Prgress In Electrmagnetics Research Letters, Vl. 71, 53 6, 217 Synthesis f a Bradband Rat-Race Hybrid Using Transmissin Lines and Lumped-Element Cmpnents Ry Ueda * and Hitshi Hayashi Abstract This letter presents the synthesis f a bradband rat-race cnsisting f a miniaturized bradband rat-race hybrid and transmissin line cascades. This bradband technique invlves cnnecting a cascade f transmissin lines with lengths equal t a quarter f the wavelength at the design frequency t each prt f a previusly prpsed rat-race hybrid. Butterwrth and Chebyshev perfrmances f the bradband rat-race hybrid are als reprted. The bradband rat-race hybrid was implemented n an FR4 substrate using spiral inductrs and chip capacitrs. Fr the frequency range f 42 8 MHz, which crrespnds t a relative bandwidth f mre than 62%, the bradband rat-race hybrid exhibited pwer splits f 3.8±1., return lsses f greater than 19, and islatin between utput prts f greater than 2. The phase difference between S 21 and S 41 was 18 ± 3. 1. INTRODUCTION Rat-race hybrids have a wide range f applicatins in micrwave-balanced mixers, amplifiers, and antenna arrays [1 7]. Because wireless systems must be f substantially lw mass and vlume, the miniaturizatin f such hybrids is f great interest. Fig. 1(a) shws a cnventinal rat-race hybrid cnsisting f three 9 transmissin lines and a 27 transmissin line with a characteristic impedance 2Z at a design frequency f,wherez is the reference characteristic impedance. The reductin methds depend n the equivalent circuits f these transmissin lines, which include T-type, Π-type, and lumped-element circuits. Mst rat-race hybrids miniaturized by cnventinal methds are nt sufficiently cmpact, because three 9 equivalent circuits are substituted fr a 27 transmissin line. T vercme this prblem, we adpted the miniaturized bradband rat-race hybrid shwn in Fig. 1(b) [8] and made the fllwing substitutins. 1. The lng 27 high-frequency transmissin line was replaced by a 9 transmissin line. 2. The 9 transmissin line was replaced by a lumped-element circuit with a 9 phase lead using inductrs and capacitrs. Cmpared with a cnventinal rat-race hybrid, the phase lead and lag f the prpsed rat-race hybrid are cmpletely reversed. In a previus study, we reprted simulatin and measurement results fr a miniaturized bradband rat-race hybrid fr bimedical applicatins and televisin white space systems [8]. Figure 2 shws a cnventinal transmissin line and its equivalent T-type circuit cnsisting f tw series capacitrs and a shunt inductr. By applying a matrix frmulatin, the ABCD parameters f the equivalent circuit shwn in Fig. 2(b) can be deduced frm Fig. 2(a). Furthermre, equating the parameters f each circuit yields the relatin cs( θ) jz sin( θ) j sin( θ) = 1 1 1 jω C 1 cs( θ) Z 1 jω 1 1 jω C. (1) 1 Received 2 August 217, Accepted 29 September 217, Scheduled 2 Octber 217 * Crrespnding authr: Ry Ueda (ry1643@eagle.sphia.ac.jp). The authrs are with the Sphia University, Tky 12-8554, Japan.
