New π–T generalised metamaterial negative refractive index transmission line for a compact...

$: New π–T generalised metamaterial negative refractive index transmission line for a compact coplanar waveguide triple band pass filter applications$
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Published in IET Microwaves, Antennas & PropagationReceived on 23rd June 2013Revised on 28th March 2014Accepted on 14th May 2014doi: 10.1049/iet-map.2013.0698

T Microw. Antennas Propag., 2014, Vol. 8, Iss. 13, pp. 1097–1104oi: 10.1049/iet-map.2013.0698

ISSN 1751-8725

New π–T generalisedmetamaterial negative refractiveindex transmission line for a compact coplanarwaveguide triple band pass filter applicationsMohammed A. Fouad, Mahmoud Abdelrahman Abdalla

Electromagnetic Fields Group, Electronic Engineering Department, MTC College, Cairo, Egypt

E-mail: [email protected]

Abstract: This study presents, for the first time, a novel π− T generalised negative refractive index (NRI) transmission line (TL)configuration. It is innovated for increasing the possible passbands in designing microwave components. It is proved that theproposed transmission line can introduce up to seven passbands for completely unbalanced transmission line condition. Thedetailed mathematical analysis of that configuration based on the periodic network analysis and equivalent circuit model isintroduced. As an application for the novel π− T generalised NRI TL configuration, a new compact triple band coplanarwaveguide (CPW) metamaterial filter is introduced. The proposed triple bands CPW filter design steps are introduced and itsperformance is validated using equivalent circuit model simulation, electromagnetic full wave simulation and experimentalmeasurements. Good agreements between the circuit modelling, electromagnetic full wave simulation and practicalmeasurement results are achieved. All the results confirm that the proposed filter has triple passbands from 900 to 960 MHz,1.4 to 1.48 GHz and 2.4 to 2.45 GHz. Moreover the filter size is compact whose length is only 12.1% lg at first passbands,18.2 lg% at second passbands and 31.7 lg% at third passbands.

1 Introduction

Metamaterials are artificial constructed periodic structureswhich are characterised with unusual electromagneticwave propagation properties. These structures are mainlysatisfying sub-wavelength dimensions condition. Indefinitions they can be called an effective media becauseof their equivalent medium permittivity and permeability.The type having simultaneous negative permittivity andpermeability is the most common metamaterials types. Itstheory has been predicted in 1960s by the Russianphysicist Viktor Veselago [1]. He pointed out that suchmedium can have negative refractive index (NRI) (n).Hence, the propagated electric field (E), magnetic field(H) components and wave number vector (K) form aleft-handed triplet. In the beginning of the 2000s, thismedium has been realised practically in three-dimensional(3D) configurations [2]. However, this configuration isbulky and resonant narrow band. Hence, it has been laterfabricated in different planar configurations. In 2002, thetransmission line (TL) approach for realising this mediumwas presented by loading a transmission line periodicallywith series capacitor and shunt inductor [3, 4]. Such TLhas been called an NRI TL [5] or a composite right–left-handed (CLRH) TL [6]. These TLs have demonstratedvery novel electromagnetic properties such as anti-parallelphase and group velocities, non-linear phase dispersionproperties. Hence they have been applied in differentcompact and multi-band RF components such as

resonators [7, 8], filters [8–10], couplers [11, 12], powerdividers [13] and antennas [14–18].The need in RF systems for multi-band components has

encouraged the researchers for more and deep developmentsin planar metamaterial structures. As a consequence, CRLHTL has been modified as extended CRLH TL [19] and alsothe NRI TL has been modified to generalised NRI TL [20]and its π version [21]. They have been claimed that thesecan introduce up to quad different passbands, and hencefew researches have been started to design multi-bandcomponents making use of such new left-handed propertiessuch as dual coupled line coupler [21], dual band pass filter[22, 23] and quad power divider [24].Most of these components were realised in microstrip

configurations. However, realising simple series and shuntconnections in coplanar waveguides (CPWs) structuresmakes them attractive in designing microwave componentsbased on CRLH TL and of course the G-NRI TL. Inaddition, more operating bands are still a challenge forresearchers.In this paper, we introduce a new modified configuration

for the generalised NRI TL named as a π–T generalisedmetamaterial NRI transmission line (π–T G-metamaterialNRI TL). In this context, the π generalised NRI TL isinvestigated to prove it can introduce five passbands TL[25] not only four as claimed in [21]. In addition, our newπ–T G-metamaterial NRI TL was analysed and proven tointroduce up to seven passbands. Such new left handed(LH) TL can be applied in designing multi-band microwave

