Research Article Design of a Novel Ultrawide Stopband

Research ArticleDesign of a Novel Ultrawide Stopband Lowpass Filter Usinga DMS-DGS Technique for Radar Applications

Ahmed Boutejdar1 Ahmed A Ibrahim2 and Edmund P Burte3

1Microwave Engineering Department University of Magdeburg 39106 Magdeburg Germany2Electronic and Communication Engineering Department Minia University Minia 61519 Egypt3Micro and Sensor Department University of Magdeburg 39106 Magdeburg Germany

Correspondence should be addressed to Ahmed Boutejdar ahmedboutejdarovgude

Received 18 June 2015 Accepted 31 August 2015

Academic Editor Giancarlo Bartolucci

Copyright copy 2015 Ahmed Boutejdar et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A novel wide stopband (WSB) low pass filter based on combination of defected ground structure (DGS) defected microstripstructure (DMS) and compensated microstrip capacitors is proposed Their excellent defected characteristics are verified throughsimulation andmeasurements Additionally to a sharp cutoff the structure exhibits simple design and fabrication very low insertionloss in the pass band of 03 dB and it achieves a wide rejection bandwidth with overall 20 dB attenuation from 15GHz up to 83GHzThe compact low pass structure occupies an area of (040120582119892 times 024120582119892) where 120582119892 = 148mm is the waveguide length at the cut-offfrequency 11 GHz Comparison between measured and simulated results confirms the validity of the proposed method Such filtertopologies are utilized in many areas of communications systems and microwave technology because of their several benefits suchas small losses wide reject band and high compactness

1 Introduction

With the rapid progress inmodern communications systemsdesign goals such as compact size low cost good qualityfactor and high performance components are highly con-sidered To achieve these targets many filtering structuresas open-circuited stubs hi-low impedances parallel coupledand end coupled filters have been investigated Neverthelessthese methods keep the satisfactory results unattainable Inorder to approach the desired results aDGS-DMSfilter couldbe an effective solution Due to their improved performancecharacteristics many filter techniques and methodologieshave been proposed and successfully realized Defectedground structures (DGSs) with and without periodic arrayhave been realized by etching a pattern in the backside of themetallic ground plane to obtain the stopband effect [1ndash13]DGS often consisted of two large defected areas and a narrowconnecting slot channel which corresponds to its equivalentL-C elements [14] The DGS with periodic or nonperiodictopology leads to a reject band in some frequency rangedue to the slow wave effect as a result of increasing the

effective capacitance and inductance of the transmission lineIn general DMS-unit [15ndash18] is used as a complementaryelement for the DGS-unit to achieve required filter responseDMS compared to DGS is etched on the microstrip line andexhibits same frequency behavior Additionally the design issimpler than theDGS and ismore easily integratedwith othermicrowave circuits Moreover it has an effective reducedcircuit size compared to DGS

In this paper a new compact microstrip low pass filterusing coupled DMS DGS resonators and compensatedcapacitors is reportedThe compensated capacitors are addedon the top layer in order to get a sharp transmission domainand to regenerate transmission zeros to obtain a large rejectband Dimensions of the microstrip capacitors were com-puted according to the desired equivalent circuit and usingRichardrsquos-Kuroda transformation and TX-Line software [19]afterwards they were optimized by AWR EM simulator [20]The measured results agree well with simulated results TheDGS-DMS technique (see Figure 1) in this research canbe applied in microwave coupler antennas and in MRItechnology

Hindawi Publishing CorporationInternational Journal of Microwave Science and TechnologyVolume 2015 Article ID 101602 7 pageshttpdxdoiorg1011552015101602

2 International Journal of Microwave Science and Technology

Metallic ground plane

DGS-unit

DMS-unit

Substrate

microstrip line50Ω

Figure 1 Three-dimensional view of the DMS-unit and DGS cell

2 Characteristics and Modeling ofDMS Resonators

Top layer of Figure 1 shows the proposed DMS cell which iscomposed of wide and narrow etched sections in the feed lineplaced on the top layer The extremes of this resonator areconnected throughmicrostrip linewith SMAconnectorsThewidths of themicrostrip lines at port 1 and port 2 are designedto match the characteristic impedance of 50Ω The etchedsurface presents the capacitance while the arms correspondto the inductance The DMS cell acts as a band stop elementwith a resonance frequency of 48GHz and an insertionloss of minus05 dB as shown in Figure 4 The structure hasbeen designed on RO4003 substrate with a relative dielectricconstant 120576

