Novel Compact Dual-Band Rat-Race Coupler ...

Novel Compact Dual-Band Rat-Race Coupler Combining Fractal Geometry and CRLH TLs He-Xiu Xu, Guang-Ming Wang, XiaoKuan Zhang & Xiao-Lei Yang

Wireless Personal Communications An International Journal ISSN 0929-6212 Volume 66 Number 4 Wireless Pers Commun (2012) 66:855-864 DOI 10.1007/s11277-011-0411-7

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Author's personal copy Wireless Pers Commun (2012) 66:855–864 DOI 10.1007/s11277-011-0411-7

Novel Compact Dual-Band Rat-Race Coupler Combining Fractal Geometry and CRLH TLs He-Xiu Xu · Guang-Ming Wang · Xiao-Kuan Zhang · Xiao-Lei Yang

Published online: 8 October 2011 © Springer Science+Business Media, LLC. 2011

Abstract A super compact fractal-shaped composite right/left handed (CRLH) rat-race coupler (RRC) is proposed for the first time by skillfully combining two circuit schematics of the RRC operating at two arbitrary frequencies. For dual-band (DB) purpose, novel circuit schematics of RRC are deducted, and close-form formula and design procedures are derived in detail. The CRLH transmission line (TL) consists of lumped elements for the left handed part and Koch-shaped microstrip lines (MLs) for the right handed part. Since conventional RRC exhibits two types of unique branches, the DB design often suffers a tedious process. By employing the CRLH TL, the realization of a DB RRC becomes much easier. Moreover, constructing the microstrip lines as Koch curves enables the compactness of the circuit. For verification, a coupler operating at 0.75 and 1.8 GHz is fabricated and measured. Consistent results between simulation and measurement have confirmed the design and shown that the RRC with an area of 10.2% of its conventional counterpart owns excellent in-band performances. Keywords Rat-race coupler · Compact · Dual-band · Fractals · Composite right/left handed transmission line (CRLH TL) · Lumped elements

1 Introduction The rapid development of modern wireless communication has imposed an increasing demand for multi-standard and compact RF/microwave devices, not to mention the rat-race couplers (RRC). A survey of covered literatures suggests that the multiband components with miniaturized dimensions have aroused a wide of particular interest. As one type of 180◦ hybrids, conventional RRC was generally categorized as one of the most important microwave passive devices. Moreover, the compact dual-band (DB) RRC enables low cost, high reliability and integrity. Up to date, numerous approaches have been developed for

H.-X. Xu (B) · G.-M. Wang · X.-K. Zhang · X.-L. Yang Missile Institute of Air Force Engineering University, 713800 Sanyuan, People’s Republic of China e-mail: [email protected]

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compact issue, e.g., RRCs were implemented based on the capacitor loading [1] and periodic slow-wave loading [2], by using periodic stepped-impedance ring resonators [3] and T-shaped photonic bandgap (PBG) cells [4], however, the most used technique should be fractals [5–7]. Although these RRCs feature compact size, they are remarkably restricted to DB applications and thus deserve further investigations. As to the DB design, much fewer literatures were reported, e.g., using tri-section branch-line [8], stepped-impedance-stub units [9] and two T-shape open-stub units [10]. However, these implementations were either tedious or much difficult to be followed and typically featured large size. The lack of literatures concerning both the DB and size reduction property makes the design of a compact DB RRC a pressing task. The concept of composite right/left handed transmission line (CRLH TL) has been extensively applied to develop broadband and DB components [11–13]. However, the circuit size of these devices is even larger than their conventional counterparts, which certainly deviates from current requirements of microwave integrated circuits (MIC). Most recently, the concept of combining fractal geometries and CRLH TL has been popularized by the authors and demonstrated as a preferable strategy to engineer super compact devices with comparable DB and broadband performances [14–16]. Nevertheless, neither DB RRC has been experimentally reported yet by using the technique of CRLH TL because of the unique phase relation of the two types of branches. In this paper, we proposed a novel DB RRC based on the strategy of combining the fractal geometry and CRLH TL inspired by [14–16]. However, current DB design using CRLH TL is different from any previous one. To this end, two possible circuit schematics are deducted firstly in Sect. 2, followed by elaborate derivation of the design procedures and close-form equations. In Sect. 3, illustrative results of simulation and measurement and discussions are provided. Finally, the major conclusion is highlighted in Sect. 4.

