In this paper, compact microwave components, including a Wilkinson power divider and a 3 dB branch-line coupler based onartificial transmission lines (ATLs) with harmonic suppression, are presented. A section ATL is consisted of microstripstepped impedance transmission lines and a microstrip interdigital capacitor. To achieve a compact size, the steppedimpedance transmission lines are folded into a right-angled triangle shape. For the ATL, the interdigital capacitor is usedto suppress harmonics. By employing two sections of 70.7Ω ATLs with a right-angled triangle shape to replaceconventional transmission lines, the proposed power divider working at 0.9GHz achieves a size miniaturization with the58.8% area of a conventional case. In addition, the power divider has good harmonic suppression performance. In thedesign of a branch-line coupler, two pairs of ATLs with 50Ω and 35.4Ω are utilized. For 50Ω ATLs, the ATLs aredesigned to a right-angled triangle shape. Meanwhile, to obtain a more compact size, these 35.4Ω ATLs are modified toan isosceles trapezoid shape. The proposed branch-line coupler operating at 0.9 GHz accounts for merely 33.4% of acoupler adopting conventional microstrip transmission lines. Moreover, the harmonics of a branch-line coupler aresuppressed effectively as well. Finally, measured results of the proposed Wilkinson power divider and branch-line couplerdisplay good performance and agree with their simulated results well.
1. Introduction
The rapid development of the modern communicationsystem makes a high requirement for size miniaturizationof microwave components [1–3]. At present, size minia-turization methods of microwave components includeloading lumped elements [4], using right/left-handedtransmission lines [5], employing a defected ground struc-ture (DGS) [6], utilizing a microstrip electromagneticbandgap (EBG) [7], and applying slow-wave transmissionlines with inductive and capacitive loading [8]. In theseminiaturization methods, using artificial transmission lines(ATLs) is a good solution due to a flexible design and easyfabrication on a printed circuit broad. Besides, harmonicsuppression can improve the signal-to-noise ratio of thecommunication system, which is also a hot research spotfor microwave components. To achieve harmonic suppres-sion, these methods are proved to be effective, such asusing an ultra-wideband band-stop filter [9], an
electromagnetic bandgap [10], open stubs [11], a defectedground structure [12], and inductively loaded slow-wavetransmission lines [13].
The Wilkinson power divider, which works as adivider and combiner of power, is extensively used in afeed network for an antenna [14]. The conventional Wil-kinson power divider consists of two sections of 70.7Ωquarter-wavelength transmission lines and an insolationresistor. Therefore, the size of the Wilkinson power divideris mainly determined by the size of quarter-wavelengthtransmission lines at operating frequency, which resultsin a large occupied area, especially when operating atlow frequency. Besides, the conventional Wilkinson powerdivider realized by microstrip lines cannot suppressharmonics. Therefore, some miniaturization methods ofWilkinson power dividers are reported, such as using shortcircuited half-wavelength and quarter-wavelength resona-tors [15], loading coupled resonator topology [16], utiliz-ing topology consisted of half-wavelength resonators and
HindawiInternational Journal of Antennas and PropagationVolume 2019, Article ID 4923964, 16 pageshttps://doi.org/10.1155/2019/4923964
quarter-wavelength resonators [17], and using open dual-transmission line stub and L-type artificial lowpass transmis-sion line structures [18]. These power dividers mentionedabove not only have an obvious reduced size but also have agood harmonic suppression performance. In [15], harmonicsuppression is realized by using lowpass filters. In [16], anet-type resonator is designed to obtain rejection ofharmonic responses. In [17], the mixed electric and magneticcoupling and cross-coupling between three quarter-wavelength resonators generate three transmission zeroes tosuppress harmonics. In [18], open dual-transmission linestub, L-type artificial lowpass transmission lines, open stub,and extension line modules are designed to suppress har-monics. These power dividers mentioned above can achievea compact size and good harmonic suppression, but -15 dBbandwidths of these cases are narrow, which are, respectively,only 2.4%, 4.5%, 6.5%, and 21.1%.