119903= 338 and thicknesses ℎ = 0813mm and a loss

tangent of 00027 The equivalent circuit of the DMS cell actsas a parallel LC resonator as shown in Figure 2

The values 119877 119871 and 119862 of the circuit parameters canbe computed using result that is matched to the one-pole Butterworth-type low pass response [7] Furthermoreradiation effects are more or less neglected The reactancevalues of DMS and filter first order can be expressed as

119883LC = [1205960119862(1205960

120596minus120596

1205960

)]

minus1

(1)

The series inductance (reactance) of one-pole Butterworthlow pass filter can be derived as follows

119883119871= 120596119871 = 120596(

11989211198850

120596119892

) (2)

where 1205960 120596119892 1198850 and 119892

1are the resonant frequency

cutoff frequency the scaled characteristic impedance andprototype value of the Butterworth-type LPF respectivelyBy matching the two previous reactance values the parallel

XLC

Z0

Z0

C

R

L

PortP = 1Z =

PortP = 2Z = 50Ohm50Ohm

Figure 2 Equivalent circuit of the DMSDGS-unit

S21S11

EM simulationCircuit simulation

S-pa

ram

eter

s (dB

)

Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus401086420

Figure 3 119878-parameters of the DMS-element and its equivalentcircuit

capacitance and the inductance of the equivalentDMS-circuitcan be derived using the following equations

119862 =120596119888

21198850(12059620minus 1205962119888)

119871 =1

12059620119862

119877 =21198850

radic1100381610038161003816100381611987811 (1205960)

10038161003816100381610038162

minus (21198850(1205960119862 minus 1120596

0119871))2

minus 1

(3)

The computed values of parameters 119862 119871 and 119877 are respec-tively 064 pF 173 nH and 742 kΩ The simulation results ofthe investigated EM structure and its corresponding circuitare illustrated in Figure 3 which shows identical values of 3dB cutoff frequency (119891

119888) and pole frequency (119891

119901) at 337GHz

and 483GHz respectively The transmit band shows aninsertion loss pass of 05 dB All dimensions of DMS-unit aredepicted in Table 1The proposed DMS resonator is shown inFigure 4

International Journal of Microwave Science and Technology 3

Table 1 Dimensions of the defected microstrip structure- (DMS-)element

Dimensions of DMS-unit Values (mm)ℎ 050119901 188119892 040119896 060119897 950

l

h

p

kg

Figure 4 Layout of the DMS-element

r

Figure 5 Layout of the cascaded DMS-band stop filter

3 Design of Band Stop Filter UsingCascaded DMS

AnewBSFwas designed using two cascadedDMS resonatorswhich are positioned one to the other by 180 degrees and aredirectly connected with the ports through 50Ω microstriplines Figure 5 shows the 3D view of the proposed BSF Thegeometry of each DMS-unit is equal to the dimensions indi-cated inTable 1 while themicrostrip distance (119903) between twoDMS resonators is 05mmThe 50Ω feed line has a line widthof 119908 The band stop structure is simulated and optimized byusing Microwave Studio CST [21] Microwave Office AWRThe dimensions are calculated using filter theory TX-Linesoftware and EM simulator Figure 6 shows the designedequivalent circuit of the BSF employing circuit simulatorAWR The extracted circuit parameters are computed basedon the EM simulations and empirical method and defined asfollows 119871 = 62 nH 119862 = 077 pF 119877 = 051 kΩ 119862

119901= 096 pH

and 1198620= 332 pF

The simulated results depicted in Figures 7(a) and 7(b)prove that the proposed filter has a 3 dB cutoff frequency at

27 GHz and a suppression level of 20 dB from 45 to 55 GHzthe insertion loss in the pass band is about 065 dB Goodagreement is verified between the EM simulations and thecircuit simulations