2 Theory and Design Conventional RRC whose circuit topology outlined in Fig. 1 is a lossless reciprocal four-port network with two applications, namely a power divider and a power combiner.√ It consists of three −90◦ branches and one −270◦ branch with characteristic impedance of 2Z 0 , where Z 0 is the reference port impedance corresponding to 50. As a power divider, it can be used for in-phase operation and 180◦ out-of-phase operation, respectively. In the case of in-phase operation, a signal applied to port 1 divides equally into ports 2 and 3 with identical phase while port 4 is isolated, whereas in out-of-phase operation a signal injected into port 4 separates evenly in ports 2 and 3 with 180◦ phase discrepancy while port 1 is isolated. As a power combiner, two signals with 180◦ phase difference injected simultaneously into ports 2 and 3 are outputted through port 4, whereas the sum of inputs will be formed at port 1 when the two signals are with the same phase. The network with four pairs of transmission port and two pairs of isolation port (ports 1 and 4, ports 2 and 3) can be expressed by a scatting matrix [S] ⎤ ⎡ 0 1 1 0 j ⎢ 1 0 0 −1 ⎥ ⎥ (1) [S] = √ ⎢ 2 ⎣1 0 0 1 ⎦ 0 −1 1 0 Unlike previous DB implementations by adopting CRLH TL [12–14], the design of current DB RRC is less direct and more complicated to be carried out. The discrepancy appears mainly because the synthesis of a DB RRC requires combining two different networks with

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Fig. 1 Circuit schematics of the RRCs a conventional one; derivative ones with b one +90◦ branch and c three +90◦ branches

two types of branches in each network, whereas two different networks each with identical branches are combined in already covered DB devices such as quarter-wavelength open-circuited and short-circuited stubs, branch-line coupler and Wilkinson power divider [12–14]. To begin with, two circuit schematics with corresponding behavior are compulsory if one embarks on designing a DB RRC. With a deep insight into the essence, another two types of RRCs with schematics shown in Fig. 1b, c are derived. Three possible combinations of any two networks are obtained, and the two networks shown in Fig. 1a, c are examined as the exclusive selection which will be specified later. To develop a DB RRC, we consider using two types of CRLH branches with specified phases to combine these two networks operating at two arbitrary frequencies, respectively. For convenience, the specified two frequencies 0.75 and 1.8 GHz are denoted as f L and f H , respectively. For better understanding, let us begin with the basic concept and dispersion relation of CRLH TL to briefly derive the fundamental DB theory. The circuit model of a CRLH cell, not reproduced here for brevity, is comprised of a left handed (LH) inductanceL L in parallel with a parasitic right handed (RH) capacitor C R in shunt branch, and a LH capacitor C L in series with a RH inductor L R in series branch. The C L and L L are associated with antiparallel group and phase velocities. In practice, CRLH TLs can be realized by either using chip components based on surface mounted technology (SMT) [11–16] or using distributed elements. In the former case, SMT chip components guarantee good performance up to 4–6 GHz due to the self-resonance effect. Otherwise, it is beneficial to substitute distributed elements for them at higher frequencies. In this work, we consider constituting the RH and LH contribution of the 70.7 CRLH branches by microstrip lines (MLs) and SMT chip elements, respectively. The phase shift of CRLH TL endures a broad range of values varying from positive to negative ones across the frequency domain from DC to high frequency and can be predicted by the hyperbolic-linear dispersion relation. N ϕ CRLH (ω) = √ − N ω L RCR (2) ω L L CL Note that N is the number of CRLH cell. Controllable dispersion diagram enables the CRLH TL an attractive candidate to design four branches of the DB RRC. It is extremely useful to mention that (2) is valid under the balanced condition L R × C L = L L × C R which has eased the design to a great extent, otherwise the CRLH TL can not be decoupled into separate LH and RH part, respectively. In this condition, the LH band switches to RH region without a gap. Moreover, the impedance of LH and RH part, and the characteristic impedance of the CRLH cell are quantitatively the same. √ LR LL CRLH Z = Zc = = = 2Z 0 (3) CR CL

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At f L , the RRC operates in the state of Fig. 1c with three +90◦ branches and one −90◦ branch, whereas at f H , the RRC operates in the state of Fig. 1a with three −90◦ branches and one −270◦ branch. For convenience, we denote the CRLH branch whose phase is +90◦ at f L while −90◦ at f H as CRLH TL1 , whereas CRLH TL2 is corresponding to the CRLH branch with phase −90◦ at f L while −270◦ at f H . Consequently, the DB RRC is composed of three branches of CRLH TL1 and one CRLH TL2 . ϕ L and ϕ H are the required phases at f L and f H , respectively and are formulated by ϕ CRLH (ω = ω L = 2π f L ) = ϕ L , ϕ

CRLH

(ω = ω H = 2π f H ) = ϕ H .

