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A novel Wilkinson power divider using lowpass filter with harmonics suppression and high fractional bandwidth
Microelectronics Journal 71 (2018) 61–69
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Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo
A novel Wilkinson power divider using lowpass filter with harmonics suppression and high fractional bandwidth Gholamreza Karimi *, Samira Menbari Department of Electrical Engineering, Faculty of Engineering, Razi University Kermanshah, 67149, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: Wilkinson power divider Harmonics suppression High fractional bandwidth Miniaturization
In this paper, a new compact Wilkinson power divider using lowpass filter is presented. The proposed structure suppresses from 2nd to 6th harmonics with an attenuation level less than 20 dB and reduces the occupied area to 43.5% in comparison to the conventional Wilkinson power divider. Also, it generates a wide stop-band bandwidth (5.1 GHz–16 GHz). In addition, fractional bandwidth is equal to 44%. According to the measured frequency responses, input and output return losses are more than 27 dB and isolation is better than 46 dB at a center frequency of 2.55 GHz.
1. Introduction Wilkinson and Gysel are the most famous kinds of power dividers which have several applications in microwave systems, such as radars and wireless connections. Using quarter-wavelength transmission lines in conventional Wilkinson power divider cause counterfeit frequencies generation and occupy a wide area [1]. For improved performance of power dividers; such as the size reduction and harmonics suppression, several methods are expressed. In Refs. [2–4] Wilkinson and Gysel power dividers with open stubs for harmonics suppression are presented. Harmonics suppression also is obtained by adding transmission lines to the conventional Wilkinson power divider [5]. Fractal geometry has also been shown as an effective approach to harmonics suppression in microstrip-based structures [6]. In Refs. [7,8] Gysel power dividers using lowpass filters instead of the transmission lines are proposed to suppress unwanted harmonics and reduce the size. A dual band power divider was designed by a parallel RLC circuit and two two-section transmission lines to decrease the occupied area in Ref. [9]. Also, two-section transmission lines and inductor are used in the structure of the Wilkinson power divider to reduce the occupied area, suppress the unwanted harmonics, and/or provide the arbitrary power division ratios in Ref. [10]. Quasi-elliptic filters [11] and hook-shaped resonators [12] are used to improve out-of-band rejection and suppress the harmonics. Filtering power dividers using short-circuit stubs and coupled lines with open-circuit stubs [13] and distributed stepped-impedance resonator network [14] are presented to achieve wide stopband bandwidth and
harmonics suppression. Stepped-impedance interdigital coupling element, adding asymmetric spiral defected ground structure (DGS), front coupled tapered compact microstrip cell (FCTCMRC), microstrip electromagnetic bandgap cells (EBG), and combination of half-wavelength resonators and short-stub-loaded resonator (SSLR) [15–20] are certain different methods for designing a compact power divider with harmonics suppression. A dual-band unequal filtering power divider (DUFPD) is proposed to realize the dual-band filtering response with arbitrary power division, arbitrary frequency ratio, and independently controllable bandwidth in Ref. [21]. Negative refractive index transmission lines (NRI-TL) were used to achieve high fractional bandwidth in Ref. [22]. Also, extended composite right and left handed transmission line (E-CRLH-TL) is used to reach high fractional bandwidth and exhibit the benefits of bandwidth enlargement [23]. Lowpass filters including T-shaped, Z-shaped, and circular patch -shaped resonators, Hilbert-shaped complementary single split ring resonator (H-CSSRR), and transverse resonance type lowpass filter (TR-LPF) were presented to achieve wide stop-band bandwidth [24–27]. In Ref. [28], a tri-band T-junction power divider (TTPD) using L network (LN) is presented to obtain arbitrary tri-band application, independent power division ratios, and small size. In Ref. [29] massive state-of-the-art planer power dividers are discussed that it might be helpful for the development of power dividers. But the main problems are a large size, unwanted harmonics and low fractional bandwidth (FBW). In this paper, a compact Wilkinson power divider with high fractional bandwidth is proposed in which two lowpass filters (LPF) are used
* Corresponding author. E-mail addresses: [email protected] (G. Karimi), [email protected] (S. Menbari). https://doi.org/10.1016/j.mejo.2017.11.011 Received 9 July 2017; Received in revised form 10 October 2017; Accepted 21 November 2017 0026-2692/© 2017 Published by Elsevier Ltd.
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Microelectronics Journal 71 (2018) 61–69
Fig. 1. Schematic of (a) the conventional Wilkinson power divider (b) the proposed power divider using lowpass filters.
Fig. 2. Layout and LC equivalent circuit of (a) high- and low-impedance lossless line, (b) open-end, (c) microstrip line T-junction, (d) microstrip line with a gap, and (e) optimal right-angle mitered bend [31].
Design of a basic resonator; the first step is to consider transmission line to attain a lowpass filter. Design of primary lowpass filter; it consists of adding circular patchshaped resonator to suppress higher unwanted harmonics and achieving wide stop-band bandwidth.
instead of the quarter-wavelength transmission lines in the conventional power divider. These lowpass filters suppress from 2nd to 6th unwanted harmonics and generate a wide stop-band bandwidth (5.1 GHz–16 GHz). The proposed power divider improves fractional bandwidth to 44% and reduces the size of the circuit to 43.5% in comparison to the conventional Wilkinson power divider. The design procedure of the proposed Wilkinson power divider with harmonics suppression is summarized as follows:
Fig. 4. (a) Layout of the first section of the LPF, (b) LC equivalent circuit of the first section of the LPF.
Fig. 3. Layout of (a) semicircular resonator (b) circular patch-shaped resonator.
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Fig. 5. Full-wave EM and LC circuit model performances of the first section of the LPF.
Design of finally lowpass filter; it is done by adding T-shaped resonators with inductor property to suppress lower unwanted harmonics and obtain sharpness in transition band. Design of the proposed Wilkinson power divider; using the proposed lowpass filter instead of the quarter-wavelength transmission lines in the structure of the conventional Wilkinson power divider.
Fig. 7. (a) Layout of the second section of the LPF, (b) LC equivalent circuit of the second section of the LPF.
2. Proposed structure Fig. 1 shows the conventional Wilkinson power divider and structure of the proposed power divider which consists of two lowpass filters instead of the quarter-wavelength transmission lines. The impedances of the quarter-wavelength transmission lines and isolation resistor are equal to 70.7 (√2Z0) and 100 Ω, respectively. Ports 1 and 2 are shunting with 50 and 100 Ω, respectively, at resonator cells and lowpass filter designing (such as Figs. 4, 7 and 9), while all ports of Wilkinson power divider are shunting with 50 Ω. This creative design technique causes the lowpass filters act as quarter-wavelength transmission lines in the structure of the power divider and the resonator cells and lowpass filters frequency responses achieve similarity to the power divider frequency responses, to
Fig. 6. (a) Primary structure of the two T-shaped resonators (b) modified T-shaped resonators with inductor property.