4 Band Stop to Low Pass UsingCompensated Capacitors

In order to demonstrate the effectiveness of the compensatedmicrostrip capacitor in transforming a structure with bandstop to low pass behaviors the added parallel microstripcapacitors to the previous structure (Figure 5) are designedand optimized as shown in Figure 8 A new DMS low passfilter is composed of three compensated parallel microstripcapacitors which are separated through two identical DMSresonators All components are cascaded on the top layer anddirectly connected with the SMAs through the two 50Ω feedlines of width 188mm as shown in Figure 8 The filter hasbeen designed and simulated in order to improve the rejectband and to minimize the pass band losses The DMS lowpass structure is designed for cutoff frequency at 155GHzand is simulated on the Rogers RO4003 substrate with thedielectric constant of 338 and thickness of 0813mm Thetotal size of the filter is 59 times 35mm2 Simulations have beenperformed using the full-wave EM Microwave Studio CSTand Microwave Office AWR

Figures 9 and 10 represent the equivalent circuit and the S-parameters of the DMS low pass filter According to the sim-ulation response we can conclude that the equivalent circuithas the characteristics of quasielliptic function because thefrequency response of the elliptic function filters is knownwith its generated transmission zeros in pass band and thus itshigh sharpness in transition response as shown in Figure 10

The values of119877 119871 and119862 are obtained as 4 kΩ 13 nH and06 pF respectively after using an optimization techniquewhile the values of three parallel open-circuit capacitors arecalculated using TX-Line software or exactly calculated usingthe following equation

119862 =1

1198850119862120596119888

sin (120573119862119897119862) +

2

1198850119871120596119888

tan (120573119871119897119871) (4)

where1198850119862120573119862 119897119862 120573119871 and 119897

119871are the characteristic impedance

the phase constant and the physical length of the com-pensated capacitor (low-impedance line) and the phaseconstant and the physical width of the series reactance (high-impedance line) respectively Both series reactance values ofthe low-impedance line are negligible thus the length of stubcapacitors is approximated as the following

119897119862=120582119892119862

2120587sinminus1 (120596

1198881198850119871119862)

119882119862asymp 119891 (119885

0119862 120579 119905 ℎ 120576

119903)

(5)

where 119882119862 120582119892119862 120579 119905 ℎ and 120576

119903are the width of the open-

circuit stub capacitance the guided wavelengths the electri-cal length the thickness of metal thickness of the substrateand the relative dielectric constant respectively As shownin Figure 10 two reflection zeros at 1 GHz and 15 GHz are


RR

CC

L LPortP = 1Z =

PortP = 2Z =

Cp CpC0

50Ohm 50Ohm

Figure 6 Equivalent circuit of the DMS-band stop filter

0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60

S11S21

(a)

0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60

S11 circuit simulationS21 circuit simulation

(b)

Figure 7 Simulation results of the DMS-band stop filter (a) EM simulation (b) circuit simulation

Table 2 Dimensions of the DMS low pass filter structure

Dimensions of DMS-unit Values (mm)119886 905119887 10119888 3119890 2119894 20

generated thus the insertion loss is less than 02 dB fromDC up to 155GHz The return loss in the pass band is lessthan minus12 dB The stopband rejection is higher than minus20 dBfrom 215GHz up to 425GHz As illustrated in Figure 10 anundesired peak appeared around the frequency of 44GHz Inorder to suppress this undesired harmonic another techniquebased on DGS will be used The dimensions of the proposedstructure are depicted in Table 2

5 Improvement of the Low Pass Filter

In order to suppress the undesired peak at 44GHz of theDMS low pass filter a pair of DGS-units has been used Theidea is to choose DGS resonators having resonance frequency

Compensated capacitors

ab

e

i

c


DMS-unit

Substrate

microstrip line50Ω

Figure 8 3D view of the proposed DMS low pass filter

around the unwanted frequency 44GHz thus to realizestructure with a wide reject band As shown in Figure 11 amultilayer structure is used to improve the performance of


PortP = 1Z = 50Ohm

PortP = 2Z = 50OhmR R

C C

L L

C1 C0 C2

Figure 9 Equivalent circuit of DMS low pass filter

S 11

andS 2

1(d

B)

minus10

0

minus20

minus30

minus40

minus50

minus60

minus700 2 4 6 8 10

Frequency (GHz)

