research article investigation of compact balun-bandpass...
TRANSCRIPT
Research ArticleInvestigation of Compact Balun-Bandpass Filter Using FoldedOpen-Loop Ring Resonators and Microstrip Lines
Chia-Mao Chen1 Shoou-Jinn Chang2 Sung-Mao Wu3
Yuan-Tai Hsieh4 and Cheng-Fu Yang5
1 Institute of Microelectronics and Department of Electrical Engineering National Cheng Kung University Tainan 701 Taiwan2 Institute of Microelectronics and Department of Electrical Engineering Center for MicroNano Science and TechnologyAdvanced Optoelectronic Technology Center National Cheng Kung University Tainan 701 Taiwan
3Department of Electrical Engineering National University of Kaohsiung Kaohsiung 811 Taiwan4Department of Electronic Engineering Southern Taiwan University Tainan 710 Taiwan5Department of Chemical and Materials Engineering National University of Kaohsiung Kaohsiung 811 Taiwan
Correspondence should be addressed to Cheng-Fu Yang cfyangnukedutw
Received 2 May 2014 Accepted 7 June 2014 Published 1 July 2014
Academic Editor Teen-Hang Meen
Copyright copy 2014 Chia-Mao Chen et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A balun-bandpass filter was proposed by using two folded open-loop ring resonators (OLRRs) to couple three microstrip lines Bytuning the size of the OLRR the operating frequency of the balun-bandpass filter could be tuned to the needed value By tuningthe size of open stub at the end of microstrip lines the balanced impedance of the balun-bandpass filter could also be tuned Thefabricated balun-bandpass filter had a wide bandwidth and a low insertion loss at center frequency of the passband The balun-bandpass filter presented an excellent in-band balanced performance with common-mode rejection ratio more than 20 dB in thepassbands An advanced design methodology had been adopted based on EM simulation for making these designed parametersof OLRRs and microstrip lines Good correlation was seen between simulation and measurement and the result was that first runpass had been achieved in the majority of our designs
1 Introduction
A mass of RFmicrowave modules is designed for portableterminals such as handsets e-readers and tablet PCs Inte-gration of two functional blocks in a single circuit is the mostintuitive way to reduce the cost as well as the circuit sizeBandpass filters (BPFs) and baluns are critical componentsin the RF channels because most of the RF-front end mod-ules require bandpass filters and baluns Some balun BPFsare evolved from the classic quarter- and half-wavelengthresonators with folding topology [1] To cater for dual-bandwireless systems plenty of researches focus on the balun BPFswith two passbands [2] In [3 4] single dual-mode resonatorsare employed to construct a compact balun BPF To extendthe ability of the microwave components to support multiplefrequency bands tunable or reconfigurable techniques havedrawn much attention for researches and developments To
achieve the requirement of the compact and low-cost RFmodule for the modern wireless communication system thebalun BPFs with the balance-to-unbalance conversion arehighly desired Accordingly all kinds of tunable BPFs havebeenunder intensive developments [5] but relatively only fewresearches have been done on the tunable balun BPFs [6]
In the present study a generalized methodology fordesigning a novel and simple single passband balun BPFwas investigated The low-loss balun BPF was using twofolded open-loop ring resonators (OLRRs) with equal phys-ical dimensions to couple three microstrip lines as Figure 1shows Each OLRR is placed between two microstrip linesand has a perimeter of about a half wavelength of the designedresonant frequency Each of the foldOLRRs has its maximumelectric field density near the open ends of the line andhas its maximum magnetic field density around the centervalley of the microstrip line The resonant frequencies can
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 679538 6 pageshttpdxdoiorg1011552014679538
2 Mathematical Problems in Engineering
L
g
g
s
balanced
balanced
unbalancedPort 1
Port 2
Port 3
Figure 1 Proposed balun-bandpass filter (BPF) based on OLRRs
be adjusted via the length of the OLRRs to provide a high-performance passband response The proposed balun BPFhas low insertion loss a wide tunable range of passbandtransmission zeros and simple design By tuning the sizeof open stub at the end of microstrip line the balancedimpedance of the balun BPF can be tuned Finally wefabricated a high-performance balun BPF on FR4 substratesto demonstrate the proposed structure
2 Design Methodology