1097& The Institution of Engineering and Technology 2014

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components with up to seven different passbands dependingon the application. As an application of our novel LH TLconfiguration, a new compact and triple passbands filter isintroduced. The design relation between the triple passbandfilter and the seven passband TL is explained. The tripleband filter was designed to cover the frequencies from 900to 960 MHz, 1.4 to 1.48 GHz and 2.4 to 2.45 GHz. Thedetailed design procedures, electromagnetic full wavesimulation and experimental measurements of the proposedtriple passbands filter are introduced.
2 Theory

In this section, we introduce our new proposed modificationof the generalised NRI TL. In our paper, the generalised πversion of G-NRI TL has been analysed and proven that itcan introduce up to five different passbands for completelyunbalanced TL condition. Next, our proposed modificationis introduced and explained in details. This will prove thatour new modification can introduce up to seven passbands.In the next sections, we point out this modificationproperties using the theoretical analysis and the equivalentcircuit model.

2.1 Generalised NRI TL theory

The generalised NRI TL equivalent circuit is shown in Fig. 1a[19]. The electromagnetic wave propagation through this TLcan be explained by applying the periodic analysis ofmicrowave structures [26] and extracting the dispersion forthe propagation phase constant (β) over a periodic distance

Fig. 1 Circuit model of

a Conventional G-NRI TLb π G-NRI TL


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(d ) using the ABCD matrix of Fig. 1b as

cos bd = (1+ ZBYB) (1)

where

ZB = ZS + 1/YS (2)

ZS = JvLS + 1/JvCS (3)

Ys = JvCSH + 1/JvLSH (4)

YB = YSH + 1/ZSH (5)

YSH = JvCHH + 1/JvLHH (6)

ZSH = JvLHS + 1/JvCHS (7)

The possible passbands for the G-NRI TL can bedemonstrated by plotting the dispersion diagram, using (1).On the other hand, we can solve (1) mathematically for thesame purpose by expressing it as

0 = M + ZBYB (8)

where M is a constant whose value can be specified to thefollowing criteria:

† M = 1; it indicates the centre frequencies of the passbands(which is corresponding to βd = π/2).† M = 0 or 2; it indicates the two cut off frequencies of thepassbands (it is corresponding to βd = 0 or π).

The dispersion equation in (1) is fourth order, and hencesuch TL can demonstrate four possible passbands [20].However, the propagation within these passbands isdependent on the Bloch impedance at each band and howmuch it is matched with the input impedance.The π configuration of G-NRI TL is as illustrated in

Fig. 1b. The dispersion equation can be also obtained usingperiodic analysis of the equivalent circuit in Fig. 1b.Accordingly, we have deduced the dispersion equation fromthe ABCD matrix of Fig. 3 as

cosbd = 1+ ZY + ZSY + ZSZaddsY2( )

(9)

where

Z = ZS + ZaddS (10)

ZS = JvLS + 1/JvCS (11)

Zadds = 1/ JvCSH + 1

JvLSH

( )(12)

Y = YSH + 1/ZSH (13)

ZSH = JvLHS + 1/JvCHS (14)

YSH = JvCHH + 1/JvLHH (15)

To identify the possible number of passbands of π G-NRI TL,we can solve the dispersion equation in (9) as follows

0 = M + ZY + ZSY + ZSZaddsY2 (16)

T Microw. Antennas Propag., 2014, Vol. 8, Iss. 13, pp. 1097–1104doi: 10.1049/iet-map.2013.0698

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where M is the same conditioned constant used in (8). As aresult of such dispersion equation investigation, we canconfirm that there are five possible passbands, In otherwords, the π G-NRI TL configuration has succeeded inadding one extra passband compared with conventionalgeneralised NRI TL in Fig 1a.It is worth to mention that the frequencies associated with
these bands are completely controlled with the lumpedcomponent values. To illustrate our idea, we have solved(16) for M = 1, assuming the loading elements as Cs = 0.48pF, Ls = 2.45 nH, Lsh = 10 nH, Csh = 0.3405 pF, Lhs = 5.1nH, Chs = 0.06 pF, Lhh = 20 nH and Chh = 0.2104 pF. Thefive frequency solutions of (16) are f1 = 1.68 GHz, f2 = 2.4GHz, f3 = 6 GHz, f4 = 9.65 GHz and f5 = 10.6 GHz. Moreinvestigations can be extracted using the dispersion diagramof the equivalent circuit model in Fig. 1b. This has beenobtained by plotting (16) as shown in Fig. 2a. As shown inthe figure, we can note five passbands. The first bandextends from 1.26 to 2.05 GHz and is an LH passband. The