S11S21

Figure 10 Comparison of simulated results of DMS low pass filter

the previous low pass filter The proposed element is similarto the DMS-unit with the difference that the new structureconsists of additional two DGS-units which are locatedbetween the microstrip capacitors as shown in Figure 11

The dimensions of the two DGS shapes which are etchedin the ground have been defined as follows 119904 = 06mm119902 = 6mm 119905 = 10mm and 119911 = 10mm The coupleddistance (119889 = 26mm) between the cascaded DGS resonatorsis obtained based on the empirical method This proposedgeometrical idea is based on using several stacked layers andit was able to improve the performance of the filter Theproposed DGS-DMS low pass filter has been simulated on aRogers RO4003 substrate with a relative dielectric constant120576119903of 338 and a thickness ℎ of 0813mm As depicted in

Figure 12 the proposed LPF behaves well in the pass bandand the stopband The filter has a minus3 dB cutoff frequency at11 GHz an insertion loss of 01 dB and a return loss less thanminus20 dB in the whole pass band

In addition an ultrawide suppression level approximatelyequal to minus20 dB in the frequency stopband ranging from15GHz to more than 85GHz is achieved Simulationswere performed using Microwave Office AWR and CSTMicrowave Studio simulators

Substrate



c

Z

q

tds

DMS-unit microstrip line50Ω

Figure 11 3D view of the proposed DMS-DGS low pass filter

6 Field Distribution along the Filter Structure

The investigation of this EMfield distribution has an objectiveof showing the frequency behaviour of this proposed filterand to prove the validity of the intuitive equivalent circuitFigure 13(a) shows the field distribution in the pass bandregion at the frequency of 05 GHz The magnetic field isconcentrated along theDMS resonators and on the 50Ω lineswhile a negligible electric field appears between both polesof this DMS structureThe transmission power between bothports ismagneticThe armof theDMS represents an inductorFigure 13(b) shows a filter with stopband behaviour at aresonant frequency of 4GHzThe electric andmagnetic fieldsshow same distribution densitiesThe electric field is concen-trated between extremities of the first slot which representsthe capacity Based on this EM field investigation the parallelLC circuit can be an approach model for the DMS-unit

7 Fabrication and Measurement

Figure 14 shows photographs of the fabricated LPF filter Thesimulations of the proposed DMS-DGS-UWRB-LPF are car-ried out using CST Microwave Studio and AWR Microwave


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50

S11 simulationS21 simulation

S 11

andS 2

1(d

B)

Figure 12 Simulation results of the proposed DMS-DGS low passfilter

(a)

(b)

Figure 13 Field distribution (a) magnetic field at 119891 = 05GHz (b)magnetic field at 119891 = 4GHz

OfficeThe simulation results show that the designed filter hasa high sharpness factor small losses in the pass band anda wide reject band as shown in Figure 15 In order to verifythe validity of the proposedDMS-DGS combination idea thefilter has been fabricated and measured using an HP8722Dnetwork analyzerThe LPF has been fabricated on a substratewith a relative dielectric constant 120576

119903of 338 and a thickness

(a)

(b)

Figure 14 Photograph of the fabricated DMS-DGS LPF (a) toplayer (b) bottom layer

0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)


S11 measurementS21 measurement

Figure 15 Comparison of simulation and measurement results ofproposed DMS-DGS LPF

ℎ of 0813mm The comparison between measured andsimulated results is depicted in Figure 15 In the pass bandthemeasured insertion and return losses are less than ndash03 dBand minus17 dB respectively The stopband rejection is higherthan minus20 dB from 13GHz up to 89GHz The compact lowpass structure occupies an area of (040120582119892 times 024120582119892) where120582119892 = 148mm is the guided wavelength at cutoff frequency


A very good agreement between simulations and mea-surements has been obtained Some discrepancy betweenthem can be interpreted as unexpected fabrication tolerancesThe observed deviation between simulation and experimen-tal results which also means the loss of transmission line hasbeen caused by mismatching effects and the manufacturingtolerance errors