54 Ueda and Hayashi 9 transmissin Prt 4 line Prt 3 9 transmissin line Prt 1 Prt 2 27 transmissin line (a) 9 transmissin line A lumped-element circuit with a 9 Prt 4 phase lead Prt 3 A lumpedelement circuit with a 9 phase lead A lumpedelement circuit with a 9 phase lead Prt 1 9 Prt 2 transmissin line (b) Figure 1. (a) Cnventinal rat-race hybrid. (b) Miniaturized bradband rat-race hybrid [7]. C C Z,-θ L (a) (b) Figure 2. (a) Cnventinal transmissin line and (b) its equivalent T-netwrk, which cnsists f tw capacitrs and an inductr. Prt 4 C 1 C 1 Prt 3 C 1 C 1 /2 C 1 C 1 /2 C 1 /2 C 1 C 1 9 transmissin line Prt 1 Prt 2 Figure 3. Miniaturized bradband rat-race hybrid using a transmissin line and lumped-element cmpnents [8]. where ω is the angular frequency crrespnding t the design frequency f. Equatin (1) yields the relatin Z L = 2πf sin θ, C = sin θ 2πf Z (1 cs θ). (2) Thus, a lumped-element circuit with a 9 phase lead can be cnstructed by cnnecting tw stages f lumped-element circuits with a 45 phase lead, as shwn in Fig. 3. The circuit parameters can be calculated as fllws at the design frequency f : = Z 2πf, C 1 = 1 2πf Z( 2 1). (3)
Prgress In Electrmagnetics Research Letters, Vl. 71, 217 55 A miniaturized rat-race hybrid with a bandwidth wider than that f a cnventinal rat-race hybrid can be realized because the frequency characteristics f the phase slpe f the 9 transmissin line and thse f the lumped-element circuit are almst the same near the design frequency f [7]. 2. SYNTHESIS OF BROADBAND RAT-RACE HYBRID Figure 4 shws a bradband rat-race hybrid in which a cascade f transmissin lines is cnnected t each prt f the previusly reprted rat-race hybrid shwn in Fig. 3. The length f each transmissin line is a quarter f the wavelength at the design frequency f, and characteristic impedances Z 1 Z n+1 are nrmalized by Z. Rehnmark studied the Butterwrth and Chebyshev perfrmances f the wideband hybrid cnsisting f a reversed-phase hybrid ring and transmissin-line cascades [9]. Tables 1 and 2 give the nrmalized characteristic impedances calculated using the synthesis prcedure prpsed by Rehnmark. Fr example, with nrmalized characteristic impedances Z 1 =.793, Z 2 =.932, and Z 3 =.932 fr n = 2 in Table 2, with input reflectin cefficient S 11 f less than 2, a bandwidth f.838 will be btained. Nte that this relative bandwidth f the prpsed circuit cnfiguratin des nt increase in prprtinal t n, while that f the cnventinal wide-band hybrid cnsisting f a reversed-phase hybrid ring and transmissin-line cascades is in prprtinal t n [9]. Z L n 1 Prt 4 Z 1 Z 2 Z n-1 C 1 C 1 Z n-1 Z 2 Z 1 Prt 3 Prt 1 C 1 C 1 /2 C 1 Z n+1 Z n+1 C 1 /2 C 1 /2 C 1 Z n C 1 Z 1 Z 2 Z n-1 Z n-1 Z 2 Z 1 9 Transmissin line Prt 2 Figure 4. Bradband rat-race cnsisting f a miniaturized bradband rat-race hybrid and transmissin line cascades. Table 1. Nrmalized characteristic impedances f hybrid shwn in Fig. 4 Butterwrth case (3 cupling). Z 1 Z n 1 Z n+1 Z n Cupling Relative bandwidth Relative bandwidth Relative bandwidth n [] f S 11 < 2 f S 11 < 15 f S 11 < 1 1.4142 1.4142 3.1.52.6679.8431 1.92 1.156 1.156 3.1.7155.825.93 2.976.85.973.973 3.1.7995.8842.9685 3.9915.9246.718.8385.8385 3.1.8344.9178.9895 4.9976.9735.874.6412.731.731 3.1.7744.9374 1.21 5
56 Ueda and Hayashi Table 2. Nrmalized characteristic impedances f hybrid shwn in Fig. 4 Chebyshev case (3 cupling). Relative Relative Relative Z 1 = Z n 1 Z n+1 Z n bandwidth bandwidth bandwidth Cupling f f f [] S 11 < 2 S 11 < 15 S 11 < 1 n 1.47 1.47 3.1.529.673.844 1.871 1.78 1.78 3.1.765.853.947 2.926.71.85.85 3.1.768.927.995 3.949.787.532.585.585 3.1.75.837 1.14 4.96.836.622.387.413.413 3.1.765.84.923 5 1.38 1.38 3.1.558.728.851 1.828.993.993 3.1.812.887.967 2.876.621.694.694 3.1.733.846 1.9 3.898.691.439.472.472 3.1.757.826.918 4.91.734.54.297.312.312 3.1.785.851.918 5 1.348 1.348 3.1.59.78.859 1.793.932.932 