An Area efficient structure for a Dual band Wilkinson power divider with flexible frequency ratios

1 An Area efficient structure for a Dual band Wilkinson power divider with flexible frequency ratios Jafar Sadique, Under Guidance of Ass. Prof.K.J.Vinoy.E.C.E.Department Abstract In this paper a new design of Wilkinson power divider for dual band applications made using stub-loaded transmission line is presented. Dual-band quarter-wavelength (λ/4) transmission lines are proposed first, where both open- and short-ended stubs are applied. By replacing the conventional λ/4-line with the Dualband lines, the desired dual-band Wilkinson power dividers can be realized. The dual band designs are there. However, the design with a large frequency ratio, becomes a challenge in engineering because of the impractical realization of the high- or lowimpedance transmission lines on a dielectric substrate. In this paper, we first introduce a transmission-line structure and perform theoretical analysis. For the designed stub a closed form solution has made to minimize the area. A power divider working at 2/ 6.44 GHz is designed using this method. Its measured performance verifies the designed concepts. Index Terms Open and short stub, transmission line, Wilkinson power divider, dual-band, ABCD matrix W I. INTRODUCTION the rapid advancement of wireless/wireline communication, various functionalities such as bandwidth, multi band are increased with much more stringent requirements suffering from the system cost, compactness, stability, reliability, and other specifications. It is known that any wireless/wireline (RF) system is generally composed of passive and active circuits [1] [2], [3]. Among various RF passive circuits, Wilkinson power divider [4] is a basic and important component in application to RF power amplifiers, mixers, phased-array antennas, and many kinds of equipment. To enable a Wilkinson power divider with dual-band characteristics, several topologies [5] [7] have been reported to date. In [5] - [6], dual-band power dividers working at the fundamental frequency and its first harmonic (the frequency ratio: f2 / f1 = 2) are discussed, where lumped element equivalent circuit [3] and stepped impedance transformers [5], [8], [6] are used. In [9] and [6], Wilkinson power dividers with controllable frequency ratios are discussed, but additional lumped components such as capacitors and inductors are needed for these designs. To address this issue, a Wilkinson power divider based on dual-band transmission line is proposed in [7]. However, to satisfy the corresponding matching conditions and to keep the size compact, the realizable frequency ratio for this topology is limited. Fig. 1. General topology of the conventional Wilkinson power divider.. Fig. 2 Transmission line (a) with a loading and (b) without a loading. In this paper, we propose a novel dual-band λ/4-line using both open- and short-ended stubs. It is found that these modifications lead to large frequency. Closed form design equations are derived for the dual band lines. To increase the frequency ration we loaded transmission line instead of normal stubs. Based on these equations, new dual-band Wilkinson power dividers are designed. To verify the design concepts, a Wilkinson power divider working at 2 / 6 GHz is fabricated on the FR-4 board. The measurement results agree very well with the theoretical predictions

2 where n1 = 1, 2, 3, Z1-A, Zopen_A, Zshort_A, θ1_a, θopen_a, θshort_a are as labeled in Fig. 3 Fig. 3. Schematics of the proposed dual-band λ/4-lines. II. MATHEMATICAL ANALYSIS. A. Dual-band λ/4-lines. The realizable frequency ratios of the proposed power dividers are constrained by the realizable transmission line characteristic impedances. To understand this limitation, the corresponding stub impedances are calculated as a function of the frequency ratio (f2 / f1). The results are plotted in Fig. 4, where Eqs. (3) (5) are applied. In the calculations, we have assumed that n1 = n2 = 1 for the compactness of the circuit. It should be pointed out that, since there are two variables in Eqs. (4) (Zopen-A and Zshort-A ), one more degree of freedom in the selections of the stub values is introduced by the new designs. This leads to the different combinations of stub impedances (Zopen-A vs Zshort-A,) as shown in Fig.4, which increases the range of frequency ratio. The structure of the conventional single band Wilkinson power divider is shown in Fig. 1. It is composed of two λ/4-lines with characteristic impedance of 70.7Ω (assuming a Z0 = 50Ω system). To realize the dual-band power divider a dual band transmission lines are proposed. Fig. 2 shows the schematics of these lines. The theoretical analyses of these structures are presented below. On the other side we have the ABCD-matrix of a conventional λ/4-line as Where Zc is the characteristic impedance of the conventional λ/4 line. By equating (1) with (2) at the two desired working frequencies (f1 and f2), we have: Fig. 4. Calculated stub impedances of the proposed dual-band λ/4 lines as a function of frequency ratio, B. Loaded Transmission Line Fig. 2(a) shows a transmission line with a loading. The loading is centrally located and can be capacitive or inductive, Which is denoted as jb. The line has a characteristic impedance of Z and an electric length of 2θ. The structure is actually a T-network. Fig. 2(b) shows a conventional transmission line without a loading. It is denoted by a characteristic impedance of Zc and an electric length of 2θc.Perfoming same analysis as that of dual band structure using ABCD matrix