(4a) (4b)

We obtain four equations while own four unknowns, therefore explicit expressions for circuit parameters can be acquired after some manipulations [12]. Z c [ϕ L ( f L / f H ) − ϕ H ]

, 2π N f H 1 − ( f L / f H )2 ϕL ( f L / f H ) − ϕ H

, CR = 2π N f H Z c 1 − ( f L / f H )2

N Z c 1 − ( f L / f H )2 , LL = 2π f L [ϕ L − ϕ H ( f L / f H )] N [1 − ( f L / f H )2 ] . CL = 2π f L Z c [ϕ L − ϕ H ( f L / f H )] LR =

(5a) (5b) (5c) (5d)

Referring to (5), the following condition should be satisfied to maintain the L R and C R positive. ϕL f L ≥ ϕ H f H

(6)

Consulting (6), circuit schematics of Fig. 1b, c are theoretically predicted impossible to be combined. With a further observation, we find that the schematics of Fig. 1a, c are the exclusive selection in terms of combination. For verification, novel designed RRC is built on F4B-2 microstrip substrate with a dielectric constant of 2.65 and a thickness of 1 mm based on standard print circuit board (PCB) fabrication process. For simplicity, two CRLH cells are utilized. For the implementation of the LH contribution, two cascaded T-networks with schematics depicted in Fig. 2 are adopted. Note that CRLH TL terminated by two capacitors of 2C L in each end is from the point of view of an easy impedance match and improved transmission performances. As to the design of fractal-shaped RH contribution, the design procedures are mainly involved three steps. First, with computed L R and C R , the electrical length of conventional ML is determined. ϕ RH = −N ω L L R C R (7) Also the width of ML is fixed according to Z c and dielectric substrate. Table 1 summarizes the circuit parameters and dimensions of ML of the designed CRLH TLs. Second, Koch curves whose iteration factor and iteration order are 1/4 and 2, respectively are applied to facilitate a super compact size. Since the middle raised fractal sections are removed to load SMT capacitors, the length Q corresponding to the removed fractal sections should be added to conventional ML P for compensation. Right-angle bends are replaced by chamfered ones to connect the resultant fractal sections for the sake of minimizing current discontinuity. However, it is just these bends that results in additional phase shift. The phase-shifting property of fractals has been demonstrated [14] and is not negligible. Here the phase-equalizing

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Fig. 2 Circuit configuration of the RRCs, a conventional design; b novel design and c circuit confifuration of the LH part of the two-cell CRLH TLs

Table 1 Detailed circuit parameters and dimensions of ML of the designed CRLH TLs TL type

L L (n H )

C L ( p F)

2C L ( p F)

L R (n H )

C R ( p F)

ϕ RH (deg)

P

W

1.68

−64.3

49.1

1.5

3.1

−117.2

89.6

1.5

CRLH TL1 TC

11.1

2.2

4.4

PU

12

2

4.7

8.42

CRLH TL2 TC

63.1

12.6

25.2

PU

56 + 6.8

12

12 + 12

15.3

TC means theoretically computed and PU means practically used, P and W are length and width of the ML in mm

method developed in [14] can be extended directly in this work. A slight physical length b corresponding to the phase shift generated by each bend is applied to take into account this effect. The value of b evaluated at f 0 is formulated after some manipulations from [17] 19.2π h

2 − ( f 0 h/0.4Z C )2 b = √ εe f f Z C

(8)

where εe f f is the effective dielectric constant, h is the height of substrate in millimeters. With determined b, the length of Koch-shaped ML should be reduced by b per bend. L = P + Q − n × b

(9)

Third, the optimization is actually very essential and is performed around L to accurately design fractal curve through MOM (moment of method)-based solver Ansoft Designer. The final stage is considered to locate the four branches in an appropriate configuration to maximize the size reduction. Since the necessary space accommodating CRLH TL1 is much smaller than that of CRLH TL2 , we consider changing orientations of several chamfered bends of CRLH TL2 to form a closed-loop, which allows us an additional degree of freedom to facilitate a super compact circuit. The engineered configuration of the fractal-shaped RRC is depicted in Fig. 2. As can be observed, the proposed DB RRC with an occupied square area of 52.2 × 39.4 mm2 is only 10.2% of 150 × 135 mm2 that its conventional circular counterpart occupies, therefore the combined technology shrinks the circuit by 89.8%.

