J Electromagn Eng Sci Search

CLOSE


J Electromagn Eng Sci > Volume 19(3); 2019 > Article
Yoon and Kim: Miniaturized Multi-Section Power Divider with Parallel RC Isolation Circuit

Abstract

This paper proposes a miniaturized multi-section power divider with parallel resistor and capacitor isolation circuits. Each of the section transmission lines constituting the proposed multi-section power divider has a length less than a quarter wavelength and the impedance of the transmission lines can be controlled within a certain range while avoiding high impedance. In addition, each circuit connected between the transmission lines consists of a parallel resistor and capacitor to satisfy the matching and isolation characteristics between output ports. To validate the proposed power divider, two circuits at a frequency of 2 GHz were designed with two- and three-section dividers. In comparison to a conventional power divider, the proposed divider showed broadband performances with a small structure.

I. Introduction

The power divider is a vital element in communication systems such as power amplifiers, mixers, and transceivers, owing to its simple design and superior performance. The conventional power divider has good matching of input and output, isolation performance, and low loss in narrow band operation. Due to its narrow band characteristics, its application has been limited in the current large-capacity communication systems of WCDMA, LTE, and 5G.
To address this limitation, a multi-section divider [15] has been proposed. Although the multi-section divider has broadband characteristics with an achievable bandwidth greater than 100%, it has the disadvantages of a large circuit and increased insertion loss.
Recently, various designs to reduce the circuit size of power dividers have been researched, such as a structure using short uniform transmission line [6, 7], an isolation circuit positioned in a quarter-wavelength transformer [8, 9], and artificial transmission lines built up with lumped elements [10].
However, since these dividers use a λ/4 transformer between the input and output or between the input or output and 50 Ω termination, they cannot achieve an overall reduction in size. In addition, the bandwidth is reduced due to the impedance transformer, and the parasitic uncertainty of lumped elements is not desirable.
The power divider proposed in this paper has a multi-section structure to realize broadband characteristics, with the electrical length of each power splitting section less than a quarter wavelength to reduce the circuit size. The characteristic impedance of each power-splitting section can be controlled within a certain range while avoiding high impedance. All input and output ports are designed with 50 Ω termination, so there is no need for an impedance transformer. In addition, a parallel resistorcapacitor circuit structure is adopted to obtain the broadband output matching and isolation characteristics of the proposed power divider.