3 Now, assuming that the studied structure is equivalent to a Conventional transmission line shown in Fig. 2(b), which yields by equating corresponding elements in (1) and (2), we have With normalization, one can find where z = Z/Zc and b = B Zc are the normalized impedance and susceptance, respectively, as referred to the conventional transmission line in Fig. 2(b). Equation (9) is shown in Fig. 5. The following cases are observed. Case I : When the normalized impedance z < 1, the investigated structure can replace a conventional highimpedance transmission line; its electric length θ will be greater than that of the conventional one. For a given electric length θ, a smaller z corresponds to a smaller θc, as shown in Fig. 5.Furthermore, for a smaller electric length θc, the curve slope in z < 1 region is steeper than that of a larger θc. This means that the translated impedance z will be less sensitive to the change of the electric length θ. Case II : When the normalized impedance z 1, which is an opposite case compared to Case I; a smaller electric length θ is achieved, and the structure is compact. As shown in Fig. 5, the smaller θc for the conventional transmission line is, the more compact for the studied structure would be Therefore case II (z 1) can be used to avoid low-impedance transmission lines and to realize size reduction. By fully utilizing these characteristics, Dual frequency Wilkinson power divider with large frequency division could be practically achieved, as will be demonstrated later. Fig. 5. Characteristics of the loaded transmission line, Electric lengths against characteristic impedances. C. Area minimization The important thing to be observed in the loaded based transmission line technique to reduce the width of transmission line by increasing the Characteristic Impedance is that as we keep on increasing z (normalized impedance, Sec. II. Part.b), the width required for the jb (shunt load connected to the transmission) increasing by countering the effect of overall size reduction. So there is an optimal point of z that we can use for the overall size reduction in terms total area. Let Making impedance of transmission line same as shunt stub ie = Then Putting And let Then we have (10) Solving the Eqn.10 for the different Zc we can find the optimal Characteristic impedance (Z) for the transmission line and loaded stub.

4 III. DESIGN AND FABRICATION OF DUAL FREQUENCY WILKINSON POWER DIVIDER WITH UNLOADED TRANSMISSION LINE The design procedures of the proposed Wilkinson power dividers is, Using Eqn. (5) the suitable stub electrical length for the desired frequency ratio (f2 / f1) calculated Then using Eqn. (3), and Eqn. (4) the desired characteristic impedance (Zc = 70.7Ω) is calculated to compute the characteristic impedances of the corresponding stubs. To validate the theoretical design of the proposed dual band Wilkinson power divider, an experimental prototype was designed and fabricated on FR-4 board with a thickness of 1.56mm, a dielectric constant of 4.4,. The schematic of the designed power divider is shown in Fig. 6. It works at 2 and 6.44 GHz, with a frequency ratio of 3.22. Following the design procedures discussed previously, the characteristic impedances and electrical lengths of the stubs for the power divider are: Fig.7. The photo of the Layout of the topology shown in fig.6 (11) Where the parameters are labeled in Fig.6 By converting these parameters into physical dimensions, the experimental dual-band Wilkinson power divider is fabricated as shown in Fig. 7 with a total size of 23mm x 28mm. The open- / short-ended stubs are folded to reduce the total size. Fig. 8.The photo of the fabricated of the dual-band Wilkinson power divider Fig. 6.. The topology of the designed dual-band Wilkinson powerdivider employing the type A dual-band line. IV. SIMULATION AND MEASUREMENT RESULTS The simulation from momentum ADS and measurement results of this power divider are plotted in Figs.8-11.The measured center frequencies are found to be 1.94 GHz and 6.53 GHz, which are very close to the design frequencies. The measured input return loss (S11) as shown in Fig. 8 is more than at 20dB 1.94 GHz and below -15 db at 6.53 GHz. The insertion losses at the two output ports are: S21 = -3.27 db at 1.94 GHz and S21 = -6 db at 6 GHz. Figs. 10 plot the output return losses (S22, S33) and isolation (S23),showing that all of these parameters are below -15 db at the two working frequencies.

Mag. [db] 5 0 S11-10 -20-30 -40 0 1 2 3 4 5 6 7 Frequency Fig. 9. Simulated and measured output insertion losses (S12, S13) of the designed dual-band Wilkinson power divider. Fig 8. Simulated and measured input return loss (S11) of the designed dual-band Wilkinson power Divider Fig. 10. Simulated and measured output return losses (S22, S33) of the designed dual-band Wilkinson power divider.

