Design and Analysis of Compact Unequal-Split Wilkinson Power Divider Using Non-Uniform Transmission Lines

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1 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) Design and Analysis of Compact Unequal-Split Wilkinson Power Divider Using Non-Uniform Transmission Lines Derar Hawatmeh, Khair Al Shamaileh and Nihad Dib Department of Electrical Engineering Jordan University of Science and Technology P. O. Box 33, Irbid 2211, Jordan Abstract In this paper, the design of miniaturized unequal-split Wilkinson power divider (), with 1:2 split ratio, using nonuniform transmission lines (NTLs) is presented. To achieve compactness, the uniform transmission lines of the conventional are substituted by their equivalent NTLs. Two extra compact NTLs transformers are incorporated in each arm of the divider for output ports matching purposes. To prove the validity of the design procedure, the proposed divider is simulated using full-wave simulators, fabricated and tested. Both simulation and measurement results are in good agreement. Using NTLs, a size reduction of 22.2% is achieved, besides odd harmonics suppression. Keywords divider; Wilkinson power divider; non-uniform transmission line I. INTRODUCTION Microwave power dividers are essential components in modern microwave applications, such as antenna feed networks, phase shifters, and frequency mixers. Since its invention back in 196 [1], the Wilkinson power divider () has been considered as one of the most important dividers in microwave circuits. Recently, s have been notably addressed by researchers in many different aspects, such as reducing the size of their overall circuit area. The use of non-uniform transmission lines (NTLs) as one of the miniaturization techniques was presented in many papers [2-6]. In [2], an equal-split was miniaturized using NTLs, and a size reduction of 52% was achieved. In [3], and as an extension to what was done in [2], a dual band was proposed with 26% reduction in size (compared to the conventional dual-band ). In [4] and [5], NTL-based Bagley power divider and branch line coupler were presented, respectively. A general design procedure for NTLs-based compact multi-band equal-split was proposed in [6]. Moreover, many miniaturization techniques were introduced in the literature to accomplish compactness, such as the use of stubs. In [7, 8], dual band compact s were proposed in which stubs were incorporated to gain a significant size reduction of the circuit area. In [9], has been miniaturized using stubs too, where artificial TLs have been used to accomplish the design. In [1], a stepped impedance interdigital coupling element has been used to achieve the compactness for a single band and to suppress the odd harmonics. In this paper, based on NTLs theory, compact unequal-split, with 1:2 split ratio, is presented. This is in contrast to [2, 6], where an equal-split was considered. To achieve compactness, the conventional uniform arms of the divider are replaced by their equivalent NTLs at a specific design frequency. The proposed divider is then, simulated using two full-wave simulators to prove the validity of the design procedure. Moreover, the designed unequal-split is fabricated and measured, and both simulation and measurement results are in good agreement. II. DESIGN OF CMPACT NTLS The key step in designing compact NTLs is to find an equivalent NTL for a certain uniform transmission line (UTL) at a specific design frequency, keeping in mind that the length of the equivalent NTL (d) should be less than the UTL length (d ), as illustrated in Figure 1. Figure 1. Uniform TL and its equivalent NTL As shown in Figure 1, the equivalent NTL has a varying characteristic impedance Z(z), and propagation constant β(z), compared to the conventional uniform TL, that has a constant characteristic impedance Z, and propagation constant β. The ABCD matrix of the UTL is given as follows [11]: /11/$ IEEE

2 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) cos sin 1 sin cos where θ is the electrical length of the UTL at the design frequency. In order to characterize the NTL section, it is firstly subdivided into K uniform electrically short sections. The overall ABCD matrix of the whole NTL can be obtained by multiplying the ABCD matrices of these uniform sections as follows [11]: 2 where the ABCD parameters of the i th section can be expressed as follows [12]: cos 1 2 sin sin where Δ b 3. Then, the normalized characteristic impedance is expanded as follows [1]: ln cos 2 4 So, an optimum designed compact length NTL has to have its ABCD parameters as close as possible to the ABCD parameters of the UTL at a specific frequency. Therefore, the optimum values of the Fourier coefficients F n s can be obtained through minimizing the following error function [12]: So, the goal is to find the Fourier coefficients values (F n s) that give an NTL that has its ABCD parameters approximately equal to those of the UTL by minimizing the above error function at a specific design frequency. To solve the above constrained minimization problem, the MATLAB function fmincon.m is used. III. 1:2 NTL-BASED The conventional unequal-split parameters can be calclulated using the following equations [11]: 1 7. a 1 7. b 7. where is the power ratio between ports 3 and 2, i. e.,. Since the designed divider is of unequal-split type, output port 2 has an impedance of, while output port 3 has an impedance of [11]. To obtain 1:2 split ratio (k 2 =.5), the unequal-split parameters are found to be: Z 2 =51.5 Ω, Z 3 =13 Ω, R=16.6 Ω, R 2 =35.36 Ω and R 3 =7.71 Ω (considering a reference impedance Z = 5 Ω). Finally, to match the output ports to 5 Ω, quarter-wavelegnth matching transfromers are needed. The characteristic impedances of these matching transofrmers are calculated as follows: for port 2: Ω; and for port 3: Ω. Considering an FR-4 susbtrate (with a thickness of 1.6 mm and dielectric constant of 4.6), and a design frequency of 1 GHz, a schematic diagram for the conventional 1:2 (using Ansoft Designer [13]) including the output ports matching transformers is shown in Figure This error function should be restricted by some constraints, such as reasonable fabrication and physical matching, as follows: ( ) max ( ) Z( d) 1 Z min Z z Z (6.a) Z = = (6.b) Figure 2. Schematic diagram of the 1:2 including the output ports matching transformers. The rectangles represent uniform microstrip lines with W as the microstrip line width and P its physical length.