A branch-line coupler is another important microwavecomponent used in a modern communication system.However, the conventional 3 dB branch-line coupler is alsoconfronted with the problem of a large occupied areabrought in by two pairs of quarter-wavelength transmissionlines with 50Ω and 35.4Ω. In order to reduce the size, somesolutions are reported, such as loading a π-equivalent artifi-cial transmission line [19], using asymmetrical T-structures[20], utilizing high-impedance transmission lines and inter-digitated shunt capacitors [21], applying artificial transmis-sion line combined with meandered lines and resonators[22], and employing transmission lines loaded resonators[23]. However, only the couplers in [21–23] can realize har-monic suppression. In [21], the second-order harmonic issuppressed to 20 dB by using interdigitated shunt capaci-tors. In [22], shunt LC resonators generate suppression forhigh-frequency harmonics, but a second-order harmonicand third-order harmonic cannot be suppressed. In [23],harmonics are suppressed due to the transmission zeros ofresonators. In addition, these cases in [19, 21] are realizedwith size reduction, but 15 dB bandwidths are only 8.9%and 7.2%. These methods are difficult to achieve a reducedsize, good bandwidth, and harmonic suppression at thesame time.
In this paper, a method of using ATLs for size minia-turization and harmonic suppression employed on theWilkinson power divider and 3dB branch-line coupler ispresented. These ATLs consist of stepped impedancetransmission lines and interdigital capacitors. In the designof ATLs, these stepped impedance lines are folded into aright-angled triangle shape or isosceles trapezoid shapefor a more compact size. Then, the interdigital capacitorplays a function of harmonic suppression. Finally, the pro-posed Wilkinson power divider and branch-line couplerhave similar bandwidths of 58.2% and 17% compared withconventional components, while a compact size and har-monic suppression are realized at the same time.
2. Theoretical Analysis of an ATL
2.1. Design Concepts. As shown in Figure 1(a), a section ofthe 70.7Ω ATL with a right-angled triangle shape is
composed of five sections of microstrip low-impedancetransmission lines and six sections of microstrip high-impedance transmission lines. Additionally, there are twosections of uniform transmission lines connected to ports.The low-impedance lines and high-impedance lines arecascaded alternately and then folded into a right-angledtriangle shape for a compact size. Meanwhile, an interdigi-tal capacitor is placed in the middle of an ATL to suppressharmonics. The equivalent circuit of the 70.7Ω ATL isgiven by Figure 1(b). Each uniform transmission line con-nected to a port can be equivalent to a series inductor Las1and a shunt capacitor Cas1 to ground. Correspondingly,the high-impedance lines can be equivalent to seriesinductors Las2, Las3, and Las4, and these low-impedancelines work as equivalent shunt capacitors Cas2, Cas3, andCas4 to ground. The interdigital capacitor is placedbetween several high-impedance lines and between low-impedance lines, so it can be equivalent to several seriescapacitors in parallel and parasitic capacitors to ground.For the sake of simplicity, as marked in Figure 1(a), themicrostrip interdigital capacitor is divided into two parts asinterdigital A1 and interdigital A2 and then be equivalentto series capacitors Cap1 and Cap2. Besides, the shunt capaci-tors Ca11, Ca12, Ca21, and Ca22 represent parasitic capacitorsof the interdigital capacitor.
For the equivalent circuit of the 70.7Ω ATL, the totalinductance of equivalent series inductors can be repre-sented by Lt1, and the total capacitance of equivalentshunt capacitors can be presented by Ct1. And they canbe given by
In the design of the 3 dB branch-line coupler, 50Ωand 35.4Ω ATL are designed. For a 50Ω ATL, the layoutand its equivalent circuit are given by Figure 2. It hassimilar layout and equivalent circuit as a 70.7Ω ATL.The total inductance Lt2 of equivalent series inductorsand total capacitance Ct2 of equivalent shunt capacitorsare calculated by
The layout and equivalent circuit of the 35.4Ω ATLare shown in Figure 3. The 35.4Ω ATLs are modified toan isosceles trapezoid shape to realize a more compact sizefor the branch-line coupler. Referring to its layout, the35.4Ω ATL is comprised of three sections of low-impedance transmission lines and four sections of high-impedance transmission lines. The two transmission linesconnected to ports can be equivalent to series inductorLcs1 and shunt capacitor Ccs1 to ground. In order toanalyze the interdigital capacitor more accurately, the
2 International Journal of Antennas and Propagation
