APPLICATION OF EMPIRICAL MODELS TO DESIGN MICROSTRIP TEE JUNCTIONS WITH PRESPECIFIED POWER-DIVIDER RATIOS
B.P. Kumar and G.R. Branner Department of Electrical and Computer Engineering University of California, Davis, CA-956 16 Tel: (916)-752-1423 Fax: (916)752-8428
[email protected] Abstract: This paper validates the accuracy of a set of empirical models developed for the design of a class of microstrip T junction power-divider circuits in the frequency range of 1-8 GHz. These models were developed by the authors earlier for three distinct designs: the asymmetrical tee (narrow band circuit), the 2-step tee and the linearly tapered tee(broad band circuits). The models are used to obtain the dimensions of each of these circuits, given some desired transmission characteristics, and then compared with computer simulation.
(0.0508 cm) thickness microstrip board with a dielectric constant of 2.17. The simulated and measured results on the 3 designs were used to generate the following empirical model equations [4] for the circuit dimensions, with a prescribed power ratio k dB. Q AsymmetricalTee The circuit dimensions (Figure lb) held constant are P = 2 cm, 11 = 1 cm and w = 0.1534 cm. The design equation for the width w l is given by: wl = 0.036k + 0.1534 where k, the specified power ratio is in dB and w 1 is in cm. I. INTRODUCTION (ii) 2- Step Tee Microstrip T junction circuits can be designed to act as The circuit dimensions (Figure IC) held constant are P = 2 either equal or uneuqal power-dividers [l]. The standard cm, Pl = 42 = 1 cm and w = 0.1534 cm. The design symmetrical T junction circuit is shown in Figure 1a, and all equation for the width wl is given by: 3 arms have the same characteristicimpedance of 50 ohms. wl = 0.0187 k + 0.1534 This circuit is used as a basis for the design of unequal w2 = 0.0468 k + 0.1534 power dividers, in which the requirement is as follows: for a Qii) Linearly Tapered Tee given power input into port 1, the power transmission to The circuit dimensions (Figure Id) held constant are P = 2 ports 2 and 3 of the junction should maintain a prespecified difference IS211 IS311 = k, dJ3 over the frequencyrange of cm, P1 = 3 cm and w = 0.1534 cm. The design equation for interest, 1 -8Ghz. Uneuqal power division is very useful in the width wl is given by: wl = 0.0694 k + 0.1534 many microwave measurement devices and applications.
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111. APPLICATION AND VALIDATION OF THE MODEL EQUATIONS
11. DEVELOPMENT OF EMPIRICAL MODELS In the past [2-31considerable simulation studies on the modifications required on the basic 50 ohm T junction circuit led to the evolution of 3 uneuqal power divider geometries: the asymmetrical tee, the 2-step tee, and the linearly tapered tee shown in Figures lb-ld respectively. These circuits were designed initially by direct gradient optimization on the softwareTouchstone to yield the appropriate lengths and widths of the 3 circuits. The specified optimization goal was the maintain the transmission characteristics over the frequency band close to the desired power ratio k dB. Subsequently, these designs were relaized on a 20 mil
0-7803-3694-1 /97/$10.00 1997 IEEE
The testing of the empirical model equations was done in two steps: (i) The model equations were applied for a range of values of power-divider ratios: k = 0.5 dB, 3.0 dB and 6 dB, and the circuit dimensions were obtained for all the 3 T junction realizations. (ii) Using these dimensions, the circuits were simulated on Touchstone to yield the predicted value of the divider ratios k (pred.), dB.
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The predicted divider ratio for the asymmetrical tee, 2-step tee and the linearly tapered tee are plotted in Figures 2-4 respectively. The latter figures illustrate, that as stated in [4], the asymmetrical tee acts as a narrow band circuit whereas the 2-step tee and linearly tapered tee function as broadband circuits. Further work in this direction is continuiung, with the aim of improving the response flatness over the frequency band of interest.
REFERENCES [l] S . Wu, H. Yang, N.G. Alexopoulus and I. Wolff, ‘A Rigorous Dispersive Characterization of Microstrip Cross and T Junctions’, IEEE Trans. Microwave Theory Tech. vol. 38, No. 12, 1990. [2] M. Villegas, G.R. Branner, B.P. Kumar and W.O. Keese, ‘Analysis and Design of Microwave T Junction Circuits for Prescribed Response Characteristics’, Proc. 36th Midwest Symp. Circuits and Systems 1993. [3] B.P. Kumar, G.R. Branner, G. Razmafiouz and D. Brody, ‘Optimization of Microwave T Junction PowerDivider Circuits’, Proc. 37th Midwest Symp. Circuits and Systems, 1994. [4] G,R Branner, B.P. Kumar and D. James, ‘Design Formulae for a class of Microstrip Tee Junction PowerDivider Circuits’, Proc. 39th Midwest Symp. Circuits and Systems, 1996.
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Figure lc. 2-Step Tee
Figure la. Basic 50 ohm Tee
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Figure Id. Linearly Tapered Tee
Figure lb. Asymmetrical Tee 578
FIGURE 2. POWER DIVIDER PERFORMANCE OF ASYMMETRICAL TEE 6
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FIGURE 3. POWER DIVIDER PERFORMANCE OF %STEP TEE
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FIGURE 4. POWER DIVIDER PERFORMANCE OF LINEARLY TAPERED TEE 6
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