II. Theory and Design

The structure of the proposed N-section power divider is shown in Fig. 1. It consists of transmission lines with electrical lengths (θ 1, θ 2, … , θ N ) less than 90° and isolation circuits with parallel resistors (R 1, R 2, … , R N ) and capacitors (C 1, C 2, … , C N ). The proposed power divider is analyzed using the even-and odd-mode analysis methods; Fig. 2(a) and (b) show the even- and odd-mode equivalent circuits, respectively.
To obtain the electrical lengths and characteristic impedances of the transmission lines, the matching mechanism of the cascade transmission lines [11] is presented in Fig. 3. As seen in Fig. 3(a) and (b), it is possible to convert a part of the impedance transformer with Z a and 90° to another impedance Z b and electrical length θ b . To match the conversion portion of the impedance transformer, the admittance values of Y in,a and Y in,b must be the same. By solving the equation for the real and imaginary parts of the admittance (Y in,a , Y in,b ), the impedance Z b and terminating impedance Z Lb of the proposed two-section transformer for θ b change can be obtained as:
(1)
Zb=ZLb·(B-BZa2/ZLa2)2+4Za2/ZLa2-B(1-Za2/ZLa2)2Za/ZLa
(2)
ZLb=(1+(Za2/ZLa2)tan2θa)(1+tan2θb)(1+tan2θa)(1+(Zb/ZLb)2tan2θb)/ZLa
where
B=tan θa(1+tan2θb)tan θb(1+tan2θa).
Ahn [12] confirmed that when the electrical length (θ a < θ b < 90°) and termination conditions (Z La < Z oS ) are satisfied, Z b and Z Lb should satisfy Z b < Z a and Z Lb < Z La . Using the above conditions, the impedance Z c and electrical length θ d of the three-section transformer can be obtained in the same way, as seen in Fig. 3(c). Using this method, all the electrical lengths of the multi-section transmission line, which is the proposed divider with each section length less than λ/4 wavelength, can be obtained.
In addition, for the odd-mode equivalent circuit shown in Fig. 2(b), the following equations can be obtained:
(3)
Yin,N=GN+jBN-jYNtanθN
(4)
Yin,N-1=GN-1+jBN-1+YN-1Yin,N+jYN-1tan θN-1YN-1+jYin,Ntan θN-1
(5)
Γii=Yo-Yin,1Yo+Yin,1
where GN=2RN , B N = 2ωC N , YN=1ZN , and Γ ii is the reflection coefficient at port 2 (i = 2) and port 3 (i = 3).
The conductance (G 1, G 2, …, G N ) and susceptance (B 1, B 2, …, B N ) values can be obtained to satisfy the condition that the reflection coefficient of Eq. (5) becomes zero.
To achieve isolation performance between ports 2 and 3, the S-parameter S 32 should be minimized as shown in Fig. 4. To calculate the isolation characteristic of the divider network, ABCD and admittance parameters are used. The ABCD matrix of the circuit Net N , which is composed of two transmission lines (Z N , θ N ) and a shunt resistor Z o , can be expressed as:
(6)
(ANetNBNetNCNetNDNetN)=(cosθNjZNsinθNjYNsinθNcosθN)(10Yo1)(cosθNjZNsinθNjYNsinθNcosθN)
The admittance matrix of the composite network Net RCN resistor-capacitor can be represented by:
(7)
(y11y12y21y22)NetRCN=(1RN-1RN-1RN1RN)RN+(jωCN-jωCN-jωCNjωCN)CN
Since the network Net N is connected in parallel with network Net RCN , we needed to transform Eq. (6) from an ABCD matrix to an admittance matrix. Finally, the composite admittance matrix of Net N and Net RCN can be obtained as follows:
(8)
(y11y12y21y22)NetN+NetRCN=(y11y12y21y22)NetN+(y11y12y21y22)NetRCN
To obtain the equation of the networks, which are connected by two cascade transmission lines (Z N- 1, θ N- 1) and the composite network of Net N and Net RCN , the composite network parameters are needed to convert the ABCD matrix. We can compute the ABCD parameters of the networks Net N- 1 and Net RCN- 1 as previously calculated. Through this process, the admittance parameters of the entire network can be obtained. The S-parameter value of isolation, S 32, is finally obtained by parameter conversion, and the isolation circuit values of the resistor and capacitor are selected to satisfy the S 32 parameter condition of |S 32| ≤ −25 dB at the same time among the values satisfying Eq. (5).

III. Simulation and Experimental Results

To confirm the validation of the design rule, we designed two- and three-section power dividers operating at a frequency of 2 GHz and implemented on the substrate of Rogers RO4350B PCB (ɛ r = 3.48 and h = 0.762 mm). The simulation was performed using the Microwave Office software developed by National Instruments.
The two-section power divider configuration process is summarized as follows. First λ/4 impedance transformer of Z oT = 50 Ω, Z LT = 35.35 Ω, Z T = 42.04 Ω and θ T = 90° is chosen as shown in Fig. 5(a).
Based on the decomposition theory of a single transmission line [13], the impedance transformer can be divided into two transmission lines of Z oTD = 100 Ω, Z LTD = 70.7 Ω, Z TD = 84.08 Ω, and θ TD = 90°, as shown in Fig. 5(b). To constitute the two-section transmission line of the divider, the following parameters are set: Z a = 84.1 Ω and θ a = 60°. The parameters of Z b = 69.56 Ω, Z Lb = 50 Ω, and θ b = 76° can be calculated using Eqs. (1) and (2). To obtain the parameter values for the three-section lines, we used a similar method as follows:
The following parameters are set: Z a = 84.1 Ω and θ a = 50°. The three-section parameters of Z b = 74.44 Ω, Z Lb = 59.22 Ω, θ b = 66°, Z c = 67.60 Ω, Z Lc = 50 Ω, and θ d = 73° can be calculated as described previously. Finally, the resistor-capacitor values satisfying the reflection and isolation characteristics of the output ports are obtained using MATLAB and summarized as follows: In the case of the two-section divider, R 1 = 120 Ω, C 1 = 0.02 pF, R 2 = 110 Ω, and C 2 = 0.18 pF. In the case of the three-section divider, R 1 = 820 Ω, C 1 = 0.01 pF, R 2 = 180 Ω, C 2 = 0.02 pF, R 3 = 150 Ω, and C 3 = 0.17 pF.
Fig. 6(a) and (b) show photographs of the two- and three-section proposed power dividers. The total length of the two-section divider is 106°, and that of the three-section divider is 179°. Fig. 7(a) and (b) show the measured and simulated S-parameters of the two-section power divider. The insertion losses of |S 21| and |S 31| were −3.10 dB, and the isolation of |S 32| was greater than 25 dB. The input return loss of |S 11| was better than −25 dB, and the output return losses of |S 22| and, |S 33| were better than −30 dB at the center frequency of 2 GHz. The measured −15 dB bandwidths of |S 11|, |S 22|, |S 33|, and |S 32| were in the ranges of 1.33–2.46 GHz, 0.5–3.63 GHz, 0.5–3.35 GHz, and 1.26–2.6 GHz, featuring fractional bandwidths of 56.5%, 156%, 142%, and 67%. In addition, Fig. 8(a) and (b) show the measured and simulated S-parameters of the three-section power divider. The insertion losses of |S 21| and |S 31| were −3.20 dB, and the isolation of |S 32| was greater than 22 dB. The input return loss of |S 11| was better than −19 dB, and output return losses of |S 22| and, |S 33 | were better than −24 dB at center frequency of 2 GHz. The measured −15 dB bandwidth of |S 11|, |S 22|, |S 33|, and |S 32| were in the ranges of 1.1–3.42 GHz, 0.54–3.76 GHz, 0.52–3.76 GHz, and 0.95–3.29 GHz, featuring fractional bandwidths of 116%, 161%, 162%, and 117%. Fig. 9 shows that the phase difference between the output ports in the two- and three-section power dividers was measured within ±2.5°. Table 1 shows a comparison of the proposed divider with conventional multi-section divider.

