VOL.6, NO., 211 228 Enhanced Balance Bandwidth Quadrature Cupler Using Parallel Cupled Micrstrip Lines Vamsi Krishna Velidi, Girja Shankar and Subrata Sanyal Department f Electrnics and Electrical Cmmunicatin Engineering Indian Institute f Technlgy Kharagpur, Kharagpur, WB 72132, INDIA. E-mail: vvamsi.iitkgp@gmail.cm Abstract-A single stage quadrature hybrid cupler with enhanced flat balance ver a wide bandwidth is presented in this article. The present cupler is realized by replacing the transmissin line sectins f the cnventinal tw-branch cupler by their equivalent parallel cupled micrstrip lines (PCML). The impedance cntrlled wide-bandpass respnse prduced by the PCML is utilized t achieve flat balanced respnse ver wider bandwidth that is cmparable t that f a furbranch cnventinal cupler. A lssless transmissin line mdel is used t derive the design equatins alng with design graphs. A prttype micrstrip cupler having a wide ±1. db amplitude balance f 71% is fabricated at 2.4 GHz t validate theretical predictins. Index Terms- Micrstrip cupler, quadrature hybrid, parallel cupled line, balance bandwidth. I. INTRODUCTION The Quadrature hybrid cuplers, knwn as 9 hybrids, are imprtant devices in wireless cmmunicatin systems. They are widely emplyed in many applicatins such as imagereject mixers, balanced amplifiers, and reflectintype phase shifters. The cnventinal cupler is frmed by using quarter-wavelength transmissin line (TL) sectins, arranged in ring frm, resulting in narrw bandwidths f 1-2% and a large circuit area [1]. Much effrt has been made t size reductin [2]. Hwever, in mst f the cases, the size reductin is achieved at the cst f reduced bandwidth. In [3], a reduced size cupler with varius bandwidths that are almst same as the cnventinal cupler was presented by replacing the lw impedance series arms with their equivalent high impedance parallel lines. The cupler bandwidth can be increased by using Fig.1. Equivalent circuit f a quarter-wavelength transmissin line with the prpsed parallel cupled micrstrip line. multiple sectins in cascade [4]. At lw frequencies, bradband cuplers are therefre physically very large sized. Further, this is als limited by the fabricatin limit f the high impedance line as the required vertical branch impedances increase drastically with increase in number f sectins. Als, the cupling varies cnsiderably ver the usable bandwidth. Cnsequently the cupler applicatin t wideband system as well as t systems demanding cmpact size devices is limited. Early investigatins have shwn that if the junctins f a tw-branch cupler can be matched at any frequency by an suitable matching netwrk, then the cupling must be the same at all frequencies [5]. Instead f using multiple branches, wide bandwidth can be achieved by adding external matching netwrks, cnsisting f either quarter-wavelength transfrmers shunted by half-wavelength pencircuited stubs [5]. On the ther way, several methds [6] [9] have been reprted, t design reduced sized wideband multi-sectin cuplers, such as using defected grund structure (DGS) [6], lumped distributed elements [7], integrated swap [8], and fractal gemetry [9] etc. T be effective, the design using DGS [6] requires a IJMOT-211-1-64 211 ISRAMT