Fig. 2 Five passbands

a Dispersion diagram for the circuit model of the five passbands π G-NRI TLb Simulated transmission coefficient (magnitude and phase) of the generalisedπ NRI metamaterial TL using circuit model

IET Microw. Antennas Propag., 2014, Vol. 8, Iss. 13, pp. 1097–1104doi: 10.1049/iet-map.2013.0698

second band extends from 2.15 to 2.59 GHz and is an RHpassband. The third band extends from 5.8 to 7.2 GHz andis an RH passband. The fourth band extends from 9.42 to9.5 GHz and is an LH passband. The fifth band extendsfrom 10.4 to 11.4 GHz and is an RH passband.For further confirmation of the calculated results, the

equivalent circuit, shown in Fig. 1b, was simulated usingthe equivalent circuit modelling. The commercial software(advanced design system (ADS)) was employed in thesimulation. However, we should know that the simulatedstructure is not an infinite structure as periodic structuresanalysis requires. In other words, it is expected that the TLillustrates the five passbands, but the 90° phase shiftcondition may change a little bit compared with idealperiodic structure requirement. The simulatedscattering-parameter magnitudes and phase of transmissioncoefficient (S21) were extracted and plotted as shown inFig. 2b. During the simulation, the terminals were assumedto be matched to 50 Ω. As shown in the figure, there arequite clear five passbands whose centre frequencies havescattering transmission coefficient (S21) magnitudeapproaching the 0 dB level, approximately. The centrefrequencies for the five passbands are 1.29, 2.02, 6.28, 9.49and 11.3 GHz. As predicted, the condition of the (π/2) forthe five passbands is satisfied at 1.48, 2.5, 6.65, 9.46 and10.86 GHz. We can see that the frequencies shift is verysmall. Hence, we can confirm the validation of theanalytical five passbands by the circuit simulation results.From the results comparison in Figs. 2a and b, we can

claim the good agreements between the circuit modellingand analytical results. In other words, the π generalised NRITL configuration is capable of introducing dual left-handedbands and triple right-handed bands.

2.2 New modified π− T generalised NRI TL

Based on our analysis for the π G-NRI TL and its increase ofits possible passbands, we have suggested a new modificationfor the generalised NRI-TL for the sake of increasing thepossible passbands. The proposed new TL configurationcan introduce up to seven passbands. The equivalent circuitof the proposed new TL configuration is shown in Fig. 3a.The added modification in the new TL configuration can beexplained as replacing the series impedance (Zadds) inFig. 1b with a T section formed as shown in Fig. 3a.Therefore the idea of the new configuration is to introduce acombined π− T G-NRI TL.For the sake of explaining the performance of the new

π− T NRI TL configuration, the middle T loaded sectioncan be replaced with its equivalent π model as shown inFig. 3b. Hence, the total equivalent circuit is illustrated inFig. 3c which is similar to the previously explained as πG-NRI TL in Fig. 1b. However, comparing this equivalentcircuit model in Fig. 3c to that introduced in Fig. 1b, weobserve that two equal shunt impedances (Zaddsh) have beenadded at the centre of the new π− T G-NRI TL. This newconfiguration changes the shunt admittance (Y ) defined in(3) to include a new term (1/Zaddsh). This new added termincreases the order of loaded elements, and hence adds onemore degree of freedom. Therefore it is expected that thenew configuration would introduce higher passbands.Thanks to this T–π conversion, the analysis of the proposednew configuration, shown in Fig. 3a, can be done based onits equivalent model in Fig. 3c. Thus, the dispersionequation for our new proposed πT-G-NRI TL can beobtained using the periodic network analysis as in (16).