interdigital capacitor is divided into two parts. As markedin Figure 3(a), interdigital capacitor C1 and interdigitalcapacitor C2 can be equivalent to series capacitors Ccp1
and Ccp2 and parasitic capacitors Cc11, Cc12, Cc21, andCc22 to ground. The total series inductance Lt3 and totalshunt capacitance Ct3 are given by
Port2Port1
Wa2
Wa3
Wa4
Wa7
Wa6
La4
La3
La2Wa5
Section A4
Section A3
Section A2
Section A1
Interdigital capacitor A2
La1
La5
Wa1
La6
Interdigital capacitor A1
(a)
Cas1
Las1Cas1
Las1
Cas2Cas2
Cas3Cas3
Cap2
Cap1
Las4Las4
Cas4
Las2
Las3
Las2
Las3Ca11Ca12
Ca21Ca22
Section A4
Section A2
Section A1
Interdigitalcapacitor A1
Interdigitalcapacitor A2
Section A3
Port1 Port2
(b)
Figure 1: A section of 70.7Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
Interdigitalcapacitor B1Interdigital
capacitor B2
Section B
Lb3 Wb4
Wb3
Wb7
Wb8
Wb5
Lb4
Lb2Wb6
Port2Port1Wb1
Wb2Lb5Lb1
(a)
Cbs1 Cbs1Lbs1Lbs1
Cbs2
Cbs3 Cbs3
Cbp1
Lbs4Lbs4
Cbs4
Lbs2Lbs2
Lbs3Lbs3 Cb11Cb12
Cb21Cb22
Cbp2
Lbs5 Lbs5
Cbs2
Interdigitalcapacitor B1
Interdigitalcapacitor B2
Section B
Port1 Port2
(b)
Figure 2: A section of 50Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
Port2Port1
Wc3
Wc8
Wc4
Wc7
Lc3Lc2
Wc6
Lc1
Lc4
Wc2
Wc1
Interdigitalcapacitor C1
Interdigitalcapacitor C2Section C
Wc5
(a)
Lcs5
Lcs4Ccs3
Lcs3Ccs2
Lcs1
Lcs2
Ccs1 Ccs1Lcs1
Lcs2Cc21 Cc22
Ccp2
Cc11Cc12Ccp1
Lcs5
Ccs4
Lcs4Ccs3
Lcs3 Interdigitalcapacitor C1
Interdigitalcapacitor C2
Section C
Port1 Port2
Ccs2
(b)
Figure 3: A section of 35.4Ω ATL with an isosceles trapezoid shape: (a) layout and (b) equivalent circuit.
3International Journal of Antennas and Propagation
According to the uniform transmission line theory,characteristic impedance Zi (i = 1,2,3) and phase propaga-tion constant βi (i = 1,2,3) of per unit length are deter-mined by Zi = Li/Ci and βi = ω Li ⋅ Ci, where Li andCi are the inductance and capacitance per unit lengthalong the transmission line and ω represents the operatingangular frequency. For ununiform transmission lines suchas ATLs, when the physical length of the ATL is less thanone-eighth of a guided wavelength, the ununiform trans-mission lines can approximate to uniform transmission lines[24]. Then, for the ATL, Lti = Lili and Cti = Cili, where Lti andCti are the total series inductance and shunt capacitance andli is the physical length of a unit ATL. The characteristicimpedance Zi and electrical length θi of a unit of an ATLcan be calculated as
Zi =LiCi
= LtiCti
, 4
θi = βili = ω Li ⋅ Cili = ω Lti ⋅ Cti 5
From formulas (4) and (5), we can find, for a unit ATLwith the same length, if Lti and Cti increase proportionally,that Zi would remain unchanged, while the electrical lengthθi would increase. In turn, with a given characteristic imped-ance Zi and electrical length θi of a unit of an ATL, when Liand Ci are increased proportionally, characteristic imped-ance Zi would be unchanged, while phase propagation con-stant βi of per unit length would be increased, so therequired physical length li is significantly reduced.
For stepped impedance transmission lines, using thelines with high characteristic impedance is equivalent toloading more inductance per unit length, while employingthe lines with low characteristic impedance is equivalent toloading more capacitance per unit length than conven-tional microstrip transmission lines. In the design of anATL, stepped impedance transmission lines folded into aright-angled triangle shape would add more capacitanceand inductance for per physical length, so the requiredphysical length can be further reduced. In a practicaldesign, the 35.4Ω ATL is modified to an isosceles trape-zoid shape to realize a more compact size of a branch-line coupler.
Owing to the impedance invariance of half wavelengths,conventional transmission lines including stepped imped-ance transmission lines have many harmonic pass-bands atmultiples of central frequency. In order to suppress har-monics effectively, a microstrip interdigital capacitor is usedin the ATL, which is equivalent to several series capacitors.These series capacitors are shunted with inductors, formingLC parallel-resonant circuits, as shown in Figures 1(b),2(b), and 3(b). According to the stopband characteristic ofLC parallel-resonant circuits at resonant frequency, these
high-order harmonics at multiples of central frequency willbe suppressed effectively by this way. Besides, the perfor-mance of harmonic suppression can be changed by chang-ing the number and size of an interdigital capacitor’sfingers. Finally, in order to realize a more compact struc-ture of the proposed components using ATLs, eachquarter-wavelength line is replaced by one unit ATL with90°, though the optimum number of ATL units is provedto be two in [8, 13].
