IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 4, APRIL 2018
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Dual-/Tri-Band Branch Line Couplers With High Power Division Isolation Using Coupled Lines Wenjie Feng, Yu Zhao, Wenquan Che, Senior Member, IEEE, Haidong Chen, and Wanchen Yang
Abstract—Two novel dual-/tri-band branch line couplers with high power division isolation using coupled lines are proposed in this brief. Two conventional couplers loaded with quarterwavelength open/shorted coupled lines are adopted to realize the dual or triple bands. Each band has a high isolation due to the introduced transmission zeros. The center frequencies of the two planar couplers can be adjusted over a wide frequency band by changing the even/odd-mode characteristic impedances of the coupled lines. Two planar dual-/tri-band couplers located at 0.75/1.32 GHz, 0.69/1.0/1.4 GHz are designed and fabricated for verification. Good agreement can be observed between measured results and theoretical expectations. Index Terms—Branch line coupler, high isolation, open/shorted coupled lines, dual-/tri-band operation.
I. I NTRODUCTION HE BRANCH-LINE coupler is one of the most important components in various fields of microwave systems. It is a four-port microwave device, which is frequently used for power combining/splitting. For example, they are widely used in balanced circuits, antennas, rectifiers, power amplifier and so on [1]–[4]. Recently, several new approaches are developed for the branch line couplers operating at two or three arbitrary frequencies. The most common approach to design a dual/triband coupler is by directly substituting dual/tri-band blocks, composite right/left-handed (CRLH) transmission lines for the single/dual-band λ/4 transmission line sections [2]–[5]. The Pi-network, T-network are a few examples of dualband quarter-wave blocks [6]–[8]. To achieve the tri operating frequency band, the open- and shorted-ended stubs are tapped at the center of the Pi-type lines [9]–[12]. The above published researches mainly use extra stubs to realize the dual or tri-band passbands for the branch line couplers [6]–[12]. However, the loaded stubs are often with
T
Manuscript received April 4, 2017; revised July 3, 2017; accepted August 10, 2017. Date of publication August 15, 2017; date of current version March 26, 2018. This work was supported in part by the National Natural Science Foundation of China under Grant 61401206, Grant 61571231, and Grant 61627802; in part by the Qing Lan Project of Jiangsu Province under Grant 2017-2020; and in part by the Open Funding of State Key Laboratory of Millimeter Waves under Grant K201804. This brief was recommended by Associate Editor A. Cilardo. (Corresponding author: Wenjie Feng.) The authors are with the Department of Communication Engineering, Nanjing University of Science and Technology, Nanjing 210094, China (e-mail:
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCSII.2017.2739751
Fig. 1.
Ideal circuit of the proposed planar dual-band coupler.
different electrical wavelengths, thus it is difficult to derive the design equations. In addition, it is hard for tri-band couplers to realize the power division effect at the center frequency, and the isolations between different frequencies are usually not so high. Little research has described the applications of using coupled lines to design multi-band planar branch line couplers with high isolation between each passband. In this brief, two planar couplers for dual-band and tri-band demands are proposed. Using quarter-wavelength open/shorted coupled lines connected to the conventional branch line coupler, dual-band and tri-band performances can be easily realized for the planar couplers. Each passband has high isolation degrees by adding extra transmission zeros. Closedform design equations are derived and the specific frequency of each passband is given. The dual-band planar coupler is located at 0.75/1.32 GHz, and the tri-band coupler is located at 0.69/1.0/1.4 GHz. All the circuits and structures are simulated with Ansoft Designer v3.0 and Ansoft HFSS v13.0, and constructed on the dielectric substrate with εr = 2.65, h = 1.0 mm, and tanδ = 0.003. II. A NALYSIS OF THE P ROPOSED C OUPLERS In this section, two branch line couplers using open/shorted coupled lines are analyzed in detail; even-odd-mode analysis [13] is employed to simplify the analysis and to derive the operating frequencies of the passbands. A. Dual-Band Coupler and Circuit Analysis Fig. 1 shows the structure of the proposed dual-band coupler. The loaded open coupled line (Z oe , Z oo , θ ) is attached to each port of the conventional branch-line coupler that consists
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 4, APRIL 2018
Substituting (10) into (11), the relationship between the Y ee1 , Y eo1 , Y oe1 , Y oo1 can be obtained and simplified as Z02 Yee Yeo = 1
(12)
=1
(13)
Z02 Yoe Yoo
From (12)-(14) can be obtained as: Yee Yeo = Yoe Yoo
(14)
Substituting (2)∼(5) into (14), the expression of YC can be obtained and simplified as: θ 1 Z1 + Z2 θ (15) (cot − tan ) 2 Z1 Z2 2 2 To realize the dual-band operation, four open coupled lines are connected at Ports 1, 2, 3 and 4 respectively, as shown in Fig. 1. The admittance of the open coupled line YC1 can be represented as: YC = j
Fig. 2. Decomposed equivalent circuits of the proposed dual-band coupler. (a) Even–even-mode circuit. (b) Even–odd-mode circuit. (c) Odd–even-mode circuit. (b) Odd–odd-mode circuit.
