# Compact Microwave Components with Harmonic Suppression Based on Artificial Transmission Lines

Authors: Wen Huang; Jia Li; Ping Li; Xi Guo
Journal: International Journal of Antennas and Propagation
 (2019)

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## Abstract

In this paper, compact microwave components, including a Wilkinson power divider and a 3 dB branch-line coupler based on artificial transmission lines (ATLs) with harmonic suppression, are presented. A section ATL is consisted of microstrip stepped impedance transmission lines and a microstrip interdigital capacitor. To achieve a compact size, the stepped impedance transmission lines are folded into a right-angled triangle shape. For the ATL, the interdigital capacitor is used to suppress harmonics. By employing two sections of 70.7 Ω ATLs with a right-angled triangle shape to replace conventional transmission lines, the proposed power divider working at 0.9 GHz achieves a size miniaturization with the 58.8% area of a conventional case. In addition, the power divider has good harmonic suppression performance. In the design of a branch-line coupler, two pairs of ATLs with 50 Ω and 35.4 Ω are utilized. For 50 Ω ATLs, the ATLs are designed to a right-angled triangle shape. Meanwhile, to obtain a more compact size, these 35.4 Ω ATLs are modified to an isosceles trapezoid shape. The proposed branch-line coupler operating at 0.9 GHz accounts for merely 33.4% of a coupler adopting conventional microstrip transmission lines. Moreover, the harmonics of a branch-line coupler are suppressed effectively as well. Finally, measured results of the proposed Wilkinson power divider and branch-line coupler display good performance and agree with their simulated results well.


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## Body

## 1. Introduction

The rapid development of the modern communication system makes a high requirement for size miniaturization of microwave components [1–3]. At present, size miniaturization methods of microwave components include loading lumped elements [4], using right/left-handed transmission lines [5], employing a defected ground structure (DGS) [6], utilizing a microstrip electromagnetic bandgap (EBG) [7], and applying slow-wave transmission lines with inductive and capacitive loading [8]. In these miniaturization methods, using artificial transmission lines (ATLs) is a good solution due to a flexible design and easy fabrication on a printed circuit broad. Besides, harmonic suppression can improve the signal-to-noise ratio of the communication system, which is also a hot research spot for microwave components. To achieve harmonic suppression, these methods are proved to be effective, such as using an ultra-wideband band-stop filter [9], an electromagnetic bandgap [10], open stubs [11], a defected ground structure [12], and inductively loaded slow-wave transmission lines [13].The Wilkinson power divider, which works as a divider and combiner of power, is extensively used in a feed network for an antenna [14]. The conventional Wilkinson power divider consists of two sections of 70.7 Ω quarter-wavelength transmission lines and an insolation resistor. Therefore, the size of the Wilkinson power divider is mainly determined by the size of quarter-wavelength transmission lines at operating frequency, which results in a large occupied area, especially when operating at low frequency. Besides, the conventional Wilkinson power divider realized by microstrip lines cannot suppress harmonics. Therefore, some miniaturization methods of Wilkinson power dividers are reported, such as using short circuited half-wavelength and quarter-wavelength resonators [15], loading coupled resonator topology [16], utilizing topology consisted of half-wavelength resonators and quarter-wavelength resonators [17], and using open dual-transmission line stub and L-type artificial lowpass transmission line structures [18]. These power dividers mentioned above not only have an obvious reduced size but also have a good harmonic suppression performance. In [15], harmonic suppression is realized by using lowpass filters. In [16], a net-type resonator is designed to obtain rejection of harmonic responses. In [17], the mixed electric and magnetic coupling and cross-coupling between three quarter-wavelength resonators generate three transmission zeroes to suppress harmonics. In [18], open dual-transmission line stub, L-type artificial lowpass transmission lines, open stub, and extension line modules are designed to suppress harmonics. These power dividers mentioned above can achieve a compact size and good harmonic suppression, but -15 dB bandwidths 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 microwave component used in a modern communication system. However, the conventional 3 dB branch-line coupler is also confronted with the problem of a large occupied area brought in by two pairs of quarter-wavelength transmission lines with 50 Ω and 35.4 Ω. In order to reduce the size, some solutions are reported, such as loading aπ-equivalent artificial transmission line [19], using asymmetrical T-structures [20], utilizing high-impedance transmission lines and interdigitated shunt capacitors [21], applying artificial transmission line combined with meandered lines and resonators [22], and employing transmission lines loaded resonators [23]. However, only the couplers in [21–23] can realize harmonic suppression. In [21], the second-order harmonic is suppressed to 20 dB by using interdigitated shunt capacitors. In [22], shunt LC resonators generate suppression for high-frequency harmonics, but a second-order harmonic and third-order harmonic cannot be suppressed. In [23], harmonics are suppressed due to the transmission zeros of resonators. In addition, these cases in [19, 21] are realized with size reduction, but 15 dB bandwidths are only 8.9% and 7.2%. These methods are difficult to achieve a reduced size, good bandwidth, and harmonic suppression at the same time.In this paper, a method of using ATLs for size miniaturization and harmonic suppression employed on the Wilkinson power divider and 3 dB branch-line coupler is presented. These ATLs consist of stepped impedance transmission lines and interdigital capacitors. In the design of ATLs, these stepped impedance lines are folded into a right-angled triangle shape or isosceles trapezoid shape for a more compact size. Then, the interdigital capacitor plays a function of harmonic suppression. Finally, the proposed Wilkinson power divider and branch-line coupler have similar bandwidths of 58.2% and 17% compared with conventional components, while a compact size and harmonic suppression are realized at the same time.