8 Conclusion

In this work a novel DMS-DGS wide stopband low pass filterhas been introduced and investigated The filter structurewith strong suppression of undesired harmonic responses hasbeen presented which is based on stopband behaviors of theDMS and DGS cells It is demonstrated that low insertionloss (03 dB) deep return loss (greater than 17 dB) and awide rejection bandwidthwith overall 20 dB attenuation from13GHz up to 89GHz and bandwidth with overall 40 dBattenuation from 19GHz up to 77GHz have been achieved inthis type of filter It has been shown that the simulated resultsachieved by full-wave EM were in excellent agreement withthe measured onesThe newly proposed DMS-DGS-LPF andthe related design method are compatible with monolithicmicrowave integrated circuit (MMIC) or multilayer technol-ogy and can be used in a wide range of microwave andmillimeter wave applications

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors thank the German Research Foundation (DFG)for financial support The authors thank Ms Eng SonjaBoutejdar for her assistance and help andMr HaraldDempe-wolf the Lab Manager of the Institute for Electronics SignalProcessing and Communication (IIKT) at the University ofMagdeburg Germany for his support

References

[1] H Liu X Sun and Z Li ldquoNovel two-dimensional (2-D)defected ground array for planar circuitsrdquo Active and PassiveElectronic Components vol 27 no 3 pp 161ndash167 2004

[2] A K Arya M V Kartikeyan and A Patnaik ldquoDefected groundstructure in the perspective of microstrip antennas a reviewrdquoFrequenz vol 64 no 5-6 pp 79ndash84 2010

[3] A Boutejdar ldquoDesign of broad-stop band low pass filter usinga novel quasi-Yagi-DGS-resonators and metal box-techniquerdquoMicrowave and Optical Technology Letters vol 56 no 3 pp523ndash528 2014

[4] F Karshenas A R Mallahzadeh and J Rashed-MohasselldquoSize reduction and harmonic suppression of parallel coupled-line bandpass filters using defected ground structurerdquo AppliedComputational Electromagnetics Society Journal vol 25 no 2pp 149ndash155 2010

[5] A Boutejdar A Omar and E Burte ldquoHigh-performance widestop band low-pass filter using a vertically coupled DGS-DMS-resonators and interdigital capacitorrdquo Microwave and OpticalTechnology Letters vol 56 no 1 pp 87ndash91 2014

[6] M KMandal and S Sanyal ldquoA novel defected ground structurefor planar circuitsrdquo IEEE Microwave and Wireless ComponentsLetters vol 16 no 2 pp 93ndash95 2006

[7] A Boutejdar ldquoNew method to transform band-pass to low-pass filter using multilayer- and U-slotted ground structure-techniquerdquo Microwave and Optical Technology Letters vol 53no 10 pp 2427ndash2433 2011

[8] H Liu B Ren X Xiao Z Zhang S Li and S PengldquoHarmonic-rejection compact bandpass filter using defectedground structure for GPS applicationrdquo Active and PassiveElectronic Components vol 2014 Article ID 436964 4 pages2014

[9] M Challal A Boutejdar M Dehmas A Azrar and A OmarldquoCompact microstrip low-pass filter design with ultra-widereject band using a novel quarter-circle dgs shaperdquo AppliedComputational Electromagnetics Society Journal vol 27 no 10pp 808ndash815 2012

[10] A Boutejdar A Batmanov M H Awida E P Burte and AOmar ldquoDesign of a new bandpass filter with sharp transitionband using multilayer-technique and U-defected ground struc-turerdquo IET Microwaves Antennas and Propagation vol 4 no 9pp 1415ndash1420 2010

[11] G E Al-Omair S F Mahmoud and A S Al-Zayed ldquoLowpassand bandpass filter designs based on DGS with complementarysplit ring resonatorsrdquo Applied Computational ElectromagneticsSociety Journal vol 26 no 11 pp 907ndash914 2011

[12] Z Pan and J Wang ldquoDesign of the UWB bandpass filterby coupled microstrip lines with U-shaped defected groundstructurerdquo in Proceedings of the International Conference onMicrowave and Millimeter Wave Technology (ICMMT rsquo08) vol1 pp 329ndash332 April 2008

[13] A Boutejdar A B A Omar and E Burte ldquoLPF builds on quasi-yagi DGSrdquoMicrowaves amp RF vol 52 no 9 pp 72ndash77 2013