Based on the above analysis, taking the ATL with therequired 70.7Ω characteristic impedance and 90° electriclength as an illustration, the design procedure of ATL canbe described as follows:
Step 1. Based on the layout of an ATL just like that inFigure 1(a), create a rough model of an ATL inthe software of IE3D. Obviously, the physicaldimensions of each section in the model as shownin Figure 4 are arbitrary.
Step 2. The ATL is simulated by software of IE3D. Thevalue of characteristic impedance Z1 can beobtained by simulation directly, and electriclength θ1 can be got by simulated Ang(S21).
Step 3. Compare the simulated characteristic impedanceand electric length with the required goals. Whenrequired goals are not achieved, then, accordingto equations (4) and (5), decide the value of Lt1and Ct1 should be increased or reduced.
In tuning of characteristic impedance Z1, when the sim-ulated characteristic impedance Z1 is lower than 70.7Ω,according to equation (4), we can increase total inductanceLt1 or reduce total capacitance Ct1. When the simulated char-acteristic impedance Z1 is higher than 70.7Ω, we can reducetotal inductance Lt1 or increase total capacitance Ct1.
In tuning of electric length θ1, when electric length θ1 issmaller than 90°, according to equation (5), we can increasetotal inductance Lt1 or total capacitance Ct1. When simulatedelectric length θ1 is larger than 90
°, we can reduce total induc-tance Lt1 or total capacitance Ct1.
According to equation (1), changing the total inductanceLt1 or total capacitance Ct1 can be realized by changing theinductance and capacitance of each related section. For exam-ple, extending line length or reducing line width of these high-impedance lines can increase inductance of Las2, Las3, and Las4,and reducing the area of low-impedance lines can reducecapacitance of Cas2, Cas3, and Cas4 as shown in Figure 1(b).
So tuning physical dimensions of each section can changetotal inductance Lt1 and total capacitance Ct1, to obtain thedesigned 70.7Ω and 90°.
Step 4. Tune fingers of interdigital capacitors to adjust theperformance of harmonic suppression, includingfrequency of transmission zero and range ofstopband.
Step 5. To obtain equivalent inductance and capacitance ofATL to verify our design, with designated 70.7Ω
4 International Journal of Antennas and Propagation
Las1
Cas1
Port Port
Port Port
(a)
Las2
Cas2
Port
Port
Port
Port
(b)
Port
Port
Port
Port
Las3
Cas3
(c)
Port PortLas4
Cas4
Las4
Port Port
(d)
Figure 4: Continued.
5International Journal of Antennas and Propagation
characteristic impedance and 90° electric length, weuse formulas (4) and (5) to obtain Lt1 and Ct1.
Step 6. Each section as shown in Figure 4 is simulated bythe simulation software of IE3D and converted toL-, T-, or π-equivalent circuit. And then parame-ter extraction of equivalent elements is based onimpedance or admittance matrices.
2.2. Parameter Extraction. The process of parameter extrac-tion is similar for the ATL of 70.7Ω, 50Ω, and 35.4Ω, sowe take the 70.7Ω ATL as an example to analyze. In orderto analyze the equivalent circuit of the 70.7Ω ATL easily,the ATL is divided into several sections, as shown inFigure 1. Each section and their equivalent circuit are givenin Figure 4. Obviously, a more accurate equivalent circuitcan be achieved by dividing the ATL into more sections whenanalyzing the ATL. To extract the equivalent element valuesof each section, full-wave simulation software IE3D is appliedto calculate impedance or admittance matrices from the cor-responding equivalent circuits of each section.
The admittance matrix of the equivalent circuit for sec-tion A1 in Figure 4(a) is expressed as
YA111 YA1
12
YA121 YA1
22=
−j
ωLas1
jωLas1
jωLas1
jωCas1 −j
ωLas1
6
From the formula above, the equivalent value of elementscan be obtained by
Las1 =1
2πf 0 Im YA112
,
Cas1 =Im YA1
22 + Im YA121
2πf0
7
Due to similar L-type circuit, the equivalent value of ele-ments in Figures 4(b) and 4(c) can be readily calculated basedon the admittance matrix by the same way.