## 2. Theoretical Analysis of an ATL

### 2.1. Design Concepts

As shown in Figure1(a), a section of the 70.7 Ω ATL with a right-angled triangle shape is composed of five sections of microstrip low-impedance transmission lines and six sections of microstrip high-impedance transmission lines. Additionally, there are two sections of uniform transmission lines connected to ports. The low-impedance lines and high-impedance lines are cascaded alternately and then folded into a right-angled triangle shape for a compact size. Meanwhile, an interdigital capacitor is placed in the middle of an ATL to suppress harmonics. The equivalent circuit of the 70.7 Ω ATL is given by Figure 1(b). Each uniform transmission line connected to a port can be equivalent to a series inductor Las1 and a shunt capacitor Cas1 to ground. Correspondingly, the high-impedance lines can be equivalent to series inductors Las2, Las3, and Las4, and these low-impedance lines work as equivalent shunt capacitors Cas2, Cas3, and Cas4 to ground. The interdigital capacitor is placed between several high-impedance lines and between low-impedance lines, so it can be equivalent to several series capacitors in parallel and parasitic capacitors to ground. For the sake of simplicity, as marked in Figure 1(a), the microstrip interdigital capacitor is divided into two parts as interdigital A1 and interdigital A2 and then be equivalent to series capacitors Cap1 and Cap2. Besides, the shunt capacitors Ca11, Ca12, Ca21, and Ca22 represent parasitic capacitors of the interdigital capacitor.Figure 1
A section of 70.7 Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
(a)
(b)For the equivalent circuit of the 70.7 Ω ATL, the total inductance of equivalent series inductors can be represented byLt1, and the total capacitance of equivalent shunt capacitors can be presented by Ct1. And they can be given by
(1)Lt1=2Las1+2Las2+2Las3+2Las4,Ct1=2Cas1+2Cas2+2Cas3+Cas4+Ca11+Ca12+Ca21+Ca22.In the design of the 3 dB branch-line coupler, 50 Ω and 35.4 Ω ATL are designed. For a 50 Ω ATL, the layout and its equivalent circuit are given by Figure2. It has similar layout and equivalent circuit as a 70.7 Ω ATL. The total inductance Lt2 of equivalent series inductors and total capacitance Ct2 of equivalent shunt capacitors are calculated by
(2)Lt2=2Lbs1+2Lbs2+2Lbs3+2Lbs4+2Lbs5,Ct2=2Cbs1+2Cbs2+2Cbs3+Cbs4+Cb11+Cb12+Cb21+Cb22.Figure 2
A section of 50 Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
(a)
(b)The layout and equivalent circuit of the 35.4 Ω ATL are shown in Figure3. The 35.4 Ω ATLs are modified to an isosceles trapezoid shape to realize a more compact size for the branch-line coupler. Referring to its layout, the 35.4 Ω ATL is comprised of three sections of low-impedance transmission lines and four sections of high-impedance transmission lines. The two transmission lines connected to ports can be equivalent to series inductor Lcs1 and shunt capacitor Ccs1 to ground. In order to analyze the interdigital capacitor more accurately, the interdigital capacitor is divided into two parts. As marked in Figure 3(a), interdigital capacitor C1 and interdigital capacitor C2 can be equivalent to series capacitors Ccp1 and Ccp2 and parasitic capacitors Cc11, Cc12, Cc21, and Cc22 to ground. The total series inductance Lt3 and total shunt capacitance Ct3 are given by
(3)Lt3=2Lcs1+2Lcs2+2Lcs3+2Lcs4+2Lcs5,Ct3=2Ccs1+2Ccs2+2Ccs3+Ccs4+Cc11+Cc12+Cc21+Cc22.Figure 3
A section of 35.4 Ω ATL with an isosceles trapezoid shape: (a) layout and (b) equivalent circuit.
(a)
(b)According to the uniform transmission line theory, characteristic impedanceZi (i=1,2,3) and phase propagation constant βi (i=1,2,3) of per unit length are determined by Zi=Li/Ci and βi=ωLi⋅Ci, where Li and Ci are the inductance and capacitance per unit length along the transmission line and ω represents the operating angular frequency. For ununiform transmission lines such as ATLs, when the physical length of the ATL is less than one-eighth of a guided wavelength, the ununiform transmission lines can approximate to uniform transmission lines [24]. Then, for the ATL, Lti=Lili and Cti=Cili, where Lti and Cti are the total series inductance and shunt capacitance and li is the physical length of a unit ATL. The characteristic impedance Zi and electrical length θi of a unit of an ATL can be calculated as
(4)Zi=LiCi=LtiCti,(5)θi=βili=ωLi⋅Cili=ωLti⋅Cti.From formulas (4) and (5), we can find, for a unit ATL with the same length, if Lti and Cti increase proportionally, that Zi would remain unchanged, while the electrical length θi would increase. In turn, with a given characteristic impedance Zi and electrical length θi of a unit of an ATL, when Li and Ci are increased proportionally, characteristic impedance Zi would be unchanged, while phase propagation constant βi of per unit length would be increased, so the required physical length li is significantly reduced.For stepped impedance transmission lines, using the lines with high characteristic impedance is equivalent to loading more inductance per unit length, while employing the lines with low characteristic impedance is equivalent to loading more capacitance per unit length than conventional microstrip transmission lines. In the design of an ATL, stepped impedance transmission lines folded into a right-angled triangle shape would add more capacitance and inductance for per physical length, so the required physical length can be further reduced. In a practical design, the 35.4 Ω ATL is modified to an isosceles trapezoid 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 impedance transmission lines have many harmonic pass-bands at multiples of central frequency. In order to suppress harmonics effectively, a microstrip interdigital capacitor is used in 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 of LC parallel-resonant circuits at resonant frequency, these high-order harmonics at multiples of central frequency will be suppressed effectively by this way. Besides, the performance of harmonic suppression can be changed by changing the number and size of an interdigital capacitor’s fingers. Finally, in order to realize a more compact structure of the proposed components using ATLs, each quarter-wavelength line is replaced by one unit ATL with 90°, though the optimum number of ATL units is proved to be two in [8, 13].Based on the above analysis, taking the ATL with the required 70.7 Ω characteristic impedance and 90° electric length as an illustration, the design procedure of ATL can be described as follows:Step 1.
Based on the layout of an ATL just like that in Figure1(a), create a rough model of an ATL in the software of IE3D. Obviously, the physical dimensions of each section in the model as shown in Figure 4 are arbitrary.
Step 2.
The ATL is simulated by software of IE3D. The value of characteristic impedanceZ1 can be obtained by simulation directly, and electric length θ1 can be got by simulated Ang(S21).
Step 3.
Compare the simulated characteristic impedance and electric length with the required goals. When required goals are not achieved, then, according to equations (4) and (5), decide the value of Lt1 and Ct1 should be increased or reduced.Figure 4
Each section of the 70.7 Ω ATL and their equivalent circuit: (a) section A1, (b) section A2, (c) section A3, (d) section A4, and (e) interdigital capacitorAj (j=1,2).
(a)
(b)
(c)
(d)
(e)In tuning of characteristic impedanceZ1, when the simulated characteristic impedance Z1 is lower than 70.7 Ω, according to equation (4), we can increase total inductance Lt1 or reduce total capacitance Ct1. When the simulated characteristic impedance Z1 is higher than 70.7 Ω, we can reduce total inductance Lt1 or increase total capacitance Ct1.In tuning of electric lengthθ1, when electric length θ1 is smaller than 90°, according to equation (5), we can increase total inductance Lt1 or total capacitance Ct1. When simulated electric length θ1 is larger than 90°, we can reduce total inductance Lt1 or total capacitance Ct1.According to equation (1), changing the total inductance Lt1 or total capacitance Ct1 can be realized by changing the inductance and capacitance of each related section. For example, 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 reduce capacitance of Cas2, Cas3, and Cas4 as shown in Figure 1(b).So tuning physical dimensions of each section can change total inductanceLt1 and total capacitance Ct1, to obtain the designed 70.7 Ω and 90°.
Step 4.
Tune fingers of interdigital capacitors to adjust the performance of harmonic suppression, including frequency of transmission zero and range of stopband.
Step 5.
To obtain equivalent inductance and capacitance of ATL to verify our design, with designated 70.7 Ω characteristic impedance and 90° electric length, we use formulas (4) and (5) to obtain Lt1 and Ct1.
Step 6.
Each section as shown in Figure4 is simulated by the simulation software of IE3D and converted to L-, T-, or π-equivalent circuit. And then parameter extraction of equivalent elements is based on impedance or admittance matrices.


