Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

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TABLE

CAUER-PARAMETER

LOW-PASS

DEGREE=4

9.60283

6.73180

4.82 1 64

4.22622

3.56970

3.09392

2.73382

2.37 170

2.09956

1.84278

75.2

62.7

50.9

46.2

40.2

35.0

30.4

25.0

20.3

15.2

0.4738

0.4654

0.4494

0.4393

0.4215

0.4003

0.3756

0.3367

0.2908

0.2223

0.0091

0.0187

0.0377

0.0500

0.0726

0.1007

0.1355

0.1953

0.2757

0.4207

0.9888

0.9745

0.9476

0.9306

0.9010

0.8661

0.8260

0.7644

0.6938

0.5939

10.546

7.3903

5.2892

4.6338

3.9107

3.3861

2.9885

2.5880

2.2863

2.0006

0.9978

0.9929

0.9839

0.9782

0.9685

0.9572

0.9446

0.9257

0.9052

0.8784

0.4828

0.4838

0.4857

0.4869

0.4890

0.4914

0.4941

0.4980

0.5021

0.5068

7.4757 1

5.18854

3.76399

3.39504

2.96326

2.53903

2.22655

1.93651

1.72025

1.52527

74.4

61.5

50.1

46.3

41.3

35.6

30.6

25.1

20.2

15.0

0.6236

0.6112

0.5891

0.5782

0.5595

0.5301

0.4954

0.4440

0.3830

0.2957

0.0125

0.0266

0.0523

0.0654

0.0886

0.1269

0.1754

0.2552

0.3650

0.5609

1.183

1.162

1.124

1.106

1.074

1.025

0.9675

0.8844

0.7889

0.6591

8.2082

5.6929

4.1248

3.7182

3.2419

2.7732

2.4272

2.1050

1.8637

1.6446

1.196

1.188

1.174

1.168

1.156

1.139

1.119

1.091

1.060

1.021

0.6360

0.6371

0.6391

0.6401

0.6418

0.6443

0.6471

0.6508

0.6545

0.6578

8.40608

6.12348

4.50395

3.23721

2.84368

2.45229

2.16100

1.88831

1.68355

1.49794

84.5

73.4

62.5

50.6

45.9

40.3

35.5

30.1

25.3

20.1

0.7912

0.7838

0.7704

0.7422

0.7245

0.6968

0.6645

0.6171

0.5615

0.4829

0.0088

0.0167

0.0314

0.0634

0.0844

0.1183

0.1604

0.2270

0.3146

0.4606

1.340

1.327

1.304

1.256

1.226

1.179

1.125

1.047

0.9568

0.8337

9.2310

6.7213

4.9396

3.5441

3.1099

2.6772

2.3545

2.0514

1.8226

1.6137

1.348

1.344

1.335

1.316

1.305

1.287

1.267

1.239

1.206

1.164

0.7999

0.8003

0.8011

0.8027

0.8037

0.8052

0.8068

0.8090

0.81 11

0.8129

1.146

1.145

1.144

1.143

1.142

1.140

1.136

1.129

6.73180

4.82164

3.39504

2.63260

2.29663

1.98762

1.75892

1.58398

1.423 10

1.28267

84.9

73.1

60.6

51.2

46.0

40.3

35.3

30.8

25.8

20.4

7.3903

5.2892

3.7182

2.8767

2.5049

2.1619

1.9070

1.7108

1.5289

1.3678

1.505

1.498

1.482

1.460

1.442

1.417

1.387

1.354

1.309

1.250

1.134

1.122

1.097

1.062

1.034

0.9923

0.9437

0.8875

0.8095

0.7018

0.0123

0.0243

0.0505

0.0877

0.1197

0.1691

0.2313

0.3102

0.4356

0.6497

1.493

1.474

1.433

1.377

1.332

1.266

1.189

1.101

0.9820

0.8227

FILTERS, MODERN-NETWORK-THEORY DESIGN

TABLE

CAUER-PARAMETER

LOW-PASS,

DEGREE=5

c3 c4

5.24084

3.86370

3.07155

2.45859

2.20269

2.00000

1.78829

1.62427

1.49448

1.36733

85.7

72.1

61.7

51.3

46.0

41.3

35.5

30.3

25.6

20.1

0.5764

0.5691

0.5595

0.5441

0.5329

0.5203

0.5010

0.4787

0.4532

0.4163

0.01 10

0.0206

0.0335

0.0544

0.0697

0.0874

0.1151

0.1480

0.1875

0.2492

1.158

1.148

1.135

1.114

1.099

1.082