3.1.838.99.98 2.836.571.628.628 3.1.718.816 1.15 3.857.631.388.413.413 3.1.765.824.93 4.87.669.441.253.263.263 3.1.8.862.92 5 1.291 1.291 3.1.736.869 1.742.852.852 3.1.934.996 2.779.59.552.552 3.1.796.922 3.798.558.332.349.349 3.1.824.89 4.89.589.371.28.215.215 3.1.876.925 5 1.24 1.24 3.1.758.879 1.72.796.796 3.1.797 1.7 2.735.468.53.53 3.1.763.899 3.753.51.298.311.311 3.1.824.882 4 1.195 1.195 3.1.775.886 1.67.751.751 3.1.77 1.14 2.7.437.467.467 3.1.714.892 3.716.474.273.284.284 3.1.877 4 1.155 1.155 3.1.891 1.642.715.715 3.1 1.2 2.67.413.438.438 3.1.886 3.685.446.254.263.263 3.1.874 4 3. SIMULATION AND MEASUREMENT RESULTS FOR BROADBAND RAT-RACE HYBRID The validity f the prpsed circuit cnfiguratin was investigated by simulating its frequency characteristics using radi frequency (RF) and micrwave design sftware (Micrwave Office and ADS). Fig. 5 shws the simulatin results fr the ideal bradband rat-race hybrid shwn in Fig. 4 with nrmalized characteristic impedances Z 1 =.793, Z 2 =.932, and Z 3 =.932 fr n =2inTable2. Assuming a design frequency f is 59 MHz and a reference characteristic impedance Z is 5 Ω, a
Prgress In Electrmagnetics Research Letters, Vl. 71, 217 57 S21 [] S41 [] S41 S21 [ ] -2 19-4 -6-8 185 18 175 17 (a) Phase difference [ ] S23 [] S43 S23 [ ] -2-4 -6-8 S43 [] 2 1-2 (b) Phase difference [ ] S11 [] S31 [] S44 [] -2-3 -4 (c) Figure 5. Simulated results fr ideal bradband rat-race hybrid shwn in Fig. 4 (n = 2). (a) S 21, S 41, and S 41 S 21.(b)S 23, S 43,andS 43 S 23.(c)S 11, S 44,andS 31. capacitance C 1 is 13.98 pf and an inductance is 17.78 nh, respectively. Fr the frequency range f 42 8 MHz, which crrespnds t a relative bandwidth f mre than 62%, the bradband rat-race hybrid exhibits pwer splits f 3.1 ±.6, return lsses f greater than 21, islatin between utput prts f greater than 23, and errrs in the desired relative phase differences between utput prts f less than 3. The feasibility f perating the circuit was experimentally investigated by fabricating the prpsed bradband rat-race hybrid n a cmmercially available 1.6-mm-thick 2-layer FR4 substrate (dimensins f 146 mm 5 mm = 73 cm 2 ) [1]. We selected a 2-layer substrate fr lw-cst fabricatin. A phtgraph f the fabricated bradband rat-race hybrid is shwn in Fig. 6. The relative permittivity and lss tangents at 1 GHz typically range between 4. and 4.2 and between.12 and.14, respectively. The thickness f the uter cpper was 35 µm. We used spiral inductrs and chip capacitrs (15 pf and 7 pf) which were sldered by hand. Figure 7 shws the simulatin and measurement results fr the fabricated bradband rat-race hybrid shwn in Fig. 6. The simulatin used S-parameters f the cmmercial chip capacitrs and threedimensinal electrmagnetic analysis f the vias and the spiral inductrs. Fr the frequency range f 42 8 MHz, which crrespnds t a relative bandwidth f mre than 62%, the rat-race hybrid exhibited pwer splits f 3.8 ± 1., return lsses f greater than 19, and islatin between utput prts f greater than 2. The phase difference between S 21 and S 41 was 18 ± 3, and that between S 23 and S 43 was 4 ± 3. The discrepancies between the measurement and simulatin results are caused by the parasitic effects f the spiral inductrs and sldering. Table 3 cmpares the results f this study and
58 Ueda and Hayashi 146 mm 5 mm Figure 6. Phtgraph f fabricated rat-race hybrid. -2 19 Sim S21 [] -4 185-6 18-8 175 17 (a) -2 2 Phase difference [ ] Meas S21 [] Sim S41 [] Meas S41 [] Sim S41 S21 [ ] Meas S41 S21 [ ] Sim S23 [] -4 1-6 -8-2 (b) Phase difference [ ] Meas S23 [] Sim S43 [] Meas S43 [] Sim S43 S23 [ ] Meas S43 S23 [ ] Sim S11 [] Meas S11 [] -2-2 -3-3 -4-4 (c) Sim S44 [] Meas S44 [] Sim S31 [] Meas S31 [] Figure 7. EM Simulated and measured results fr fabricated bradband rat-race hybrid shwn in Fig. 6. (a) S 21, S 41,andS 41 S 21.(b)S 23, S 43,andS 43 S 23.(c)S 11, S 44,andS 31.