To obtain the maximummagnetic coupling the center valleyof the OLRRs must be positioned in the proper locationalong the microstrip line with the maximum magnetic fieldintensity which can be determined by studying wavemotionson a microstrip line For the transverse electromagnetic(TEM) field structure both the electric and magnetic fieldvectors lie in the transverse plane which is perpendicular tothe uniform propagation axis Under the assumptions of theTEMmode of propagation and a lossless line the fields 119864 and119867 are uniquely related to voltage and current respectivelyBased on transmission line theory the magnitudes of voltageand current on the microstrip line can be expressed in termsof the incident wave and the reflection coefficient
|119881 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1 + |Γ| 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(1)
|119868 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1198850
1003816
1003816
1003816
1003816
1003816
1 minus |Γ| 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(2)
where 119897 = minus119911 is measured away from the load at 119911 = 0 and120579 is the phase of the reflection coefficient When 120579 minus 2120573119889 hasa magnitude of zero or any multiple of 2120587 radian voltage in(1) is at its maximum magnitude and current in (2) is at itsminimum magnitude respectively For the case of an open-circuited line (1) and (2) respectively become
|119881 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1 + 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
|119868 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1198850
1003816
1003816
1003816
1003816
1003816
1 minus 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(3)
At a distance of a quarter wavelength from the receivingend the voltage becomes zero while the current is at its
Open end
rarr
Hmax
Input26GHz
Figure 2 Current distribution inmicrostrip line terminated at openend
balanced
balanced
unbalancedPort 1
Port 2
Port 3
Figure 3 Simulation of current distribution and coupling pathsoscillating at 26GHz
maximum If the line has a value of half wavelength thecurrent distribution near the center of the transmission lineis at its maximum High magnetic coupling results from ahigh conduction current Once the point of 119868max is foundthe point of 119867max can be easily determined Figure 2 showsa uniform section of a transmission line of length 119871 where119871 is about 05120582 under operation frequency of 26GHz Thisresult suggests that the resonant frequency of the designedbalun BPFs can be adjusted by changing the dimension of theOLRRs
To demonstrate that the proposed structure is availablebalun BPF is designed using OLRRs to couple microstriptransmission lines To excite the passbands two pairs ofguided half-wavelength OLRRs should be located betweentwo microstrip lines and the microstrip lines are terminatedwith open ends Each OLRR provides a path coupled sig-nal energy from one microstrip line to another at aroundresonance frequency When the signal is above and belowresonance frequency most of the energy is reflected back andthe standing waves are said to exist on the line as Figure 3shows After the designed balun BPFs are simulated usingthe HFSS simulator with loss factors (conductor loss anddielectric loss) included in the simulated response to find theoptimal parameters the coupling paths shown in Figure 3 arechosen specifically for resonant frequency
Besides having good match in input impedance andgood amplitude and phase balances between the two outputports the match in output balanced impedance will makebalun BPFs have more attraction in the sense of the systemintegration ability This structure is very easy for designer totune balanced impedance because we only need to adjust thewidth (119882
119861) of balanced-port microstrip line and add open-
stub line as the structure shown in Figure 4
Mathematical Problems in Engineering 3
L1
L1
W2
L2
W1
W1
WUB
Unit (mm)
Open stub
Open stub
WB
WB
Figure 4 Balun BPF with open stub
To characterize the balance characteristic of the balunBPFs the mode conversion between the unbalanced three-port network and the unbalanced-to-balanced two-port net-work is applied to obtain the single-ended to differential-mode and common-mode parameters [7 8]
11987811990411990411= 11987811
11987811988911990421=
(11987821minus 11987831)
radic2
11987811988811990421=
(11987821minus 11987831)
radic2
(4)
where 11987811988911990421
and 11987811988811990421
are the couplings of mixed-modeparameters 119878
11988911990421is from the unbalanced input port 1 to
the differential-mode output port 2 and 11987811988811990421
is from theunbalanced input port 1 to the common-mode output port2 respectively
3 Design of Balun-Bandpass Filters