1.056

1.026

0.9896

0.9334

8.8625

6.4997

5.1318

4.0631

3.6119

3.2508

2.8683

2.5662

2.3213

2.0733

1.349

1.332

1.310

1.277

1.254

1.230

1.197

1.163

1.132

1.103

0.0292

0.0557

0.0922

0.1551

0.2045

0.2652

0.3693

0.5110

0.7118

1.111

1.128

1.092

1.046

0.9728

0.9212

0.8638

0.7789

0.6851

0.5836

0.4495

1.259

1.212

1.149

1.056

1.002

0.9214

0.8332

0.7125

0.6091

0.4467

5.5057

4.0559

3.2212

2.5743

2.3038

2.0892

1,8646

1.6901

1.5515

1.4150

0.5587

0.5360

0.5059

0.4575

0.4223

0.3821

0.3200

0.2470

0.1610

0,0304

4.44541

3.23607

2.55930

2.06266

1.88708

1.70130

1.55573

1.41421

1.32501

1.22078

86.4

72.1

61.2

50.8

46.3

40.8

35.8

30.2

26.0

20.0

0.7556

0.7456

0.7321

0.71 12

0.6987

0.6798

0.6581

0.6265

0.5973

0.5460

0.0137

0.0266

0.0441

0.0718

0.0887

0.1148

0.1456

0.1920

0.2372

0.3242

1.295

1.280

1.261

1.231

1.214

1.187

1.156

1.110

1.067

0.9858

7.4994

5.4168

4.2397

3.3629

3.0476

2.7089

2.4377

2.1660

1.9881

1.7689

1.558

1.531

1.496

1.444

1.415

1.373

J.328

1.271

1.225

1.166

0.0365

0.0716

0.1211

0.2038

0.2574

0.3456

0.4590

0.6535

0.8756

1.419

4.6684

3.3946

2.6807

2.1556

1.9695

1.7721

1.6170

1.4654

1.3693

2.2561

0.7336

0.7033

0.6628

0.6004

0.5632

0.5070

0.4427

0.3494

0.2628

0.1073

3.86370

2.92380

2.20269

1.83608

1.66164

1.52425

1.39016

1.28676

1.20622

1.14335

0.0175

0.0315

0.0587

0.0899

0.1155

0.1454

0.1902

0.2451

0.3141

0.4039

1.352

1.337

1.307

1.273

1.247

1.216

1.172

1.119

1.056

0.9778

6.4997

4.8753

3.6119

2.9553

2.6356

2.3781

2.1187

1.9095

1.7368

1.5913

1.760

1.727

1.666

1.601

1.552

1.498

1.427

1.352

1.278

1.207

0.0464

0.0843

0.1607

0.2534

0.3337

0.4338

0.5976

0.8269

1.168

1.723

1.310

1.262

1.173

1.076

1.001

0.9195

0.8075

0.6858

0.5567

0.4234

4.0559

3.0653

2.3038

1.9154

1.7299

1.5833

1.4396

1.3279

1.2402

1.1708

0.9312

0.8983

0.8363

0.7678

0.7140

0.6533

0.5670

0.4679

0.3534

0.2197

86.2

73.5

60.1

50.9

45.6

40.7

35.1

30.0

25.1

80.4

101

86.3

73.5

60.5

50.1

45.5

40.2

35.2

30.5

25.9

0.9590

0.9479

0.9265

0.9024

0.8833

0.8613

0.8296

0.7924

0.7488

0.6973

1.444

1.433

1.416

1.383

1.340

1.313

1.275

1.231

1.179

1.118

4.44541

3.23607

2.45 859

1.88708

1.55573

1.43956

1.32501

1.23607

1.16663

1.1

1260

0.0137

0.0266

0.0480

0.0879

0.1430

0.1775

0.2288

0.2914

0.3693

0.4695

1.293

1.281

1.261

1.225

1.177

1.148

1.106

1.057

0.9986

0.9290

7.4994

5.4168

4.0631

3.0476

2.4377

2.2154

1.9881

1.8021

1.6467

1.5142

2.244

2.209

2.151

2.050

1.923

1.851

1.752

1.646

1.534

1.417

1.268

1.234

1.177

1.079

0.9543

0.8830

0.7859

0.6808

0.5689

0.4518

4.6684

3.3946

2.5743

1.9695

1.6170

1.4926

1.3693

1.2728

1,1966

1.1364

1.422

1.391

1.341

1.253

1.139

1.072

0.9789

0.8749

0.7586

0.6280

0.0362

0.0703

0.1282

0.2390

0.4007

0.5083

0.6786

0.9067

1.228

1.714

TABLE

CAUER-PARAMETER

