**Zheng Zhang, Yong-Chang Jiao, Peng Fei, Shun-Feng Cao, and Fu-Shun Zhang**

Power dividers create the multiple versions of high-frequency signals so essential for signal processing in modern communications systems. Ideally, they can channel moderately high levels of power while still in compact circuit sizes. And at times, unequal division ratios are needed for use with amplifiers, antennas, and numerous other components within a system design. In this report, a novel three-way power divider with an unequal dividing ratio of 4:1:1 achieves a bandwidth of about 143.63% centered at 4.045 GHz in a compact size of only 27.5 x 18.0 mm. Compared to conventional designs employing double-sided parallel striplines (DSPSL), grooved substrates, or defected ground structures (DGSs) to achieve the unequal power dividing ratio, this three-way design makes use of a straightforward implementation based on inserting three slots onto the middle microstrip line and laying a pair of parasitical metallic strips alongside microstrip lines.

As communications systems have diversified in recent years, demand has grown for a greater variety of power dividers, and noteworthy research has been devoted to the search for effective unequal power-divider designs.^{1,2} For achieving high-impedance lines having realistic strip widths, a number of approaches have been tried, including the use of offset double-sided parallel strip lines (DSPSLs),^{3} grooved substrates,^{4 }and defected ground structures (DGSs) in microstrip circuits.^{5}

Unfortunately, when using the DSPSL method, it can be difficult to realize a proper transition between the two transmission-line technologies: microstrip and double-sided parallel stripline. In the other approaches, grooved substrates are difficult to implement in a practical way, and when applying the DGS approach, those structures should be kept as far away as possible from other conductors on the ground plane for best results. In addition, although many advances have been made in the design of unequal power dividers, only a small number of these designs have involved power dividers with an odd number of output ports,^{6-8} especially those with unequal power-division ratios.

The current design represents a departure from those three earlier power divider design approaches. This new approach was used to create a three-way unequal power divider with usable frequency range from 1.14 to 6.95 GHz. With the slots inserted onto the middle microstrip line and the two metallic strips laid aside the edge ones, a 4:1:1 dividing ratio was achieved while also avoiding the disadvantages of the earlier three design approaches. Over the full operating-frequency band, the proposed PD exhibits less than 1-dB insertion loss, better than 10-dB return loss at the input/output ports, and better than 12-dB isolation between the output ports.

The circuit schematic for a conventional three-way unequal Wilkinson power divider can be seen in Fig. 1. For the proposed ratio 4:1:1, = k_{1}: k_{2}: k_{3} (k_{1}+k_{2}+k_{3}=1), these values can be found by solving for Eqs. 1 and 2 and the following design parameters can be obtained: Z_{01} = 51.49 Ω, Z_{02} = Z_{03} = 183.14 Ω, R_{1} = R_{int1} = 35.35 Ω, R_{2} = R_{int2} = R_{3} = R_{int3} = 111.8 Ω. Here, Z_{0i}, R_{i}, and R_{inti} are denoted as the transmission-line impedances, termination impedance, and isolation resistor value, respectively:

Z_{0i} = 0.5Z_{0}>/n_{i} = Z_{0}/{k_{i}i/(1 k_{i})>^{0.5}}^{0.5}

I = 1, 2, 3 (1)

R_{inti} = R_{i} = Z_{0}i)/k_{i}>^{0.5}

I = 1, 2, 3 (2)

The design steps for the novel power divider are shown in Fig. 2. Computer-aided-engineering (CAE) simulations of performance were performed with the help of Version 11 of the High-Frequency Structure Simulator (HFSS) software from Ansoft (www.ansoft.com/hfss); the overall size of each power divider was maintained at 27.5 x 18.0 mm.

Due to fabrication limitations, the 183.14-Ω microstrip line, with its 0.068-mm width, is difficult to fabricate. According to the impedance values calculated above, by fixing path 1/3 to a width of 0.2 mm (the smallest practical value), changing the length of path 1/2/3 and width of path 2 to more practical values, the unequal power divider shown in Fig. 2(a) resulted. However, this original configuration of the power divider exhibited too-narrow an operating frequency range and insertion/return loss of around 3/9 dB (Fig. 3), which was considered unacceptable for broadband applications for this unequal dividing ratio.

For the proposed power divider design, a pair of metallic strips were laid partway along the side of the microstrip lines and three slots inserted onto the path 2 signal path to overcome the fabrication problems of the other power-divider design approaches and provide improved transmission characteristics. In one way, the additional metallic strip provides capacitive loading to the sideward microstrip, increasing the capacitance of the nearby microstrip lines. The metallic strip also works together with the microstrip as a coupled line, producing a higher characteristic impedance. Because the added equivalent inductance is dominant over the capacitance in this approach, a higher impedance can be obtained with a 0.2-mm-wide microstrip line.

