A Tri-band Wilkinson Power Divider using Step-Impedance Resonator

Xin-Huai Wang, Yan-Fu Bai, He Xu, Wei Cheng, Zhi-Qing Lv, and Xiao-Wei Shi

National Key Laboratory of Science and Technology on Antennas and Microwave, Xidian University

Xi’an 710071, Shaanxi, P. R.China

Abstract-A novel planar tri-band power divider using step-

impedance resonator with band-pass response is proposed in this paper. The topology of the circuit, different from conventional Wilkinson power divider, is the couple lines and resonators instead of the transmission lines. It can provide good isolation, good amplitude balance simultaneously at three arbitrary frequencies and direct current (DC) block characteristic. The proposed structure is analyzed and simulated. The validity of the design is demonstrated by experimental results on a 930/2300/3600 MHz power divider.

I. INTRODUCTION

Power dividers are fundamental components applied in various microwave circuits and subsystems. In 1960, the conventional Wilkinson power divider was developed with the equivalent amplitude and in-phase outputs by Ernest. J. Wilkinson [1]. The circuits have been widely utilized in microwave designs. In recent years, some new types of power dividers using couple line are proposed [2, 3]. At the same time, much more dual-frequency power dividers are developed [4-6]. To realize dual-frequency operations, the dividers are often modified using two-section transformers or stub lines. However, due to the rapid development of multi-standard operation in wireless practical applications and so components that work at three or more frequencies are of great interest. Unfortunately, the previous mentioned power divider only can operate at one or two design frequency. Therefore, these are not suitable for some triple band or multi-band operations. In 2005, a three-section transmission-line transformer was introduced by M.Chongcheawchamnan [7], which can operate at any three frequencies f1, f2, and f3. Two kinds of tri-band Wilkinson power divider using this transformer section has been reported in [8, 9].

This paper presents a new technique to design a three-way tri-band power divider using couple lines and triple section step-impedance resonator (TSSIR). The proposed power divider operates at three arbitrary frequencies of interest f1, f2, and f3, which supplies high isolation, good amplitude balance simultaneously. In additional, the couple line procedure can provide the DC block functions, which further reduce the parasitic effects from using extra blocking capacitors. The formulas, which used to determine design parameters of the tri-band power divider, are given out. It can be considered as considered as an integration of a conventional divider and a

tri-band filter. The technique is validated by experimental results on a 930/2300/3600MHz power divider.

II. STRUCTURE AND ANALYTICAL EQUATIONS

The structure of the proposed dual-frequency power divider is shown in Fig. 1. The topology of the circuit is three triple section step-impedance resonators, and a planar isolation resistor. Assuming all the impedances of the input and output ports to be Z0 = 50 Ω, the planar isolation resistors are selected as R = 2Z0 = 100 Ω.

Figure 1. The structure of the proposed tri-band power divider.

A. Triple section step-impedance resonator As shown in Fig. 2, the basic geometry of a triple section

step-impedance resonator is symmetrical. It consists of five microstrip lines of three different characteristic impedances Z1, Z2, Z3 and of electrical lengths 1 , 2 and 3 .

Figure 2. The basic geometry of tri-section SIR.

Ignoring discontinuity and open-edge capacitance of the

microstrip lines, the admittance looking into the TSSIR is derived as:

2 21 2 2 2 3 2 1 3 1 2 1 2

1 2 22 3 1 2 2 1 2 2 2 1 2 3

tan tan tan tan tan tan

tan tan tan tan tan tanin

K K K K K KY jY

K K K K K K

(1)

where 1 3 2/K Z Z , 2 2 1/K Z Z are impedance ratios. For practical consideration, 1 , 2 , 3 is chosen to have

equal electrical lengths , (1) can be describe as: 2

1 2 1 21 2

1 1 2 2

tan (1 )

tan [1 tan ]in

K K K KY jY

K K K K

(2)

From the resonance condition can be obtained by 0inY or

inY , the first three resonant modes of the TSSIR can be derived as:

1 1 201

1 2

tan1

K K

K K

(3)

1 1 1 202

2

1tan

K K K

K

(4)

03 2

(5)