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3 Illustrative Results For characterization, the eventually designed DB RRC is analyzed through the dynamic links and solver of planar EM and Circuit cosimulation in Ansoft Designer. For verification, the RRC is fabricated and measured by Anritsu ME7808A vector network analyzer. Figure 3 illustrates the photograph of fabricated prototype for experimental use. The SMT chip capacitors and inductors with 0805 and 0603 packages are adopted in the experimental circuit. Figure 4 compares the S-parameters and output phase and amplitude imbalances between simulation and measurement for in-phase operation, whereas the comparison of simulated and measured results for out-of-phase operation is illustrated in Fig. 5. Reasonable agreement can be observed across the entire frequency band of interest except a slight frequency shift of the fundamental band toward higher frequencies in the measurement case which has confirmed the effectiveness of the design. The slight discrepancy is mainly attributable to the slight value deviation of the marketable chip components from the theoretically calculated ones, and the non-ideal components with a variation of ±10% applied in the experiment while partially to the soldering pad which contributes to the phase delay, and the tolerances that are inherent in the fabrication process. Nevertheless, the discrepancy is in a normal acceptable range. Referring to Figs. 4 and 5, the DB performance can be clearly seen around 0.75 and 1.8 GHz. For in-phase operation, the measured return loss |S11 | is 24.2 dB, insertion losses |S21 | & |S31 | are 3.4 and 3.1 dB, respectively, and isolation |S41 | is 28.3 dB at 0.75 GHz,

Fig. 3 Fabricated prototype of the proposed DB RRC

Fig. 4 Comparison between simulation and measurement for in-phase operation, a S-parameters; b output magnitude and phase imbalance

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Fig. 5 Comparison between simulation and measurement for 180◦ out-of-phase operation, a S-parameters; b output magnitude and phase imbalance

Table 2 Summary of the performances of the proposed RRC for in-phase operation

RL

IL

Isolation

MI

PI

S

18.2

2.9 & 3.3

33.1

0.35

−0.3

M

24.2

3.4 & 3.1

28.3

−0.4

−4.2

CF1

FBW1 S

0.66–0.94

0.61–0.99

0.57–0.97

0.62–0.87

0.66–0.99

M

0.7–0.92

0.64–1.01

0.54–1.1

0.63–1

0.73–1.1

S

29.3

3.1 & 3.2

33.3

0.15

0.5

M

19.9

3.2 & 3.5

28.5

0.6

−0.15

CF2

FBW2 S

1.58–2.14

1.48–2.29

1.45–2.31

1.57–2.44

1.4–2.36

M

1.56–2.16

1.46–2.3

1.11–2.33

1.5–2.4

1.37–2.04

whereas at 1.8 GHz, the measured |S11 | is 19.9 dB, |S21 | & |S31 | are 3.2 and 3.5 dB, respectively, and |S41 | is 28.5 dB. The out-of-phase performances at 0.75 and 1.8 GHz are found very comparable to the in-phase performances and thus are not listed for brevity. Tables 2 and 3 summarize the simulated and measured results in detail for in-phase and out-of-phase operation, respectively. In the former case, measured results indicate that the |S11 | better than 15 dB, |S21 | & |S31 | less than 5 dB, |S41 | larger than 20 dB and magnitude and phase imbalances varying within 1 dB and 5◦ are obtained from 0.73 to 0.92 GHz. Therefore, a fractional bandwidth (FBW) of 190 MHz (a relative bandwidth of 25.3%) is achieved for the fundamental lower band, whereas a FBW of 26.7% is obtained from 1.56 to 2.04 GHz for the higher band. In the latter case, a FBW of 32% characterized by |S44 | better than 15 dB, |S24 | & |S34 | less than 5 dB, |S14 | larger than 20 dB and magnitude and phase imbalances varying within 1 dB and 5◦ is acquired from 0.69 to 0.93 GHz for the fundamental lower band while a FBW of 28.3% from 1.59 to 2.1 GHz is achieved in the higher band. In general, the developed DB RRC demonstrated with a modest operation bandwidth and excellent in-band performances in terms of low insertion loss and return loss should be highlighted.