Fig. 3 Equivalent circuit of the proposed new TL configuration

a Equivalent circuit model of the proposed new seven order π− T G-NRI TLb Equivalent T– π section transformationc π.format of the proposed π− T G-NRI TL

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However, in (16), the definition of the shunt loading elementsY used in (13) will be replaced to be as in (17). This can bewritten as

Y = YSH + 1/ZSH + 1/Zaddsh (17)

where the definition of new added impedance (Zaddsh), andsimilarly the expression for the series impedance (Zadds),can be extracted from the π to T conversion as

Zaddsh = (2× (YSH1 + 1/ZSH1))+ 1/YS( )

(18)

Zadds = 2/YSH1( )+ 1/YS

( )2× YSH1 + 1/ZSH1( )( )

(19)

where

ZSH1 = JvLHS1 + 1/JvCHS1 (20)

YSH1 = JvCHH1 + 1/JvLHH1 (21)

On the other hand, the employed definitions in (16) for ZS,ZSH and YSH are still as given in (11), (14) and (15),respectively.The analysis of the new dispersion equation for our new

π− T G-NRI TL can be solved for the value of the constantM = 1. In this case, it can be proven that we have aseventh-order equation. In other words, our new modifiedconfiguration can introduce seven resonance frequencies


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associated with (βd = π/2). To confirm our idea, thedispersion equation in (16) has been solved for M = 1 andassuming the following lumped component values Cs =0.45 pF, Ls = 2.49 nH, Lsh = 0.95 nH, Csh = 0.5 pF, Lhs =7.98 nH, Chs = 0.42 pF, Lhh = 12.5 nH and Chh = 0.03 pF,Lhs1 = 6 nH, Chs1 = 0.079 pF, Lhh1 = 4.92 nH and Chh1 =0.214 pF. The solutions for (16) introduces seven differentfrequencies which are f1 = 1.885 GHz, f2 = 2.578 GHz, f3 =3.63 GHz, f4 = 5.92 GHz, f5 = 7.74 GHz, f6 = 8.34 GHz andf7 = 12.2 GHz. These frequencies should represent the centrefrequency of the passbands introduced as a consequence ofour new modified G-NRI TL.A deep investigation for our proposed new π− T G-NRI

TL configuration, for the same aforementioned lumpedvalues, its dispersion diagram has been plotted, employing(16), in Fig. 4a. In addition, the circuit model in Fig. 3ahas been simulated using ADS and magnitude and phase ofscattering-parameter magnitudes has been extracted asshown in Fig. 4b. From observation in Fig. 4a, it is quiteclear that our new configuration has seven passbands. Thefirst band extends from 1.76 to 2.03 GHz and it is an LHpassband. The second band extends from 2.56 to 2.59 GHzand it is an RH passband. The third band extends from 3.44to 4.05 GHz and it is an RH passband. The fourth bandextends from 5.55 to 6.11 GHz and it is an LH passband.The fifth band extends from 7.72 to 7.81 GHz and it is anRH passband. The sixth passbands extends from 8.05 to9.3 GHz and it is LH passband. The seventh passbandsextends from 9.8 to 13.5 GHz and it is an RH passband. Inother words, we can claim that our new combined π− T


Fig. 4 Dispersion diagram

a Dispersion diagram for the proposed new seven passband new π− T G-NRITLb Simulated transmission coefficient (magnitude and phase) of the proposednew seven passbands new π− T G-NRI TL circuit model

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G-NRI TL configuration has added new LH and RHpassbands compared with the π G-NRI TL.In addition, the simulated circuit model results in Fig. 4b

confirm the seven passbands centre frequencies at 1.79,2.57, 3.94, 6.05, 8.05, 9.28 and 13.1 GHz. It can be notedthat the magnitude of the transmission coefficient is ∼0 dBat these frequencies. The frequencies of 90° phase shift of(S21) for the seven passbands are 1.88, 2.58, 3.63, 5.93,7.75, 8.33 and 12.1 GHz, respectively. As explained before,the slight variation in the phase results is because of thesimplification of the periodic analysis that should be appliedfor infinite periodic structures.

Fig. 5 General triple passband filter design curves employing oneunit cell of the new π–T G-NRI TL

a Filter dispersion diagram for indicating the passbands cut off frequenciesb Designed filter transmission coefficients at the three bands

3 Tri-band pass filter

In this section, we introduce a new compact tri passbandCPW filter based on our new π− T G-NRI TLconfiguration. The proposed filter has been designed so thatit operates in the low-frequency applications; hence thefilter compactness becomes very obvious. The first band iscentred at 930 MHz with 900–960 MHz bandwidth, second


passband is centred at 1.44 GHz with bandwidth from 1.4–1.48 GHz and third band is centred at 2.43 GHz with itsbandwidth ranging from 2.4 to 2.45 GHz. These threebands were selected as three different examples such asGSM, universal mobile telecommunication system andradio frequency identification applications. The proposeddetailed filter design procedures and its structure analysisare introduced. Next the filter performance has beenvalidated using both circuit, full wave simulations andconfirmed by practical measurements.