The simulated frequency response of the 26GHz-basedbalun BPFwith better design parameters is shown in Figure 5with layout pattern shown in the inset The designed balunBPF is based on two pairs of half-wavelength OLRRs Electriccoupling can be obtained if the open sides of the two coupledresonators are placed near each other andmagnetic couplingcan be obtained if the sides with the maximum magneticfield of two coupled resonators are placed near each otherThe coupling spacing 119904 between the main microstrip line andOLRRs is 02mmand the spacing119892 between two resonators is061mmThe center frequency of the designed balun BPF canbe accurately controlled to a desired band once the correctposition is chosen The balanced impedance is about (78 +11989518) Ohm at 26GHz The simulation result of the designedbalun BPF shows good match in input impedance goodamplitude and phase balances between the two output portsand a wide passband Those simulated results prove that we
Table 1 Balanced impedance of the balun BPFs with open stub
119882UB 119882119861 1198821119871111988221198712
Balanced impedance Ω15 15 0 0 0 0 78 + 1198951815 1125 0 0 075 2 10015 15 095 5 075 1 50
only need to find the optimum width (119882119861) of balanced-port
microstrip line and add open-stub line and then we can tunebalanced impedance the balanced impedance of the balunBPFs with open stub is shown in Table 1
Both patterns in Figures 6 and 7 have the same designedstructures In order to design the balanced impedance thatis needed the sizes of open stub and 119882
119861are different from
each otherThe balun BPF using OLRRs was fabricated on anFR4 substrate with a relative permittivity of 44 and thicknessbetween the two electrodes was 12mm The dimensionfor the proposed balun BPF with balanced impedance of100Ohm is 41mm times 2221mm as shown in Figure 6(a) andthe photograph of the fabricated balun BPF is shown inFigure 6(b) Similarly the dimension for the proposed balunBPF with balanced impedance of 50 Ohm is about 41mm times3296mm as shown in Figure 7(a) and the photograph of thefabricated balun BPF is shown in Figure 7(b) Measurementswere carried out using an Agilent N5071C network analyzerFigures 8(a) and 8(b) show the full-wave simulated andmeasured results of the 119878-parameters and phaseamplitudedifferences for the circuit with balanced impedance of100Ohm Figures 9(a) and 9(b) show those for the circuitwithbalanced impedance of 50Ohm respectively The measured11987811988911990421
values at the center frequencies of each passband inFigures 8(a) and 9(a) are 198 and 219 dB respectively Themeasured 3 dB band-edge frequencies of 119878
11988911990421values are
observed at 119891119871100Ω= 243GHz and 119891
119867100Ω= 288GHz for
Figure 8(a) and at 11989111987150Ω= 249GHz and 119891
11986750Ω= 277GHz
for Figure 9(a) respectively The simulated and measured11987811988811990421
values are smaller than 20 dB within operating bands oftwo balun BPFs which demonstrates good common-modesuppression at the differential output port Figures 8(a) and9(a) also show that the amplitude difference between 119878
21and
11987831
is below 2 dB and the phase difference between 11987821
and11987831is within 180 plusmn 100 at each operating band The proposed
balun BPFs present a wide bandwidth because they havetwo resonant frequencies within the passband The balanceimpedance will affect the electrical performance of returnloss as shown in Figures 8(a) and 9(a) for that there is onepeak or two peaksThe little difference between the simulatedandmeasured results ismainly caused by the fabrication error(circuit etching) the SMA connector and numerical error
4 Conclusions
We presented a simple and effective method for designing amicrostrip balun BPF with differential outputs By adjustingthe physical dimensions of the OLRRs the center frequenciesof the balun BPF could be tuned over a wide range Thebalanced impedance was tuned easily by open stub and119882
119861
The balun-bandpass filter not only possessed good bandpass
4 Mathematical Problems in Engineering
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
S-p
aram
eter
(dB)
Sss11Sds21Scs21
(a)
20 22 24 26 28 30
190
185
180
175
170
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
2
1
0
minus1
minus2
(b)
Figure 5 Simulated results of the designed balun BPF (a) 119878-parameters and (b) magnitude and phase differences
41
061
04174
1543
411
923
1125
15
Unit (mm)
923
1125
0220
075
(a) (b)
Figure 6 (a) Layout pattern and (b) photograph of the designed balun BPF with about 100-Ω balanced impedance
41
061
04174
1543
411
923
15
Unit (mm)
0210
075
15
923
15
095
50
(a) (b)
Figure 7 (a) Layout pattern and (b) photograph of the designed balun BPF with about 50-Ω balanced impedance
Mathematical Problems in Engineering 5
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 8 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 100-Ω balanced impedance
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 9 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 50-Ω balanced impedance