3 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) Now, each uniform microstrip line section in Figure 2 is replaced by its equivalent compact NTL. Table I shows the parameters used in the optimization process. It should be pointed out here that the optimized NTL arms lengths were originally chosen as mm and 3 mm, respectively. A frequency shift in the design frequency appeared due to the discontinuities effects, and to overcome this frequency shift, the arms lengths were shortened such that each NTL arm becomes equivalent to a uniform arm at the design frequency. Figure 3 shows both sections before and after shortening the arms lengths. Two output ports NTL matching transformers have been also designed. The length (d) of these transformers is 24.3 mm and 25.7 mm. Figure 4 shows the the layout of the compact NTL-based 1:2. TABLE V Ω TRANSFORMER FOURIER COEFFICIENTS TABLE I. PARAMETERS OF THE UTL AND NTL USED IN THE OPTIMIZATION section1 section2 UTL NTL Constraints Ω Ω The optimized Fourier coefficients of the NTL-based main arms and output ports matching transformers are shown in Tables II-V. TABLE II: OPTIMIZED FOURIER COEFFICIENTS FOR ARM TABLE III. OPTIMIZED FOURIER COEFFICIENTS FOR ARM 2 Figure 3. The two NTL arms of the before and after length reduction (a) upper arm (b) lower arm. The proposed is simulated using IE3D [14] and HFSS [15] full-wave simulators. Simulation results are shown in Figure 5 which validates the design. Specifically, at the design frequency (1 GHz), S 11 = db using IE3D, while it equals.55 db using HFSS. S 21 equals db and -2.4 db using IE3D and HFSS, respectively, which are close to the theoretical value of db. S 31 equals to db in IE3D and db using HFSS, which are almost equal the theoretical value of db. S 22 and S 33 are db and db, respectively, using IE3D; and around.1 db and db, respectively, using HFSS. Finally, S 23 equals db using IE3D, and -23 db using HFSS. The differences between the theoretical and simulation results are due to dielectric losses, coupling effects, and discontinuities effects TABLE IV Ω TRANSFORMER FOURIER COEFFICIENTS Figure 4. The proposed NTL-based layout. (Dimensions are in mm)

4 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) S11 IE3D S11 HFSS S21 IE3D S21 HFSS S31 IE3D S31 HFSS S22 IE3D S22 HFSS (a) (b) from -1.5 GHz). Figure 6 shows the measured results of the 1:2, while Figure 7 shows a picture of the fabricated. Experimental results show an acceptable agreement between both simulated and measured results. The small discrepancies in the measured results could be due to conductor and dielectric losses, the use of the connectors and the errors in the measurements, keeping in mind that a spectrum analyzer (not a network analyzer) was used Figure 6. Measured S-parameters of the fabricated NTLbased S11 S21 S31 S22 S23 S33-35 S23 IE3D -4 S23 HFSS -45 S33 IE3D S33 HFSS Figure 5. S-parameters of the proposed NTL-based using IE3D and HFSS (c) For verification purposes, the NTL-based is fabricated and measured using an Agilent Spectrum Analyzer (with a built in tracking generator extending Figure 7. Fabricated NTL-based 1:2 IV. COMPARISON BETWEEN CONVENTIONAL AND COMPACT Figure 8 shows the layout of the conventional 1:2 structure and Figure 9 shows the simulated S- parameters using IE3D. Using NTLs instead of UTLs, two main advantages are obtained: (1) the size reduction and (2) the odd harmonics suppression. A total size