[14] M Al Sharkawy A Boutejdar F Alhefnawi and O LuxorldquoImprovement of compactness of lowpassbandpass filter usinga new electromagnetic coupled crescent defected ground struc-ture resonatorsrdquo Applied Computational Electromagnetics Soci-ety Journal vol 25 no 7 pp 570ndash577 2010

[15] H-H Xie Y-C Jiao B Wang and F-S Zhang ldquoDMS struc-tures stop band pass filter harmonicsrdquoMicrowaves and RF vol50 pp 72ndash76 2011

[16] J-K Xiao and W-J Zhu ldquoNew defected microstrip structurebandstop filterrdquo in Proceedings of the Electromagnetics ResearchSymposium pp 1471ndash1474 Suzhou China September 2011

[17] J-K Xiao and W-J Zhu ldquoNon-uniform defected microstripstructure lowpass filterrdquoMicrowave Journal vol 14 2012

[18] J-K Xiao X Xirsquoan and W-J Zhu ldquoNew bandstop filter usingsimple defected microstrip structurerdquo Microwave Journal vol11 2011

[19] AWR Corporation TX-LINE Transmission Line CalculatorAWR Corporation San Jose Claif USA 2015

[20] Microwave Office AWR httpwebawrcorpcom[21] Microwave Studio Software version 12 CST Corporation

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks




DGS-unit

DMS-unit

Substrate

microstrip line50Ω

Figure 1 Three-dimensional view of the DMS-unit and DGS cell

2 Characteristics and Modeling ofDMS Resonators

Top layer of Figure 1 shows the proposed DMS cell which iscomposed of wide and narrow etched sections in the feed lineplaced on the top layer The extremes of this resonator areconnected throughmicrostrip linewith SMAconnectorsThewidths of themicrostrip lines at port 1 and port 2 are designedto match the characteristic impedance of 50Ω The etchedsurface presents the capacitance while the arms correspondto the inductance The DMS cell acts as a band stop elementwith a resonance frequency of 48GHz and an insertionloss of minus05 dB as shown in Figure 4 The structure hasbeen designed on RO4003 substrate with a relative dielectricconstant 120576

119903= 338 and thicknesses ℎ = 0813mm and a loss

tangent of 00027 The equivalent circuit of the DMS cell actsas a parallel LC resonator as shown in Figure 2

The values 119877 119871 and 119862 of the circuit parameters canbe computed using result that is matched to the one-pole Butterworth-type low pass response [7] Furthermoreradiation effects are more or less neglected The reactancevalues of DMS and filter first order can be expressed as

119883LC = [1205960119862(1205960

120596minus120596

1205960

)]

minus1

(1)

The series inductance (reactance) of one-pole Butterworthlow pass filter can be derived as follows

119883119871= 120596119871 = 120596(

11989211198850

120596119892

) (2)

where 1205960 120596119892 1198850 and 119892

1are the resonant frequency

cutoff frequency the scaled characteristic impedance andprototype value of the Butterworth-type LPF respectivelyBy matching the two previous reactance values the parallel

XLC

Z0

Z0

C

R

L

PortP = 1Z =

PortP = 2Z = 50Ohm50Ohm

Figure 2 Equivalent circuit of the DMSDGS-unit

S21S11

EM simulationCircuit simulation

S-pa

ram

eter

s (dB

)

Frequency (GHz)

0

minus5

minus10

minus15

minus20

minus25

minus30

minus35

minus401086420

Figure 3 119878-parameters of the DMS-element and its equivalentcircuit

capacitance and the inductance of the equivalentDMS-circuitcan be derived using the following equations

119862 =120596119888

21198850(12059620minus 1205962119888)

119871 =1

12059620119862

119877 =21198850

radic1100381610038161003816100381611987811 (1205960)

10038161003816100381610038162

minus (21198850(1205960119862 minus 1120596

0119871))2

minus 1

(3)

The computed values of parameters 119862 119871 and 119877 are respec-tively 064 pF 173 nH and 742 kΩ The simulation results ofthe investigated EM structure and its corresponding circuitare illustrated in Figure 3 which shows identical values of 3dB cutoff frequency (119891