### 2.2. Parameter Extraction

The process of parameter extraction is similar for the ATL of 70.7 Ω, 50 Ω, and 35.4 Ω, so we take the 70.7 Ω ATL as an example to analyze. In order to analyze the equivalent circuit of the 70.7 Ω ATL easily, the ATL is divided into several sections, as shown in Figure1. Each section and their equivalent circuit are given in Figure 4. Obviously, a more accurate equivalent circuit can be achieved by dividing the ATL into more sections when analyzing the ATL. To extract the equivalent element values of each section, full-wave simulation software IE3D is applied to calculate impedance or admittance matrices from the corresponding equivalent circuits of each section.The admittance matrix of the equivalent circuit for section A1 in Figure4(a) is expressed as
(6)Y11A1Y12A1Y21A1Y22A1=−jωLas1jωLas1jωLas1jωCas1−jωLas1.From the formula above, the equivalent value of elements can be obtained by(7)Las1=12πf0ImY12A1,Cas1=ImY22A1+ImY21A12πf0.Due to similarL-type circuit, the equivalent value of elements in Figures 4(b) and 4(c) can be readily calculated based on the admittance matrix by the same way.For section A4 in Figure4(d), its impedance matrix can be given by
(8)Z11A4Z12A4Z21A4Z22A4=jωLas4−jωCas4−jωCas4−jωCas4jωL−jωCas4.Then, the value of equivalent elements can be calculated as(9)Las4=ImZ11A4−ImZ12A42πf0,Cas4=−12πf0ImZ12A4.For interdigital capacitorAj (j=1,2) as shown in Figure 4(e), its admittance matrix can be expressed by
(10)Y11intjY12intjY21intjY22intj=jωCaj1+jωCapj−jωCapj−jωCapjjωCaj2+jωCapj.Then, the equivalent capacitance value can be calculated by(11)Capj=-ImY12intj2πf0,Caj1=ImY11intj+ImY12intj2πf0,Caj2=ImY22intj+ImY12intj2πf0.All values of equivalent elements as marked in Figures1(b), 2(b), and 3(b) are given in Table 1.Table 1
Detailed element parameters of ATLs.
70.7 Ω
Las1
Las2
Las3
Las4
Cas1
Cas2
Cas3
Cas4
3.56 nH
0.97 nH
2.33 nH
2.01 nH
0.34 pF
0.41 pF
0.39 pF
0.46 pF
Cap1
Cap2
Ca11
Ca12
Ca21
Ca22
0.24 pF
0.99 pF
0.09 pF
0.12 pF
0.34 pF
0.41 pF
50 Ω
Lbs1
Lbs2
Lbs3
Lbs4
Lbs5
Cbs1
Cbs2
Cbs3
2.46 nH
1.31 nH
1.01 nH
1.02 nH
1.18 nH
0.79 pF
0.51 pF
0.72 pF
Cbs4
Cbp1
Cbp2
Cb11
Cb12
Cb21
Cb22
0.32 pF
0.42 pF
0.51 pF
0.19 pF
0.19 pF
0.24 pF
0.25 pF
35.4 Ω
Lcs1
Lcs2
Lcs3
Lcs4
Lcs5
Ccs1
Ccs2
Ccs3
1.52 nH
0.33 nH
0.78 nH
0.91 nH
1.01 nH
1.75 pF
0.51 pF
0.83 pF
Ccs4
Ccp1
Ccp2
Cc11
Cc12
Cc21
Cc22
0.62 pF
0.95 pF
0.19 pF
0.42 pF
0.41 pF
0.11 pF
0.14 pFThe final optimized size of ATLs used in the proposed Wilkinson power divider and branch-line coupler are listed in Table2 as marked in Figures 1(a), 2(a), and 3(a). The physical lengths of the 70.7 Ω, 50 Ω, and 35.4 Ω ATLs are 0.098λg, 0.104λg, and 0.124λg, respectively.Table 2
Optimized dimensions of ATLs (unit: mm).
70.7 Ω
La1
La2
La3
La4
La5
La6
Wa1
Wa2
Wa3
Wa4
Wa5
Wa6
Wa7
22.2
2.3
6.9
11.7
21.6
5.2
5.4
0.2
1.7
1.7
0.7
0.2
0.2
50Ω
Lb1
Lb2
Lb3
Lb4
Lb5
Wb1
Wb2
Wb3
Wb4
Wb5
Wb6
Wb7
Wb8
23.4
5.8
12.1
15.2
22.6
3.8
4
0.6
0.3
0.3
2.9
0.3
0.4
35.4 Ω
Lc1
Lc2
Lc3
Lc4
Wc1
Wc2
Wc3
Wc4
Wc5
Wc6
Wc7
Wc8
28.6
12.7
16.1
27
6.4
6.6
0.2
0.2
4.6
4.7
2
0.5


### 2.3. Harmonic Suppression

For the proposed ATLs, the interdigital capacitors can play a role of harmonic suppression. For the interdigital capacitors, the performance of harmonic suppression is mainly determined by the number, length, width of finger, and gap width between fingers [24]. In order to realize the compact size and easy fabrication, the gap width between fingers is chosen to be 0.2 mm. Then, other factors affecting harmonic suppression would be discussed.Taking the 70.7 Ω ATL mentioned above as an example, the interdigital capacitors have 19 fingers and the lengthLa6=5.2mm and width Wa6=0.2mm as marked in Figure 1(a). The 70.7 Ω ATLs with different fingers’ numbers, lengths, and widths of interdigital capacitors are simulated.When the fingers’ number of interdigital capacitors changes, while their lengthLa6=5.2mm and width Wa6=0.2mm remain unchanged, the simulated S21 are shown in Figure 5(a). It can be observed that when the fingers’ number is reduced, the frequency of transmission zero in stopband becomes higher. In addition, compared to the ATL without interdigital capacitors, the ATL with interdigital capacitors has obvious harmonic suppression. The influence of fingers’ length on harmonic suppression is given in Figure 5(b). When the number of fingers equals to 19 and fingers’ width Wa6=0.2mm, it can be seen that the frequency of transmission zero becomes higher as fingers’ length is shortened. Figure 5(c) reveals that the frequency of transmission zero varies as fingers’ width Wa6 changes when the interdigital capacitors have 7 fingers with 5.2 mm length. When fingers’ width increases, the frequency of transmission zero would be lower slightly.Figure 5
Harmonic suppression of the 70.7 Ω ATL: (a) different number, (b) different length, and (c) different width.
(a)
(b)
(c)The result of such simulations is because the reduction of fingers’ number, length, and width would reduce the capacitance ofCap1 and Cap2. The reduced capacitance of Cap1 and Cap2 would make the resonant frequency of the parallel resonant circuit higher, which is composed of Cap1, Cap2, and Las4. And the resonant frequency is the frequency of transmission zero in a stopband, so the harmonic suppression is affected.


### 2.4. Propagation Characteristics

All of these proposed ATLs are designed to operate at 0.9 GHz and with 90° phase delay. The layout of ATLs are simulated by the electromagnetic simulation solver of IE3D, while their corresponding equivalent lumped circuits as given in Figures1(b), 2(b) and 3(b) are simulated by software of ADS. The comparisons of simulated S-parameters between the layout and equivalent lumped circuit are given in Figure 6. Additionally, when the 70.7 Ω, 50 Ω and 35.4 Ω ATLs are simulated, the reference impedances of the ports are set to 70.7 Ω, 50 Ω, and 35.4 Ω, respectively.Figure 6
SimulatedS-parameter of the proposed ATLs: (a) 70.7 Ω, (b) 50 Ω, and (c) 35.4 Ω.
(a)
(b)
(c)As shown in Figure6(a), for the 70.7 Ω ATL, the simulated S-parameters show that it has a 152.2% bandwidth of 0.9 GHz, from 0 GHz to 1.37 GHz. At 0.9 GHz, the return loss is 45.63 dB while insertion loss is less than 0.1 dB. Moreover, harmonic suppression performance is also shown in Figure 6(a). For the second-order harmonic frequency at 1.8 GHz, S21 is -10.66 dB, while for the third-order harmonic frequency at 2.7 GHz, S21 is -17.71 dB. For these harmonic frequencies, there are no pass-bands.For 50 Ω ATL as shown in Figure6(b), the layout simulation displays a 170% bandwidth of 0.9 GHz, from 0 GHz to 1.53 GHz. At 0.9 GHz, the ATL achieves 39.56 dB return loss and insertion loss less than 0.1 dB. Moreover, its harmonic suppression performance is verified by 12.5 dB harmonic suppression at the third-order harmonic frequency at 2.7 GHz.For the 35.4 Ω ATL as exhibited in Figure6(c), it has a 161.1% bandwidth of 0.9 GHz, from 0 GHz to 1.45 GHz. When operating at 0.9 GHz, 52.7 dB return loss and less than 0.1 dB insertion loss are realized. For the 35.4 Ω ATL, the third-order harmonic is suppressed to 26.63 dB, which displays good harmonic suppression performance.The simulated characteristic impedance and phase delay are exhibited in Figures7 and 8. For the 70.7 Ω ATL, at 0.9 GHz, the real part of characteristic impedance is 70.7 Ω and the imaginary part is 0.42 Ω, while the simulated results of the equivalent circuit are 70.93 Ω and 2.08 Ω. For the 50 Ω ATL, the 50.0 Ω real part and -0.56 Ω imaginary part of characteristic impedance can be obtained, while the results of equivalent circuit simulation are 50.5 Ω and -0.1 Ω. For the 35.4Ω ATL, the real part of characteristic impedance is 35.4 Ω and the imaginary part is 0.24 Ω, while the corresponding results of the equivalent circuit are 35.85 Ω and -0.15 Ω.Figure 7
Simulated characteristic impedance of the proposed ATLs.Figure 8
Simulated phase delay of the proposed ATLs.Figure8 indicates that the 70.7 Ω ATL has 90.0° phase delay at 0.9 GHz while 90.13° for the equivalent circuit. The 50 Ω ATL has 90.0° phase delay at 0.9 GHz while 91.52° for the equivalent circuit. The 35.4 Ω ATL has 90.1° phase delay and 91.15° for the equivalent circuit.From the analysis above, these proposed ATLs not only have the similar performance like conventional transmission lines within the bandwidth but also have effective suppression ability for the harmonics. For the ATLs, the simulatedS-parameters of the layout agree well with that of the lumped equivalent circuit at low frequency. However, at high frequency, there is a deviation of insertion losses, due to the equivalent circuit of the interdigital capacitor. In addition, the precision of the equivalent circuit would be improved by dividing the interdigital capacitor into more numbers of equivalent series capacitors. The simulation comparisons between the layout and lumped model indicate the accuracy of extracting parameters of the equivalent circuit.