For section A4 in Figure 4(d), its impedance matrix canbe given by
ZA411 ZA4
12
ZA421 ZA4
22=
jωLas4 −j
ωCas4−
jωCas4
−j
ωCas4jωL −
jωCas4
8
Then, the value of equivalent elements can be calculatedas
Las4 =Im ZA4
11 − Im ZA412
2πf0,
Cas4 = −1
2πf0 Im ZA412
9
For interdigital capacitor Aj (j = 1, 2) as shown inFigure 4(e), its admittance matrix can be expressed by
Port Port
Port Port
Caj1 Caj2
Capj
(j=1,2)
(e)
Figure 4: Each section of the 70.7Ω ATL and their equivalent circuit: (a) section A1, (b) section A2, (c) section A3, (d) section A4, and (e)interdigital capacitor Aj (j = 1, 2).
6 International Journal of Antennas and Propagation
Y int j11 Y int j
12
Y int j21 Y int j
22
=jωCaj1 + jωCapj −jωCapj
−jωCapj jωCaj2 + jωCap j
10
Then, the equivalent capacitance value can be calculatedby
Capj =Im Y int j
12
2πf0,
Caj1 =Im Y int j
11 + Im Y int j12
2πf0,
Caj2 =Im Y int j
22 + Im Y int j12
2πf0
11
All values of equivalent elements as marked inFigures 1(b), 2(b), and 3(b) are given in Table 1.
The final optimized size of ATLs used in the proposedWilkinson power divider and branch-line coupler are listedin Table 2 as marked in Figures 1(a), 2(a), and 3(a). Thephysical lengths of the 70.7Ω, 50Ω, and 35.4Ω ATLs are0.098λg, 0.104λg, and 0.124λg, respectively.
2.3. Harmonic Suppression. For the proposed ATLs, the inter-digital capacitors can play a role of harmonic suppression.For the interdigital capacitors, the performance of harmonicsuppression is mainly determined by the number, length,width of finger, and gap width between fingers [24]. In orderto realize the compact size and easy fabrication, the gap widthbetween fingers is chosen to be 0.2mm. Then, other factorsaffecting harmonic suppression would be discussed.
Taking the 70.7Ω ATL mentioned above as an example,the interdigital capacitors have 19 fingers and the lengthLa6 = 5 2mm and width Wa6 = 0 2mm as marked inFigure 1(a). The 70.7Ω ATLs with different fingers’ num-bers, lengths, and widths of interdigital capacitors aresimulated.
When the fingers’ number of interdigital capacitorschanges, while their length La6 = 5 2mm and width Wa6 =0 2mm remain unchanged, the simulated S21 are shownin Figure 5(a). It can be observed that when the fingers’ num-ber is reduced, the frequency of transmission zero in stop-band becomes higher. In addition, compared to the ATLwithout interdigital capacitors, the ATL with interdigitalcapacitors has obvious harmonic suppression. The influenceof fingers’ length on harmonic suppression is given inFigure 5(b).When the number of fingers equals to 19 and fin-gers’ width Wa6 = 0 2mm, it can be seen that the frequencyof transmission zero becomes higher as fingers’ length isshortened. Figure 5(c) reveals that the frequency of transmis-sion zero varies as fingers’ width Wa6 changes when theinterdigital capacitors have 7 fingers with 5.2mm length.When fingers’ width increases, the frequency of transmissionzero would be lower slightly.
The result of such simulations is because the reductionof fingers’ number, length, and width would reduce thecapacitance of Cap1 and Cap2. The reduced capacitance ofCap1 and Cap2 would make the resonant frequency of theparallel resonant circuit higher, which is composed ofCap1, Cap2, and Las4. And the resonant frequency is the fre-quency of transmission zero in a stopband, so the har-monic suppression is affected.
2.4. Propagation Characteristics. All of these proposed ATLsare designed to operate at 0.9GHz and with 90° phase delay.The layout of ATLs are simulated by the electromagneticsimulation solver of IE3D, while their corresponding equiva-lent lumped circuits as given in Figures 1(b), 2(b) and 3(b)are simulated by software of ADS. The comparisons of simu-lated S-parameters between the layout and equivalentlumped circuit are given in Figure 6. Additionally, when the70.7Ω, 50Ω and 35.4Ω ATLs are simulated, the referenceimpedances of the ports are set to 70.7Ω, 50Ω, and 35.4Ω,respectively.
As shown in Figure 6(a), for the 70.7Ω ATL, the sim-ulated S-parameters show that it has a 152.2% bandwidthof 0.9GHz, from 0GHz to 1.37GHz. At 0.9GHz, thereturn loss is 45.63 dB while insertion loss is less than
7International Journal of Antennas and Propagation
0.1 dB. Moreover, harmonic suppression performance isalso shown in Figure 6(a). For the second-order harmonicfrequency at 1.8GHz, S21 is -10.66 dB, while for thethird-order harmonic frequency at 2.7GHz, S21 is-17.71 dB. For these harmonic frequencies, there are nopass-bands.