Fig. 8. Full-wave EM and LC circuit model simulation results of the second section of the LPF.
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Microelectronics Journal 71 (2018) 61–69
λg ¼
300 pffiffiffiffiffi ðmmÞ fðGHzÞ εre
(3)
where λg is the guided wavelength at the cut-off frequency, Zs and l are the characteristic impedance and length of the line, respectively. Semicircular resonator produces a wide stop-band bandwidth that angle reduction of it causes to increase stop-band bandwidth and convert it to circular patch-shaped resonator. The first section of the proposed LPF is a circular patch-shaped resonator that is shown in Fig. 3. As seen in Fig. 4(a), optimal bend are used in designing of the circular patch-shaped resonator to reduce the resonator's size and increase stopband bandwidth. Layout and LC equivalent circuit of the first section of the LPF are shown in Fig. 4, so that C1 is the sum of the equivalent capacitances of open-end and high- and low-impedance lossless line. L1, L2, and C2 are inductances and capacitance of high- and low-impedance lossless lines. L3a is inductance of transmission line, and C3a is the sum of the equivalent capacitances of high- and low-impedance lossless line and transmission lines. LC equivalent circuit of the first section of the LPF is obtained using
Fig. 9. (a) Layout of the proposed lowpass filter, (b) LC equivalent circuit of the proposed lowpass filter.
recognize the center frequency of the Wilkinson power divider. Developing the efficiency of the power divider is the main purposes of the used lowpass filters. The proposed lowpass filters suppress up to 6th unwanted harmonics and improve the fractional bandwidth. 3. Lowpass filter design The layout and LC equivalent circuit of the high- and low-impedance lossless line, open-end, gap, microstrip line T-junction, and optimal rightangle mitered bend used in the proposed structure are shown in Fig. 2 [30,31]. The values of the inductors and capacitors can be calculated using the presented procedure in Refs. [30,31]. Fig. 2(a) shows that a high- and low-impedance lossless line terminated at both ends by relatively low impedance lines is presented by a Π-equivalent circuit [31]. The values of the inductors and capacitors can be calculated as [31]:
Ls ¼
1 2π zs sin l ω λg
(1)
Cs ¼
1 1 π tan l ω zs λg
(2)
Table 1 Calculated values for LC equivalent circuit of the proposed lowpass filter (Units: C, fF; L, nH). Parameters Calculations Parameters Calculations
L1 0.27 C1 188
L2 0.28 C2 129.2
L3 1.88 C3 114.8
L4 0.94 C4 152.4
L5 2.54 C5 149.8
L6 0.285 C6 78.93
Cg 26 Fig. 10. Full-wave EM and LC circuit model simulation results of the proposed lowpass filter (a) around the operating frequency (b) in the target range. 64
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Microelectronics Journal 71 (2018) 61–69
resonator cell (CMRC) consists of two T-shaped resonators with inductor property. Sharpness in transition band can be obtained using the improved T-shaped resonators. Fig. 6(a) shows primary structure of the two T-shaped resonators used in the CMRC. As seen in Fig. 6(b), optimal bend and gap are used in the structure of the resonator cell to reduce the size of the second section of the LPF and obtain more sharpness in transition band. The final proposed lowpass filter is a compound of compact microstrip resonator cell (CMRC), circular patch-shaped resonator and transmission lines, so a small change in the structure of CMRC is applied to prevention of contact with circular patch-shaped resonator. The layout and LC equivalent circuit of the second section of the LPF are shown in Fig. 7, so that L3b and L4 are inductances of transmission lines. C4b is the sum of the equivalent capacitances of high- and low-impedance lossless line and transmission lines. L5, L6, and C5 are inductances and capacitance of high- and low-impedance lossless lines. C6 is the sum of the equivalent capacitances of high- and low-impedance lossless line and shunt capacitance of gap, and Cg is the series capacitance of gap. LC equivalent circuit of the second section of the LPF is obtained using present procedure in Fig. 2. The full-wave EM and LC circuit model simulation results of the second section of the LPF are shown in Fig. 8. The lower unwanted harmonics at the frequency response of the proposed lowpass filter can be suppressed by the second section of it. This figure shows that frequency response has good sharpness in transition band. Harmonics suppression and sharpness in transition band are also obvious from the LC equivalent simulation result of the second section of the LPF. Fig. 9 (a) shows the layout of the proposed lowpass filter that is used in the proposed power divider. This structure is a compound of the first and second sections. In Fig. 9 (b) the LC equivalent circuit of the proposed lowpass filter is presented to demonstrate the circuit operation in the frequency response. The values of the capacitors and inductors of the LC equivalent circuit of the proposed lowpass filter are calculated using Equations of 1–3 and expressed in Table 1. The lowpass filter dimensions of Fig. 6 are: W1 ¼ 0.26, W2¼W3¼W4 ¼ 0.2, W5 ¼ 2.24, W6 ¼ 1.57, W7 ¼ 0.21, La1 ¼ 1.8, La2 ¼ 0.49, La3 ¼ 5.18, La4 ¼ 0.65, La5 ¼ 1.51, La6 ¼ 3.22, La7 ¼ 1.08, La8 ¼ 1.44, g ¼ 0.14 (all in millimeters), Ө ¼ 150 deg. Fig. 10 shows the comparison between the full-wave EM and LC circuit model simulation results of the proposed lowpass filter. As seen, a combination of the first and second sections suppresses the unwanted harmonics and reduces the level of the input return loss around the operating frequency to less than 35 dB. Sharpness and wide transition band at the frequency response of the proposed lowpass filter are obvious so that it is a desirable result of insertion loss of the lowpass filter. According to this frequency response, transmission zeros are equal to 5.37, 6.63, and 15.04 GHz, respectively. Also, these points can be obtained from the transfer function of the LC equivalent circuit of the lowpass filter. The transfer function of the proposed lowpass filter is computed and shown in equation (4). “Z0 ” expresses the value of matched impedance of the transmission line (Z0). The transmissions zeros can be calculated using the transfer function.