characteristics as the results shown in Figures 8 and 9 thetwo balun BPFs had the good performance A prototype wasdesigned and fabricated with the measured results given
Conflict of Interests
The authors declare that they have no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors acknowledge financial supports of NSC 102-2622-E-390-002-CC3 NSC 102-2221-E-390-027 and NSC102-2221-E-218-036
References
[1] L K Yeung and K L Wu ldquoA dual-band coupled-line balunfilterrdquo IEEE Transactions on Microwave Theory and Techniquesvol 55 no 11 pp 2406ndash2411 2007
[2] G S Huang and C H Chen ldquoDual-band balun bandpassfilter with hybrid structurerdquo IEEE Microwave and WirelessComponents Letters vol 21 no 7 pp 356ndash358 2011
[3] E Y Jung and H Y Hwang ldquoA balun-BPF using a dual modering resonatorrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 652ndash654 2007
[4] L-H Zhou H Tang J-X Chen and Z-H Bao ldquoTunable filter-ing balun with enhanced stopband rejectionrdquo EEE ElectronicsLetters vol 48 no 14 pp 845ndash847 2012
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
2 Mathematical Problems in Engineering
L
g
g
s
balanced
balanced
unbalancedPort 1
Port 2
Port 3
Figure 1 Proposed balun-bandpass filter (BPF) based on OLRRs
be adjusted via the length of the OLRRs to provide a high-performance passband response The proposed balun BPFhas low insertion loss a wide tunable range of passbandtransmission zeros and simple design By tuning the sizeof open stub at the end of microstrip line the balancedimpedance of the balun BPF can be tuned Finally wefabricated a high-performance balun BPF on FR4 substratesto demonstrate the proposed structure
2 Design Methodology
To obtain the maximummagnetic coupling the center valleyof the OLRRs must be positioned in the proper locationalong the microstrip line with the maximum magnetic fieldintensity which can be determined by studying wavemotionson a microstrip line For the transverse electromagnetic(TEM) field structure both the electric and magnetic fieldvectors lie in the transverse plane which is perpendicular tothe uniform propagation axis Under the assumptions of theTEMmode of propagation and a lossless line the fields 119864 and119867 are uniquely related to voltage and current respectivelyBased on transmission line theory the magnitudes of voltageand current on the microstrip line can be expressed in termsof the incident wave and the reflection coefficient
|119881 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1 + |Γ| 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(1)
|119868 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1198850
1003816
1003816
1003816
1003816
1003816
1 minus |Γ| 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(2)
where 119897 = minus119911 is measured away from the load at 119911 = 0 and120579 is the phase of the reflection coefficient When 120579 minus 2120573119889 hasa magnitude of zero or any multiple of 2120587 radian voltage in(1) is at its maximum magnitude and current in (2) is at itsminimum magnitude respectively For the case of an open-circuited line (1) and (2) respectively become
|119881 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1 + 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
|119868 (119911)| =
1003816
1003816
1003816
1003816
119881
+
0
1003816
1003816
1003816
1003816
1198850
1003816
1003816
1003816
1003816
1003816
1 minus 119890
119895(120579minus2120573119897)100381610038161003816
1003816
1003816
(3)
At a distance of a quarter wavelength from the receivingend the voltage becomes zero while the current is at its
Open end
rarr
Hmax
Input26GHz
Figure 2 Current distribution inmicrostrip line terminated at openend
balanced
balanced
unbalancedPort 1
Port 2
Port 3
Figure 3 Simulation of current distribution and coupling pathsoscillating at 26GHz
maximum If the line has a value of half wavelength thecurrent distribution near the center of the transmission lineis at its maximum High magnetic coupling results from ahigh conduction current Once the point of 119868max is foundthe point of 119867max can be easily determined Figure 2 showsa uniform section of a transmission line of length 119871 where119871 is about 05120582 under operation frequency of 26GHz Thisresult suggests that the resonant frequency of the designedbalun BPFs can be adjusted by changing the dimension of theOLRRs
To demonstrate that the proposed structure is availablebalun BPF is designed using OLRRs to couple microstriptransmission lines To excite the passbands two pairs ofguided half-wavelength OLRRs should be located betweentwo microstrip lines and the microstrip lines are terminatedwith open ends Each OLRR provides a path coupled sig-nal energy from one microstrip line to another at aroundresonance frequency When the signal is above and belowresonance frequency most of the energy is reflected back andthe standing waves are said to exist on the line as Figure 3shows After the designed balun BPFs are simulated usingthe HFSS simulator with loss factors (conductor loss anddielectric loss) included in the simulated response to find theoptimal parameters the coupling paths shown in Figure 3 arechosen specifically for resonant frequency