The inserted slots produce an increased equivalent capacitance (C) across the microstrip line and ground, so that the characteristic impedance 0.5> of the microstrip reaches a lower value. This makes it possible to obtain the appropriate impedance for the path 2 line without using too wide of a microstrip line. The use of the slots helps simplify the overall fabrication of the power divider while also achieving acceptable insertion-loss performance.

### Page Title

Figure 4 shows a detailed view of the final power divider design. The three-way, 4:1:1 ratio unequal power divider was fabricated on a dielectric substrate material measuring 27.5 x 18.0 mm with 0.6-mm thickness and relative dielectric constant (e_{r}) of 2.65 and dissipation factor (loss) of 0.002. The final values for all of the power dividers dimensional values are shown in the table, in which a pair of L_{x} and W_{x} (x = 1, 2, 38) dimensional parameters indicates the length and width of the same microstrip segment of the power divider. It should be pointed out that the length L_{1} is the entire length of the zigzag side of the microstrip.

Figure 5 shows the simulated and measured S-parameter data for the novel unequal power divider, with the results in close agreement. The excursion of the high resonant frequency may be caused by the nonuniformity of the dielectric substrate's relative permittivity, as well as the effects of the SMA connector and the manufacturing limitations in achieving the desired tolerances and dimensional requirements. For operating frequencies that apply to applications in IMT systems (2 GHz), WiMAX (3.5 GHz), and wireless-local-area-network (WLAN) applications (2.4, 5.2, and 5.8 GHz), the return loss was better than 10 dB. Additionally, the measured insertion losses of the power divisions at ports 2/4 and 3 are equal to 8.280.5 dB and 2.260.5 dB, respectively, indicating that the power divider can effectively separate an incoming signal into three parts with the desired division ratio. The results of simulated and measured isolation were nearly better than 12 dB across all operating frequencies.

In conclusion, it was possible to realize a compact, broadband three-way power divider with unequal division ratio (4:1:1) by means of symmetric metallic strips placed alongside microstrip lines and inserting three slots in the middle microstrip line. Measured results for a fabricated component agreed closely with the simulated performance parameters, with impressive results for insertion loss, return loss, and isolation. Good division ratios were achieved at ports 2, 3, and 4 across the full operating-frequency range, making the final design a good candidate for use in applications in IMT-2000, WiMAX, and WLAN bands.

ZHENG ZHANG, Researcher

YONG-CHANG JIAO, Researcher

PENG FEI, Researcher

SHUN-FENG CAO, Researcher

FU-SHUN ZHANG, Researcher

**Key Laboratory of Antennas and Microwave Technology **

Xidian University

Xi'an, Shaanxi, 710071, People's Republic of China

+86(029)88202669

FAX: +86(029)88202662

e-mail: zhangzh_lucky@163.com

**References**

- Bo Li, Xidong Wu, and Wen Wu, "A 10:1 Unequal Wilkinson Power Divider Using Coupled Lines with Two Shorts," IEEE Microwave & Wireless Component Letters, Vol. 19, No. 12, December 2009, pp. 789791.
- Yongle Wu, Yuanan Liu, Yaxing Zhang, Jinchun Gao, and Hui Zhou, "A dual band unequal Wilkinson power divider without reactive components," IEEE Transactions on Microwave Theory & Techniques, Vol. 57, No. 1, January 2009, pp. 216222.
- J.-X. Chen and Q. Xue, "Novel 5:1 unequal Wilkinson power divider using offset double-sided parallel-strip lines," IEEE Microwave & Wireless Component Letters, Vol. 17, No. 3, March 2007, pp. 175177.
- M. Moradian and H. Oaraizi, "Application of grooved substrates for design of unequal Wilkinson power dividers," IET Electronics Letters, Vol. 44, No. 1, January 2008, pp. 3233.
- J. S. Lim, S. W. Lee, C. S. Kim, J. S. Park, D. Ahn, and S. W. Nam, "A 4:1 Unequal Wilkinson Power Divider," IEEE Microwave & Wireless Component Letters, Vol. 11, No. 3, March 2001, pp. 124126.
- J.-C. Chiu, J.-M. Lin, and Y.-H. Wang, "A novel planar three-way power divider," IEEE Microwave & Wireless Component Letters, Vol. 16, No. 8, August 2006, pp. 449-451.
- Xinhuai Wang, Dongzhou Chen, Xiaowei Shi, Feng Wei, and Xiaoqun Chen, "A compact three-way dual-frequency power divider," Microwave and Optical Technology Letters, Vol. 51, No. 4, April 2009, pp. 913-915.
- Yu-Ann Lai, Chi-Ming Lin, Jui-Chieh Chiu, Che-Hung Lin, and Yeong-Her Wang, "A Compact Ka-Band Planar Three-Way Power Divider," IEEE Microwave & Wireless Component Letters, Vol. 17, No. 12, December 2007, pp. 840-842.