Fig. 11. (a) EM simulated response of S12 of the proposed lowpass filter as a function of “g” (b) LC simulated response of S12 of the LC equivalent circuit of the proposed lowpass filter as a function of “Cg”.
present procedure in Fig. 2. The full-wave EM and LC circuit model performances of the first section of the LPF are shown in Fig. 5. The higher unwanted harmonics at the frequency response of the proposed lowpass filter can be suppressed by the first section of it. As seen, it has a wide stop-band bandwidth so that the LC equivalent simulation results of the first section of the LPF express this note. The second section of the proposed LPF is a compact microstrip
vo ¼ vi
ðABCZ0 Þ ðL4 sðBð2L3 sðZ0 þ L4 sÞ þ CðZ0 þ 2L3 s þ L4 sÞÞ þ L3 sðL3 sðZ0 þ L4 sÞþ CðZ0 þ ðL3 þ L4 ÞsÞÞÞ þ AððL3 þ L4 ÞsðL3 sðZ0 þ L4 sÞ þ CðZ0 þ ðL3 þ L4 ÞsÞÞþ Bðð2L3 þ L4 ÞsðZ0 þ L4 sÞ þ CðZ0 þ 2ðL3 þ L4 ÞsÞÞÞÞ
65
(4)
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Microelectronics Journal 71 (2018) 61–69
where
A¼
1 þ C5 L5 s2 þ Cm L5 s2 þ Cm L6 s2 þ C5 Cm L5 L6 s4 C4 s þ C5 s þ Cm s þ C4 C5 L5 s3 þ C4 Cm L5 s3 þ C4 Cm L6 s3 þ C5 Cm L6 s3 þ C4 C5 Cm L5 L6 s5
B¼
C1 s þ C2 s þ C3 s þ C1 C2 L1 s3 þ C1 C3 L1 s3 þ C1 C3 L2 s3 þ C2 C3 L2 s3 þ C1 C2 C3 L1 L2 s5 1 þ C1 L1 s2 þ C1 L2 s2 þ C2 L2 s2 þ C1 C2 L1 L2 s4
C¼
ð1 þ C5 L5 s2 þ Cn L5 s2 þ Cn L6 s2 þ C5 Cn L5 L6 s4 Þ C4 s þ C5 s þ Cn s þ C4 C5 L5 s3 þ C4 Cn L5 s3 þ C4 Cn L6 s3 þ C5 Cn L6 s3 þ C4 C5 Cn L5 L6 s5
5. Simulated and measured results
Fig. 11 (a) shows that the insertion loss (S12) of the proposed lowpass filter is a function of “g” and the second harmonic can be suppressed by tuning the coupling gap “g” as the optimized value of “g” is equal to 0.14 mm, also Fig. 11 (b) shows that the insertion loss (S12) of the LC equivalent circuit is a function of “Cg” and the second harmonic can be suppressed by setting the value of “Cg” to 26 fF.
The used substrate is an RT/Duroid 5880 which has the following characteristics: dielectric constant of 2.2, the thickness of 0.508 mm,
4. Wilkinson power divider design The proposed Wilkinson power divider consists of two lowpass filters as shown in Fig. 12. This structure suppresses up to 6th unwanted harmonics and is significantly smaller than the conventional one. It provides a wide stop-band and high fractional bandwidth at a center frequency of 2.55 GHz. The proposed Wilkinson power divider dimensions of Fig. 12 are A1 ¼ 0.25, A2 ¼ A6 ¼ 1.56, A3 ¼ 8.78, A4 ¼ A5 ¼ 0.2, A7 ¼ 0.91, A8 ¼ 1.72, (all in millimeters). R is equal to 100 Ω. Comparison between the full-wave EM and LC circuit model simulation results of the proposed power divider is illustrated in Fig. 13. Frequency responses show that using the proposed lowpass filters instead of the quarter-wavelength transmission lines of the conventional Wilkinson power divider caused the suppression from 2nd to 6th harmonics with desirable attenuation level. It has a wide stop-band and high fractional bandwidth. These results are considered positive distinction for the Wilkinson power divider.
Fig. 13. Full-wave EM and LC circuit model simulation results of (a) input return loss and insertion loss (b) output return loss and isolation.
Fig. 12. Layout of the proposed Wilkinson power divider.
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Fig. 14. Photograph of the proposed Wilkinson power divider.
and loss tangent of 0.0009. The photograph of the fabricated power divider with operating frequency of 2.55 GHz for harmonics suppression and high FBW is shown in Fig. 14. The size of the fabricated power divider is 9.05 mm 10.88 mm (98.464 mm2) that the size reduction is over 43.5% in comparison to the conventional Wilkinson power divider. The S-parameters are measured using Agilent's E8361C network analyzer. Fig. 15 shows the comparison between simulated and measured Sparameters of the proposed power divider. As it is shown, the measured input return loss (S11), output return loss (S22), and isolation (S23), are less than 15 dB from 1.87 GHz to 2.93 GHz. Also according to their measured conclusions, fractional bandwidth (FBW) is equal to 44%. This is a good result to improve the operation of the conventional Wilkinson power divider. As it is shown in Fig. 15 (a), the measured insertion loss (S12), unwanted harmonics from 5.1 GHz to 16 GHz have been suppressed; in the other word, from 2nd to 6th harmonics have been suppressed with a level less than 20 dB. This expresses that the insertion loss has a wide stop-band bandwidth. The measured input return loss (S11), output return loss (S22), isolation (S23), and insertion loss (S12) at operating frequency of 2.55 GHz, are 28 dB, 27 dB, 46.5 dB, and 3.017 dB, respectively. This topology suppresses undesirable harmonics, in this case: the suppressed harmonics from 2nd to 6th are 20.6 dB, 20.1 dB, 23.3 dB, 24.4 dB, and 32.1 dB, respectively. In Fig. 16, a proper phase performance between two output ports around operating frequency is shown. According to the simulated parameters of ports 2 and 3, as output ports, the phase difference of output ports is equal to 0.05 and magnitude of S12 and S22 are equal to S13 and S33, respectively. Fig. 17 shows the circuit's operation at a center frequency of 2.55 GHz. As seen, the electrical current densities in both lowpass filters are equal. Also, E-field distribution shows when the signal passes from the input port, the power is leading between the two output ports equally, but the lost power at isolation resistance is zero which is indicative the principles of transmission and isolation. These results also confirm that the proposed power divider is symmetrical and output ports are isolated from each other entirely. At operating frequency, the current density distribution in the transmission line is more than one in modified T-
Fig. 15. Simulated and measured (a) input return loss and insertion loss (b) output return loss and isolation.