## 2.1. Design Concepts

As shown in Figure1(a), a section of the 70.7 Ω ATL with a right-angled triangle shape is composed of five sections of microstrip low-impedance transmission lines and six sections of microstrip high-impedance transmission lines. Additionally, there are two sections of uniform transmission lines connected to ports. The low-impedance lines and high-impedance lines are cascaded alternately and then folded into a right-angled triangle shape for a compact size. Meanwhile, an interdigital capacitor is placed in the middle of an ATL to suppress harmonics. The equivalent circuit of the 70.7 Ω ATL is given by Figure 1(b). Each uniform transmission line connected to a port can be equivalent to a series inductor Las1 and a shunt capacitor Cas1 to ground. Correspondingly, the high-impedance lines can be equivalent to series inductors Las2, Las3, and Las4, and these low-impedance lines work as equivalent shunt capacitors Cas2, Cas3, and Cas4 to ground. The interdigital capacitor is placed between several high-impedance lines and between low-impedance lines, so it can be equivalent to several series capacitors in parallel and parasitic capacitors to ground. For the sake of simplicity, as marked in Figure 1(a), the microstrip interdigital capacitor is divided into two parts as interdigital A1 and interdigital A2 and then be equivalent to series capacitors Cap1 and Cap2. Besides, the shunt capacitors Ca11, Ca12, Ca21, and Ca22 represent parasitic capacitors of the interdigital capacitor.Figure 1
A section of 70.7 Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
(a)
(b)For the equivalent circuit of the 70.7 Ω ATL, the total inductance of equivalent series inductors can be represented byLt1, and the total capacitance of equivalent shunt capacitors can be presented by Ct1. And they can be given by
(1)Lt1=2Las1+2Las2+2Las3+2Las4,Ct1=2Cas1+2Cas2+2Cas3+Cas4+Ca11+Ca12+Ca21+Ca22.In the design of the 3 dB branch-line coupler, 50 Ω and 35.4 Ω ATL are designed. For a 50 Ω ATL, the layout and its equivalent circuit are given by Figure2. It has similar layout and equivalent circuit as a 70.7 Ω ATL. The total inductance Lt2 of equivalent series inductors and total capacitance Ct2 of equivalent shunt capacitors are calculated by
(2)Lt2=2Lbs1+2Lbs2+2Lbs3+2Lbs4+2Lbs5,Ct2=2Cbs1+2Cbs2+2Cbs3+Cbs4+Cb11+Cb12+Cb21+Cb22.Figure 2
A section of 50 Ω ATL with a right-angled triangle shape: (a) layout and (b) equivalent circuit.
(a)
(b)The layout and equivalent circuit of the 35.4 Ω ATL are shown in Figure3. The 35.4 Ω ATLs are modified to an isosceles trapezoid shape to realize a more compact size for the branch-line coupler. Referring to its layout, the 35.4 Ω ATL is comprised of three sections of low-impedance transmission lines and four sections of high-impedance transmission lines. The two transmission lines connected to ports can be equivalent to series inductor Lcs1 and shunt capacitor Ccs1 to ground. In order to analyze the interdigital capacitor more accurately, the interdigital capacitor is divided into two parts. As marked in Figure 3(a), interdigital capacitor C1 and interdigital capacitor C2 can be equivalent to series capacitors Ccp1 and Ccp2 and parasitic capacitors Cc11, Cc12, Cc21, and Cc22 to ground. The total series inductance Lt3 and total shunt capacitance Ct3 are given by
(3)Lt3=2Lcs1+2Lcs2+2Lcs3+2Lcs4+2Lcs5,Ct3=2Ccs1+2Ccs2+2Ccs3+Ccs4+Cc11+Cc12+Cc21+Cc22.Figure 3
A section of 35.4 Ω ATL with an isosceles trapezoid shape: (a) layout and (b) equivalent circuit.
(a)
(b)According to the uniform transmission line theory, characteristic impedanceZi (i=1,2,3) and phase propagation constant βi (i=1,2,3) of per unit length are determined by Zi=Li/Ci and βi=ωLi⋅Ci, where Li and Ci are the inductance and capacitance per unit length along the transmission line and ω represents the operating angular frequency. For ununiform transmission lines such as ATLs, when the physical length of the ATL is less than one-eighth of a guided wavelength, the ununiform transmission lines can approximate to uniform transmission lines [24]. Then, for the ATL, Lti=Lili and Cti=Cili, where Lti and Cti are the total series inductance and shunt capacitance and li is the physical length of a unit ATL. The characteristic impedance Zi and electrical length θi of a unit of an ATL can be calculated as
(4)Zi=LiCi=LtiCti,(5)θi=βili=ωLi⋅Cili=ωLti⋅Cti.From formulas (4) and (5), we can find, for a unit ATL with the same length, if Lti and Cti increase proportionally, that Zi would remain unchanged, while the electrical length θi would increase. In turn, with a given characteristic impedance Zi and electrical length θi of a unit of an ATL, when Li and Ci are increased proportionally, characteristic impedance Zi would be unchanged, while phase propagation constant βi of per unit length would be increased, so the required physical length li is significantly reduced.For stepped impedance transmission lines, using the lines with high characteristic impedance is equivalent to loading more inductance per unit length, while employing the lines with low characteristic impedance is equivalent to loading more capacitance per unit length than conventional microstrip transmission lines. In the design of an ATL, stepped impedance transmission lines folded into a right-angled triangle shape would add more capacitance and inductance for per physical length, so the required physical length can be further reduced. In a practical design, the 35.4 Ω ATL is modified to an isosceles trapezoid 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 impedance transmission lines have many harmonic pass-bands at multiples of central frequency. In order to suppress harmonics effectively, a microstrip interdigital capacitor is used in 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 of LC parallel-resonant circuits at resonant frequency, these high-order harmonics at multiples of central frequency will be suppressed effectively by this way. Besides, the performance of harmonic suppression can be changed by changing the number and size of an interdigital capacitor’s fingers. Finally, in order to realize a more compact structure of the proposed components using ATLs, each quarter-wavelength line is replaced by one unit ATL with 90°, though the optimum number of ATL units is proved to be two in [8, 13].Based on the above analysis, taking the ATL with the required 70.7 Ω characteristic impedance and 90° electric length as an illustration, the design procedure of ATL can be described as follows:Step 1.
Based on the layout of an ATL just like that in Figure1(a), create a rough model of an ATL in the software of IE3D. Obviously, the physical dimensions of each section in the model as shown in Figure 4 are arbitrary.
Step 2.
The ATL is simulated by software of IE3D. The value of characteristic impedanceZ1 can be obtained by simulation directly, and electric length θ1 can be got by simulated Ang(S21).
Step 3.
Compare the simulated characteristic impedance and electric length with the required goals. When required goals are not achieved, then, according to equations (4) and (5), decide the value of Lt1 and Ct1 should be increased or reduced.Figure 4
Each section of the 70.7 Ω ATL and their equivalent circuit: (a) section A1, (b) section A2, (c) section A3, (d) section A4, and (e) interdigital capacitorAj (j=1,2).
(a)
(b)
(c)
(d)
(e)In tuning of characteristic impedanceZ1, when the simulated characteristic impedance Z1 is lower than 70.7 Ω, according to equation (4), we can increase total inductance Lt1 or reduce total capacitance Ct1. When the simulated characteristic impedance Z1 is higher than 70.7 Ω, we can reduce total inductance Lt1 or increase total capacitance Ct1.In tuning of electric lengthθ1, when electric length θ1 is smaller than 90°, according to equation (5), we can increase total inductance Lt1 or total capacitance Ct1. When simulated electric length θ1 is larger than 90°, we can reduce total inductance Lt1 or total capacitance Ct1.According to equation (1), changing the total inductance Lt1 or total capacitance Ct1 can be realized by changing the inductance and capacitance of each related section. For example, 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 reduce capacitance of Cas2, Cas3, and Cas4 as shown in Figure 1(b).So tuning physical dimensions of each section can change total inductanceLt1 and total capacitance Ct1, to obtain the designed 70.7 Ω and 90°.
Step 4.
Tune fingers of interdigital capacitors to adjust the performance of harmonic suppression, including frequency of transmission zero and range of stopband.
Step 5.
To obtain equivalent inductance and capacitance of ATL to verify our design, with designated 70.7 Ω characteristic impedance and 90° electric length, we use formulas (4) and (5) to obtain Lt1 and Ct1.
Step 6.
Each section as shown in Figure4 is simulated by the simulation software of IE3D and converted to L-, T-, or π-equivalent circuit. And then parameter extraction of equivalent elements is based on impedance or admittance matrices.