Besides having good match in input impedance andgood amplitude and phase balances between the two outputports the match in output balanced impedance will makebalun BPFs have more attraction in the sense of the systemintegration ability This structure is very easy for designer totune balanced impedance because we only need to adjust thewidth (119882
119861) of balanced-port microstrip line and add open-
stub line as the structure shown in Figure 4
Mathematical Problems in Engineering 3
L1
L1
W2
L2
W1
W1
WUB
Unit (mm)
Open stub
Open stub
WB
WB
Figure 4 Balun BPF with open stub
To characterize the balance characteristic of the balunBPFs the mode conversion between the unbalanced three-port network and the unbalanced-to-balanced two-port net-work is applied to obtain the single-ended to differential-mode and common-mode parameters [7 8]
11987811990411990411= 11987811
11987811988911990421=
(11987821minus 11987831)
radic2
11987811988811990421=
(11987821minus 11987831)
radic2
(4)
where 11987811988911990421
and 11987811988811990421
are the couplings of mixed-modeparameters 119878
11988911990421is from the unbalanced input port 1 to
the differential-mode output port 2 and 11987811988811990421
is from theunbalanced input port 1 to the common-mode output port2 respectively
3 Design of Balun-Bandpass Filters
The simulated frequency response of the 26GHz-basedbalun BPFwith better design parameters is shown in Figure 5with layout pattern shown in the inset The designed balunBPF is based on two pairs of half-wavelength OLRRs Electriccoupling can be obtained if the open sides of the two coupledresonators are placed near each other andmagnetic couplingcan be obtained if the sides with the maximum magneticfield of two coupled resonators are placed near each otherThe coupling spacing 119904 between the main microstrip line andOLRRs is 02mmand the spacing119892 between two resonators is061mmThe center frequency of the designed balun BPF canbe accurately controlled to a desired band once the correctposition is chosen The balanced impedance is about (78 +11989518) Ohm at 26GHz The simulation result of the designedbalun BPF shows good match in input impedance goodamplitude and phase balances between the two output portsand a wide passband Those simulated results prove that we
Table 1 Balanced impedance of the balun BPFs with open stub
119882UB 119882119861 1198821119871111988221198712
Balanced impedance Ω15 15 0 0 0 0 78 + 1198951815 1125 0 0 075 2 10015 15 095 5 075 1 50
only need to find the optimum width (119882119861) of balanced-port
microstrip line and add open-stub line and then we can tunebalanced impedance the balanced impedance of the balunBPFs with open stub is shown in Table 1
Both patterns in Figures 6 and 7 have the same designedstructures In order to design the balanced impedance thatis needed the sizes of open stub and 119882
119861are different from
each otherThe balun BPF using OLRRs was fabricated on anFR4 substrate with a relative permittivity of 44 and thicknessbetween the two electrodes was 12mm The dimensionfor the proposed balun BPF with balanced impedance of100Ohm is 41mm times 2221mm as shown in Figure 6(a) andthe photograph of the fabricated balun BPF is shown inFigure 6(b) Similarly the dimension for the proposed balunBPF with balanced impedance of 50 Ohm is about 41mm times3296mm as shown in Figure 7(a) and the photograph of thefabricated balun BPF is shown in Figure 7(b) Measurementswere carried out using an Agilent N5071C network analyzerFigures 8(a) and 8(b) show the full-wave simulated andmeasured results of the 119878-parameters and phaseamplitudedifferences for the circuit with balanced impedance of100Ohm Figures 9(a) and 9(b) show those for the circuitwithbalanced impedance of 50Ohm respectively The measured11987811988911990421
values at the center frequencies of each passband inFigures 8(a) and 9(a) are 198 and 219 dB respectively Themeasured 3 dB band-edge frequencies of 119878
11988911990421values are
observed at 119891119871100Ω= 243GHz and 119891
119867100Ω= 288GHz for
Figure 8(a) and at 11989111987150Ω= 249GHz and 119891
11986750Ω= 277GHz
for Figure 9(a) respectively The simulated and measured11987811988811990421
values are smaller than 20 dB within operating bands oftwo balun BPFs which demonstrates good common-modesuppression at the differential output port Figures 8(a) and9(a) also show that the amplitude difference between 119878
21and
11987831