of four quarter-wave length transmission lines with the electrical length θ and characteristic impedance Z 1 or Z 2 . Thus the electrical length θ equals to 90◦ at the center frequency. Due to the symmetry of the dual-band coupler, the even-odd- mode analysis is employed to simplify the analysis and to derive the operating frequencies [13], which are required to meet the following properties: S11 = S41 = 0, |S21 | = |S31 |
(1)
By placing electric wall (E-wall) and E-wall, magnetic wall (H-wall) and H-wall, E-wall and H-wall, H-wall, and E-wall along the symmetry lines A-A and B-B , respectively [13], the eigen-admittances Y ee , Y eo , Y oe , Y oo of Fig. 2 can be illustrated as follows(YC : the admittance of the coupled line): tan(θ/2) tan(θ/2) +j + YC Z1 Z2 tan(θ/2) cot(θ/2) Yeo = j −j + YC Z1 Z2 cot(θ/2) tan(θ/2) Yoe = −j +j + YC Z1 Z2 cot(θ/2) cot(θ/2) Yee = −j −j + YC Z1 Z2 The S-parameters of the crossover can simply be derived Yee = j
(2) (3) (4) (5) as:
ee1 + eo1 + oe1 + oo1 (6) S11 = 4 ee1 − eo1 + oe1 − oo1 S21 = (7) 4 ee1 − eo1 − oe1 + oo1 (8) S31 = 4 ee1 + eo1 − oe1 − oo1 (9) S41 = 4 and Γee1 , Γeo1 , Γoe1 and Γoo1 are the corresponding input reflection coefficients under different excitations, where 1 − Z0 Yee1,eo1,oe1,oo1 ee1,eo1,oe1,oo1 = (10) 1 + Z0 Yee1,eo1,oe1,oo1 Using (1) and the relationship (6)-(9) to acquire ee + eo = 0 oe + oo = 0
(11)
Yc1 = j
2 tan θ Zoe + Zoo
(16)
From (15)-(17) can be obtained and simplified as: Zoe + Zoo =
4 tan θ cot
θ 2
− tan
θ 2
tan2 θ2 Z1 Z2 8Z1 Z2 = ··· = Z1 + Z2 Z1 + Z2 (1 − tan2 θ2 )2
(17) When Z oe , Z oo , Z 1 , and Z 2 are determined, we can obtain the equation about θ : θ 2 (1 − tan2 θ2 )2
tan2
(Zoe + Zoo)(Z1 + Z2 ) (18) 8Z1 Z2 (Zoe + Zoo)(Z1 + Z2 ) =m (19) Setting 8Z1 Z2 Solve the equation (18), we have √ (2m + 1) ± 4m + 1 2 θ tan = (20) 2 2m Thus, we can obtain the two operating frequencies of the dual-band coupler: √ (2m + 1) + 4m + 1 , θ( f2 ) = π − θ( f1 ) θ( f1 ) = 2 arctan 2m (21) =
and the transmission zero is at the center of two operating frequencies calculated in (21). The simulated results of the dual-band coupler are shown in Figs. 3(a)(b), good power division for |S21 |&|S31 | = 3dB @Zoe /Zoo = 80/40 , 100/60 , 150/80 can be easily realized with perfect match and isolation |S11 |/|S41 | > 20 dB@ Zoe /Zo o=80/40 , 100/60 , 150/80 . In addition, we can clearly observe that the passband center frequencies adjusted over a wide band by changing the even/odd-mode characteristic impedances of the coupled lines. B. Tri-Band Coupler and Circuit Analysis By substituting the shorted coupled lines for the open ones to connect at Ports 1, 2, 3 and 4, we can easily realize the tri-band demand. Fig. 4 shows the structure of the proposed
FENG et al.: DUAL-/TRI-BAND BRANCH LINE COUPLERS WITH HIGH POWER DIVISION ISOLATION USING COUPLED LINES
Fig. 3. The simulated results of the dual-band coupler. (a) |S11 |&|S21 | versus Zoe & Zoo, (b) |S31 |&|S41 | versus Zoe & Zoo. (Z1 = 50 , Z2 = 35.36 , θ = 90◦ ).