## 2.2. Parameter Extraction

The process of parameter extraction is similar for the ATL of 70.7 Ω, 50 Ω, and 35.4 Ω, so we take the 70.7 Ω ATL as an example to analyze. In order to analyze the equivalent circuit of the 70.7 Ω ATL easily, the ATL is divided into several sections, as shown in Figure1. Each section and their equivalent circuit are given in Figure 4. Obviously, a more accurate equivalent circuit can be achieved by dividing the ATL into more sections when analyzing the ATL. To extract the equivalent element values of each section, full-wave simulation software IE3D is applied to calculate impedance or admittance matrices from the corresponding equivalent circuits of each section.The admittance matrix of the equivalent circuit for section A1 in Figure4(a) is expressed as
(6)Y11A1Y12A1Y21A1Y22A1=−jωLas1jωLas1jωLas1jωCas1−jωLas1.From the formula above, the equivalent value of elements can be obtained by(7)Las1=12πf0ImY12A1,Cas1=ImY22A1+ImY21A12πf0.Due to similarL-type circuit, the equivalent value of elements in Figures 4(b) and 4(c) can be readily calculated based on the admittance matrix by the same way.For section A4 in Figure4(d), its impedance matrix can be given by
(8)Z11A4Z12A4Z21A4Z22A4=jωLas4−jωCas4−jωCas4−jωCas4jωL−jωCas4.Then, the value of equivalent elements can be calculated as(9)Las4=ImZ11A4−ImZ12A42πf0,Cas4=−12πf0ImZ12A4.For interdigital capacitorAj (j=1,2) as shown in Figure 4(e), its admittance matrix can be expressed by
(10)Y11intjY12intjY21intjY22intj=jωCaj1+jωCapj−jωCapj−jωCapjjωCaj2+jωCapj.Then, the equivalent capacitance value can be calculated by(11)Capj=-ImY12intj2πf0,Caj1=ImY11intj+ImY12intj2πf0,Caj2=ImY22intj+ImY12intj2πf0.All values of equivalent elements as marked in Figures1(b), 2(b), and 3(b) are given in Table 1.Table 1
Detailed element parameters of ATLs.
70.7 Ω
Las1
Las2
Las3
Las4
Cas1
Cas2
Cas3
Cas4
3.56 nH
0.97 nH
2.33 nH
2.01 nH
0.34 pF
0.41 pF
0.39 pF
0.46 pF
Cap1
Cap2
Ca11
Ca12
Ca21
Ca22
0.24 pF
0.99 pF
0.09 pF
0.12 pF
0.34 pF
0.41 pF
50 Ω
Lbs1
Lbs2
Lbs3
Lbs4
Lbs5
Cbs1
Cbs2
Cbs3
2.46 nH
1.31 nH
1.01 nH
1.02 nH
1.18 nH
0.79 pF
0.51 pF
0.72 pF
Cbs4
Cbp1
Cbp2
Cb11
Cb12
Cb21
Cb22
0.32 pF
0.42 pF
0.51 pF
0.19 pF
0.19 pF
0.24 pF
0.25 pF
35.4 Ω
Lcs1
Lcs2
Lcs3
Lcs4
Lcs5
Ccs1
Ccs2
Ccs3
1.52 nH
0.33 nH
0.78 nH
0.91 nH
1.01 nH
1.75 pF
0.51 pF
0.83 pF
Ccs4
Ccp1
Ccp2
Cc11
Cc12
Cc21
Cc22
0.62 pF
0.95 pF
0.19 pF
0.42 pF
0.41 pF
0.11 pF
0.14 pFThe final optimized size of ATLs used in the proposed Wilkinson power divider and branch-line coupler are listed in Table2 as marked in Figures 1(a), 2(a), and 3(a). The physical lengths of the 70.7 Ω, 50 Ω, and 35.4 Ω ATLs are 0.098λg, 0.104λg, and 0.124λg, respectively.Table 2
Optimized dimensions of ATLs (unit: mm).
70.7 Ω
La1
La2
La3
La4
La5
La6
Wa1
Wa2
Wa3
Wa4
Wa5
Wa6
Wa7
22.2
2.3
6.9
11.7
21.6
5.2
5.4
0.2
1.7
1.7
0.7
0.2
0.2
50Ω
Lb1
Lb2
Lb3
Lb4
Lb5
Wb1
Wb2
Wb3
Wb4
Wb5
Wb6
Wb7
Wb8
23.4
5.8
12.1
15.2
22.6
3.8
4
0.6
0.3
0.3
2.9
0.3
0.4
35.4 Ω
Lc1
Lc2
Lc3
Lc4
Wc1
Wc2
Wc3
Wc4
Wc5
Wc6
Wc7
Wc8
28.6
12.7
16.1
27
6.4
6.6
0.2
0.2
4.6
4.7
2
0.5


