Branch-Line Coupler Designs PDF

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Summary

Tittle : Branch-Line Coupler Designs Objective : Design of microwave branch-line couplers using transmission line concept. Theory: Generally, the directional coupler is one of the fundamental components for Microwave Integrated Circuit (MIC), especially; the equal power-split coupler is used for bal...

Description

Tittle

: Branch-Line Coupler Designs

Objective

: Design of microwave branch-line couplers using transmission line concept.

Theory: Generally, the directional coupler is one of the fundamental components for Microwave Integrated Circuit (MIC), especially; the equal power-split coupler is used for balanced-type components such as balanced mixers. A basic microstrip branch-line coupler is made by two main horizontal transmission lines shunt-connected by two secondary lines (vertical branch lines) as shown in Figure 1.

Figure 1. Basic branch-line directional coupler Normally, there are four parameters describe the characteristics and performance of the branch-line directional coupler as: 1) Reflection coefficient (so-called return loss), |S11| at Port-1 2) Transmission coefficient (so-called insertion loss), |S21| at Port-2 3) Coupling, |S31| at Port-3 4) Isolation, |S41| at Port-4 By appropriately selecting the characteristic impedance, (Zo, Z1 and Z2) of the transmission lines, uneven power split between the two output ports (Port-2 and Port-3) at the centre frequency can be achieved. At center frequency, fo, power applied to the input port (Port-1) is transferred equally to the two output ports (Port-2 and Port-3), with the fourth port in isolation (Port-4). Input match (|S11| = 0 at Port-1) is perfect at fo. The upper output (| S21| = -3 dB or 1/√2 at Port-2) leads the lower output (| S31| = -3 dB or 1/√2 at Port-3) by phase shift of 90°. The bandwidth can be enhanced by increasing the branch sections. Here, students are required to create two types of coupler, which are two- and three-branch line couplers as shown in Figure 2. The required values of characteristic impedances Z1, Z2 and Z3 for the both couplers are listed in Table 1.

Z1 90o

50 Ω

90o

Z2

Z2

90o Z1

50 Ω

50 Ω

90o

50 Ω

Z1 90o

50 Ω

90o

Z3 90o

Z2

50 Ω

(a)

Z1 90o

90o Z1

50 Ω

Z2

90o Z1

90o

50 Ω

(b)

Figure 2. Microstrip transmission line design of (a) two- and (b) three-branch line couplers.

Table 1: Characteristic impedance of the transmission line for two- and three-branch line couplers. Type fo (GHz) Z1 (Ω) Z2 (Ω) Z3 (Ω) 3-dB two-branch line coupler 2 Zo /√2 Zo 3-dB three-branch line coupler 2 Zo (√2+1)Zo √2Zo The Zo in Table 1 is equal to 50 Ω. The width, W of the each microstrip branch line at fo = 2 GHz can be calculated as: 8h exp  A    exp  2 A  2  W    1 0.61   2 h    1 ln  2B  1  r  ln B  1  0.39    B  r   2 r   

W 2 h W 2 for h for

(1) where A

Z n  r 1  r  1  0.11    0.23   60 2 r  1 r 

and

B

376.7 2 Zn  r

Symbol Zn is the characteristic impedance of the branch line and the subscript n = 0, 1, 2, and 3. The εr and h are the dielectric constant and thickness of the subtract, respectively. The line length, l of transmission line for a 90o phase shift can be found as:

l

c 4 fo  eff

   eff  0.3  W h  0.264    0.412h     eff  0.258  W h  0.8 

(2) o

-1

eff

where c, f , and ε are the speed of light in free space (299792458 ms ), center frequency and effective dielectric constant of coupler circuit, respectively.  eff 

 1  r 1  r  1      2 2  1 12  h W    

Equipments: 1. 2. 3. 4. 5. 6. 7.