shaped and circular patch-shaped resonators. Also, the current density distribution in modified T-shaped resonators is very weak. The comparison between the proposed power divider and other available works is expressed in Table 2. 6. Conclusion In this paper, a new design for improved performance of Wilkinson power divider with higher order harmonics suppression has been proposed using lowpass filters instead of the quarter-wavelength transmission lines in the conventional Wilkinson power divider. The proposed power divider operating at 2.55 GHz has been designed, fabricated and measured which has harmonics suppression from 2nd to 6th with an attenuation level less than 20 dB and wide stop-band bandwidth (5.1 GHz - 16 GHz). This structure reduces the size to 43.5% in comparison to the conventional one. High fractional bandwidth (FBW) equal
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to 44% are obtained from this topology. The proposed power divider is proper for using in communication systems which required a compact structure with harmonics suppression, wide stop-band, and high fractional bandwidth. References [1] D.M. Pozar, Microwave Engineering, third ed., Wiley, New York, 2005, pp. 333–337. Ch. 7. [2] M. Hayati, S. Roshani, A novel Wilkinson power divider using open stubs for the suppression of harmonics, ACES J. 28 (6) (June 2013) 501–505. [3] K.-H. Yi, B. Kang, Modified Wilkinson power divider for nth harmonic suppression, IEEE Microw. Wirel. Components Lett. 13 (5) (May 2003) 178–180. [4] H. Shahi, H. Shamsi, Compact wideband Gysel power dividers with harmonic suppression and arbitrary power division ratios, Int. J. Electron. Commun. (AEÜ) 79 (September 2017) 16–25. [5] M.G. Kim, J.S. Kim, R. Mittra, Modified Wilkinson power divider for suppression of nth harmonics, Electron. Lett. 48 (24) (January 2013) 1540–1542. [6] A. Lalbakhsh, A.-A. Lotfi Neyestanak, M. Naser-Moghaddasi, Microstrip hairpin bandpass filter using modified minkowski fractal-shape for suppression of second harmonic, IEICE Trans. Electron. 95 (3) (2016) 378–381. [7] Gh. Karimi, H. Siahkamari, F. Khamin Hamedani, A novel miniaturized Gysel power divider using lowpass filter with harmonic suppression, Int. J. Electron. Commun. (AEÜ) 69 (5) (February 2015) 856–860. [8] H. Siahkamari, S. Vahab, A. Makki, S.-A. Malakooti, Using microstrip LPF in Gysel power divider for extreme size reduction and higher order harmonic suppression, Freq. –Berlin 69 (7–8) (May 2015) 323–328. [9] X. Wang, I. Sakagami, Z. Ma, A. Mase, M. Yoshikawa, Generalized, miniaturized, dual-band Wilkinson power divider with a parallel RLC circuit, Int. J. Electron. Commun. (AEÜ) 69 (1) (January 2015) 418–423. [10] R. Mirzavand, M.M. Honari, A. Abdipour, Gh. Moradi, Compact microstrip Wilkinson power dividers with harmonic suppression and arbitrary power division ratios, IEEE Trans. Microw. Theory Tech. 61 (1) (January 2013) 61–68. [11] J.-Y. Shao, S.-C. Huang, Y.-H. Pang, Wilkinson power divider incorporating quasielliptic filters for improved out-of-band rejection, Electron. Lett. 47 (23) (November 2011) 1288–1289. [12] Z. Zhang, Y.-C. Jiao, Z.-B. Weng, Design of 2.4 GHz power divider with harmonic suppression, Electron. Lett. 48 (12) (June 2012) 705–707. [13] Y. Wu, Z. Zhuang, Y. Liu, L. Deng, Z. Ghassemlooy, Wideband filtering power divider with ultra-wideband harmonic suppression and isolation, IEEE Access 4 (September 2016) 6876–6882. [14] Y. Deng, J. Wang, L. Zhu, W. Wu, Filtering power divider with good isolation performance and harmonic suppression, IEEE Microw. Wirel. Components Lett. 26 (12) (December 2016) 984–986. [15] P. Cheong, K.-I. Lai, K.-W. Tam, Compact Wilkinson power divider with simultaneous bandpass response and harmonic suppression, in: Microwave Symposium Digest (MTT), 2010 IEEE MTT-s International, July 2010, pp. 1588–1591. [16] D.-J. Woo, T. Lee, Suppression of harmonics in Wilkinson power divider using dualband rejection by asymmetric DGS, IEEE Trans. Microw. Theory Tech. 53 (6) (June 2005) 2139–2144. [17] M. Hayati, S. Roshani, S. Roshani, Miniaturized Wilkinson power divider with nth harmonic suppression using front coupled tapered CMRC, ACES J. 28 (3) (March 2013) 221–227. [18] C.M. Lin, H.H. Su, J.C. Chiu, Y.H. Wang, Wilkinson power divider using microstrip EBG cells for the suppression of harmonics, IEEE Microw Wirel. Components Lett. 17 (10) (October 2007) 700–702. [19] F. Zhang, C.F. Li, Power divider with microstrip electromagnetic bandgap element for miniaturization and harmonic rejection, Electron. Lett. 44 (6) (March 2008) 422–423. [20] M. Luo, X. Xu, X.-H. Tang, Y.-H. Zhang, A compact balanced-to-balanced filtering Gysel power divider using λg/2 resonators and short-stub-loaded resonator, IEEE Microw. Wirel. Components Lett. 27 (7) (July 2017) 645–647. [21] Y. Wu, Z. Zhuang, G. Yan, Y. Liu, Z. Ghassemlooy, Generalized dual-band unequal filtering power divider with independently controllable bandwidth, IEEE Trans. Microw. Theory Tech. 65 (10) (October 2017) 3838–3848. [22] M. Bemani, S. Nikmehr, S. Hosseinzadeh, Arbitrary dual-band unequal Wilkinson power divider based on negative refractive index transmission lines, Int. J. Electron. Commun. (AEÜ) 67 (5) (May 2013) 382–386. [23] H. Younesiraad, M. Bemani, M. Fozi, A novel fully planar quad band Wilkinson power divider, Int. J. Electron. Commun. (AEÜ) 74 (April 2017) 75–82. [24] Gh. Karimi, A. Lalbakhsh, H. Siahkamari, Design of sharp roll-off lowpass filter with ultra wide stopband, IEEE Microw. Wirel. Components Lett. 23 (6) (May 2013) 303–305. [25] Gh. Karimi, H. Siahkamari, F. Khamin Hamedani, A. Lalbakhsh, Design of modified Z-shaped and TShaped microstrip filter based on transfer function analysis, Wirel. Personal. Commun. 82 (4) (February 2015) 2005–2016. [26] H.-X. Xu, G.-M. Wang, C.-X. Zhang, Q. Peng, Hilbert-shaped complementary single split ring resonator and low-pass filter with ultra-wide stopband, excellent
Fig. 16. Simulated phase difference between S12 and S13 of the proposed power divider.
Fig. 17. Simulated current density distribution of the proposed power divider.
Table 2 Comparison between the performance of the proposed power divider and previous works. Ref.
FWB (%)
Size Reduction (%)
Harmonic suppression (dB) 2nd
3rd
4th
5th
6th
[2] [5] [9] [10] [11] [12] [17] [18] [21] [28]
– 27 5 27 – – – – 17, 10.8 10.1, 3.2, 1.7 44
35 – – 40 – 40 34.5 39 – –
– 45.3 – 28 – – – 26 – –
45 46.4 – 32 46.2 24 32.5 25 – –
– – – 20 – – – – – –
43 – – – 37.35 – 12 – – –
– – – – – – – – – –
43.5
20.6
20.1
23.3
24.4
32.1
This work
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Microelectronics Journal 71 (2018) 61–69 [29] Y. Wu, L. Jiao, Z. Zhuang, Y. Liu, The art of power dividing: a review for state-ofthe-art planar power dividers, China Commun. 14 (5) (May 2017) 1–16. [30] B.C. Wadell, Transmission Line Design Handbook, British library cataloging in publishing data, 1991. [31] J.S. Hong, M.J. Lancaster, Microstrip Filters for RF/Microwave Applications, second ed., Wiley, New York, 2011.
selectivity and low insertion-loss, Int. J. Electron. Commun. (AEÜ) 65 (11) (November 2011) 901–905. [27] A.K. Verma, N.P. Chaudhari, A. Kumar, Improved performance step impedance lowpass filter, Int. J. Electron. Commun. (AEÜ) 67 (9) (September 2013) 761–770. [28] Y. Wu, Y. Guan, Z. Zhuang, W. Wang, Y. Liu, A novel tri-band T-junction impedance-transforming power divider with independent power division ratios, Plos One 12 (6) (June 2017) 1–7.