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Fig. 6. The simulated results of the tri-band coupler. (a) |S11 |&|S21 | versus Zoe & Zoo, (b) |S31 |&|S41 | versus Zoe & Zoo. (Z1 = 50 , Z2 = 35.36 , θ = 90◦ ).
Setting Z1 + Z2 =n (24) 2Z1 Z2 When Z oe , Z oo , Z 1 , and Z 2 are determined, simplify and solve the equation (23) and we can express the equation about θ : n(Zoe − Zoo)2 + (Zoe + Zoo) , cos θ2 = 0 n(Zoe + Zoo)2 + (Zoe + Zoo) Thus we have three roots of θ : n(Zoe − Zoo)2 + (Zoe + Zoo) , θ ( f1 ) = arccos n(Zoe + Zoo)2 + (Zoe + Zoo) θ ( f2 ) = 90◦ , θ ( f3 ) = π − θ ( f1 ) cos2 θ =
Fig. 4.
Ideal circuit of the proposed planar tri-band coupler.
Fig. 5. Decomposed equivalent circuits of the proposed tri-band coupler. (a) Even–even-mode circuit. (b) Even–odd-mode circuit. (c) Odd–even-mode circuit. (b) Odd–odd-mode circuit.
tri-band coupler. Similarly, due to the symmetry of the dualband coupler, the even-odd- mode analysis is employed to simplify the analysis and to derive the operating frequencies, and the equivalent circuits of the proposed tri-band coupler are shown in Fig. 5. The previous part of the derivations of the tri-band coupler are the same as the dual-band one, as (1)∼(15) shown. The difference lies in the choice of the open or shorted coupled lines. The admittance of the shorted coupled line YC2 can be represented as: Yc2 = j
(Zoe + Zoo ) sin 2θ (Zoe + Zoo )2 cos2 θ − (Zoe − Zoo )2
(22)
From (15) and (22), (23) can be obtained as: 1 Z1 + Z2 θ θ = (1 − tan2 ) 2 2 Z1 Z2 2 × [(Zoe + Zoo )2 cos2 θ − (Zoe − Zoo )2 ] (23)
2(Zoe + Zoo ) sin θ cos θ tan
(25)
(26)
and the transmission zeros introduced by the coupled lines are obtained as: Zoe − Zoo , θtz2 = π − θtz (27) θtz = arccos Zoe + Zoo The simulated results of the tri-band coupler are shown in Figs. 6(a)(b), good power division for |S21 |&|S31 | = 3dB @Zoe/Zoo=80/40 , 100/60 , 150/90 can be easily realized with perfect match and isolation |S11 |/|S41 | > 20 dB@ Zoe/Zoo=80/40 , 100/60 , 150/80 . In addition, we can clearly observe that the passband center frequencies adjusted over a wide band by changing the even/odd-mode characteristic impedances of the coupled lines. C. Proposed Two Planar Couplers Based on the above discussions and analysis, the simple design procedures of the two couplers can be summarized as: (1) Based on the equations (19)-(21), (24)-(26), choose the desired center frequency f 0 of the two couplers and the passband frequency ratio; determine the characteristic impedances Z 1 , Z 2 according to the conventional branch line coupler; determine the even/odd -mode values Z oe , Z oo according to the desired frequency ratio; (2) When Z oe , Z oo , Z 1 , and Z 2 are determined, using the commercial software in Ansoft Designer to determine the original values, and convert the characteristic impedance to the physical dimensions of coupled lines and transmission lines; (3) According to the schematic simulation results from Ansoft Designer, to choose the proper layouts and routing of the two couplers in the commercial software
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 4, APRIL 2018
TABLE I PARAMETERS OF THE P ROPOSED T WO C OUPLERS (εr = 2.65, h = 1.0 mm, AND tan δ = 0.003)
(a) Fig. 7.