Copper tape [3 pieces: (6.5×4) cm2, (5×5.5) cm2 and (7×5.5) cm2] 1 mm thickness of Teflon plate [2 pieces: (4.5×5) cm2 and (6.5×5) cm2 ] PCB mount 50 Ω SMA connector (8 units) 50 Ω match load (2 units) Knife Kits (1 unit) Ruler (1 unit) N9928A FieldFox Vector Network Analyzer.

Procedures: 1. Each group students will be supplied two piece of h = 0.001 m thick Teflon plate (as PCB subtract), three piece of 0.06 mm thick copper tapes and eight units of end launch jack SMA connectors as shown in Figure 3.

Figure 3

o

1

2

3

2. For a given characteristic impedance, (Z , Z , Z , and Z from Table 1) and the dielectric r

constant, ε = 2.06 and thickness, h = 0.001 m of the Teflon plate, the width, W of the transmission line (width of copper tape) can be calculated using equation (1).

3. On the other hand, the length, l of each branch line section can be found by equation (2).

4. Cut the designed dimensions of copper line from the copper tape and attached the line to the Teflon plate surface.

5. Another surface of the Teflon will be used as a ground and fully affixed with copper tape.

6. Finally, four SMA connectors will merge the four terminals of the coupler by soldering iron as shown in Figure 4.

Figure 4. Branch-line coupler fabrications.

7. The performances of both designed couplers are tested by N9928A FieldFox Vector Network Analyzer from 1.5 GHz to 2.5 GHz. Since all four ports of the coupler are going to be tested and the Network Analyzer has only two test-ports, hence, two 50 Ω terminators will also be supplied to students. 8. The performance in term of reflection coefficient, |S11| (port-1), transmission coefficient, | S21| (port-2), coupling, |S31| (port-3) and isolation, | S41| (port-4) for both coupler are respectively measured and recorded in Table 2 and Table 3. From the measured data, plot the graph for: a) |S11| versus operating frequency (from 1.5 to 2.5 GHz) b) |S21| versus operating frequency (from 1.5 to 2.5 GHz) c) |S31| versus operating frequency (from 1.5 to 2.5 GHz) d) |S41| versus operating frequency (from 1.5 to 2.5 GHz) e) | 21-31| versus operating frequency (from 1.5 to 2.5 GHz) 9. The measurement will be compared to the ideal values. The ideal values of |S11|, |S21|, |S31|, |S41| and |21- 31| at 2 GHz are given as: |S11| = 0; |S21| = 1/√2;

|S31| = 1/√2;

|S41| = 0

and

|21-31| = 90˚

Table 2. Measurement results for one-branch line coupler (15 Marks). |S11|

|S21|

|S31|

|S41|

1500000000

-10.2802

-7.56016

-6.68197

-10.0032

154.9228824

1530000000

-7.10092

-13.983

-6.5834

-6.89912

152.6474639

1560000000

-6.77961

-20.8725

-6.65691

-6.64681

150.356592

1590000000

-6.90447

-29.8819

-6.76201

-6.83393

147.6106771

1620000000

-7.12114

-43.6152

-6.92517

-7.02699

146.2639736

1650000000

-7.5094

-29.5486

-7.31825

-7.44989

144.605294

1680000000

-8.14524

-25.4561

-7.96374

-8.04616

142.8590856

1710000000

-8.63464

-22.9989

-8.59112

-8.48795

141.6306405

1740000000

-9.14653

-21.4617

-9.2499

-9.0326

140.9013318

1770000000

-9.83497

-20.2778

-10.2033

-9.66301

140.1399114

f (GHz)

|21-31| (degree)