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A novel Wilkinson power divider using lowpass filter with harmonics suppression and high fractional bandwidth Gholamreza Karimi *, Samira Menbari Department of Electrical Engineering, Faculty of Engineering, Razi University Kermanshah, 67149, Iran
A R T I C L E I N F O
A B S T R A C T
Keywords: Wilkinson power divider Harmonics suppression High fractional bandwidth Miniaturization
In this paper, a new compact Wilkinson power divider using lowpass filter is presented. The proposed structure suppresses from 2nd to 6th harmonics with an attenuation level less than 20 dB and reduces the occupied area to 43.5% in comparison to the conventional Wilkinson power divider. Also, it generates a wide stop-band bandwidth (5.1 GHz–16 GHz). In addition, fractional bandwidth is equal to 44%. According to the measured frequency responses, input and output return losses are more than 27 dB and isolation is better than 46 dB at a center frequency of 2.55 GHz.
1. Introduction Wilkinson and Gysel are the most famous kinds of power dividers which have several applications in microwave systems, such as radars and wireless connections. Using quarter-wavelength transmission lines in conventional Wilkinson power divider cause counterfeit frequencies generation and occupy a wide area [1]. For improved performance of power dividers; such as the size reduction and harmonics suppression, several methods are expressed. In Refs. [2–4] Wilkinson and Gysel power dividers with open stubs for harmonics suppression are presented. Harmonics suppression also is obtained by adding transmission lines to the conventional Wilkinson power divider [5]. Fractal geometry has also been shown as an effective approach to harmonics suppression in microstrip-based structures [6]. In Refs. [7,8] Gysel power dividers using lowpass filters instead of the transmission lines are proposed to suppress unwanted harmonics and reduce the size. A dual band power divider was designed by a parallel RLC circuit and two two-section transmission lines to decrease the occupied area in Ref. [9]. Also, two-section transmission lines and inductor are used in the structure of the Wilkinson power divider to reduce the occupied area, suppress the unwanted harmonics, and/or provide the arbitrary power division ratios in Ref. [10]. Quasi-elliptic filters [11] and hook-shaped resonators [12] are used to improve out-of-band rejection and suppress the harmonics. Filtering power dividers using short-circuit stubs and coupled lines with open-circuit stubs [13] and distributed stepped-impedance resonator network [14] are presented to achieve wide stopband bandwidth and
harmonics suppression. Stepped-impedance interdigital coupling element, adding asymmetric spiral defected ground structure (DGS), front coupled tapered compact microstrip cell (FCTCMRC), microstrip electromagnetic bandgap cells (EBG), and combination of half-wavelength resonators and short-stub-loaded resonator (SSLR) [15–20] are certain different methods for designing a compact power divider with harmonics suppression. A dual-band unequal filtering power divider (DUFPD) is proposed to realize the dual-band filtering response with arbitrary power division, arbitrary frequency ratio, and independently controllable bandwidth in Ref. [21]. Negative refractive index transmission lines (NRI-TL) were used to achieve high fractional bandwidth in Ref. [22]. Also, extended composite right and left handed transmission line (E-CRLH-TL) is used to reach high fractional bandwidth and exhibit the benefits of bandwidth enlargement [23]. Lowpass filters including T-shaped, Z-shaped, and circular patch -shaped resonators, Hilbert-shaped complementary single split ring resonator (H-CSSRR), and transverse resonance type lowpass filter (TR-LPF) were presented to achieve wide stop-band bandwidth [24–27]. In Ref. [28], a tri-band T-junction power divider (TTPD) using L network (LN) is presented to obtain arbitrary tri-band application, independent power division ratios, and small size. In Ref. [29] massive state-of-the-art planer power dividers are discussed that it might be helpful for the development of power dividers. But the main problems are a large size, unwanted harmonics and low fractional bandwidth (FBW). In this paper, a compact Wilkinson power divider with high fractional bandwidth is proposed in which two lowpass filters (LPF) are used
* Corresponding author. E-mail addresses: [email protected] (G. Karimi), [email protected] (S. Menbari). https://doi.org/10.1016/j.mejo.2017.11.011 Received 9 July 2017; Received in revised form 10 October 2017; Accepted 21 November 2017 0026-2692/© 2017 Published by Elsevier Ltd.
G. Karimi, S. Menbari
Microelectronics Journal 71 (2018) 61–69
Fig. 1. Schematic of (a) the conventional Wilkinson power divider (b) the proposed power divider using lowpass filters.
Fig. 2. Layout and LC equivalent circuit of (a) high- and low-impedance lossless line, (b) open-end, (c) microstrip line T-junction, (d) microstrip line with a gap, and (e) optimal right-angle mitered bend [31].
Design of a basic resonator; the first step is to consider transmission line to attain a lowpass filter. Design of primary lowpass filter; it consists of adding circular patchshaped resonator to suppress higher unwanted harmonics and achieving wide stop-band bandwidth.
instead of the quarter-wavelength transmission lines in the conventional power divider. These lowpass filters suppress from 2nd to 6th unwanted harmonics and generate a wide stop-band bandwidth (5.1 GHz–16 GHz). The proposed power divider improves fractional bandwidth to 44% and reduces the size of the circuit to 43.5% in comparison to the conventional Wilkinson power divider. The design procedure of the proposed Wilkinson power divider with harmonics suppression is summarized as follows:
Fig. 4. (a) Layout of the first section of the LPF, (b) LC equivalent circuit of the first section of the LPF.
Fig. 3. Layout of (a) semicircular resonator (b) circular patch-shaped resonator.
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Fig. 5. Full-wave EM and LC circuit model performances of the first section of the LPF.
Design of finally lowpass filter; it is done by adding T-shaped resonators with inductor property to suppress lower unwanted harmonics and obtain sharpness in transition band. Design of the proposed Wilkinson power divider; using the proposed lowpass filter instead of the quarter-wavelength transmission lines in the structure of the conventional Wilkinson power divider.
Fig. 7. (a) Layout of the second section of the LPF, (b) LC equivalent circuit of the second section of the LPF.