IV. Conclusion

This paper presents a multi-section power divider with a parallel RC isolation circuit. Because each section of the power divider is less than λ/4 wavelength, the power divider is implemented in a reduced size. In addition, the bandwidth of the matching and isolation characteristic showed that a fractional bandwidth above 100% is achievable in the three-section divider. By choosing the proper source and load impedance, the power divider can be implemented while avoiding the use of high impedance. By adopting decomposition and the improved transformer, the proposed power divider was demonstrated good performance, and the simulated and measured results were confirmed to be in good agreement.

Fig. 1
Schematic of the proposed power divider.
jees-19-3-147f1.jpg
Fig. 2
Equivalent circuits of even-mode (a) and odd-mode (b).
jees-19-3-147f2.jpg
Fig. 3
Matching mechanism of the cascade transmission lines: (a) conventional λ/4 transformer, (b) proposed transformer with two sections, and (c) proposed transformer with three sections.
jees-19-3-147f3.jpg
Fig. 4
Equivalent circuit of the entire schematic.
jees-19-3-147f4.jpg
Fig. 5
Decomposition of transmission lines: (a) λ/4 transformer and (b) decomposition of single λ/4 transformer.
jees-19-3-147f5.jpg
Fig. 6
Photographs of two-section (a) and three-section (b) proposed power dividers.
jees-19-3-147f6.jpg
Fig. 7
Measured and simulated S-parameters of the two-section power divider: (a) |S 21|, |S 31|, |S 32|, and (b) |S 11|, |S 22|, |S 33|.
jees-19-3-147f7.jpg
Fig. 8
Measured and simulated S-parameters of the three-section power divider: (a) |S 21|, |S 31|, |S 32|, and (b) |S 11|, |S 22|, |S 33|.
jees-19-3-147f8.jpg
Fig. 9
Measured phase difference between the output ports of the two- and three-section power dividers.
jees-19-3-147f9.jpg
Table 1
Comparison of the proposed divider with conventional multi-section divider
Ref. Center freq. (GHz) Section no. Total length (º) 15 dB BW (%) Insertion loss (dB)
[2] 30 2 180 100 −5.0
[3] 1 3/4 270 / 360 110 −2.2 / −5.5
[4] 1 3 183 55 −0.5 / −10
[5] 0.8 / 2 2 90 40 −2.06 / −4.88
This work 2 2 106 156 max. −3.1
3 179 162 max. −3.2

References

1. JS. Lim, UH. Park, S. Oh, JJ. Koo, YC. Jeong, and D. Ahn, "A 800- to 3,200-MHz wideband CPW balun using multistage Wilkinson structure," In: Proceedings of 2006 IEEE MTT-S International Microwave Symposium Digest; San Francisco, CA. 2006; pp 1141–1144.