is below 2 dB and the phase difference between 11987821
and11987831is within 180 plusmn 100 at each operating band The proposed
balun BPFs present a wide bandwidth because they havetwo resonant frequencies within the passband The balanceimpedance will affect the electrical performance of returnloss as shown in Figures 8(a) and 9(a) for that there is onepeak or two peaksThe little difference between the simulatedandmeasured results ismainly caused by the fabrication error(circuit etching) the SMA connector and numerical error
4 Conclusions
We presented a simple and effective method for designing amicrostrip balun BPF with differential outputs By adjustingthe physical dimensions of the OLRRs the center frequenciesof the balun BPF could be tuned over a wide range Thebalanced impedance was tuned easily by open stub and119882
119861
The balun-bandpass filter not only possessed good bandpass
4 Mathematical Problems in Engineering
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
S-p
aram
eter
(dB)
Sss11Sds21Scs21
(a)
20 22 24 26 28 30
190
185
180
175
170
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
2
1
0
minus1
minus2
(b)
Figure 5 Simulated results of the designed balun BPF (a) 119878-parameters and (b) magnitude and phase differences
41
061
04174
1543
411
923
1125
15
Unit (mm)
923
1125
0220
075
(a) (b)
Figure 6 (a) Layout pattern and (b) photograph of the designed balun BPF with about 100-Ω balanced impedance
41
061
04174
1543
411
923
15
Unit (mm)
0210
075
15
923
15
095
50
(a) (b)
Figure 7 (a) Layout pattern and (b) photograph of the designed balun BPF with about 50-Ω balanced impedance
Mathematical Problems in Engineering 5
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 8 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 100-Ω balanced impedance
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 9 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 50-Ω balanced impedance
characteristics as the results shown in Figures 8 and 9 thetwo balun BPFs had the good performance A prototype wasdesigned and fabricated with the measured results given
Conflict of Interests
The authors declare that they have no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors acknowledge financial supports of NSC 102-2622-E-390-002-CC3 NSC 102-2221-E-390-027 and NSC102-2221-E-218-036
References
[1] L K Yeung and K L Wu ldquoA dual-band coupled-line balunfilterrdquo IEEE Transactions on Microwave Theory and Techniquesvol 55 no 11 pp 2406ndash2411 2007
[2] G S Huang and C H Chen ldquoDual-band balun bandpassfilter with hybrid structurerdquo IEEE Microwave and WirelessComponents Letters vol 21 no 7 pp 356ndash358 2011
[3] E Y Jung and H Y Hwang ldquoA balun-BPF using a dual modering resonatorrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 652ndash654 2007
[4] L-H Zhou H Tang J-X Chen and Z-H Bao ldquoTunable filter-ing balun with enhanced stopband rejectionrdquo EEE ElectronicsLetters vol 48 no 14 pp 845ndash847 2012
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
L1
L1
W2
L2
W1
W1
WUB
Unit (mm)
Open stub
Open stub
WB
WB
Figure 4 Balun BPF with open stub
To characterize the balance characteristic of the balunBPFs the mode conversion between the unbalanced three-port network and the unbalanced-to-balanced two-port net-work is applied to obtain the single-ended to differential-mode and common-mode parameters [7 8]
11987811990411990411= 11987811
11987811988911990421=
(11987821minus 11987831)
radic2
11987811988811990421=
(11987821minus 11987831)
radic2
(4)
where 11987811988911990421
and 11987811988811990421
are the couplings of mixed-modeparameters 119878
11988911990421is from the unbalanced input port 1 to
the differential-mode output port 2 and 11987811988811990421
is from theunbalanced input port 1 to the common-mode output port2 respectively
3 Design of Balun-Bandpass Filters
The simulated frequency response of the 26GHz-basedbalun BPFwith better design parameters is shown in Figure 5with layout pattern shown in the inset The designed balunBPF is based on two pairs of half-wavelength OLRRs Electriccoupling can be obtained if the open sides of the two coupledresonators are placed near each other andmagnetic couplingcan be obtained if the sides with the maximum magneticfield of two coupled resonators are placed near each otherThe coupling spacing 119904 between the main microstrip line andOLRRs is 02mmand the spacing119892 between two resonators is061mmThe center frequency of the designed balun BPF canbe accurately controlled to a desired band once the correctposition is chosen The balanced impedance is about (78 +11989518) Ohm at 26GHz The simulation result of the designedbalun BPF shows good match in input impedance goodamplitude and phase balances between the two output portsand a wide passband Those simulated results prove that we