Note (3)-(5) that have been given in [10] are shown here for convenience. In a tri-band design, f1, f2 and f3 presented the first three resonant frequencies which are usually set to the center frequencies of the three passbands. With the discontinuity of the TSSIR neglected, they are expressed as:

1 1 1 2

2022

1 01 1 1 2

1 2

1tan

tan1

K K K

Kf

f K K

K K

(6)

3 03

1 01 1 1 2

1 2

2tan1

f

f K K

K K

(7)

From (6) and (7) it is obvious that f1, f2 and f3 are controlled by impedance ratio K1, K2. When the value of K1 and K2 are varied, the first three resonant frequencies are changed. The relationships are shown in Fig. 3 and Fig. 4.

Figure 3. f2 / f1 with K1, K2. relationships.

Figure 4. f3 / f1 with K1, K2. relationships.

In actual designs of the tri-band power divider, when the f1, f2 and f3 are specified, the desired impedance ratios for the TSSIR are given as follow:

1 1

N M NK

N

(8)

12

1

1 KK

M K

(9)

where

2 2

3

tan ( )2

fM

f

(10)

2 1

3

tan ( )2

fN

f

(11)

Note that (8)-(11) have been given in [11].The (10) is simpler than that given in [11].

B. Analysis of coupling network The coupling network1 and coupling network2 can be

predigested as two parallel-couple microstrip lines. EM procedure as given in [12, 13] could be used to obtain the coupling length L0 and gap S. As shown in Fig. 5 and Fig. 6, the bandwidth and the power level of each band also can be tuned by adjusting the gap S1 and S2 between the two microstrip couple lines. When the gap becomes wider, the coupling strength becomes weaker, the bandwidth becomes narrower.

Figure 5. S21-magnitude with varied coupling gap S1.

Figure 6. S21-magnitude with varied coupling gap S2.

III. IMPLEMENT AND RESULTS

In this section, in order to demonstrate the validity of the proposed design concept for a tri-band power divider, a proposed tri-band power divider is designed on PTFE substrate with relative dielectric constant of 2.65 and thickness h = 1 mm. The center frequencies of the three bands are f1 = 0.93 GHz, f2 = 2.30 GHz, and f3 = 3.6 GHz. As shown in Fig. 1, based on the real transmission line, substrate, and resistor, the model is built up with the dimension marked and simulation has been carried out by the full-wave EM simulator (Ansoft HFSS 11.0). The measured data are collected from the Agilent N5230A network analyzer.

On the basis of the earlier-mentioned discussion, the parameters of the power divider are calculated by using (8)-(11), in which M = 2.46, N = 0.18, K1 = 0.54, K2 = 0.80. After the initial dimensions are chosen, the dimensions are optimized in the actual implementation. The minimum the gap and width of the coupling line is limited to 0.2 mm due to tolerances of PCB fabrication. The final optimum dimensions shown in Fig. 1 are listed as follows: L0 = 15.7 mm, L1 = 14.54 mm, L2 = 14.32 mm, L3 = 14.1 mm, W0 = 2.73 mm, W1 = 0.88 mm, W2 = 1.56 mm, W3 = 2.73 mm, S1 = 0.2 mm, S2 = 0.2 mm. Fig. 7 shows the photograph of the fabricated power divider. The area of the proposed power divider is 18×4 cm2. The simulated S-parameters are presented in Figure 8 and the measured S-parameters are presented in Fig. 9.

Figure 7. Photograph of the fabricated tri-band power divider.

Figure 8. Simulated performance of the tri-band power divider.

Figure 9. Measured results of the tri-band power divider.

The measured results of the return loss are about -13.0

dB at 0.93 GHz, -14.5dB dB at 2.3 GHz and -23.4 dB at 3.6 GHz, respectively. The |S21| and | S31| are about - 4.56±0.01 dB at 0.93 GHz, - 4.35±0.02 dB and -4.25±0.02 dB at 3.6 GHz. The measured isolation between port3 and port2 (|S32|) are better than -16.0 dB at 0.93 GHz, -17.0 dB at 2.3 GH and -18.6 dB at 3.6 GHz. Except for triple passband, it has the fourth passband at 4.9GHz, which is resulted by the third spurious frequency. It is to say that this design also can be considered as a quad-band power divider. Some slight differences between measured and simulated result, which is due to dielectric loss and the limited precision of fabrication and measurement.