(b)
Geometries of the two couplers (a) Dual-band, (b) Tri-band. Fig. 8. Photograph, simulated and measured results of the dual-band coupler. (a) |S11 |&|S21 |, (b) |S31 |&|S41 |.
Ansoft HFSS; carry out further full-wave electromagnetic simulation and dimension optimization. Two prototypes of the proposed couplers both with sizes of 100 mm× 100 mm, are shown in Figs. 7 (a)-(b). The circuit and structure parameters are shown in Table I. The simulated results of two couplers are shown in Figs. 8-9. For the dual-band coupler, the passband center frequency is located at 0.75/1.32 GHz, maximal insertion losses |S21 |/|S31 | simulated for the two passbands are 3.26/3.33 dB,3.59/3.67 dB, respectively. The difference of insertion losses at output ports (|S21 |_in dB - |S31 |_in dB) is within ±0.1dB. The phase difference ∠|S21 |-∠|S31 | is within 90◦ ±2◦ . Within the frequency range 0.72∼0.78 GHz, 1.31∼1.33 GHz, the simulated |S11 | is more than 14 dB, and isolation |S41 | are more than 14 dB for 0.72∼0.78 GHz, 1.29∼1.34 GHz. For the tri-band coupler, the passband center frequency is located at 0.69/1.0/1.4 GHz, maximal insertion losses |S21 |/|S31 | simulated for the three passbands are 3.08/3.32 dB,3.34/3.53 dB,3.47/3.40 dB, respectively. The difference of insertion losses at output ports (|S21 |_in dB |S31 |_in dB) is within ±0.3 dB. The phase difference ∠|S21 | - ∠|S31 | is within 90◦ ±1.5◦ . Within the frequency range 0.665∼0.713 GHz, 0.984∼1.018 GHz, 1.388∼1.42 GHz, the simulated |S11 | is more than 16 dB, and isolation |S41 | are more than 16 dB for 0.662∼0.715 GHz, 0.982∼1.02 GHz, 1.375∼1.42 GHz.
Fig. 9. Photograph, simulated and measured results of the tri-band coupler. (a) |S11 |&|S21 |, (b) |S31 |&|S41 |.
III. E XPERIMENT AND R ESULTS D ISSCUSION For further demonstration, two coupler prototypes are fabricated and measured. The photographs, measured results of the two proposed couplers are also illustrated in Figs. 8-9. Good agreements can be observed between the simulation
and the experiments. For the dual-band coupler, the passband center frequency is located at 0.756/1.42 GHz, maximal insertion losses |S21 |/|S31 | measured for the two passbands are 3.35/3.74 dB,4.0/4.1 dB, respectively. The difference of
FENG et al.: DUAL-/TRI-BAND BRANCH LINE COUPLERS WITH HIGH POWER DIVISION ISOLATION USING COUPLED LINES
TABLE II C OMPARISONS OF M EASURED R ESULTS FOR D UAL -BAND C OUPLERS
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wavelengths of the stubs, it is difficult to derive the design equations and calculate each passband center frequencies. In this brief, we use quarter-wavelength coupled lines for dual/tri-band operation and the calculations become more convenient. In addition, compared with other couplers, the proposed dual/tri-band branch line couplers have high isolation degrees between different passbands. IV. C ONCLUSION
TABLE III C OMPARISONS OF M EASURED R ESULTS FOR S OME T RI -BAND C OUPLERS
In this brief, two novel planar couplers with high isolation using open/shorted coupled lines are proposed for dual/tri-band operation. The center frequency of the two planar couplers can be adjusted over a wide frequency band by changing the even/odd-mode characteristic impedance of the coupled lines. The proposed couplers have advantages of multiband operation, simple structures and high isolation. Good agreements between simulated and measured responses of the structures are demonstrated, indicating good candidates for planar microwave circuits and systems. R EFERENCES