1800000000

-10.5826

-19.3727

-11.2078

-10.4182

137.9009212

1830000000

-11.2585

-18.5147

-12.1381

-10.9817

137.1159638

1860000000

-12.0073

-17.7698

-13.429

-11.6522

136.0208294

1890000000

-12.9471

-17.0789

-14.805

-12.5695

133.7648272

1920000000

-13.8671

-16.552

-16.1704

-13.4699

130.8699147

1950000000

-14.6353

-15.9119

-17.3775

-14.0133

128.0523685

1980000000

-15.5952

-15.4583

-18.5991

-14.6617

124.7710569

2010000000

-16.4354

-14.9418

-18.9725

-15.7019

120.1482111

2040000000

-16.9232

-14.3971

-18.4331

-16.1477

115.388587

2070000000

-17.1831

-13.8429

-17.5608

-16.3518

109.803095

2100000000

-17.4435

-13.3527

-16.6408

-16.709

103.7730474

2130000000

-16.8487

-12.7741

-15.4936

-16.5856

96.77701895

2160000000

-16.1945

-12.1136

-14.5815

-16.0489

89.31557192

2190000000

-15.4255

-11.4761

-13.7994

-15.3768

81.87660541

2220000000

-14.5217

-10.7343

-13.0723

-14.8876

73.9659223

2250000000

-13.4171

-9.87806

-12.3932

-13.8955

66.26165684

2280000000

-12.2484

-9.00732

-12.0469

-12.6938

58.69282958

2310000000

-10.9772

-8.01562

-11.7125

-11.435

50.93255245

2340000000

-9.72247

-6.97857

-11.4839

-10.0896

43.55205757

2370000000

-8.26988

-6.01438

-14.9508

-19.8214

-164.4904222

2400000000

-7.28182

-5.42455

-13.6234

-17.0731

-176.3182286

2430000000

-6.92351

-5.5145

-12.2076

-14.2196

171.7095257

2460000000

-7.42884

-6.51008

-11.2589

-12.0798

159.5271349

2490000000

-8.39093

-8.09839

-10.4861

-10.5242

146.9518838

2520000000

-9.78664

-9.92615

-9.53123

-9.20724

134.8016402

2550000000

-11.1018

-11.598

-8.70426

-7.84667

122.9387975

2580000000

-12.2676

-13.302

-7.94409

-6.75105

111.1054194

2610000000

-13.6841

-14.8528

-7.24601

-6.06487

99.26692506

2640000000

-15.0369

-16.1632

-6.574

-5.45009

88.08788937

2670000000

-16.1543

-17.3163

-5.85845

-4.75429

77.60360629

2700000000

-17.6532

-18.3922

-5.2736

-4.25918

67.17855742

2730000000

-19.1713

-18.9764

-4.80166

-3.97405

57.15001816

2760000000

-20.7576

-19.3728

-4.32282

-3.683

48.16794274

2790000000

-21.9592

-19.4818

-3.83854

-3.33456

39.71122597

2820000000

-22.3939

-19.2665

-3.46674

-3.11558

31.8639394

2850000000

-22.2417

-18.9001

-3.23801

-3.05325

24.43094489

2880000000

-20.9167

-18.6088

-2.91513

-2.9013

17.10088848

2910000000

-19.2449

-18.1929

-2.6252

-2.67019

9.940053444

2940000000

-17.7901

-17.7265

-2.53747

-2.62042

3.379705333

2970000000

-16.6305

-17.3414

-2.31564

-2.45215

-3.278444938

3000000000

-15.1787

-16.8903

-2.26592

-2.35979

-9.795697053

Table 3. Measurement results for two-branch line coupler (15 Marks). |21-31| (degree)

|S11|

|S21|

|S31|

|S41|

1500000000

-10.2802

-7.56016

-6.68197

-10.0032

38.25887075

1530000000

-7.10092

-13.983

-6.5834

-6.89912

16.84598327

1560000000

-6.77961

-20.8725

-6.65691

-6.64681

2.927518657

1590000000

-6.90447

-29.8819

-6.76201

-6.83393

-8.118727541

1620000000

-7.12114

-43.6152

-6.92517

-7.02699

-16.65592092

1650000000

-7.5094

-29.5486

-7.31825

-7.44989

-24.74586416

1680000000

-8.14524

-25.4561

-7.96374

-8.04616

-32.89380052

1710000000

-8.63464

-22.9989

-8.59112

-8.48795

-41.06107117

1740000000

-9.14653

-21.4617

-9.2499

-9.0326

-48.94554804

1770000000

-9.83497

-20.2778

-10.2033

-9.66301

-56.80897093

f (GHz)