2. Proposed structure Fig. 1 shows the conventional Wilkinson power divider and structure of the proposed power divider which consists of two lowpass filters instead of the quarter-wavelength transmission lines. The impedances of the quarter-wavelength transmission lines and isolation resistor are equal to 70.7 (√2Z0) and 100 Ω, respectively. Ports 1 and 2 are shunting with 50 and 100 Ω, respectively, at resonator cells and lowpass filter designing (such as Figs. 4, 7 and 9), while all ports of Wilkinson power divider are shunting with 50 Ω. This creative design technique causes the lowpass filters act as quarter-wavelength transmission lines in the structure of the power divider and the resonator cells and lowpass filters frequency responses achieve similarity to the power divider frequency responses, to
Fig. 6. (a) Primary structure of the two T-shaped resonators (b) modified T-shaped resonators with inductor property.
Fig. 8. Full-wave EM and LC circuit model simulation results of the second section of the LPF.
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λg ¼
300 pffiffiffiffiffi ðmmÞ fðGHzÞ εre
(3)
where λg is the guided wavelength at the cut-off frequency, Zs and l are the characteristic impedance and length of the line, respectively. Semicircular resonator produces a wide stop-band bandwidth that angle reduction of it causes to increase stop-band bandwidth and convert it to circular patch-shaped resonator. The first section of the proposed LPF is a circular patch-shaped resonator that is shown in Fig. 3. As seen in Fig. 4(a), optimal bend are used in designing of the circular patch-shaped resonator to reduce the resonator's size and increase stopband bandwidth. Layout and LC equivalent circuit of the first section of the LPF are shown in Fig. 4, so that C1 is the sum of the equivalent capacitances of open-end and high- and low-impedance lossless line. L1, L2, and C2 are inductances and capacitance of high- and low-impedance lossless lines. L3a is inductance of transmission line, and C3a is the sum of the equivalent capacitances of high- and low-impedance lossless line and transmission lines. LC equivalent circuit of the first section of the LPF is obtained using
Fig. 9. (a) Layout of the proposed lowpass filter, (b) LC equivalent circuit of the proposed lowpass filter.
recognize the center frequency of the Wilkinson power divider. Developing the efficiency of the power divider is the main purposes of the used lowpass filters. The proposed lowpass filters suppress up to 6th unwanted harmonics and improve the fractional bandwidth. 3. Lowpass filter design The layout and LC equivalent circuit of the high- and low-impedance lossless line, open-end, gap, microstrip line T-junction, and optimal rightangle mitered bend used in the proposed structure are shown in Fig. 2 [30,31]. The values of the inductors and capacitors can be calculated using the presented procedure in Refs. [30,31]. Fig. 2(a) shows that a high- and low-impedance lossless line terminated at both ends by relatively low impedance lines is presented by a Π-equivalent circuit [31]. The values of the inductors and capacitors can be calculated as [31]:
Ls ¼
1 2π zs sin l ω λg
(1)
Cs ¼
1 1 π tan l ω zs λg
(2)
Table 1 Calculated values for LC equivalent circuit of the proposed lowpass filter (Units: C, fF; L, nH). Parameters Calculations Parameters Calculations
L1 0.27 C1 188
L2 0.28 C2 129.2
L3 1.88 C3 114.8
L4 0.94 C4 152.4
L5 2.54 C5 149.8
L6 0.285 C6 78.93
Cg 26 Fig. 10. Full-wave EM and LC circuit model simulation results of the proposed lowpass filter (a) around the operating frequency (b) in the target range. 64
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resonator cell (CMRC) consists of two T-shaped resonators with inductor property. Sharpness in transition band can be obtained using the improved T-shaped resonators. Fig. 6(a) shows primary structure of the two T-shaped resonators used in the CMRC. As seen in Fig. 6(b), optimal bend and gap are used in the structure of the resonator cell to reduce the size of the second section of the LPF and obtain more sharpness in transition band. The final proposed lowpass filter is a compound of compact microstrip resonator cell (CMRC), circular patch-shaped resonator and transmission lines, so a small change in the structure of CMRC is applied to prevention of contact with circular patch-shaped resonator. The layout and LC equivalent circuit of the second section of the LPF are shown in Fig. 7, so that L3b and L4 are inductances of transmission lines. C4b is the sum of the equivalent capacitances of high- and low-impedance lossless line and transmission lines. L5, L6, and C5 are inductances and capacitance of high- and low-impedance lossless lines. C6 is the sum of the equivalent capacitances of high- and low-impedance lossless line and shunt capacitance of gap, and Cg is the series capacitance of gap. LC equivalent circuit of the second section of the LPF is obtained using present procedure in Fig. 2. The full-wave EM and LC circuit model simulation results of the second section of the LPF are shown in Fig. 8. The lower unwanted harmonics at the frequency response of the proposed lowpass filter can be suppressed by the second section of it. This figure shows that frequency response has good sharpness in transition band. Harmonics suppression and sharpness in transition band are also obvious from the LC equivalent simulation result of the second section of the LPF. Fig. 9 (a) shows the layout of the proposed lowpass filter that is used in the proposed power divider. This structure is a compound of the first and second sections. In Fig. 9 (b) the LC equivalent circuit of the proposed lowpass filter is presented to demonstrate the circuit operation in the frequency response. The values of the capacitors and inductors of the LC equivalent circuit of the proposed lowpass filter are calculated using Equations of 1–3 and expressed in Table 1. The lowpass filter dimensions of Fig. 6 are: W1 ¼ 0.26, W2¼W3¼W4 ¼ 0.2, W5 ¼ 2.24, W6 ¼ 1.57, W7 ¼ 0.21, La1 ¼ 1.8, La2 ¼ 0.49, La3 ¼ 5.18, La4 ¼ 0.65, La5 ¼ 1.51, La6 ¼ 3.22, La7 ¼ 1.08, La8 ¼ 1.44, g ¼ 0.14 (all in millimeters), Ө ¼ 150 deg. Fig. 10 shows the comparison between the full-wave EM and LC circuit model simulation results of the proposed lowpass filter. As seen, a combination of the first and second sections suppresses the unwanted harmonics and reduces the level of the input return loss around the operating frequency to less than 35 dB. Sharpness and wide transition band at the frequency response of the proposed lowpass filter are obvious so that it is a desirable result of insertion loss of the lowpass filter. According to this frequency response, transmission zeros are equal to 5.37, 6.63, and 15.04 GHz, respectively. Also, these points can be obtained from the transfer function of the LC equivalent circuit of the lowpass filter. The transfer function of the proposed lowpass filter is computed and shown in equation (4). “Z0 ” expresses the value of matched impedance of the transmission line (Z0). The transmissions zeros can be calculated using the transfer function.