5 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) reduction of almost 22.2% is achieved as shown in Figure 1. Figure 8. Conventional 1:2 layout Since both structures have the same ABCD paramters at the design frequency only, the NTLs behaviour is completely different from the conventional one at other frequencies. As an illustration, Figure 11 shows the conventional input port matching parameter (S11) in an extended frequency range. As expected, the conventional operates at the design frequency (1 GHz) and its odd harmonics. The first odd harmonic is slightly above 3 GHz, and the second odd harmonic is slightly below 5 GHz. This slight frequency shift could be due to the T-junction, the right-angle bends, the step discontinuities, and the dependence of the effective permittivity on frequency. Figure 12 shows S11 for the NTL-based in an extended frequency range. It is clear that the first odd harmonic has been suppresed completely while the second odd harmonic is partially suppressed. As mentioned before, both of the NTL-based and the conventional are equivalent at the design frequency only, which justifies the suppression or partial suppression of the odd harmonics. Furthermore a performance improvement is noticeable in the NTL-based, since S11 is close to db at frequencies other than the fundamental frequency and the second odd harmonic, while in the conventional, it is about db. -4 S11 S21 S31-6 S22 S23 S Figure 9. S-parameters of the conventional 1:2 S11 (db) Figure 11. S 11 of the conventional in an extended frequency range. Figure 1. Conventional vs. NTL-based (dimensions are in mm)

6 211 IEEE Jordan Conference on Applied Electrical Engineering and Computing Technologies (AEECT) S11 (db) [9] C.-H. Tseng and C.-H. Wu, Compact planar Wilkinson power divider using pi-equivalent shunt-stub-based artificial transmission lines, Electronics Letters, Vol. 46, pp , 21. [1] P. Cheong, K. Lai, and K. Tam, Compact Wilkinson power divider with simultaneous bandpass response and harmonic suppression, IEEE MTT-S International Microwave Symposium Digest, pp , 21. [11] D. Pozar, Microwave Engineering, New York: John Wiley, 3rd edition, 25. [12] M. Khalaj, Nonuniform Transmission Lines As Compact Uniform Transmission Lines, Progress In Electromagnetics Research C, Vol. 4, pp , 28. [13] Ansoft Corporation, [14] [15] HFSS: High Frequency Structure Simulation based on Finite Element Method, V. 1, Ansoft Corporation, Figure 12. S 11 of the NTL-based in an extended frequency range V. CONCLUSION In this paper, the design and analysis of a compact 1:2 unequal-split NTL-based was presented. In order to achieve compactness, each uniform transformer was replaced by its equivalent NTL at the design frequency. Besides suppressing some of the odd harmonics of the design frequency, a size reduction of 22.2% was achieved compared to the conventional. This work will be extended to design multi-band unequal-split as was done in [6] for the equalsplit. REFERENCES [1] R. Wilkinson, An N-Way Hybrid Power Divider, IRE Transactions on Microwave theory and techniques, Vol. MTT-8, No. 1, pp , 196. [2] F. Hosseini, M. Khalaj, A. Hosseini and M. Yazdani, A Miniaturized Wilkinson Power Divider Using Non-uniform Transmission Line, Journal of Electromagnetic Waves and Applications, Vol. 23, pp , 29. [3] K. Shamaileh and N. Dib, Design Of Compact Dual-Frequency Wilkinson Power Divider Using Non-uniform Transmission Line, Progress In Electromagnetics Research C, Vol. 19, pp , 211. [4] K. Shamaileh, A. Qaroot, and N. Dib, Non-uniform Transmission Line Transformers And Their Applications In The Design Of Compact Multi- Band Bagley Power Dividers With Harmonics Suppression, Progress In Electromagnetics Research, Vol. 113, pp , 211. [5] F. Hosseini, M. Khalaj and M. Yazdany, To Compact Ring Branch- Line Coupler using Nonuniform Transmission line, Microwave And Optical Technology Letters, Vol. 51, No. 11, pp , Nov. 29. [6] K. Shamaileh, A. Qaroot, N. Dib, and A. Sheta, Design And Analysis Of Multi-Frequency Wilkinson Power Dividers Using Non-uniform Transmission Lines, International Journal of RF and Microwave Computer-Aided Engineering, Vol. 21, No. 5, pp , September 211. [7] L. Shao, H. Guo, X. Liu, W. Cai and L. Mao A Compact Dual- Frequency Wilkinson Power Divider with open-ended stubs, Signals Systems and Electronics (ISSSE), International Symposium,Vol. 1, pp. 1-4, 21. [8] Z. Wang, J. Jang and C. Park, Compact dual-band Wilkinson power divider using lumped component resonators and open-circuited stubs, Wireless and Microwave Technology Conference (WAMICON), pp. 1-4, June 211.

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