Synthesis of a Broadband Rat-Race Hybrid Using Transmission Lines and Lumped-Element Components

Transcription

1 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 ± 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) = 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 , Japan.

2 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)

3 Prgress In Electrmagnetics Research Letters, Vl. 71, 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 <

4 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 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

5 Prgress In Electrmagnetics Research Letters, Vl. 71, S21 [] S41 [] S41 S21 [ ] (a) Phase difference [ ] S23 [] S43 S23 [ ] S43 [] (b) Phase difference [ ] S11 [] S31 [] S44 [] (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 pf and an inductance is 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

6 58 Ueda and Hayashi 146 mm 5 mm Figure 6. Phtgraph f fabricated rat-race hybrid Sim S21 [] (a) -2 2 Phase difference [ ] Meas S21 [] Sim S41 [] Meas S41 [] Sim S41 S21 [ ] Meas S41 S21 [ ] Sim S23 [] (b) Phase difference [ ] Meas S23 [] Sim S43 [] Meas S43 [] Sim S43 S23 [ ] Meas S43 S23 [ ] Sim S11 [] Meas S11 [] (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.

7 Prgress In Electrmagnetics Research Letters, Vl. 71, 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 % 2.59 [8] % [11] - 36% 2 4 [12] % 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, , Mar 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, , May 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, , Mar 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, , Jul 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 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, , Jul Hayashi, H., T. Nakagawa, and K. Araki, 18 hybrid circuit, Japanese Patent Applicatin Publicatin N , 1999.

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