VOL.6, NO., 211 229 minimum space underneath, resulting in increase in the circuit vlume, while using integrated swap [8] increases fabricatin difficulties and csts. The number f branch lines used is three in [8], fur in [7], [9] and five in [6]. In [1] quadrature hybrid, having magnitude and phase balances flatter than thse f cnventinal cupler, is achieved by lading the hrizntal transmissin lines with a pair f pen-end series stubs. Hwever, the prpsed structure cannt be fabricated, fr which an equivalent circuit using edge-cupled parallel lines is used. The implemented cupled line with high even- and dd-mde impedance rati (3.36) results in fabricatin difficulties and requires high dielectric cnstant (>1) substrate fr realizatin. Furthermre, the high-frequency (upper passband) perfrmance f the cupler is nt demnstrated. In this paper, a single stage tw-branch hybrid cupler with flat magnitude balance ver a bandwidth, brader than that f the cnventinal cupler, is presented. This is achieved with the cupler neither using multiple sectins, grund plane structures, lumped elements nr seriesstubs but with a simple mdificatin f the single-sectin cnventinal cupler using parallel-cupled micrstrip lines (PCML). In cntrast t [1], the present apprach cnsiders the transmissin equivalence f PCML directly and the perfrmance f the cupler fr three different cnfiguratins by replacing all the fur, nly vertical, and nly hrizntal branches is discussed. The main advantage f the present apprach is that it significantly enhances magnitude balance bandwidth f single stage cupler that is equivalent t that f a fur-branch hybrid. Furthermre, a deeply suppressed secnd harmnic passbands is als achieved simultaneusly. A perfrmance cmparisn f the present cupler, with thse f the cnventinal single and multiple sectin cuplers as well as with the reprted designs is presented. II. TRANSMISSION LINE EQUIVALENCE OF THE PCML Fig. 1 shws the prpsed PCML sectin Z e (Ω) 2 18 16 14 12 1 8 Z = 5 Ω Z = 35.35 Ω 2 4 6 8 1 Z (Ω) Fig. 2. Impedance slutins f PCML equivalent t riginal transmissin line. equivalent t the cnventinal transmissin line (Z, θ). The even- and dd-mde electrical lengths (characteristic impedances) f the PCML are θ e and θ (Z e and Z ) respectively. The PCML sectin is assumed t have same even- and ddmde electrical lengths (θ e =θ =θ 1 ). The Z- parameters f the transmissin line and the PCML units are derived [1] as 11 = 22 = jzctθ T (1a) T 12 = 21 = jzcscθ T (1b) T j 11 = 22 ( Z Z PCML = PCML )ct 2 e + θ 1 (2a) j 12 = 21 ( Z Z PCML = PCML )csc 2 e θ 1 (2b) Equating (1) and (2) yields the fllwing impedance relatinships ( Z ) ct e + Z Z θ = ctθ 2 1 (3a) ( Z ) csc e Z Z θ = cscθ 2 1 (3b) Fr a PCML, Z e >Z at all frequencies [1]. Therefre when θ 1 =θ, nly (3b) gives the valid slutins fr the impedances. Fig.2 shws the slutins fr Z=35.35 Ω and Z=5 Ω in (3b). At an perating frequency f, the PCML unit behaves as a bandpass filter and prduces tw transmissin zers at frequencies f= and f=2f respectively. As an example, Fig. 3 plts the IJMOT-211-1-64 211 ISRAMT
VOL.6, NO., 211 23 S 21 (db) -1-2 -3 Z (Ω), Z (Ω) e 172 11.3 138.7 68 115.7 45-4.5 1 1.5 2 f/f Fig. 3. Magnitude respnses f the PCML sectin equivalent t quarter-wavelength Z=35.35Ω line. S 21 - S 31 (db) -1-2 -3 Case A (Cnv.) -4 Case B (all) Case C (nly vertical) Case D (nly hrizntal) -5.6.8 1 1.2 1.4 f/f Fig. 5. Cmparisn f circuit cmputed magnitude balance respnses f the cases shwn in Fig. 4. Balance (a) (b) (c) (d) Fig. 4. (a) Cnventinal 2- branch hybrid cupler and (b)-(d) the prpsed cupler with the equivalent embedded PCML sectins. magnitude respnses fr three different PCML equivalents f the 35.35 Ω line. The passband width increases values f Z e and Z