IV. CONCLUSION

A novel tri-band power divider is presented in this paper. The structure of the proposed power divider has been given and analyzed. By using triple section step-impedance resonator, coupling between microstrip lines and a resistor, the new circuit can provide tri-band application and DC isolation characteristic. Moreover, this design methodology allows controlling each frequency, output power level, and band width. Good agreement between the measurement and simulation has been attained. The measured results exhibit that the proposed power divider can supply the required RF performance on return loss, amplitude balance and isolation. It can be considered as an integration of a conventional divider and a tri-band filter. Thus the proposed power divider is suitable for the application of more efficient intergraded RF front ends and multi-band narrow-band systems, which are more demanding at near future.

Acknowledgments： This work is supported in part by the

National Science Foundation of China under Grant 60801039, the Fundamental Research Funds for the Central Universities K50511020021, and the Guangdong Province Major science and technology project 2009A080207006.

REFERENCES

[1] E. Wilkinson,“An N-way hybrid power divider,” IEEE Trans. Microw. Theory Tech., Vol.8, No.1, 116–118, 1960.

[2] P. K., Singh, S. Basu, et al, “Coupled line power divider with compact size and bandpass response,” Electronics Letters 45, No.17, 892-894, 2009.

[3] K.-K. M., Cheng, and C. Law, “A new approach to the realization of a dual-band microstrip filter with very wide upper stopband,” IEEE Trans. Microw. Theory Tech., Vol.56, No.6,1461-1467, 2008.

[4] X.-H.,Wang, D. Chen, X. Shi, F. Wei, and X. Chen, “A compact three-way dual frequency power divider,” Microwave and Optical Technology Letters ,Vol. 51, No. 4, 2009.

[5] Y.,Wu, Y. Liu, Y. Zhang, J. Gao, and H. Zhou, “A dual band unequal wilkinson power divider without reactive components,” IEEE Trans. Microw. Theory Tech., Vol. 57, No. 1, 216–222, 2009.

[6] Y., Wu, H. Zhou, Y. Zhang, and Y. Liu, “An unequal Wilkinson power divider for a frequency and its first harmonic,” IEEE Microw. Wireless Compon. Lett., Vol. 18, No. 11, 737-739, 2008.

[7] M. Chongcheawchamnan, S. Patisang, S.Srisathit, R. Phromloungsri, and S. Bunnjaweht, “Analysis and design of a three-section

transmission-line transformer,” IEEE Trans. Microw. Theory Tech., Vol. 53, 2458–2462, 2005.

[8] M. Chongcheawchamnan, S. Patisang, M.Krairiksh, and I.Robertson, “Tri-Band Wilkinson Power Divider Using a Three-Section Transmission-Line Transformer,” IEEE Microw. Wireless Compon. Lett., Vol. 18, 452–454, 2006.

[9] X.-H., Wang, Xiaoqun Chen, Xiao-Wei Shi, Feng Wei, and Yanfu Bai, “A novel planar three-way triband power divider,” Microwave and Optical Technology Letters, Vol. 52, No. 1, January 2010.

[10] X.- M., Lin. and Q.-X., Chu. “Design of Triple-band Bandpass Filter Using Trn-section Stepped-Impedance Resonators,” In Proc.Int.Conf. Microw.Millimeter Wave Tech.Guilin,China, 1-3,2007.

[11] C. I. G., Hsu, L. Ching-Her, et al, “Tri-Band Bandpass Filter With Sharp Passband Skirts Designed Using Tri-Section SIRs,” IEEE Microw. Wireless Compon. Lett., Vol. 18, No.1, 19-21, 2008.

[12] Y.-P., Zhang, and S. Mei, “Dual-Band Microstrip Bandpass Filter Using Stepped-Impedance Resonators With New Coupling Schemes,” IEEE Trans. Microw. Theory Tech., Vol.54, No. 10, 3779-3785, 2006.

[13] J.-S., Hong, and M. J. Lancaster, “Microstrip Filters for RF/Microwave Applications,” John Willey & Sons, Inc., New York, 2001.