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Table 3 Summary of the performances of the proposed RRC for out-of-phase operation RL

IL

Isolation

MI

PI

CF1 S

21.6

3.27 & 2.97

33.1

−0.29

−0.29

M

28.4

3.25 & 3.7

28.4

0.43

−3.3

S

0.66–0.91

0.62–0.96

0.56–0.96

0.62–0.86

0.66–0.96

M

0.68–0.93

0.63–1

0.54–1.12

0.58–0.99

0.69–1.09

S

34.8

3.2 & 3.1

33.3

−0.15

−0.34

M

31.7

3.89 & 3.22

28.57

−0.67

0.6

S

1.58–2.11

1.49–2.29

1.46–2.31

1.57–2.28

1.34–2.39

M

1.59–2.13

1.46–2.28

1.36–2.33

1.47–2.31

1.31–2.1

FBW1

CF2

FBW2

RL, IL represent return and insertion loss| in dB, while MI, PI are magnitude imbalance in dB and phase imbalance in degree, respectively. FBW1 and FBW2 are FBW in GHz at the lower and higher band characterized by |S11 | or |S44 | ≥ 15 dB, |S21 | & |S31 | ≤ 5 dB or |S24 | & |S34 | ≤ 5 dB, |S41 | ≥ 20 dB, |MI| ≤ 1 dB and |PI| ≤ 5◦

4 Conclusions It has been successfully demonstrated that a super compact CRLH RRC is engineered with good DB performances based on the derived circuit schematics of RRC. The concept of combining fractal geometry and CRLH TL has been validated in the implementation of compact DB RRC. The RRC features low insertion loss, modest operation bandwidth and good isolation between output ports. The most important aspect to note is that the DB RRC obtains a 89.8% size reduction. The design concept can be also applied to other fractal structures (Sierpinski, Hilbert, etc.) and other metamaterials in other technologies (CPW, stripline, etc.). The strategy to engineer a DB RRC by using CRLH TL should be beneficial to our engineers and technicians. Acknowledgments This work is fully supported by the National Natural Science Foundation of China under Grant Nos. 60971118. The authors would also like to extend their gratefulness to the anonymous reviewers for their valuable comments.

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Author Biographies He-Xiu Xu graduated in Radar engineering from the Missile institute of Air Force Engineering University, Xi’an, China, in 2008. From 2004 to now, he has served as a reviewer of IEEE microwave and wireless components letters, Progress in electromagnetic research, Radio Science and international journal of electronics and has authored or coauthored more than 25 conference, letter and journal papers. He is now pursing his Ph.D. Degree in the major of electromagnetic field & microwave technique. His research interests include metamaterials and fractals as well as their applications to microwave components and antennas.

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H.-X. Xu et al. Guang-Ming Wang received his B.S. and M.S. degrees from the Missile institute of Air Force Engineering University, Xi’an, China, in 1982 and 1990, respectively, and his Ph.D. degree from the electronic science and technology university, Chengdu, China, in 1994. He joined the Air Force Engineering University as an associate professor and was promoted to a full professor in 2000, and is now the head of the Microwave Laboratory center of it. He has been a senior member of Chinese Commission of Communication and Electronic. He has authored or coauthored approximately 100 conference, and journal papers. From 1994 to now, he was awarded and warranted several items supported under National Natural Science Foundation of China and fulfilled many local or military scientific research programs. His current interest includes microwave circuits, antenna, and also the new structures include EBG, PBG, Metamaterias and fractals, etc.

Xiao-Kuan Zhang received his M.S. and Ph.D. degree in the major of electromagnetic field & microwave technology from Missile institute of Air Force Engineering University, Xi’an, China, in 1999 and 2003, respectively and is now an associate professor and associate dean in Microwave Laboratory center of it. From 2001 to now, he has authored or coauthored more than 15 conference, letter and journal papers and fulfilled many local or military scientific research programs up. His research interests include target characteristic and its application research.

Xiao-Lei Yang graduated in Radar engineering from the Missile institute of Air Force Engineering University, Xi’an, China, in 2009 and is now pursing his M.S. Degree. His research interests include microwave antenna and circuit, object characteristic.

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