because f the increased (tight) cupling. The cupling cefficient, K fr the PCML is given by K = ( Z e Z ) ( Z e + Z ) (4) When the cupler is implemented using the equivalent PCML sectins, the basic peratin at perating frequency remains unchanged, but the magnitude balance varies significantly. Fig. 4 shws the cnventinal cupler alng with the three f the pssible cases f embedded PCML cupler units. Here, fr the available FR4 substrate, the realizable PCML impedance parameters equivalent t the cnventinal 5Ω and 35.35Ω lines are Z e =15Ω, Z =5Ω and Z e =115.7Ω, Z =45Ω respectively when K is maximum. Fr all cases, the crrespnding circuit simulated magnitude balance variatins with the nrmalized frequency are pltted in Fig. 5. The magnitude balance bandwidth is wider (slid line) than the than the cnventinal cupler (dtted line) is achieved nly when the hrizntal lw-impedance lines are replaced by the PCMLs S-parameters (db) -1-2 -3 S 11 S 21 S 31 S 41 suppressed 2nd harmnic -4.5 1 1.5 2 2.5 f/f Fig. 6. Circuit predicted respnses f the prpsed cupler with imprved amplitude balance fr the Case D. (Fig. 4(d)). Nw cnsider nly the cupler in Fig. 4(d). Fr this case, the circuit predicted magnitude respnses f the cupler are shwn in Fig. 6. The transmissin and cupling utputs (at prts 2 and 3) maintain excellent balance ver a wide range f cupler bandwidth. Furthermre, the secnd harmnic is deeply suppressed. The balance bandwidth varies with the cupling cefficient K f the cuple lines. Fig. 7 shws the ±1. db magnitude balance fractinal bandwidth (FBW) variatin (slid line) with K, fr embedded PCML equivalent t the 35.35Ω line. K is calculated using (4) frm the realizable PCML impedance slutins (Fig. 2) that are als shwn in the figure. The magnitude balance FBW achievable is 4-8%. This is substantially mre than that f a cnventinal cupler fr IJMOT-211-1-64 211 ISRAMT
VOL.6, NO., 211 231 Z e (Ω), Z (Ω) 2 15 1 5 Z e Z Cnventinal 4.25.3.35.4.45.5.55 Cuplin cefficient, K Fig. 7. Variatin f ±1. db magnitude balance fractinal bandwidth with cupling cefficient. Fig. 8. Phtgraph f the fabricated cupler with embedded PCML sectins. which the ±1. db magnitude balance FBW is 43.3% shwn as dtted line. III. DESIGN EXAMPLE FABRICATION AND MEASUREMENT A prttype single-sectin hybrid cupler has been fabricated n a lw cst 1.58 mm thick FR4 substrate ε r = 4.3, tanδ =.22 at 2.4 GHz. The hrizntal sectins are replaced by the equivalent PCML units having Z e =115.7Ω, Z =45Ω (K =.44). Here, the cupled-line even- and ddmde impedance rati 2.57 < 3.56 f [1] and can be implemented n substrate with lw ε r = 4.3 < 1.7 in [1] within the same fabricatin limit. The theretical ±1. db magnitude balance 9 8 7 6 5 Amplitude balance FBW (%) S-parameters (db) -5-1 -15-2 -25-3 -35 S 11 S 21 S 31 S 41-4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 Frequency (GHz) Fig. 9. Simulated (dashed) and measured (slid) scattering parameters f the prpsed BLC with enhanced flat-balanced magnitude respnse. FBW f 71% frm Fig. 7, while the ±5 phase balance is 49.2%. The vertical branch-line impedances remain unchanged (5Ω). All electrical lengths are quarter wavelength lng at perating frequency. The phtgraph f the fabricated cupler alng with physical dimensins (mm) is shwn in Fig. 8. The cupler ccupies a rectangular area f 23. 