3.1 Design producers

As mentioned above, the proposed filter has been designed todemonstrate triple passbands based on the new π− T G-NRITL model. The filter design specification is based onachieving triple band filter with centre frequencies ( f01 =0.93 GHz, f02 = 1.44 GHz and f03 = 2.43 GHz). The filtershould have 3 dB insertion loss at the two cut offfrequencies ( fc1 = 0.9 GHz and fc2 = 0.96 GHz) for the firstpassband, ( fc3 = 1.4 GHz and fc4 = 1.48 GHz) for thesecond passband and ( fc5 = 2.4 GHz and fc6 = 2.45 GHz) forthe third passband. In addition, the filter should demonstratea minimum attenuation = 15 dB before the first band ( fa1 =0.88 GHz), the middle frequencies separating the bands( fa2 = 1.16 GHz, fa3 = 2 GHz), and after the third passband( fa4 = 2.55 GHz).The general dispersion diagram for such triple passband

filter employing one unit cell of the new π–T G-NRI TLindicating the passbands cut off frequencies is shown inFig. 5a. In addition, this general design amplituderequirement for the filter insertion loss is explained inFig. 5b for general design frequencies.The design of the proposed triple band pass filter was

achieved in two different steps for initial design and further


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final design. The first design step was employing the imagemethod to determine the cut off frequencies of the threepassbands. The specific 3 dB cut off frequencies and the 15dB attenuation frequencies are re-calculated using theinsertion loss method in the second design step. This stepwas considered as a fine tuning of the pre-calculatedlumped component values from image method.
3.1.1 Cut off frequencies design using imagemethod: The initial design for the loading/ parasiticinductor and capacitor values was specified by adjusting thecut off frequencies of the proposed triple passband filter tothe limits of the dispersion equation of the new π–T G-NRITL in (9). There are six cut off frequencies for threepassbands named as ( fc1, fc2, fc3, fc4, fc5, fc6). Three of themare corresponding to βd = zero and the others arecorresponding to βd = π as illustrated in (22) and (23)

cos b d fc2, fc3,fc6

∣∣∣ = 1 (22)

cos b d fc1, fc4,fc5

∣∣∣ = −1 (23)

By using a one unit cell in Fig. 3 for designing such filter, wehave to design 12 different lumped components, whereassolutions of (22) and (23) are only possible for sixvariables. Hence, in order to solve them, we had to assumesix variables. To achieve compact filter size, we selectedthree of these variables as (Cs, Csh and Lsh). The otherselected elements are the parasitic CPW elements (Ls, Chh

and Chh1). Although the selection is arbitrary, but we haveselected the first three elements (Cs, Csh and Lsh) for filtercompactness as we will be explained in next section. Onthe other hand, the three parasitic elements were selectedbased on the CPW transmission line section which theybelong to. In more details, the shunt capacitance (CHH) isthe parasitic capacitance of the CPW section whose lengthis specified by the series capacitor (Cs). Similarly, CHH1 isthe patristic shunt capacitance of the CPW section formedby series capacitor and inductor (Csh and Lsh). Finally, Ls isthe overall of these two CPW sections parasitic seriesinductance. Equations (22) and (23) have been solvednumerically, and the solution values for the elements havebeen set as initial values for the second step of the design.

