21 (dB) of proposed filter with mixed coupling versus
L and d, respectively, where s = 0.1 mm.
3.
FABRICATION AND MEASURED RESULT
In this section, two compact and low-loss two-pole bandpass filters using hybrid resonator is
fabricated, to demonstrate the above calculations and analyses. We also discuss practical parameters that
need to be considered in actual application. In order to utilize the investigated key features above, the design
example with hardware verifications are presented in this section. The full-wave EM simulations and
optimizations for these examples are performed by the HFSS simulator. An Intel(R) Xeon(R) CPU E5-2609
(two 2.4 GHz processors) workstation with 16 GB RAM is used for all EM designs. The optimized
parameters of the proposed filters, as referring to Figure 1, are listed in the TABLE I.
By employing the symmetry structure, the design parameters are reduced to half hence helpful to
enable compact filter in implementation. The input/output is implemented based on a coupled-line structure
with a coupling gap g of 0.075 mm. The characteristic impedance of the input/output microstrip is taken as
50Ω. Two proposed BPFs prototype were designed using Ansoft HFSS and were fabricated on the substrate
Rogers 5880 with the dielectric constant of 2.2, dielectric loss tangent of 0.0019 and dielectric thickness of
0.508 mm. The measurement is accomplished with Agilent N5230A network analyzer. Good agreement
between the simulations and measurements is achieved.
Table 1. Physical dimension of two proposed filters (in mm)
Parameters
L
L1
L2
L3
r
d
BPF A
4
5.5
2.78
5.61
1.5
6.6
BPF B
1.1
6
4.53
7.58
1.5
10
Parameters
W1
W2
W3
S1
s
h
BPF A
1.74
0.5
0.3
0.14
0.1
10
BPF B
1.52
0.5
0.3
0.14
0.1
10
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Figure 8. Photograph of the fabricated proposed filter structure.
(a)
(b)
Figure 9. Simulated and measured frequency response of two proposed BPFs
(the inset shows a photograph of the PCB fabricated filter).
The simulated and measured performances of the filter A are plotted in Figure 8 (a). The measured
insertion loss includes SMA connectors is 1.5 dB with a 3.2% 3-dB bandwidth at 2.61 GHz center frequency.
The return loss is better than 12 dB within passband. The additional loss and a slightly shift in pass-band and
center frequency can be attributed to the fabrication tolerance. Two transmission zeros, located opposite each
other of the passband, can be observed which can greatly improve the selectivity and stopband suppression of
the proposed filter. Furthermore, the filter features a very compact size PCB of 15.6 mm x 12 mm, or
equivalently 0.201λg x 0.154λg, where λg is the guided wavelength at operating frequency.
Figure 8 (b) illustrates the measured results of the filter B comparing with the simulated one. The
frequency response shows 3-dB relative bandwidth of 4.8 % at 2.57 GHz center frequency. The measured
minimum insertion loss of 1.3 dB while the return loss is 19 dB within the passband. However, the position
of the transmission zeros located at 2.15 GHz and 2.85 GHz with the roll-off about -60dB as well as the
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overall response agree with the specifications. Compared to the filter A, the out-of-band performance has
been improved apparently. The over size of this filter is about 20 mm x 14 mm, less than 0.247λ g x 0.173λg.
Table 2 shows the performance comparison between this presented and referenced filters. Among
the filters under consideration, the proposed filter has an extraordinarily compact size and is able to render
full control of the transmission zeros.
Table 2. Comparison with related second-order filters
Ref.
[7]
[8] BPF A
[8] BPF B
This work BPF A
This work BPF B
f0 (GHz)
2.45
1.41
1.42
2.61
2.57
FBW (%)
5.2
5.1
6.5
3.2
4.8
Insertion loss (dB)
2.75
1.9
2.3
1.5
1.3
Return loss (dB)
15.1
17.7
14.3
12.4
21.2
PCB Size (λg2)
0.291 x 0.277
0.361 x 0.415
0.401 x 0.203
0.201 x 0.154
0.247 x 0.173
4.
CONCLUSION
Two novel miniaturized second-order bandpass filters with utilizing the hybrid resonator integrated
to shielding case is designed, fabricated and tested. Higher quality factor and smaller in size can be obtained
with easy to fabricate. Moreover, a pair of fully adjustable transmission zeros above and below the passband
which give good attenuation characteristics. With these advantages, the proposed filter is promising to apply
in many modern RF transmitted and received systems.
ACKNOWLEDGEMENTS
This research was supported in part by the National Science and Technology Major Project of China
under Grant 2013ZX03001017-003.
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