Table 1 Balanced impedance of the balun BPFs with open stub
119882UB 119882119861 1198821119871111988221198712
Balanced impedance Ω15 15 0 0 0 0 78 + 1198951815 1125 0 0 075 2 10015 15 095 5 075 1 50
only need to find the optimum width (119882119861) of balanced-port
microstrip line and add open-stub line and then we can tunebalanced impedance the balanced impedance of the balunBPFs with open stub is shown in Table 1
Both patterns in Figures 6 and 7 have the same designedstructures In order to design the balanced impedance thatis needed the sizes of open stub and 119882
119861are different from
each otherThe balun BPF using OLRRs was fabricated on anFR4 substrate with a relative permittivity of 44 and thicknessbetween the two electrodes was 12mm The dimensionfor the proposed balun BPF with balanced impedance of100Ohm is 41mm times 2221mm as shown in Figure 6(a) andthe photograph of the fabricated balun BPF is shown inFigure 6(b) Similarly the dimension for the proposed balunBPF with balanced impedance of 50 Ohm is about 41mm times3296mm as shown in Figure 7(a) and the photograph of thefabricated balun BPF is shown in Figure 7(b) Measurementswere carried out using an Agilent N5071C network analyzerFigures 8(a) and 8(b) show the full-wave simulated andmeasured results of the 119878-parameters and phaseamplitudedifferences for the circuit with balanced impedance of100Ohm Figures 9(a) and 9(b) show those for the circuitwithbalanced impedance of 50Ohm respectively The measured11987811988911990421
values at the center frequencies of each passband inFigures 8(a) and 9(a) are 198 and 219 dB respectively Themeasured 3 dB band-edge frequencies of 119878
11988911990421values are
observed at 119891119871100Ω= 243GHz and 119891
119867100Ω= 288GHz for
Figure 8(a) and at 11989111987150Ω= 249GHz and 119891
11986750Ω= 277GHz
for Figure 9(a) respectively The simulated and measured11987811988811990421
values are smaller than 20 dB within operating bands oftwo balun BPFs which demonstrates good common-modesuppression at the differential output port Figures 8(a) and9(a) also show that the amplitude difference between 119878
21and
11987831
is below 2 dB and the phase difference between 11987821
and11987831is within 180 plusmn 100 at each operating band The proposed
balun BPFs present a wide bandwidth because they havetwo resonant frequencies within the passband The balanceimpedance will affect the electrical performance of returnloss as shown in Figures 8(a) and 9(a) for that there is onepeak or two peaksThe little difference between the simulatedandmeasured results ismainly caused by the fabrication error(circuit etching) the SMA connector and numerical error
4 Conclusions
We presented a simple and effective method for designing amicrostrip balun BPF with differential outputs By adjustingthe physical dimensions of the OLRRs the center frequenciesof the balun BPF could be tuned over a wide range Thebalanced impedance was tuned easily by open stub and119882
119861
The balun-bandpass filter not only possessed good bandpass
4 Mathematical Problems in Engineering
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
S-p
aram
eter
(dB)
Sss11Sds21Scs21
(a)
20 22 24 26 28 30
190
185
180
175
170
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
2
1
0
minus1
minus2
(b)
Figure 5 Simulated results of the designed balun BPF (a) 119878-parameters and (b) magnitude and phase differences
41
061
04174
1543
411
923
1125
15
Unit (mm)
923
1125
0220
075
(a) (b)
Figure 6 (a) Layout pattern and (b) photograph of the designed balun BPF with about 100-Ω balanced impedance
41
061
04174
1543
411
923
15
Unit (mm)
0210
075
15
923
15
095
50
(a) (b)
Figure 7 (a) Layout pattern and (b) photograph of the designed balun BPF with about 50-Ω balanced impedance
Mathematical Problems in Engineering 5
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 8 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 100-Ω balanced impedance
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 9 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 50-Ω balanced impedance
characteristics as the results shown in Figures 8 and 9 thetwo balun BPFs had the good performance A prototype wasdesigned and fabricated with the measured results given
Conflict of Interests
The authors declare that they have no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors acknowledge financial supports of NSC 102-2622-E-390-002-CC3 NSC 102-2221-E-390-027 and NSC102-2221-E-218-036
References
[1] L K Yeung and K L Wu ldquoA dual-band coupled-line balunfilterrdquo IEEE Transactions on Microwave Theory and Techniquesvol 55 no 11 pp 2406ndash2411 2007
[2] G S Huang and C H Chen ldquoDual-band balun bandpassfilter with hybrid structurerdquo IEEE Microwave and WirelessComponents Letters vol 21 no 7 pp 356ndash358 2011