3.1.2 Passband slope cut off frequencies designusing insertion loss method: The second step was thedesign of the passband shape, 3 dB bandwidth and the 15dB filter attenuation frequencies. This was fulfilled based onthe insertion loss method. This is can be understood fromFig. 5b where we adjusted

(S21)∣∣ ∣∣

fc1, fc2, fc3, fc4, fc5, fc6

= 2

A+ B/Z0( )+ C × Z0 + D

∣∣∣∣∣∣∣∣∣∣ = 0.707 (24)

(S21)∣∣ ∣∣

fa2, fa3, fa4= 2

A+ B/Z0( )+ C × Z0 + D

∣∣∣∣∣∣∣∣∣∣

= 0.1778 (25)

where A, B, C and D are the elements of the filter ABCDmatrix.It is worth to mention that the frequency fa1 should lie in

the start-up of the first LH passband which has a high slop


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in NRI TL. Therefore we omitted the design constraint atthis frequency and made use of this degree of freedom forthe filter compactness. Therefore we solved (24) and (25)for nine elements values and accordingly, we have selectedthree elements and not to design them. These elements wereselected as (Cs), (Csh) and (Lsh). In addition, the reasonbehind these three elements selection is because of thefabrication miniaturisation since (Cs) was chosen to beimplemented as interdigital capacitor, whereas (Csh) and(Lsh) were chosen to be implemented using the meanderline. Hence, we can control their size and hence confirm thefilter size requirements since these three elements are thebiggest size elements. Equations (24) and (25) were solvednumerically where the initial values in the solvingalgorithm were adjusted using the pre-calculated valuesfrom initial design step employing the image method.It is worth to mention that based on the above design steps

and given that we designed the proposed triple passband filteras a narrow passband, we can control the filter amplitudewithin the passband without extra design equations.However, for wide band filters, we can zoom in thepassbands by designing the three passbands by adding threemore equations for insertion loss value at the filter centrefrequency. For example, for zero insertion loss at centrefrequencies, this can be adjusted as

(S21)∣∣ ∣∣

f01, f02, f03= 2

A+ B/Z0( )+ C × Z0 + D

∣∣∣∣∣∣∣∣∣∣ = 1 (26)

It is worth to mention that the proposed filter is based on usingthe new π− T G-NRI TL which, as proved, is capable ofintroducing up seven passbands controlled by 12 loading/parasitic elements. However, in case of the proposed filterapplication it is only triple band. This is since not only thefilter passbands cut off frequencies are designed, but alsothe centre frequencies and the attenuation level within thestopband. That means that the maximum designable filterbased on the new π− T G-NRI TL is triple or quad bandpass filter. In our paper, for the sake of compactness, wedesigned the filter to be triple band and hence we hadsolved nine non-linear equations for nine unknown elements.Finally, the obtained designed values have been optimised

using circuit modelling based on two considerations, first toachieve the wanted filter specification illustrated at thebeginning of this section and second the ability to realise.The final lumped values are examined using circuitmodelling, full wave simulation and experimentalmeasurements as will be explained in Sections 2 and 3.

3.2 Structure and analysis

The final optimised loading and the patristic elements are Cs

= 0.815 pF, Ls = 3 nH, Lsh = 2.37 nH, Csh = 0.506 pF, Lhs =0.504 nH, Chs = 2.04 pF, Lhh = 5.1 nH, Chh = 3.9 pF, Lhs1 =1.27 nH, Chs1 = 0.937 pF, Lhh1 = 3.72 nH and Chh1 = 3 pFand the filter is realised as follows.The structure of the proposed triple passbands filter has

been created based on the equivalent circuit in Fig. 3a. Theproposed filter has been employed using only one unit cellfor the sake of compactness demonstration. The proposedtriple passbands filter was realised in CPW configurations.The filter was designed using Roger RT6010 substrate withdielectric constant, εr = 10.2 and thickness, h = 0.625 mm.The 2D layout of the proposed filter is shown in Fig. 6. As

shown in the figure, the series interdigital capacitor (CS) is six


Fig. 6 Design producers

a Circuit layout of the proposed tri-band CPW π− T generalised NRI filterb Fabricated tri-band CPW π− T generalised NRI filter

Fig. 7 Simulated scattering-parameter magnitudes for circuitmodel and HFSS results for the tri-band π− T generalised NRI filter

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fingers with length = 2.9 mm. The first and last shuntbranches are symmetric and formed by the interdigitalcapacitor have ten fingers of length = 2.8 mm and connectedto the CPW ground through a strip inductor of length = 0.8mm. The two grounded shunt strip inductors are identical oflength = 4.3 mm. The series branch of the T section wasrealised using a centred shunt strip of length = 2.9 mm, twomeandered line of ten arms and width = 2 mm. The shuntbranch of the T section was realised using ten fingersinterdigital capacitor of length = 1.2 mm and connected tothe ground through a strip inductor of length = 1.4 mm. Allthe gaps and widths of employed transmission lines are 0.2mm. Two 50 Ω feeding CPW transmission lines of length =3 mm are connected at both ends of the filter. The feedingtransmission line was tapered starting from the filter to 50 Ωwidth to enhance the matching.The values of the lumped elements are realised by

equations of interdigital capacitor, metal-strip inductor andmeandered line inductor explained in [27, 28]. Thefabricated filter prototype is shown in Fig. 6b. The filterwas fabricated using wet etching employing the lithographictechnology. The proposed tri-band filter compactness isobvious whose size is only 19.6 × 20 mm2. The designprocedures will be explained in the next filter.