1800000000

-10.5826

-19.3727

-11.2078

-10.4182

-65.07733214

1830000000

-11.2585

-18.5147

-12.1381

-10.9817

-74.39761263

1860000000

-12.0073

-17.7698

-13.429

-11.6522

-82.98660453

1890000000

-12.9471

-17.0789

-14.805

-12.5695

-92.0690916

1920000000

-13.8671

-16.552

-16.1704

-13.4699

-102.4910611

1950000000

-14.6353

-15.9119

-17.3775

-14.0133

-113.9601923

1980000000

-15.5952

-15.4583

-18.5991

-14.6617

-124.079571

2010000000

-16.4354

-14.9418

-18.9725

-15.7019

-137.6004604

2040000000

-16.9232

-14.3971

-18.4331

-16.1477

-151.0679104

2070000000

-17.1831

-13.8429

-17.5608

-16.3518

-164.3440615

2100000000

-17.4435

-13.3527

-16.6408

-16.709

-177.4961853

2130000000

-16.8487

-12.7741

-15.4936

-16.5856

167.7768504

2160000000

-16.1945

-12.1136

-14.5815

-16.0489

154.8806644

2190000000

-15.4255

-11.4761

-13.7994

-15.3768

145.3930109

2220000000

-14.5217

-10.7343

-13.0723

-14.8876

133.7047642

2250000000

-13.4171

-9.87806

-12.3932

-13.8955

122.7679461

2280000000

-12.2484

-9.00732

-12.0469

-12.6938

114.0853597

2310000000

-10.9772

-8.01562

-11.7125

-11.435

104.5784482

2340000000

-9.72247

-6.97857

-11.4839

-10.0896

93.89806884

2370000000

-8.26988

-6.01438

-11.2276

-8.34633

80.40669348

2400000000

-7.28182

-5.42455

-11.3628

-6.8483

62.73118858

2430000000

-6.92351

-5.5145

-11.5266

-5.97089

41.28129219

2460000000

-7.42884

-6.51008

-11.7396

-6.22708

17.91356461

2490000000

-8.39093

-8.09839

-12.0596

-7.2694

-2.733752644

2520000000

-9.78664

-9.92615

-12.6826

-8.84017

-18.19958609

2550000000

-11.1018

-11.598

-13.1631

-10.3822

-30.94460072

2580000000

-12.2676

-13.302

-13.6449

-11.7061

-41.99764577

2610000000

-13.6841

-14.8528

-14.502

-13.1831

-51.45088704

2640000000

-15.0369

-16.1632

-15.3614

-14.7938

-60.6268577

2670000000

-16.1543

-17.3163

-16.0781

-16.102

-72.43806772

2700000000

-17.6532

-18.3922

-17.2025

-17.436

-84.28300828

2730000000

-19.1713

-18.9764

-18.1672

-19.1384

-97.90947991

2760000000

-20.7576

-19.3728

-19.2456

-21.1875

-114.973221

2790000000

-21.9592

-19.4818

-20.3788

-22.2728

-141.602227

2820000000

-22.3939

-19.2665

-20.6702

-22.4292

-164.3857771

2850000000

-22.2417

-18.9001

-20.2957

-22.5524

169.8835444

2880000000

-20.9167

-18.6088

-19.6881

-21.0046

145.2780782

2910000000

-19.2449

-18.1929

-18.8212

-19.2181

127.9939509

2940000000

-17.7901

-17.7265

-17.5563