For 50Ω ATL as shown in Figure 6(b), the layout simula-tion displays a 170% bandwidth of 0.9GHz, from 0GHz to
1.53GHz. At 0.9GHz, the ATL achieves 39.56 dB return lossand insertion loss less than 0.1 dB. Moreover, its harmonicsuppression performance is verified by 12.5 dB harmonicsuppression at the third-order harmonic frequency at2.7GHz.
For the 35.4Ω ATL as exhibited in Figure 6(c), it has a161.1% bandwidth of 0.9GHz, from 0GHz to 1.45GHz.When operating at 0.9GHz, 52.7 dB return loss and less than
Figure 5: Harmonic suppression of the 70.7Ω ATL: (a) different number, (b) different length, and (c) different width.
8 International Journal of Antennas and Propagation
0.1 dB insertion loss are realized. For the 35.4Ω ATL, thethird-order harmonic is suppressed to 26.63 dB, which dis-plays good harmonic suppression performance.
The simulated characteristic impedance and phase delayare exhibited in Figures 7 and 8. For the 70.7Ω ATL, at0.9GHz, the real part of characteristic impedance is 70.7Ωand the imaginary part is 0.42Ω, while the simulated resultsof the equivalent circuit are 70.93Ω and 2.08Ω. For the 50ΩATL, the 50.0Ω real part and -0.56Ω imaginary part of char-acteristic impedance can be obtained, while the results ofequivalent circuit simulation are 50.5Ω and -0.1Ω. For the35.4Ω ATL, the real part of characteristic impedance is35.4Ω and the imaginary part is 0.24Ω, while the correspond-ing results of the equivalent circuit are 35.85Ω and -0.15Ω.
Figure 8 indicates that the 70.7Ω ATL has 90.0° phasedelay at 0.9GHz while 90.13° for the equivalent circuit. The50Ω ATL has 90.0° phase delay at 0.9GHz while 91.52° forthe equivalent circuit. The 35.4Ω ATL has 90.1° phase delayand 91.15° for the equivalent circuit.
From the analysis above, these proposed ATLs not onlyhave the similar performance like conventional transmissionlines within the bandwidth but also have effective suppres-sion ability for the harmonics. For the ATLs, the simulatedS-parameters of the layout agree well with that of the lumpedequivalent circuit at low frequency. However, at high fre-quency, there is a deviation of insertion losses, due to theequivalent circuit of the interdigital capacitor. In addition,the precision of the equivalent circuit would be improvedby dividing the interdigital capacitor into more numbers ofequivalent series capacitors. The simulation comparisonsbetween the layout and lumped model indicate the accuracyof extracting parameters of the equivalent circuit.
3. Circuit Design and Measurements
The proposedWilkinson power divider and branch-line cou-pler are designed to operate at 0.9GHz. Simulations are per-formed by a full-wave EM simulation software of IE3D. The
|S11| of 35.4 Ω ATL by EM solver|S21| of 35.4 Ω ATL by EM solver|S11| of 35.4 Ω ATL by lumped model|S21| of 35.4 Ω ATL by lumped model
(c)
Figure 6: Simulated S-parameter of the proposed ATLs: (a) 70.7Ω, (b) 50Ω, and (c) 35.4Ω.
9International Journal of Antennas and Propagation
proposed Wilkinson power divider and branch-line couplerare fabricated on a substrate of F4B with 1mm thicknessand relative permittivity εr = 2 65 and loss tangent δ = 0 005.Measurements are carried out on an Agilent 8510C networkanalyzer.
3.1. Wilkinson Power Divider. The layout of proposedWilkinson power divider is given by Figure 9(a). The
proposed Wilkinson power divider consists of two sectionsof 70.7Ω ATLs employed to replace these conventionalquarter-wavelength transmission lines. And a chip resistorof 100Ω (type: 0805) is used in the design. The photographof the fabricated Wilkinson power divider is shown inFigure 9(b). The proposed Wilkinson power divider occupiesa size of 29 9mm × 34 7mm, that is 0 13λg × 0 16λg, whereλg is the guided wavelength on the substrate at 0.9GHz.