Fig. 8 Comparison of the measured and simulated filterscattering-parameter magnitudes

a HFSS simulated and measured scattering-parameter magnitudes of theproposed tri-band π− T generalised NRI filterb HFSS simulated and measured transmission coefficient phase of theproposed tri-band π− T generalised NRI filter

3.3 Design results and discussion

In this section, we introduce the validation of thepre-designed filter. The performance of the proposed triplebands filter has been checked first by both circuitmodelling, electromagnetic full wave simulations. Theelectromagnetic full wave simulation has been done usingthe finite elements method. The commercial softwareANSYS-high-frequency structure simulator (HFSS) wasemployed. The comparison of the circuit modelling and fullwave simulation results are introduced in Fig. 7. As shownin the figure, there is a slight shift in bands between the tworesults. The shift is about 50 MHz in the first and secondbands and 100 MHz in the third band, but it can be saidthat both results confirm first passband at 900–960 MHz,second passband at 1.4–1.48 GHz and third passband at2.4–2.45 GHz. In the circuit model simulation results, theinsertion loss is close to 0.2 dB at the three band centrefrequencies (930 MHz, 1.45 GHz and 2.43 GHz). On theother hand, the HFSS simulated results approximately agreewith the circuit model in the three band centre frequencies.However, its insertion loss is higher than the circuit model.Within the stopbands between the triple bands, the filter


attenuation (|S21|) is better than 15 dB (for both circuit andsimulated) as pre-designed. The stopband before and afterthe first and triple bands has high attenuation in bothsimulation results (better than 30 dB). The reflectioncoefficient within the passband is lower than 10 dB in allpassbands as a good measure of filter matching.The proposed filter design was further verified using

experimental measurements. A comparison of the measuredand simulated filter scattering-parameter magnitudes isshown in Fig. 8a. It is clear that there is a reasonable goodagreement between the two results. The insertion loss is ∼2dB in the first and third band centre frequencies and 0.5 dBat the second band. The measured attenuation within thestopbands is slightly higher than the simulated one, but it is


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better than 11 dB in the first stop band and 14 dB in thesecond stopband. In addition, the measured reflectioncoefficient is better than 10 dB with slightly shift in firstand third bands compared with simulation results.For further confirmation of the filter design performance, a
comparison of the measured and simulated phase of thetransmission coefficient (S21) is shown in Fig. 8b. We canobserve a good agreement with the phase and the scatteringparameters for each simulated and measurement phases.However, the slight variation between the simulated and themeasurement phases as the slight frequency shift betweenthe simulated and the measured scattering parameters.Therefore, from Figs. 7, 8a and b, we can claim that the

proposed filter design has a good agreement between circuitmodelling, electromagnetic full wave simulations andexperimental measurements results. In summary, we canclaim that the agreement between all introduced resultsconfirm the design methodology for the proposed compactsize tri passband CPW filter based on our new π− T G-NRITL configuration.

4 Conclusion

A novel π− T generalised NRI TL has been introduced. Thenew configuration can introduce up to seven differentpassbands for completely unbalanced TL condition. Thedetailed mathematical analysis of the new configurationbased on the periodic network analysis and equivalentcircuit model has been introduced. Good agreementsbetween the two analyses are achieved. As an application, anew compact tri passband CPW filter has been introduced.The filter performance has been validated usingmathematical analysis, circuit model simulations, full wavesimulations and practical measurements. The resultsdemonstrate average 1 dB insertion loss within thepassbands, 13 dB attenuation between the passbands andbetter than 11 dB return loss at the three passbands centrefrequencies. The attenuation can be enhanced using morethan one cell of the proposed π− T G_NRI TL at theexpense of the filter size. The introduced filter length isonly 12.1% lg at first passband, 18.2%lg at secondpassband and 31.7% lg at third passband.

5 References

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