2. Y. Sun, and AP. Freundorfer, "Broadband folded Wilkinson power combiner/splitter," IEEE Microwave and Wireless Components Letters, vol. 14, no. 6, pp. 295–297, 2004.
crossref
3. MM. Honari, L. Mirzavand, R. Mirzavand, A. Abdipour, and P. Mousavi, "Theoretical design of broadband multisection Wilkinson power dividers with arbitrary power split ratio," IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 6, no. 4, pp. 605–612, 2016.
crossref
4. MM. Honari, R. Mirzavand, P. Mousavi, and A. Abdipour, "Class of miniaturised/arbitrary power division ratio couplers with improved design flexibility," IET Microwaves, Antennas & Propagation, vol. 9, no. 10, pp. 1066–1073, 2015.
crossref
5. I. Sakagami, X. Wang, K. Takahashi, and S. Okamura, "Generalized two-way two-section dual-band Wilkinson power divider with two absorption resistors and its miniaturization," IEEE Transactions on Microwave Theory and Techniques, vol. 59, no. 11, pp. 2833–2847, 2011.
crossref
6. PH. Deng, and YT. Chen, "New Wilkinson power dividers and their integration applications to four-way and filtering dividers," IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 4, no. 11, pp. 1828–1837, 2014.
crossref
7. ZX. Du, XY. Zhang, KX. Wang, HL. Kao, XL. Zhao, and XH. Li, "Unequal Wilkinson power divider with reduced arm length for size miniaturization," IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 6, no. 2, pp. 282–289, 2016.
crossref
8. W. Choe, and J. Jeong, "Compact modified Wilkinson power divider with physical output port isolation," IEEE Microwave and Wireless Components Letters, vol. 24, no. 12, pp. 845–847, 2014.
crossref
9. Y. Kim, and YC. Yoon, "A modified unequal power divider with a complex isolation component for enhanced isolation," Microwave and Optical Technology Letters, vol. 57, no. 2, pp. 322–324, 2015.
crossref
10. M. Heydari, and S. Roshani, "Miniaturised unequal Wilkinson power divider using lumped component elements," Electronics Letters, vol. 53, no. 16, pp. 1117–1119, 2017.
crossref
11. T. Zhang, W. Che, and H. Chen, "Miniaturized multiway unequal power divider with controllable characteristic impedances," IEEE Microwave and Wireless Components Letters, vol. 27, no. 12, pp. 1062–1064, 2017.
crossref
12. HR. Ahn, "Complex impedance transformers consisting of only transmission-line sections," IEEE Transactions on Microwave Theory and Techniques, vol. 60, no. 7, pp. 2073–2084, 2012.
crossref
13. C. Li, and DS. Ricketts, "A low-loss, impedance matched λ/4 compact T-junction power combiner," In: Proceedings of 2012 7th European Microwave Integrated Circuit Conference; Amsterdam, The Netherlands. 2012; pp 147–150.

Biography

Young-Chul Yoon received his B.S., M.S., and Ph.D. in electronics engineering from Sogang University, Seoul, Korea, in 1978, 1982, and 1989, respectively. In 1987, he joined the Department of Electronics Engineering, Catholic Kwandong University, Gangneung, Korea, where he is currently a professor. His areas of interest are the design of high power amplifiers for the ISM band, and RF and microwave circuit analysis and design.
jees-19-3-147i1.jpg

Biography

Young Kim received his B.S., M.S., and Ph.D. in electronics engineering from Sogang University, Seoul, Korea, in 1986, 1988, and 2002, respectively. He developed cellular and PCS linear power amplifiers at Samsung Electronics Co. Ltd. In 2003, he joined the School of Electronics Engineering, Kumoh National Institute of Technology, Gumi, Korea, where he is currently a professor. His areas of interest are the design of high power amplifiers and linearization techniques, and RF and microwave circuit analysis and design.
jees-19-3-147i2.jpg
TOOLS
Share :
Facebook Twitter Linked In Google+
METRICS Graph View
  • 0 Crossref
  • 0 Scopus
  • 761 View
  • 61 Download
Related articles in JEES

ABOUT
ARTICLE CATEGORY

Browse all articles >

BROWSE ARTICLES
AUTHOR INFORMATION
Editorial Office
#706 Totoo Valley, 217 Saechang-ro, Yongsan-gu, Seoul 04376, Korea
Tel: +82-2-337-9666    Fax: +82-2-6390-7550    E-mail: admin-jees@kiees.or.kr                

Copyright © 2019 by The Korean Institute of Electromagnetic Engineering and Science. All rights reserved.

Developed in M2community

Close layer
prev next