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.120
40
50
60
70
80
90
100
110
120
Re(Zc) of 70.7 Ω ATL by EM solver Im(Zc) of 70.7 Ω ATL by EM solverRe(Zc) of 50 Ω ATL by EM solver Im(Zc) of 50 Ω ATL by EM solverRe(Zc) of 35.4 Ω ATL by EM solver Im(Zc) of 35.4 Ω ATL by EM solver Re(Zc) of 70.7 Ω ATL by lumped model Im(Zc) of 70.7 Ω ATL by lumped model Re(Zc) of 50 Ω ATL by lumped model Im(Zc) of 50 Ω ATL by lumped model Re(Zc) of 35.4 Ω ATL by lumped model Im(Zc) of 35.4 Ω ATL by lumped model
Frequency (GHz)
Re (Z
c)
−30
−25
−20
−15
−10
−5
0
5
Im (Z
c)
Figure 7: Simulated characteristic impedance of the proposed ATLs.
0.0 0.2 0.4 0.6 0.8 1.0 1.2
−120
−100
−80
−60
−40
−20
0
Phas
e del
ay (d
eg)
Frequency (GHz)Ang (S21) of 70.7Ω ATL by EM solverAng (S21) of 50Ω ATL by EM solverAng (S21) of 35.4Ω ATL by EM solverAng (S21) of 70.7Ω ATL by lumped modelAng (S21) of 50Ω ATL by lumped modelAng (S21) of 35.4Ω ATL by lumped model
Figure 8: Simulated phase delay of the proposed ATLs.
10 International Journal of Antennas and Propagation
Comparing to a power divider implemented by conventionalmicrostrip lines, the fabricated power divider only occupies a58.8% size.
Figure 10 shows the simulated and measured ∣S11∣, ∣S21∣,and ∣S31∣ of the proposed Wilkinson power divider. The sim-ulated and measured S-parameters indicate that the mea-sured results have a good agreement with simulated results.For simulation, the central frequency is 0.9GHz while mea-surements exhibit the central frequency of 0.91GHz. Thereexists a frequency deviation of 0.01GHz for central frequencydue to fabrication tolerance and measurement devices. Then,the fabricated Wilkinson power divider for 0.91GHz has abandwidth of 58.2% for S11 less than -15 dB, from0.61GHz to 1.14GHz, and the return loss at 0.91GHz is32.12 dB. At 0.91GHz, measured S21 is -3.13 dB and S31is -3.26 dB. In addition, as shown in Figure 10, the fabricatedWilkinson power divider has 12.5 dB suppression for thesecond-order harmonic of 1.82GHz and 24.7 dB suppressionfor the third-order harmonic of 2.73GHz.
Figure 11 shows isolation and phase difference (Ang(S21)-Ang(S31)). Measured results display at 0.91GHz that thepower divider has a 32.8 dB isolation, which reveals goodisolation performance between output port 2 and port 3.Besides, there is only a 0.23° phase difference between twooutput port 2 and port 3 at 0.91GHz.
Figure 12 gives the comparison of S-parameters betweenthe proposedWilkinson power divider and conventional caseoperating at 0.9GHz, which obviously indicates that theharmonic is effectively suppressed in the stopband in theproposed structure. Meanwhile, a similar bandwidth per-formance as that of the conventional case is achievedwhen size miniaturization is realized.
Finally, the performance comparisons of this proposedpower divider (this work) with several previous designs are
listed in Table 3. It indicates the proposed Wilkinson powerdivider in this work has similar electrical performance asthe conventional case and good harmonic suppression butwith a small size. Especially, the relative bandwidth is similarto the conventional one.
3.2. Branch-Line Coupler. In the design of the proposed 3 dBbranch-line coupler as shown in Figure 13(a), two sections of50Ω ATLs and two sections of 35.4Ω ATLs are employedto replace these corresponding conventional quarter-wavelength transmission lines. The two sections of 50ΩATLs are designed to be with a right-angled triangle
29.9 mm
2.7 mm
70.7 Ω 90°
2.7 mm 34.7 mmPort1
Port2
Port3
100 Ω
16.7 mm
70.7 Ω 90°
5 mm
(a) (b)
Figure 9: The proposed Wilkinson power divider: (a) layout and (b) photo.
Figure 10: Simulated and measured S11 , S21 , and S31 of theproposed Wilkinson power divider.
11International Journal of Antennas and Propagation
shape, while the two sections of 35.4Ω ATLs are modifiedto an isosceles trapezoid shape in order to realize a morecompact size. All of these ATLs are combined into a
compact rectangle shape. The photograph of the fabricated3 dB branch-line coupler is given in Figure 13(b). The sizeof the fabricated branch-line coupler is 45 2mm × 32 8
0 1 2 3 4 5−50
−40
−30
−20
−10
0
S-Pa
ram
eter
(dB)
Frequency(GHz)
|S11| of proposed design
|S21| of proposed design
|S31| of proposed design
|S11| of conventional design
|S21| of conventional design
|S31| of conventional design
Figure 12: Comparison of simulated S-parameters between the proposed and conventional Wilkinson power divider.