6 Thus the Impedance has increased and electrical length reduced as compared to the Eqn.11 and hence decreasing the size of overall structure. Other all parameters remain same as that of Sec.III. FIG.12. The photo of the Layout of the dual band Wilkinson Power Divider using loaded transmission line Fig. 11. Simulated and measured isolation (S23) of the designed dual-band Wilkinson power divider. VI. DESIGN WITH LOADED TRANSMISSION LINE. The physical dimensions for these parameter are found at 2 GHz and the layout is shown in Fig.12.It is clear from the layout that an area reduction of more than 3*28 mm is obtained by using these method and also the practical difficulties of going for higher frequency ratio is also solved For the design of Sec.III, the impedances obtained are quite low for the short circuited and open circuited stubs which are 51.95Ω and 40Ω respectively. As it is obvious from the layout the width is of these sections are so large that it is practically impossible to go beyond these frequency ratios for these given substrate. So the short and open circuited stubs are implemented using loaded transmission line sections which effectively increase the characteristic impedance of these section and hence reduces the width so that the size of these structure is reduced in a good amount. The optimal characteristic impedance is found to be Zopen=79.23Ω Zshort= 102.9Ω, θopen= 22.13Ω degree θshort= 21.9 degree IV. SIMULATION RESULTS The simulation results from momentum ADS Figs. 13-14.The measured center frequencies are found to be 2.1 GHz and 6.8 GHz, which are close to the design frequencies. The small deviation from the design is due the excessive bends in the circuit which can be corrected by suitable correction factors. Simulated input return loss (S11) as shown in Fig. 13 is more than 17 db at 2 GHz and 6.5 GHz. The insertion losses at the two output ports are: S21 = -3.4 db, at 2 GHz and S21 = -3.87 db at 6.5 GHz as shown in the Fig.14.

7 IV. REFERENCES [1] Y. Yao, J. Wu, Y. Shi, and F. F. Dai, A fully integrated 900-MHz passive RFID transponder front end with novel zero-threshold RF-DC rectifier, IEEE Trans. Ind. Electron., vol. 56, no. 7, pp. 2317 2325, Jul. 2009. [2] J.-C. Olivier, J.-C. L. Claire, and L. Loron, A nonlinear phenomenon on self-oscillating current controllers: The indirect synchronization, IEEE Trans. Ind. Electron., vol. 57, no. 3, pp. 1106 1111, Mar. 2010. Fig 13. Simulated input return loss (S11) of the dual-band Wilkinson power Divider using loaded transmission line. [3] J.-P. A. Perez, B. Calvo, and S. Celma, A high-performance CMOS feedforward AGC circuit for a WLAN receiver, IEEE Trans. Ind. Electron., vol. 57, no. 8, pp. 2851 2857, Aug. 2010. [4] E. J. Wilkinson, An N-way hybrid power divider, IEEE Trans. Microw. Theory Tech., vol. MTT-8, no. 1, pp. 116 118, Jan. 1960 [5] K. L. Wan, Y. L. Chow, and K. M. Luk, Dual-frequency power-splitter with equal phase by transmission-line theory, in IEEE Asia-Pacific Microwave Conf. (APMC) Dig., vol. 1, pp. 71-74, Dec. 2001. [6] L. Wu, H. Yilmaz, T. Bitzer, A. Pascht, and M. Berroth, A dualfrequency Wilkinson power divider: for a frequency and its first harmonic, IEEE Microw. Wireless Compon. Lett., vol. 15, no. 2, pp. 107-109, Feb. 2005. [7] K. -K. M. Cheng, and F. -L. Wong, A new Wilkinson power divider design for dual-band application, IEEE Microw. Wireless Compon. Lett., vol. 17, no. 9, pp. 664-666, Sep. 2007. Fig. 14. Simulated output insertion losses (S12) of the designed dualband Wilkinson power divider with loaded transmission line. IV. CONCLUSION. [8] S. Srisathit, S. Virunphun, K. Bandudej, M. Chongcheawchamnan, and A. Worapishet, A dual-band 3-dB three-port power divider based on a twosection transmission line transformer, in IEEE MTT-S Int Microwave Symp. Dig., vol. 1, pp. 35-38, June 2003. [9] C. -M. Tsai, C. -C. Tsai, and S. -Y. Lee, Nonsynchronous alternatingimpedance transformers, in IEEE Asia-Pacific Microwave Conf. (APMC) Dig., vol. 1, pp. 310-313, Dec. 2001. Dual-band Wilkinson power dividers with loaded and unloaded transmission line has been discussed in this paper. Novel dual-band λ/4-lines are proposed for the proper operation of the power divider. Applying the ABCD-matrix method, the explicit design equations for these dual-band lines are provided. For decreasing the size of the above dual band structure at large frequency ratios loaded transmission line structures are used. For the purpose of verification, an experimental prototype is designed, fabricated, and characterized. The measurements results demonstrate that the new power divider works well at both of the assigned operating frequencies. It has been clarified a good amount of reduction of area is obtained for the loaded transmission line structure.