Fig. 11. (a) EM simulated response of S12 of the proposed lowpass filter as a function of “g” (b) LC simulated response of S12 of the LC equivalent circuit of the proposed lowpass filter as a function of “Cg”.
present procedure in Fig. 2. The full-wave EM and LC circuit model performances of the first section of the LPF are shown in Fig. 5. The higher unwanted harmonics at the frequency response of the proposed lowpass filter can be suppressed by the first section of it. As seen, it has a wide stop-band bandwidth so that the LC equivalent simulation results of the first section of the LPF express this note. The second section of the proposed LPF is a compact microstrip
vo ¼ vi
ðABCZ0 Þ ðL4 sðBð2L3 sðZ0 þ L4 sÞ þ CðZ0 þ 2L3 s þ L4 sÞÞ þ L3 sðL3 sðZ0 þ L4 sÞþ CðZ0 þ ðL3 þ L4 ÞsÞÞÞ þ AððL3 þ L4 ÞsðL3 sðZ0 þ L4 sÞ þ CðZ0 þ ðL3 þ L4 ÞsÞÞþ Bðð2L3 þ L4 ÞsðZ0 þ L4 sÞ þ CðZ0 þ 2ðL3 þ L4 ÞsÞÞÞÞ
65
(4)
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Microelectronics Journal 71 (2018) 61–69
where
A¼
1 þ C5 L5 s2 þ Cm L5 s2 þ Cm L6 s2 þ C5 Cm L5 L6 s4 C4 s þ C5 s þ Cm s þ C4 C5 L5 s3 þ C4 Cm L5 s3 þ C4 Cm L6 s3 þ C5 Cm L6 s3 þ C4 C5 Cm L5 L6 s5
B¼
C1 s þ C2 s þ C3 s þ C1 C2 L1 s3 þ C1 C3 L1 s3 þ C1 C3 L2 s3 þ C2 C3 L2 s3 þ C1 C2 C3 L1 L2 s5 1 þ C1 L1 s2 þ C1 L2 s2 þ C2 L2 s2 þ C1 C2 L1 L2 s4
C¼
ð1 þ C5 L5 s2 þ Cn L5 s2 þ Cn L6 s2 þ C5 Cn L5 L6 s4 Þ C4 s þ C5 s þ Cn s þ C4 C5 L5 s3 þ C4 Cn L5 s3 þ C4 Cn L6 s3 þ C5 Cn L6 s3 þ C4 C5 Cn L5 L6 s5
5. Simulated and measured results
Fig. 11 (a) shows that the insertion loss (S12) of the proposed lowpass filter is a function of “g” and the second harmonic can be suppressed by tuning the coupling gap “g” as the optimized value of “g” is equal to 0.14 mm, also Fig. 11 (b) shows that the insertion loss (S12) of the LC equivalent circuit is a function of “Cg” and the second harmonic can be suppressed by setting the value of “Cg” to 26 fF.
The used substrate is an RT/Duroid 5880 which has the following characteristics: dielectric constant of 2.2, the thickness of 0.508 mm,
4. Wilkinson power divider design The proposed Wilkinson power divider consists of two lowpass filters as shown in Fig. 12. This structure suppresses up to 6th unwanted harmonics and is significantly smaller than the conventional one. It provides a wide stop-band and high fractional bandwidth at a center frequency of 2.55 GHz. The proposed Wilkinson power divider dimensions of Fig. 12 are A1 ¼ 0.25, A2 ¼ A6 ¼ 1.56, A3 ¼ 8.78, A4 ¼ A5 ¼ 0.2, A7 ¼ 0.91, A8 ¼ 1.72, (all in millimeters). R is equal to 100 Ω. Comparison between the full-wave EM and LC circuit model simulation results of the proposed power divider is illustrated in Fig. 13. Frequency responses show that using the proposed lowpass filters instead of the quarter-wavelength transmission lines of the conventional Wilkinson power divider caused the suppression from 2nd to 6th harmonics with desirable attenuation level. It has a wide stop-band and high fractional bandwidth. These results are considered positive distinction for the Wilkinson power divider.
Fig. 13. Full-wave EM and LC circuit model simulation results of (a) input return loss and insertion loss (b) output return loss and isolation.
Fig. 12. Layout of the proposed Wilkinson power divider.
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Fig. 14. Photograph of the proposed Wilkinson power divider.
and loss tangent of 0.0009. The photograph of the fabricated power divider with operating frequency of 2.55 GHz for harmonics suppression and high FBW is shown in Fig. 14. The size of the fabricated power divider is 9.05 mm 10.88 mm (98.464 mm2) that the size reduction is over 43.5% in comparison to the conventional Wilkinson power divider. The S-parameters are measured using Agilent's E8361C network analyzer. Fig. 15 shows the comparison between simulated and measured Sparameters of the proposed power divider. As it is shown, the measured input return loss (S11), output return loss (S22), and isolation (S23), are less than 15 dB from 1.87 GHz to 2.93 GHz. Also according to their measured conclusions, fractional bandwidth (FBW) is equal to 44%. This is a good result to improve the operation of the conventional Wilkinson power divider. As it is shown in Fig. 15 (a), the measured insertion loss (S12), unwanted harmonics from 5.1 GHz to 16 GHz have been suppressed; in the other word, from 2nd to 6th harmonics have been suppressed with a level less than 20 dB. This expresses that the insertion loss has a wide stop-band bandwidth. The measured input return loss (S11), output return loss (S22), isolation (S23), and insertion loss (S12) at operating frequency of 2.55 GHz, are 28 dB, 27 dB, 46.5 dB, and 3.017 dB, respectively. This topology suppresses undesirable harmonics, in this case: the suppressed harmonics from 2nd to 6th are 20.6 dB, 20.1 dB, 23.3 dB, 24.4 dB, and 32.1 dB, respectively. In Fig. 16, a proper phase performance between two output ports around operating frequency is shown. According to the simulated parameters of ports 2 and 3, as output ports, the phase difference of output ports is equal to 0.05 and magnitude of S12 and S22 are equal to S13 and S33, respectively. Fig. 17 shows the circuit's operation at a center frequency of 2.55 GHz. As seen, the electrical current densities in both lowpass filters are equal. Also, E-field distribution shows when the signal passes from the input port, the power is leading between the two output ports equally, but the lost power at isolation resistance is zero which is indicative the principles of transmission and isolation. These results also confirm that the proposed power divider is symmetrical and output ports are isolated from each other entirely. At operating frequency, the current density distribution in the transmission line is more than one in modified T-
Fig. 15. Simulated and measured (a) input return loss and insertion loss (b) output return loss and isolation.