[26] 2.4 0 17λg × 0 1λg 69 50 3.4, 3.5 33 No suppression No suppression
This work 0.91 0 13λg × 0 16λg 58.2 32.12 3.13, 3.26 32.8 12.5 24.7
λg: guided wavelength at central frequency.
12 International Journal of Antennas and Propagation
mm, that is 0 2λg × 0 15λg, where λg is the guided wave-length on the substrate at 0.9GHz. The size of the pro-posed branch-line coupler is effectively reduced to a33.4% area of a conventional one at 0.9GHz.
Figure 14 shows the simulated and measured S11 , S21 ,and S31 of the proposed coupler. The S-parameters reveala good agreement between simulated and measured results.As observed in Figure 14, the central frequency is 0.9GHzat simulation while the central frequency is 0.91GHz atmeasurement. A frequency deviation of 0.01GHz existsbetween simulation and measurement because of fabrica-tion tolerance and measurement devices. For measuredresults, at a central frequency of 0.91GHz, it has a 17%bandwidth with S11 less than -15 dB, from 0.84GHz to0.99GHz. At 0.91GHz, the return loss is 29.35 dB, whichshows its good impedance match with ports. And at0.91GHz, S21 and S31 are -3.2 dB and -3.15 dB,
respectively. In Figure 15, S41 and phase differencebetween the two output ports are given. At 0.91GHz,measured S41 is -26.3 dB. The phase difference(Ang(S21)-Ang(S31)) is 90.6°, while the 90° ± 1° bandwidthis 34MHz, from 881MHz to 915MHz.
In addition, at the second-order harmonic frequency of1.82GHz, S11 is -1.26 dB, S21 is -12.6 dB, and S31 is-11.1 dB. At the third-order harmonic frequency of2.73GHz, S11 is -0.34 dB, S21 is -29.5 dB, S31 is -33.9 dB.It is demonstrated that at the second-order and third-orderharmonic frequencies, there are no pass-bands. So harmonicsuppression performance is verified. As a comparison, S-parameters of the conventional branch-line coupler aregiven in Figure 16. By observation, the bandwidth of the pro-posed branch-coupler is comparable to that of the conven-tional one, while these harmonic pass-bands at harmonicfrequencies are effectively suppressed.
Figure 14: Simulated and measured S11 , S21 , and S31 of the proposed branch-line coupler.
Port4Isolated
35.4 Ω 90°Inputport1
Throughport2
32.8 mm
2.7mmport3
Coupled
5 mm
35.4 Ω 90°
50 Ω 90°
50 Ω
45.2 mm
90°
(a) (b)
Figure 13: The proposed 3 dB branch-line coupler: (a) layout and (b) photo.
13International Journal of Antennas and Propagation
Table 4 shows the performance comparisons of the pro-posed branch-line coupler (this work) and several previousdesigns. The performance comparisons reveal that the
proposed branch-line coupler has similar bandwidth, inser-tion loss, and isolation with other designs, but betterharmonic suppression with a miniaturized size.
14 International Journal of Antennas and Propagation
4. Conclusion
In this paper, a compact Wilkinson power divider and a com-pact 3 dB branch-line coupler with harmonic suppressionperformance based on artificial transmission lines are pro-posed. These ATLs consist of stepped impedance transmis-sion lines and interdigital capacitors. In order to reduce thesize, these ATLs are folded into a right-angled triangle shape,and especially, the 35.4Ω ATLs employed in the branch-linecoupler are modified to an isosceles trapezoid shape. Then,the feasibility of the proposed power divider and branch-line coupler design are demonstrated, and the simulatedand the measured results are in good agreement. The pro-posed Wilkinson power divider realizes the 58.8% occupiedarea of the conventional case and good harmonic suppres-sion performance. The occupied area of the proposedbranch-line coupler is reduced to 33.4% of the conventionalcase. At the same time, good harmonic suppression perfor-mance is demonstrated. Both proposed components havesimilar bandwidth as the conventional design but with com-pact size and good harmonic suppression. The proposedWilkinson power divider and branch-line coupler can beextensively used in the modern communication system.
Data Availability
All data included in this study are available from the corre-sponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
This work was supported by the Chongqing ResearchProgram of Basic Research and Frontier Technology(cstc2017jcyjAX0128), the Chongqing Postgraduate Innova-tive Research Project (CYS18243), and the National NaturalScience Foundation of China (61401054).
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