IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 7, JULY 2009 1859
Letters
Comments on “A Symmetrical Four-Port Microstrip Coupler for Crossover Application”
Yi-Chyun Chiou, Cheng-Hsiu Tsai, and Jen-Tsai Kuo
In the above paper [1], the authors demonstrate a four-port coupler for crossover application. In their eigenmode model analysis, the en-tire circuit is decomposed into tapers and two rings with four external arms. In formulation, the eigenadmittance of the inner substructure is taken account as the load of that of the outer one. A cascade ofP short sections is then used to approximate the taper and incorporated into the model of the composite structure by successively applying the input ad-mittance formula of a loaded transmission line. Finally, one prototype circuit solution obtained by an optimization process is demonstrated.
In this letter, the transmission line theory is applied to the circuit analysis. It is found that the circuit structure is so versatile for the crossover application that infinite numbers of solutions can be simply obtained by solving two simultaneous equations. In addition, the tapers for input/output matching can be saved, leading not only to circuit area reduction, but also to formulation simplification. A microstrip coupler is fabricated and measured for confirmation.
Fig. 1 shows the crossover coupler in [1]. The characteristic imped-ances of the inner and outer rings areZ3andZ1, and their circumfer-ences are43 and81, respectively. The counterparts of the sections connecting the two rings areZ2and2. In analysis, bothP P0andQQ0 planes can be either an electric or a magnetic wall since the whole struc-ture possesses bisymmetry. Four reflection coefficients can be readily derived and all theS-parameters can be formulated [2]. These reflec-tion coefficients are the eigenvalues of the eigenadmittances of the composite structure in [1]. Note that two of the four coefficients are identical since the two reduced structures with one electric and one magnetic wall have the same input admittances. This reflects the fact that the four-port circuit supports three instead of four eigenmodes. After some algebraic manipulation, on the basis of [1, eq. (1)], the fol-lowing two simultaneous equations can be used to determine the six structure parameters
R = 2t2s3 (1)
2z2(Rt3+2t2)(z12t1202t21+ 2) = z1t1(Rt2t302)(z12t21+4)
(2)
whereR = Z3=Z2,zi= Zi=Zo(i = 1; 2; and 3) denotes the char-acteristic impedances of theisections normalized with respect to the termination impedanceZo(50), ti = tan i, ands3 = tan(3=2).
Manuscript received January 28, 2009. First published June 16, 2009; current version published July 09, 2009. This work was supported in part by the Min-istry of Education, Taiwan, under the ATU Program and by the National Sci-ence Council, Taiwan, under Grant NSC 97-2221-E-009-039 and Grant NSC 98-2218-E-009-011.
The authors are with the Department of Communication Engineering, National Chiao Tung University, Hsinchu, 300 Taiwan (e-mail: ycchiou. [email protected]; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2009.2021881
Fig. 1. Crossover coupler in [1].
Fig. 2. Some solutions in term of versus z for various R, , and z .
Fig. 3. (a) Simulation and measured results of the coupler. (b) Photograph of the fabricated circuit. Geometric parameters:z = 1, z = 0:88, z = 1, = 59:21 , = 57:35 , = 40 , and = 0.
1860 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 7, JULY 2009
Here,idenotes electric length of the corresponding section at the de-sign frequency.
Fig. 2 plots some solutions in a form of variation of1versus change ofz1, given2= 30andz2= 1:0, 2= 45andz2= 0:8, and 2=
60andz
2= 1:2. In each case, five curves with R = 0:8; 0:9; . . . ; 1:2
are presented. Note that3 can be simply determined by (1) once2
andR are known. As shown in Fig. 2, all 1values decrease asR is increased. When2= 45and60,1increases whenz1is increased. For each of the three cases shown above, we have validated the so-lutions sampled atz1= 0:3; and 0:8 and R = 0:8 and 1:2 by a circuit simulator. Fig. 3(a) compares the simulation and measured results of a fabricated circuit designed atfo= 1 GHz. The substrate has a relative constant"r= 10:2 and thickness h = 1:27 mm. The software package
IE3D [3] is used for simulation. The measuredjS11j, jS21j = jS41j,
andjS31j are 025, 040, and 00.1 dB, respectively. Based on the defi-nition in [1], the experimental bandwidths ofjS11j, jS21j, and jS31j are
22%, 18% and 18%, respectively. Good agreement between simulation and measured results can be observed. Fig. 3(b) shows a photograph of the experimental circuit. Note that the fabricated circuit hasa= 0.
REFERENCES
[1] Y. Chen and S.-P. Yeo, “A symmetrical four-port microstrip coupler for crossover application,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 11, pp. 2434–2438, Nov. 2007.
[2] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. Sin-gapore: McGraw-Hill, 1992.