## 2.3. Harmonic Suppression

For the proposed ATLs, the interdigital capacitors can play a role of harmonic suppression. For the interdigital capacitors, the performance of harmonic suppression is mainly determined by the number, length, width of finger, and gap width between fingers [24]. In order to realize the compact size and easy fabrication, the gap width between fingers is chosen to be 0.2 mm. Then, other factors affecting harmonic suppression would be discussed.Taking the 70.7 Ω ATL mentioned above as an example, the interdigital capacitors have 19 fingers and the lengthLa6=5.2mm and width Wa6=0.2mm as marked in Figure 1(a). The 70.7 Ω ATLs with different fingers’ numbers, lengths, and widths of interdigital capacitors are simulated.When the fingers’ number of interdigital capacitors changes, while their lengthLa6=5.2mm and width Wa6=0.2mm remain unchanged, the simulated S21 are shown in Figure 5(a). It can be observed that when the fingers’ number is reduced, the frequency of transmission zero in stopband becomes higher. In addition, compared to the ATL without interdigital capacitors, the ATL with interdigital capacitors has obvious harmonic suppression. The influence of fingers’ length on harmonic suppression is given in Figure 5(b). When the number of fingers equals to 19 and fingers’ width Wa6=0.2mm, it can be seen that the frequency of transmission zero becomes higher as fingers’ length is shortened. Figure 5(c) reveals that the frequency of transmission zero varies as fingers’ width Wa6 changes when the interdigital capacitors have 7 fingers with 5.2 mm length. When fingers’ width increases, the frequency of transmission zero would be lower slightly.Figure 5
Harmonic suppression of the 70.7 Ω ATL: (a) different number, (b) different length, and (c) different width.
(a)
(b)
(c)The result of such simulations is because the reduction of fingers’ number, length, and width would reduce the capacitance ofCap1 and Cap2. The reduced capacitance of Cap1 and Cap2 would make the resonant frequency of the parallel resonant circuit higher, which is composed of Cap1, Cap2, and Las4. And the resonant frequency is the frequency of transmission zero in a stopband, so the harmonic suppression is affected.


## 2.4. Propagation Characteristics

All of these proposed ATLs are designed to operate at 0.9 GHz and with 90° phase delay. The layout of ATLs are simulated by the electromagnetic simulation solver of IE3D, while their corresponding equivalent lumped circuits as given in Figures1(b), 2(b) and 3(b) are simulated by software of ADS. The comparisons of simulated S-parameters between the layout and equivalent lumped circuit are given in Figure 6. Additionally, when the 70.7 Ω, 50 Ω and 35.4 Ω ATLs are simulated, the reference impedances of the ports are set to 70.7 Ω, 50 Ω, and 35.4 Ω, respectively.Figure 6
SimulatedS-parameter of the proposed ATLs: (a) 70.7 Ω, (b) 50 Ω, and (c) 35.4 Ω.
(a)
(b)
(c)As shown in Figure6(a), for the 70.7 Ω ATL, the simulated S-parameters show that it has a 152.2% bandwidth of 0.9 GHz, from 0 GHz to 1.37 GHz. At 0.9 GHz, the return loss is 45.63 dB while insertion loss is less than 0.1 dB. Moreover, harmonic suppression performance is also shown in Figure 6(a). For the second-order harmonic frequency at 1.8 GHz, S21 is -10.66 dB, while for the third-order harmonic frequency at 2.7 GHz, S21 is -17.71 dB. For these harmonic frequencies, there are no pass-bands.For 50 Ω ATL as shown in Figure6(b), the layout simulation displays a 170% bandwidth of 0.9 GHz, from 0 GHz to 1.53 GHz. At 0.9 GHz, the ATL achieves 39.56 dB return loss and insertion loss less than 0.1 dB. Moreover, its harmonic suppression performance is verified by 12.5 dB harmonic suppression at the third-order harmonic frequency at 2.7 GHz.For the 35.4 Ω ATL as exhibited in Figure6(c), it has a 161.1% bandwidth of 0.9 GHz, from 0 GHz to 1.45 GHz. When operating at 0.9 GHz, 52.7 dB return loss and less than 0.1 dB insertion loss are realized. For the 35.4 Ω ATL, the third-order harmonic is suppressed to 26.63 dB, which displays good harmonic suppression performance.The simulated characteristic impedance and phase delay are exhibited in Figures7 and 8. For the 70.7 Ω ATL, at 0.9 GHz, the real part of characteristic impedance is 70.7 Ω and the imaginary part is 0.42 Ω, while the simulated results of the equivalent circuit are 70.93 Ω and 2.08 Ω. For the 50 Ω ATL, the 50.0 Ω real part and -0.56 Ω imaginary part of characteristic impedance can be obtained, while the results of equivalent circuit simulation are 50.5 Ω and -0.1 Ω. For the 35.4Ω ATL, the real part of characteristic impedance is 35.4 Ω and the imaginary part is 0.24 Ω, while the corresponding results of the equivalent circuit are 35.85 Ω and -0.15 Ω.Figure 7
Simulated characteristic impedance of the proposed ATLs.Figure 8
Simulated phase delay of the proposed ATLs.Figure8 indicates that the 70.7 Ω ATL has 90.0° phase delay at 0.9 GHz while 90.13° for the equivalent circuit. The 50 Ω ATL has 90.0° phase delay at 0.9 GHz while 91.52° for the equivalent circuit. The 35.4 Ω ATL has 90.1° phase delay and 91.15° for the equivalent circuit.From the analysis above, these proposed ATLs not only have the similar performance like conventional transmission lines within the bandwidth but also have effective suppression ability for the harmonics. For the ATLs, the simulatedS-parameters of the layout agree well with that of the lumped equivalent circuit at low frequency. However, at high frequency, there is a deviation of insertion losses, due to the equivalent circuit of the interdigital capacitor. In addition, the precision of the equivalent circuit would be improved by dividing the interdigital capacitor into more numbers of equivalent series capacitors. The simulation comparisons between the layout and lumped model indicate the accuracy of extracting parameters of the equivalent circuit.


## 3. Circuit Design and Measurements

The proposed Wilkinson power divider and branch-line coupler are designed to operate at 0.9 GHz. Simulations are performed by a full-wave EM simulation software of IE3D. The proposed Wilkinson power divider and branch-line coupler are fabricated on a substrate of F4B with 1 mm thickness and relative permittivityεr=2.65 and loss tangent δ=0.005. Measurements are carried out on an Agilent 8510C network analyzer.