shaped and circular patch-shaped resonators. Also, the current density distribution in modified T-shaped resonators is very weak. The comparison between the proposed power divider and other available works is expressed in Table 2. 6. Conclusion In this paper, a new design for improved performance of Wilkinson power divider with higher order harmonics suppression has been proposed using lowpass filters instead of the quarter-wavelength transmission lines in the conventional Wilkinson power divider. The proposed power divider operating at 2.55 GHz has been designed, fabricated and measured which has harmonics suppression from 2nd to 6th with an attenuation level less than 20 dB and wide stop-band bandwidth (5.1 GHz - 16 GHz). This structure reduces the size to 43.5% in comparison to the conventional one. High fractional bandwidth (FBW) equal
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to 44% are obtained from this topology. The proposed power divider is proper for using in communication systems which required a compact structure with harmonics suppression, wide stop-band, and high fractional bandwidth. References [1] D.M. Pozar, Microwave Engineering, third ed., Wiley, New York, 2005, pp. 333–337. Ch. 7. [2] M. Hayati, S. Roshani, A novel Wilkinson power divider using open stubs for the suppression of harmonics, ACES J. 28 (6) (June 2013) 501–505. [3] K.-H. Yi, B. Kang, Modified Wilkinson power divider for nth harmonic suppression, IEEE Microw. Wirel. Components Lett. 13 (5) (May 2003) 178–180. [4] H. Shahi, H. Shamsi, Compact wideband Gysel power dividers with harmonic suppression and arbitrary power division ratios, Int. J. Electron. Commun. (AEÜ) 79 (September 2017) 16–25. [5] M.G. Kim, J.S. Kim, R. Mittra, Modified Wilkinson power divider for suppression of nth harmonics, Electron. Lett. 48 (24) (January 2013) 1540–1542. [6] A. Lalbakhsh, A.-A. Lotfi Neyestanak, M. Naser-Moghaddasi, Microstrip hairpin bandpass filter using modified minkowski fractal-shape for suppression of second harmonic, IEICE Trans. Electron. 95 (3) (2016) 378–381. [7] Gh. Karimi, H. Siahkamari, F. Khamin Hamedani, A novel miniaturized Gysel power divider using lowpass filter with harmonic suppression, Int. J. Electron. Commun. (AEÜ) 69 (5) (February 2015) 856–860. [8] H. Siahkamari, S. Vahab, A. Makki, S.-A. Malakooti, Using microstrip LPF in Gysel power divider for extreme size reduction and higher order harmonic suppression, Freq. –Berlin 69 (7–8) (May 2015) 323–328. [9] X. Wang, I. Sakagami, Z. Ma, A. Mase, M. Yoshikawa, Generalized, miniaturized, dual-band Wilkinson power divider with a parallel RLC circuit, Int. J. Electron. Commun. (AEÜ) 69 (1) (January 2015) 418–423. [10] R. Mirzavand, M.M. Honari, A. Abdipour, Gh. Moradi, Compact microstrip Wilkinson power dividers with harmonic suppression and arbitrary power division ratios, IEEE Trans. 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Woo, T. Lee, Suppression of harmonics in Wilkinson power divider using dualband rejection by asymmetric DGS, IEEE Trans. Microw. Theory Tech. 53 (6) (June 2005) 2139–2144. [17] M. Hayati, S. Roshani, S. Roshani, Miniaturized Wilkinson power divider with nth harmonic suppression using front coupled tapered CMRC, ACES J. 28 (3) (March 2013) 221–227. [18] C.M. Lin, H.H. Su, J.C. Chiu, Y.H. Wang, Wilkinson power divider using microstrip EBG cells for the suppression of harmonics, IEEE Microw Wirel. Components Lett. 17 (10) (October 2007) 700–702. [19] F. Zhang, C.F. Li, Power divider with microstrip electromagnetic bandgap element for miniaturization and harmonic rejection, Electron. Lett. 44 (6) (March 2008) 422–423. [20] M. Luo, X. Xu, X.-H. Tang, Y.-H. Zhang, A compact balanced-to-balanced filtering Gysel power divider using λg/2 resonators and short-stub-loaded resonator, IEEE Microw. Wirel. Components Lett. 27 (7) (July 2017) 645–647. [21] Y. Wu, Z. Zhuang, G. Yan, Y. Liu, Z. Ghassemlooy, Generalized dual-band unequal filtering power divider with independently controllable bandwidth, IEEE Trans. Microw. Theory Tech. 65 (10) (October 2017) 3838–3848. [22] M. Bemani, S. Nikmehr, S. Hosseinzadeh, Arbitrary dual-band unequal Wilkinson power divider based on negative refractive index transmission lines, Int. J. Electron. Commun. (AEÜ) 67 (5) (May 2013) 382–386. [23] H. Younesiraad, M. Bemani, M. Fozi, A novel fully planar quad band Wilkinson power divider, Int. J. Electron. Commun. (AEÜ) 74 (April 2017) 75–82. [24] Gh. Karimi, A. Lalbakhsh, H. Siahkamari, Design of sharp roll-off lowpass filter with ultra wide stopband, IEEE Microw. Wirel. Components Lett. 23 (6) (May 2013) 303–305. [25] Gh. Karimi, H. Siahkamari, F. Khamin Hamedani, A. Lalbakhsh, Design of modified Z-shaped and TShaped microstrip filter based on transfer function analysis, Wirel. Personal. Commun. 82 (4) (February 2015) 2005–2016. [26] H.-X. Xu, G.-M. Wang, C.-X. Zhang, Q. Peng, Hilbert-shaped complementary single split ring resonator and low-pass filter with ultra-wide stopband, excellent
Fig. 16. Simulated phase difference between S12 and S13 of the proposed power divider.
Fig. 17. Simulated current density distribution of the proposed power divider.
Table 2 Comparison between the performance of the proposed power divider and previous works. Ref.
FWB (%)
Size Reduction (%)
Harmonic suppression (dB) 2nd
3rd
4th
5th
6th
[2] [5] [9] [10] [11] [12] [17] [18] [21] [28]
– 27 5 27 – – – – 17, 10.8 10.1, 3.2, 1.7 44
35 – – 40 – 40 34.5 39 – –
– 45.3 – 28 – – – 26 – –
45 46.4 – 32 46.2 24 32.5 25 – –
– – – 20 – – – – – –
43 – – – 37.35 – 12 – – –
– – – – – – – – – –
43.5
20.6
20.1
23.3
24.4
32.1
This work
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Microelectronics Journal 71 (2018) 61–69 [29] Y. Wu, L. Jiao, Z. Zhuang, Y. Liu, The art of power dividing: a review for state-ofthe-art planar power dividers, China Commun. 14 (5) (May 2017) 1–16. [30] B.C. Wadell, Transmission Line Design Handbook, British library cataloging in publishing data, 1991. [31] J.S. Hong, M.J. Lancaster, Microstrip Filters for RF/Microwave Applications, second ed., Wiley, New York, 2011.
selectivity and low insertion-loss, Int. J. Electron. Commun. (AEÜ) 65 (11) (November 2011) 901–905. [27] A.K. Verma, N.P. Chaudhari, A. Kumar, Improved performance step impedance lowpass filter, Int. J. Electron. Commun. (AEÜ) 67 (9) (September 2013) 761–770. [28] Y. Wu, Y. Guan, Z. Zhuang, W. Wang, Y. Liu, A novel tri-band T-junction impedance-transforming power divider with independent power division ratios, Plos One 12 (6) (June 2017) 1–7.
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