[3] E Y Jung and H Y Hwang ldquoA balun-BPF using a dual modering resonatorrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 652ndash654 2007
[4] L-H Zhou H Tang J-X Chen and Z-H Bao ldquoTunable filter-ing balun with enhanced stopband rejectionrdquo EEE ElectronicsLetters vol 48 no 14 pp 845ndash847 2012
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
S-p
aram
eter
(dB)
Sss11Sds21Scs21
(a)
20 22 24 26 28 30
190
185
180
175
170
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
2
1
0
minus1
minus2
(b)
Figure 5 Simulated results of the designed balun BPF (a) 119878-parameters and (b) magnitude and phase differences
41
061
04174
1543
411
923
1125
15
Unit (mm)
923
1125
0220
075
(a) (b)
Figure 6 (a) Layout pattern and (b) photograph of the designed balun BPF with about 100-Ω balanced impedance
41
061
04174
1543
411
923
15
Unit (mm)
0210
075
15
923
15
095
50
(a) (b)
Figure 7 (a) Layout pattern and (b) photograph of the designed balun BPF with about 50-Ω balanced impedance
Mathematical Problems in Engineering 5
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 8 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 100-Ω balanced impedance
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 9 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 50-Ω balanced impedance
characteristics as the results shown in Figures 8 and 9 thetwo balun BPFs had the good performance A prototype wasdesigned and fabricated with the measured results given
Conflict of Interests
The authors declare that they have no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors acknowledge financial supports of NSC 102-2622-E-390-002-CC3 NSC 102-2221-E-390-027 and NSC102-2221-E-218-036
References
[1] L K Yeung and K L Wu ldquoA dual-band coupled-line balunfilterrdquo IEEE Transactions on Microwave Theory and Techniquesvol 55 no 11 pp 2406ndash2411 2007
[2] G S Huang and C H Chen ldquoDual-band balun bandpassfilter with hybrid structurerdquo IEEE Microwave and WirelessComponents Letters vol 21 no 7 pp 356ndash358 2011
[3] E Y Jung and H Y Hwang ldquoA balun-BPF using a dual modering resonatorrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 652ndash654 2007
[4] L-H Zhou H Tang J-X Chen and Z-H Bao ldquoTunable filter-ing balun with enhanced stopband rejectionrdquo EEE ElectronicsLetters vol 48 no 14 pp 845ndash847 2012
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 8 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 100-Ω balanced impedance
10 15 20 25 30 35 40 45 50
0
minus20
minus40
minus60
minus80
Frequency (GHz)
MeasurementSimulation
S-p
aram
eter
(dB)
|Sss11|
|Sds21| |Scs21|
(a)
180
160
140
120
4
2
0
minus2
minus4
200
20 22 24 26 28 30
Am
plitu
de d
iffer
ence
(dB)
Phas
e diff
eren
ce (d
eg)
Frequency (GHz)
MeasurementSimulation
(b)
Figure 9 (a) 119878-parameters and (b) phaseamplitude difference of the designed balun BPF with about 50-Ω balanced impedance
characteristics as the results shown in Figures 8 and 9 thetwo balun BPFs had the good performance A prototype wasdesigned and fabricated with the measured results given
Conflict of Interests
The authors declare that they have no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors acknowledge financial supports of NSC 102-2622-E-390-002-CC3 NSC 102-2221-E-390-027 and NSC102-2221-E-218-036
References
[1] L K Yeung and K L Wu ldquoA dual-band coupled-line balunfilterrdquo IEEE Transactions on Microwave Theory and Techniquesvol 55 no 11 pp 2406ndash2411 2007
[2] G S Huang and C H Chen ldquoDual-band balun bandpassfilter with hybrid structurerdquo IEEE Microwave and WirelessComponents Letters vol 21 no 7 pp 356ndash358 2011
[3] E Y Jung and H Y Hwang ldquoA balun-BPF using a dual modering resonatorrdquo IEEE Microwave and Wireless ComponentsLetters vol 17 no 9 pp 652ndash654 2007
[4] L-H Zhou H Tang J-X Chen and Z-H Bao ldquoTunable filter-ing balun with enhanced stopband rejectionrdquo EEE ElectronicsLetters vol 48 no 14 pp 845ndash847 2012
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
[5] J S Sun N Kaneda Y Baeyens T Itoh and Y K Chen ldquoMul-tilayer planar tunable filter with very wide tuning bandwidthrdquoIEEE Transactions onMicrowaveTheory and Techniques vol 59no 11 pp 2864ndash2871 2011
[6] XMiaoWZhang YGeng XChen RMa and JGao ldquoDesignof compact frequency-tuned microstrip balunrdquo IEEE Antennasand Wireless Propagation Letters vol 9 pp 686ndash688 2010
[7] Q Xue J Shi and J X Chen ldquoUnbalanced-to-balancedand balanced-to-unbalanced diplexer with high selectivity andcommon-mode suppressionrdquo IEEE Transactions on MicrowaveTheory and Techniques vol 59 no 11 pp 2848ndash2855 2011
[8] W R Eisenstadt R Stengel and B M Thompson MicrowaveDifferential Circuit Design Using Mixed-Mode S-ParametersArtech House Boston Mass USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of