23.3 mm 2 (.25 λ g.25 λ g, where λ g is the guided wavelength at perating frequency). Full-wave simulatins are perfrmed using IE3D electrmagnetic simulatr, while an Agilent 851C vectr netwrk analyzer is used fr measurements. The simulated and measured respnses f the prpsed cupler are shwn in Fig. 9. The measured return lss is better than 35 db, while the islatin is better than 23 db at perating frequency. The measured S 21 and S 31 are -3.24 db and -3.28 db respectively. Furthermre, as predicted a flat magnitude balance is achieved ver a wide bandwidth. The circuit predicted, full-wave simulated and the measured magnitude and phase balances are cmpared in Figs. 1 (a) and (b) respectively. The measured ±1. db magnitude balance FBW in the range 1.621 t 3.2227 is 67.2%; while the FBW fr ±5 phase balance in the range 1.83-2.88 GHz is 44.6%. The bserved slight difference in the simulated and measured FBWs is due the fabricatin tlerance. Table I cmpares the magnitude balance bandwidths and the nrmalized circuit sizes f the prpsed single IJMOT-211-1-64 211 ISRAMT
VOL.6, NO., 211 232 S 21 - S 31 (db) S 21 - S 31 (deg) -5-1 -15 Ckt. Full-wave Measured -2 1.2 1.6 2 2.4 2.8 3.2 3.6 Frequency (GHz) 12 11 1 9 8 7 (a) Ckt. Full-wave Measured 6 1.5 2 2.5 3 3.5 Frequency (GHz) (b) Fig. 1. Cmparisn f predicted and measured (a) magnitude and (b) phase balances. stage tw-branch cupler with the cnventinal tw-branch and fur-branch cuplers. It is clearly bserved that bth the 1 db and 2 db balance bandwidths f the prpsed cupler are substantially larger than that f the cnventinal single stage cupler. Furthermre, these FBWs are even larger than that f the fur-branch cupler in [4]. Table II summaries the magnitude balance and nrmalized circuit size cmparisns f the prpsed and published cuplers. It reveals that using the prpsed PCML units t replace the cnventinal micrstrip lines f the cupler can achieve the mst significant magnitude balance bandwidth with smaller circuit size. Table 1: Cmparisn with cnventinal designs Ref. Cnv. 2 branch 4 branch Mag. Bal. FBW (%) 1 db 2 db 27.8 44 43.33 54 Nrmalized Circuit Size.25.25.25.75 Harmnic Suppressi n N N Prpsed 2 branch 6.4 7.83.25.25 Yes (2 nd ) Mag. = Magnitude, Bal. = Balance, FBW = Fractinal Bandwidth Ref. Table 2: Cmparisn with the best reprted wide-band designs Branche s (N) Methd Mag. Balance FBW (%) Nrmalized Circuit Size [5] Tw matching netwrks.5 db: 12.7% >.25.75 [6] Three SWAP ± 3 db: 8%.25.5 [8] Five DGS ± 1 db: 43.3%.25 1. This Wrk Tw PCML.5 db: 14% ± 1 db: 71%.25.25 Mag. = Magnitude, FBW = Fractinal Bandwidth IV. CONCLUSION In this paper, the design f branch-line cupler with embedded parallel cupled micrstrip lines is presented. Varius cases f replacing the cnventinal cupler series and shunt arms with PCMLs are investigated and finally nly the lwimpedance line sectins are replaced by their equivalent PCMLs t achieve flatter magnitude and phase balance ver a wide frequency range. A prttype cupler perating at 2.4 GHz having a 2-dB magnitude balance f 71% is demnstrated t validate thery. The present cupler gemetry is within the size f the single stage cnventinal hybrid and is cmpact than the multi-sectin cuplers achieving the balance bandwidth ver wide bandwidth. REFERENCES [1] D. M. Pzar, Micrwave Engineering. New Yrk: Wiley, 25. [2] K. W. Ecclestn, and S. H. M. Ong, Cmpact planar micrstrip line branch-line and rat-race cuplers, IEEE Trans. Micrw.Thery Tech., vl. 51, n. 1, pp. 2119 2125, Oct. 23. [3] M. K. Mandal, V. K.Velidi, and S. Sanyal, Miniaturized quadrature hybrid cupler using high IJMOT-211-1-64 211 ISRAMT
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