### 3.1. Wilkinson Power Divider

The layout of proposed Wilkinson power divider is given by Figure9(a). The proposed Wilkinson power divider consists of two sections of 70.7 Ω ATLs employed to replace these conventional quarter-wavelength transmission lines. And a chip resistor of 100 Ω (type: 0805) is used in the design. The photograph of the fabricated Wilkinson power divider is shown in Figure 9(b). The proposed Wilkinson power divider occupies a size of 29.9mm×34.7mm, that is 0.13λg×0.16λg, where λg is the guided wavelength on the substrate at 0.9 GHz. Comparing to a power divider implemented by conventional microstrip lines, the fabricated power divider only occupies a 58.8% size.Figure 9
The proposed Wilkinson power divider: (a) layout and (b) photo.
(a)
(b)Figure10 shows the simulated and measured ∣S11∣, ∣S21∣, and ∣S31∣ of the proposed Wilkinson power divider. The simulated and measured S-parameters indicate that the measured results have a good agreement with simulated results. For simulation, the central frequency is 0.9 GHz while measurements exhibit the central frequency of 0.91 GHz. There exists a frequency deviation of 0.01 GHz for central frequency due to fabrication tolerance and measurement devices. Then, the fabricated Wilkinson power divider for 0.91GHz has a bandwidth of 58.2% for S11 less than -15 dB, from 0.61 GHz to 1.14 GHz, and the return loss at 0.91 GHz is 32.12 dB. At 0.91GHz, measured S21 is -3.13 dB and S31 is -3.26 dB. In addition, as shown in Figure 10, the fabricated Wilkinson power divider has 12.5 dB suppression for the second-order harmonic of 1.82 GHz and 24.7 dB suppression for the third-order harmonic of 2.73 GHz.Figure 10
Simulated and measuredS11, S21, and S31 of the proposed Wilkinson power divider.Figure11 shows isolation and phase difference (Ang(S21)-Ang(S31)). Measured results display at 0.91 GHz that the power divider has a 32.8 dB isolation, which reveals good isolation performance between output port 2 and port 3. Besides, there is only a 0.23° phase difference between two output port 2 and port 3 at 0.91 GHz.Figure 11
Simulated and measuredS32 and phase difference of the proposed Wilkinson power divider.Figure12 gives the comparison of S-parameters between the proposed Wilkinson power divider and conventional case operating at 0.9 GHz, which obviously indicates that the harmonic is effectively suppressed in the stopband in the proposed structure. Meanwhile, a similar bandwidth performance as that of the conventional case is achieved when size miniaturization is realized.Figure 12
Comparison of simulatedS-parameters between the proposed and conventional Wilkinson power divider.Finally, the performance comparisons of this proposed power divider (this work) with several previous designs are listed in Table3. It indicates the proposed Wilkinson power divider in this work has similar electrical performance as the conventional case and good harmonic suppression but with a small size. Especially, the relative bandwidth is similar to the conventional one.Table 3
Performance comparisons of power dividers.
Ref
Central frequency (GHz)
Size
S11 -15 dB BW (%)
At central frequency
Harmonic suppression (dB)
S11 (dB)
S21, S31(dB)
S32(dB)
Second-order harmonic
Third-order harmonic
[15]
0.9
0.1λg×0.2λg
2.4
15
4.74±0.15
23
27
36
[16]
0.9
0.11λg×0.15λg
4.5
16
4.6, 4.6
30
47
45
[17]
0.92
0.15λg×0.14λg
6.5
22
3.96, 3.99
20
45
No given
[18]
0.9
0.11λg×0.06λg
21.1
25
3.5, 3.6
19
5
41
[25]
0.77
0.042λg×0.189λg
38
20
3.52, 3.52
20.8
40
37
[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.


### 3.2. Branch-Line Coupler

In the design of the proposed 3 dB branch-line coupler as shown in Figure13(a), two sections of 50 Ω ATLs and two sections of 35.4 Ω ATLs are employed to replace these corresponding conventional quarter-wavelength transmission lines. The two sections of 50 Ω ATLs are designed to be with a right-angled triangle shape, while the two sections of 35.4 Ω ATLs are modified to an isosceles trapezoid shape in order to realize a more compact size. All of these ATLs are combined into a compact rectangle shape. The photograph of the fabricated 3 dB branch-line coupler is given in Figure 13(b). The size of the fabricated branch-line coupler is 45.2mm×32.8mm, that is 0.2λg×0.15λg, where λg is the guided wavelength on the substrate at 0.9 GHz. The size of the proposed branch-line coupler is effectively reduced to a 33.4% area of a conventional one at 0.9 GHz.Figure 13
The proposed 3 dB branch-line coupler: (a) layout and (b) photo.
(a)
(b)Figure14 shows the simulated and measured S11, S21, and S31 of the proposed coupler. The S-parameters reveal a good agreement between simulated and measured results. As observed in Figure 14, the central frequency is 0.9 GHz at simulation while the central frequency is 0.91 GHz at measurement. A frequency deviation of 0.01 GHz exists between simulation and measurement because of fabrication tolerance and measurement devices. For measured results, at a central frequency of 0.91 GHz, it has a 17% bandwidth with S11 less than -15 dB, from 0.84 GHz to 0.99 GHz. At 0.91 GHz, the return loss is 29.35 dB, which shows its good impedance match with ports. And at 0.91 GHz, S21 and S31 are -3.2 dB and -3.15 dB, respectively. In Figure 15, S41 and phase difference between the two output ports are given. At 0.91 GHz, measured S41 is -26.3 dB. The phase difference (Ang(S21)-Ang(S31)) is 90.6°, while the 90°±1° bandwidth is 34 MHz, from 881 MHz to 915 MHz.Figure 14
Simulated and measuredS11, S21, and S31 of the proposed branch-line coupler.Figure 15
Simulated and measuredS41 and phase difference of the proposed branch-line coupler.In addition, at the second-order harmonic frequency of 1.82 GHz,S11 is -1.26 dB, S21 is -12.6 dB, and S31 is -11.1 dB. At the third-order harmonic frequency of 2.73 GHz, 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-order harmonic frequencies, there are no pass-bands. So harmonic suppression performance is verified. As a comparison, S-parameters of the conventional branch-line coupler are given in Figure 16. By observation, the bandwidth of the proposed branch-coupler is comparable to that of the conventional one, while these harmonic pass-bands at harmonic frequencies are effectively suppressed.Figure 16
SimulatedS-parameters of the conventional branch-line coupler.Table4 shows the performance comparisons of the proposed branch-line coupler (this work) and several previous designs. The performance comparisons reveal that the proposed branch-line coupler has similar bandwidth, insertion loss, and isolation with other designs, but better harmonic suppression with a miniaturized size.Table 4
Performance comparisons of branch-line couplers.
Ref
Central frequency (GHz)
Size
S11 -15 dB BW (%)
At central frequency
Harmonic suppression (dB)
S11 (dB)
S21, S31 (dB)
S41 (dB)
Second-order harmonic
Third-order harmonic
[19]
0.91
0.09λg×0.11λg
8.9
33
3.2, 3.7
40
No suppression
No suppression
[20]
0.9
0.07λg×0.11λg
18.9
30
3.36, 3.25
22
No suppression
No suppression
[21]
0.8365
0.08λg×0.07λg
7.2
25
3.9, 3.9
28.9
20
No given
[22]
0.875
0.10λg×0.11λg
19.4
35
2.94, 3.72
43
5
5
[27]
1
0.19λg×0.34λg
20
34
3.5, 3.6
30
No suppression
No suppression
[28]
1.675
0.16λg×0.16λg
23.2
35.1
2.8, 3.15
34.1
No suppression
No suppression
This work
0.91
0.2λg×0.15λg
17
29.35
3.2, 3.15
26.3
12.6
29.5
λg: guided wavelength at central frequency.