119888) and pole frequency (119891

119901) at 337GHz

and 483GHz respectively The transmit band shows aninsertion loss pass of 05 dB All dimensions of DMS-unit aredepicted in Table 1The proposed DMS resonator is shown inFigure 4




l

h

p

kg


r




119901= 096 pH

and 1198620= 332 pF







119862 =1

1198850119862120596119888

sin (120573119862119897119862) +

2

1198850119871120596119888

tan (120573119871119897119871) (4)

where1198850119862120573119862 119897119862 120573119871 and 119897



119897119862=120582119892119862

2120587sinminus1 (120596

1198881198850119871119862)

119882119862asymp 119891 (119885

0119862 120579 119905 ℎ 120576

119903)

(5)

where 119882119862 120582119892119862 120579 119905 ℎ and 120576




RR

CC

L LPortP = 1Z =

PortP = 2Z =

Cp CpC0

50Ohm 50Ohm


0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60

S11S21

(a)

0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60


(b)








ab

e

i

c


DMS-unit

Substrate

microstrip line50Ω




PortP = 1Z = 50Ohm


C C

L L

C1 C0 C2


S 11

andS 2

1(d

B)

minus10

0

minus20

minus30

minus40

minus50

minus60

minus700 2 4 6 8 10

Frequency (GHz)

S11S21






Substrate



c

Z

q

tds








0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50


S 11

andS 2

1(d

B)


(a)

(b)




(a)

(b)


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)







8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












l

h

p

kg


r




119901= 096 pH

and 1198620= 332 pF







119862 =1

1198850119862120596119888

sin (120573119862119897119862) +

2

1198850119871120596119888

tan (120573119871119897119871) (4)

where1198850119862120573119862 119897119862 120573119871 and 119897



119897119862=120582119892119862

2120587sinminus1 (120596

1198881198850119871119862)

119882119862asymp 119891 (119885

0119862 120579 119905 ℎ 120576

119903)

(5)

where 119882119862 120582119892119862 120579 119905 ℎ and 120576




RR

CC

L LPortP = 1Z =

PortP = 2Z =

Cp CpC0

50Ohm 50Ohm


0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60

S11S21

(a)

0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60


(b)








ab

e

i

c


DMS-unit

Substrate

microstrip line50Ω




PortP = 1Z = 50Ohm


C C

L L

C1 C0 C2


S 11

andS 2

1(d

B)

minus10

0

minus20

minus30

minus40

minus50

minus60

minus700 2 4 6 8 10

Frequency (GHz)

S11S21






Substrate



c

Z

q

tds








0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50


S 11

andS 2

1(d

B)


(a)

(b)




(a)

(b)


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)







8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










RR

CC

L LPortP = 1Z =

PortP = 2Z =

Cp CpC0

50Ohm 50Ohm


0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60

S11S21

(a)

0 2 4 6 8 10

Frequency (GHz)

S 11

andS 2

1(d

B)

0

minus10

minus20

minus30

minus40

minus50

minus60


(b)








ab

e

i

c


DMS-unit

Substrate

microstrip line50Ω




PortP = 1Z = 50Ohm


C C

L L

C1 C0 C2


S 11

andS 2

1(d

B)

minus10

0

minus20

minus30

minus40

minus50

minus60

minus700 2 4 6 8 10

Frequency (GHz)

S11S21






Substrate



c

Z

q

tds








0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50


S 11

andS 2

1(d

B)


(a)

(b)




(a)

(b)


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)







8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PortP = 1Z = 50Ohm


C C

L L

C1 C0 C2


S 11

andS 2

1(d

B)

minus10

0

minus20

minus30

minus40

minus50

minus60

minus700 2 4 6 8 10

Frequency (GHz)

S11S21






Substrate



c

Z

q

tds








0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50


S 11

andS 2

1(d

B)


(a)

(b)




(a)

(b)


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)







8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

minus10

0

minus20

minus30

minus40

minus50


S 11

andS 2

1(d

B)


(a)

(b)




(a)

(b)


0 1 2 3 4 5 6 7 8 9

Frequency (GHz)

0

minus10

minus20

minus30

minus40

minus50

S 11

andS 2

1(d

B)







8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











8 Conclusion




Acknowledgments


References























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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