Prgress In Electrmagnetics Research Letters, Vl. 71, 217 59 Table 3. Perfrmance cmparisn f prpsed and previusly reprted rat-race hybrid. Size [mm] Relative Bandwidth Return lsses [] Design frequency [GHz] Prpsed rat race hybrid 146 5 62% 2.59 [8] 28 6 49% 14.59 [11] - 36% 2 4 [12] 12 7 111% 2 1.8 varius reprted rat-race hybrid characteristics. Cmpared t the rat-race hybrid utilizing cmpsite right/left-handed transmissin lines [11], f which the relative bandwidth is apprximately 36%, the miniaturized bradband rat-race hybrid using a transmissin line and lumped-element cmpnents [8] is very simple while achieving bth miniaturizatin and bradband characteristics sufficiently. This cmparisn demnstrates that the prpsed device achieved bradband characteristics and the verall size f the circuit is cmparable with similar design [12]. 4. CONCLUSION We reprted the synthesis f a bradband rat-race cnsisting f a miniaturized bradband rat-race hybrid and transmissin line cascades. Fr the frequency range f 42 8 MHz, which crrespnds t a relative bandwidth f mre than 62%, the bradband rat-race hybrid exhibited pwer splits f 3.8 ± 1., return lsses f greater than 19, and islatin between utput prts f greater than 2. The phase difference between S 21 and S 41 was 18 ± 3. ACKNOWLEDGMENT The results are based n the utcme f cntract research fr SCOPE (Strategic Infrmatin and Cmmunicatins R&D Prmtin Prgramme). This wrk was supprted in part by the VLSI Design and Educatin Center (VDEC) at the University f Tky in cllabratin with Keysight Technlgies Japan, Ltd. REFERENCES 1. Ahn, H. R. and S. Nam, Cmpact micrstrip 3- cupled-line ring and branch-line hybrids with new symmetric equivalent circuits, IEEE Trans. Micrw. Thery Techn., Vl. 61, N. 3, 167 178, Mar. 213. 2. Ahn, H. R. and S. Nam, Wideband micrstrip cupled-line ring hybrids fr high pwer-divisin ratis, IEEE Trans. Micrw. Thery Techn., Vl. 61, N. 5, 1768 178, May 213. 3. Hirta, T., A. Minakawa, and M. Muraguchi, Reduced-size branch-line and rat-race hybrids fr uniplanar MMIC s, IEEE Trans. Micrw. Thery Techn., Vl. 38, N. 3, 27 275, Mar. 199. 4. Piernas, B., H. Hayashi, K. Nishikawa, K. Kamgawa, and T. Nakagawa, A bradband and miniaturized V-band PHEMT frequency dubler, IEEE Micrw. Wireless Cmpn. Lett., Vl. 1, N. 7, 276 278, Jul. 2. 5. Arigng, B., J. Sha, M. Zhu, J. Ding, H. Ren, H. Kim, and H. Zhang, Design f a 18 directinal cupler with arbitrary branch lengths, Prc. 214 Texas Sympsium n Wireless and Micrwave Circuits and Systems (WMCS), 1 4, Wac, TX, Apr. 214. 6. Ahn, H. R. and B. Kim, Small wideband cupled-line ring hybrids with n restrictin n cupling pwer, IEEE Trans. Micrw. Thery Techn., Vl. 57, N. 7, 186 1817, Jul. 29. 7. Hayashi, H., T. Nakagawa, and K. Araki, 18 hybrid circuit, Japanese Patent Applicatin Publicatin N. 21-16869, 1999.
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