## 3.1. Wilkinson Power Divider

The layout of proposed Wilkinson power divider is given by Figure9(a). The proposed Wilkinson power divider consists of two sections of 70.7 Ω ATLs employed to replace these conventional quarter-wavelength transmission lines. And a chip resistor of 100 Ω (type: 0805) is used in the design. The photograph of the fabricated Wilkinson power divider is shown in Figure 9(b). The proposed Wilkinson power divider occupies a size of 29.9mm×34.7mm, that is 0.13λg×0.16λg, where λg is the guided wavelength on the substrate at 0.9 GHz. Comparing to a power divider implemented by conventional microstrip lines, the fabricated power divider only occupies a 58.8% size.Figure 9
The proposed Wilkinson power divider: (a) layout and (b) photo.
(a)
(b)Figure10 shows the simulated and measured ∣S11∣, ∣S21∣, and ∣S31∣ of the proposed Wilkinson power divider. The simulated and measured S-parameters indicate that the measured results have a good agreement with simulated results. For simulation, the central frequency is 0.9 GHz while measurements exhibit the central frequency of 0.91 GHz. There exists a frequency deviation of 0.01 GHz for central frequency due to fabrication tolerance and measurement devices. Then, the fabricated Wilkinson power divider for 0.91GHz has a bandwidth of 58.2% for S11 less than -15 dB, from 0.61 GHz to 1.14 GHz, and the return loss at 0.91 GHz is 32.12 dB. At 0.91GHz, measured S21 is -3.13 dB and S31 is -3.26 dB. In addition, as shown in Figure 10, the fabricated Wilkinson power divider has 12.5 dB suppression for the second-order harmonic of 1.82 GHz and 24.7 dB suppression for the third-order harmonic of 2.73 GHz.Figure 10
Simulated and measuredS11, S21, and S31 of the proposed Wilkinson power divider.Figure11 shows isolation and phase difference (Ang(S21)-Ang(S31)). Measured results display at 0.91 GHz that the power divider has a 32.8 dB isolation, which reveals good isolation performance between output port 2 and port 3. Besides, there is only a 0.23° phase difference between two output port 2 and port 3 at 0.91 GHz.Figure 11
Simulated and measuredS32 and phase difference of the proposed Wilkinson power divider.Figure12 gives the comparison of S-parameters between the proposed Wilkinson power divider and conventional case operating at 0.9 GHz, which obviously indicates that the harmonic is effectively suppressed in the stopband in the proposed structure. Meanwhile, a similar bandwidth performance as that of the conventional case is achieved when size miniaturization is realized.Figure 12
Comparison of simulatedS-parameters between the proposed and conventional Wilkinson power divider.Finally, the performance comparisons of this proposed power divider (this work) with several previous designs are listed in Table3. It indicates the proposed Wilkinson power divider in this work has similar electrical performance as the conventional case and good harmonic suppression but with a small size. Especially, the relative bandwidth is similar to the conventional one.Table 3
Performance comparisons of power dividers.
Ref
Central frequency (GHz)
Size
S11 -15 dB BW (%)
At central frequency
Harmonic suppression (dB)
S11 (dB)
S21, S31(dB)
S32(dB)
Second-order harmonic
Third-order harmonic
[15]
0.9
0.1λg×0.2λg
2.4
15
4.74±0.15
23
27
36
[16]
0.9
0.11λg×0.15λg
4.5
16
4.6, 4.6
30
47
45
[17]
0.92
0.15λg×0.14λg
6.5
22
3.96, 3.99
20
45
No given
[18]
0.9
0.11λg×0.06λg
21.1
25
3.5, 3.6
19
5
41
[25]
0.77
0.042λg×0.189λg
38
20
3.52, 3.52
20.8
40
37
[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.


## 3.2. Branch-Line Coupler

In the design of the proposed 3 dB branch-line coupler as shown in Figure13(a), two sections of 50 Ω ATLs and two sections of 35.4 Ω ATLs are employed to replace these corresponding conventional quarter-wavelength transmission lines. The two sections of 50 Ω ATLs are designed to be with a right-angled triangle shape, while the two sections of 35.4 Ω ATLs are modified to an isosceles trapezoid shape in order to realize a more compact size. All of these ATLs are combined into a compact rectangle shape. The photograph of the fabricated 3 dB branch-line coupler is given in Figure 13(b). The size of the fabricated branch-line coupler is 45.2mm×32.8mm, that is 0.2λg×0.15λg, where λg is the guided wavelength on the substrate at 0.9 GHz. The size of the proposed branch-line coupler is effectively reduced to a 33.4% area of a conventional one at 0.9 GHz.Figure 13
The proposed 3 dB branch-line coupler: (a) layout and (b) photo.
(a)
(b)Figure14 shows the simulated and measured S11, S21, and S31 of the proposed coupler. The S-parameters reveal a good agreement between simulated and measured results. As observed in Figure 14, the central frequency is 0.9 GHz at simulation while the central frequency is 0.91 GHz at measurement. A frequency deviation of 0.01 GHz exists between simulation and measurement because of fabrication tolerance and measurement devices. For measured results, at a central frequency of 0.91 GHz, it has a 17% bandwidth with S11 less than -15 dB, from 0.84 GHz to 0.99 GHz. At 0.91 GHz, the return loss is 29.35 dB, which shows its good impedance match with ports. And at 0.91 GHz, S21 and S31 are -3.2 dB and -3.15 dB, respectively. In Figure 15, S41 and phase difference between the two output ports are given. At 0.91 GHz, measured S41 is -26.3 dB. The phase difference (Ang(S21)-Ang(S31)) is 90.6°, while the 90°±1° bandwidth is 34 MHz, from 881 MHz to 915 MHz.Figure 14
Simulated and measuredS11, S21, and S31 of the proposed branch-line coupler.Figure 15
Simulated and measuredS41 and phase difference of the proposed branch-line coupler.In addition, at the second-order harmonic frequency of 1.82 GHz,S11 is -1.26 dB, S21 is -12.6 dB, and S31 is -11.1 dB. At the third-order harmonic frequency of 2.73 GHz, 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-order harmonic frequencies, there are no pass-bands. So harmonic suppression performance is verified. As a comparison, S-parameters of the conventional branch-line coupler are given in Figure 16. By observation, the bandwidth of the proposed branch-coupler is comparable to that of the conventional one, while these harmonic pass-bands at harmonic frequencies are effectively suppressed.Figure 16
SimulatedS-parameters of the conventional branch-line coupler.Table4 shows the performance comparisons of the proposed branch-line coupler (this work) and several previous designs. The performance comparisons reveal that the proposed branch-line coupler has similar bandwidth, insertion loss, and isolation with other designs, but better harmonic suppression with a miniaturized size.Table 4
Performance comparisons of branch-line couplers.
Ref
Central frequency (GHz)
Size
S11 -15 dB BW (%)
At central frequency
Harmonic suppression (dB)
S11 (dB)
S21, S31 (dB)
S41 (dB)
Second-order harmonic
Third-order harmonic
[19]
0.91
0.09λg×0.11λg
8.9
33
3.2, 3.7
40
No suppression
No suppression
[20]
0.9
0.07λg×0.11λg
18.9
30
3.36, 3.25
22
No suppression
No suppression
[21]
0.8365
0.08λg×0.07λg
7.2
25
3.9, 3.9
28.9
20
No given
[22]
0.875
0.10λg×0.11λg
19.4
35
2.94, 3.72
43
5
5
[27]
1
0.19λg×0.34λg
20
34
3.5, 3.6
30
No suppression
No suppression
[28]
1.675
0.16λg×0.16λg
23.2
35.1
2.8, 3.15
34.1
No suppression
No suppression
This work
0.91
0.2λg×0.15λg
17
29.35
3.2, 3.15
26.3
12.6
29.5
λg: guided wavelength at central frequency.


## 4. Conclusion

In this paper, a compact Wilkinson power divider and a compact 3 dB branch-line coupler with harmonic suppression performance based on artificial transmission lines are proposed. These ATLs consist of stepped impedance transmission lines and interdigital capacitors. In order to reduce the size, these ATLs are folded into a right-angled triangle shape, and especially, the 35.4 Ω ATLs employed in the branch-line coupler are modified to an isosceles trapezoid shape. Then, the feasibility of the proposed power divider and branch-line coupler design are demonstrated, and the simulated and the measured results are in good agreement. The proposed Wilkinson power divider realizes the 58.8% occupied area of the conventional case and good harmonic suppression performance. The occupied area of the proposed branch-line coupler is reduced to 33.4% of the conventional case. At the same time, good harmonic suppression performance is demonstrated. Both proposed components have similar bandwidth as the conventional design but with compact size and good harmonic suppression. The proposed Wilkinson power divider and branch-line coupler can be extensively used in the modern communication system.



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*Source: 4923964-2019-05-02.xml*