insertion losses at output ports (|S21 |_in dB - |S31 |_in dB) is within ±0.65dB. The phase difference ∠|S21 | - ∠|S31 | is within 90◦ ±4◦ . Within the frequency range 0.726∼0.806 GHz, 1.38∼1.46 GHz, the measured |S11 | is more than 14 dB, and isolation |S41 | are more than 14 dB for 0.716∼0.78 GHz, 1.35∼1.43 GHz. For the tri-band coupler, the passband center frequency is located at 0.736/1.02/1.44 GHz, maximal insertion losses |S21 |/|S31 | measured for the three passbands are 3.0/3.62 dB, 3.13/3.9 dB, 3.06/3.63 dB respectively. The difference of insertion losses at output ports (|S21 |_in dB - |S31 |_in dB) is within ±0.8dB. The phase difference ∠|S21 | - ∠|S31 | is within 90◦ ±1.5◦ . Within the frequency range 0.707∼0.746 GHz, 1.01∼1.04 GHz, 1.43∼1.47 GHz, the measured |S11 | is more than 16 dB, and isolation |S41 | are more than 16 dB for 0.697∼0.746 GHz, 1.01∼1.03 GHz, 1.41∼1.46 GHz. For the purpose of comparison, Table II and Table III illustrate the measured results for some other published researches on dual-band and tri-band couplers. It can be seen that, other researches above are mainly used extra stubs [6]–[12] to realize the dual or tri-band demands. Due to different electrical
[1] A. Kosuge, S. Ishizuka, M. Taguchi, H. Ishikuro, and T. Kuroda, “Analysis and design of an 8.5-Gb/s/link multi-drop bus using energyequipartitioned transmission line couplers,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 62, no. 8, pp. 2122–2131, Aug. 2015. [2] I.-H. Lin, M. De Vincentis, C. Caloz, and T. Itoh, “Arbitrary dual-band components using composite right/left-handed transmission lines,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 4, pp. 1142–1149, Apr. 2004. [3] J. Bonache et al., “Application of composite right/left handed (CRLH) transmission lines based on complementary split ring resonators (CSRRs) to the design of dual-band microwave components,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 8, pp. 524–526, Aug. 2008. [4] X. Y. Zhang, Z.-X. Du, and Q. Xue, “High-efficiency broadband rectifier with wide ranges of input power and output load based on branchline coupler,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 64, no. 3, pp. 731–739, Mar. 2017. [5] W. J. Feng, X. Gao, W. Q. Che, W. C. Yang, and Q. Xue, “High selectivity wideband balanced filters with multiple transmission zeros,” IEEE Trans. Circuits Syst. II, Exp. Briefs, to be published. [Online]. Available: http://ieeexplore.ieee.org/document/7277010/ [6] K.-K. M. Cheng and F.-L. Wong, “A novel approach to the design and implementation of dual-band compact planar 90◦ branch-line coupler,” IEEE Trans. Microw. Theory Techn., vol. 52, no. 11, pp. 2458–2463, Nov. 2004. [7] K.-S. Chin, K.-M. Lin, Y.-H. Wei, T.-H. Tseng, and Y.-J. Yang, “Compact dual-band branch-line and rat-race couplers with steppedimpedance-stub lines,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 5, pp. 1213–1221, May 2010. [8] W.-J. Zhou and J.-X. Chen, “High-selectivity tunable balanced bandpass filter with constant absolute bandwidth,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 64, no. 8, pp. 917–921, Aug. 2017. [9] H. Ren et al., “Design of tri-band branch-line couplers using novel triband transmission lines,” presented at the Wireless Microw. Circuits Syst., Waco, TX, USA, Apr. 2014, pp. 1–4. [10] H. Kim, B. Lee, and M.-J. Park, “Dual-band branch-line coupler with port extensions,” IEEE Trans. Microw. Theory Techn., vol. 58, no. 3, pp. 651–655, Mar. 2010. [11] C.-Y. Liou, M.-S. Wu, J.-C. Yeh, Y.-Z. Chueh, and S.-G. Mao, “A novel triple-band microstrip branch-line coupler with arbitrary operating frequencies,” IEEE Microw. Compon. Lett., vol. 19, no. 11, pp. 683–685, Nov. 2009. [12] F. Lin, Q.-X. Chu, and Z. Lin, “A novel tri-band branch-line coupler with three controllable operating frequencies,” IEEE Microw. Wireless Compon. Lett., vol. 20, no. 12, pp. 666–668, Dec. 2010. [13] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York, NY, USA: McGraw-Hill, 1992.