LOW-PASS,

DEGREE=6

86.1

73.1

60.6

50.2

45.6

41.3

35.8

30.8

26.0

20.3

0.5417

0.5221

0.4916

0.4518

0.4302

0.4050

0.3673

0.3242

0.2749

0.2027

0.0337

0.0562

0.0924

0.1421

0.1707

0.2050

0.2591

0.3252

0.4073

0.5435

1.179

1.150

1.106

1.049

1.019

0.9846

0.9341

0.8780

0.8157

0.7271

5.0202

3.9348

3.1279

2.5897

2.3975

2.2258

2.0329

1.8716

1.7349

1.5907

1.398

1.361

1.307

1.242

1.206

168

1.115

1.060

1.005

0.9410

0.0571

0.0959

0.1597

0.2479

0.3043

0.3714

0.4829

0.6302

0.8333

1.228

3.5830

2.8252

2.2666

1.9051

1.7692

1.6545

1.5274

1.4233

1.3371

1.2491

1.179

1.150

1.105

1.048

1.015

0.9795

0.9261

0.8658

0.7976

0.6984

0.5746

0.5762

0.5785

0.5812

0.5828

0.5842

0.586'3

0.589C

0.591

0.5934

1.365

1.307

1.219

1.111

1.049

0.9836

0.8877

0.7833

0.6712

0.5219

1.488

1.411

1.314

1.178

1.089

0.9922

0.8874

0.7749

0.6556

0.4984

3.45698

2.72832

2.19194

1.84554

1.71560

1.60614

1.48509

1.38624

1.30476

1.22215

2.97737

2.34339

1.94627

1.64063

1.51304

1.40916

1.3237

1.25292

1.19408

1.13432

2.72832

2.12408

1.75640

1.51304

1.40916

1.30476

1.23718

1.18098

1.12397

1.08733

85.9

72.4

61.4

50.6

45.1

40.0

35.1

30.5

26.0

20.5

0.6896

0.6643

0.6319

0.5844

0.5520

0.5153

0.4738

0.4267

0.3729

0.2941

0.0408

0.0692

0.1068

0.1651

0.2071

0.2572

0.3174

0.3908

0.4825

0.6368

1.321

1.283

1.235

1.165

1.118

1.067

1.009

0.9453

0.8741

0.7722

4.3068

3.3569

2.7538

2.2802

2.0777

1.9093

1.7671

1.6453

1.5398

1.4260

1.527

1.477

1.414

1.326

1.270

1.210

1.146

1.081

1.015

0.9343

0.0706

0.1206

0.1882

0.2969

0.3789

0.4810

0.6119

0.7852

1.026

1.505

3.0843

2.4244

2.0103

1.6907

1.5568

1.4475

1.3571

1.2820

1.2191

1.1546

1.321

1.283

1.235

1.167

1.121

1.070

1.013

0.9498

0.8794

0.7785

0.7294

0.7305

0.7315

0.7335

0.7347

0.7357

0.7365

0.7372

0.7373

0.7363

87.1

72.7

61.1

51.2

46.0

40.0

35.4

30.9

25.4

21.0

0.0458

0.0801

0.1266

0.1883

0.2323

0.2989

0.3643

0.4445

0.5753

0.7195

1.412

1.365

1.305

1.230

1.181

1.112

1.049

0.9794

0.8802

0.7880

3.9348

3.0250

2.4610

2.0777

,9093

1.7349

1.6175

1.5156

1.4053

1.3281

1.625

1.558

1.475

1.375

1.312

1.227

1.155

1.080

0.9831

0.9065

0.0793

0.1399

0.2240

0.3401

0.4268

0.5656

0.7121

0.9079

1.273

1.752

1.581

1.483

1.360

1.213

1.118

0.9890

0.8773

0.7585

0.6009

0.4691

2.8252

2.1959

1.8119

1.5568

1.4475

1.337 1

1.2652

1.2050

1.1434

1.1032

0.8994

0.8996

0.8993

0.8989

0.8981

3.8969

3.8951

3.8917

3.8872

0.8548

0.8231

0.7820

0.7304

0.6957

0.6461

0.6007

0.5494

0.4747

0.4040

1.238

1.213

1.167

1.110

1.036

0.9928

0.9313

0.8752

0.7939

0.7171

1.412

1.366

1.308

1.237

1.190

1.125

1.068

1.004

0.9150

0.8337

1.480

1.448

1.394

1.326

1.244

1.198

1.134

1.078

1.000

0.9305

2.97737

2.34339

1.84554

1.54246

1.34357

1.26941

1.19408

1.14518

1.09581

1.06444

100

86.7

72.5

60.7

50.6

45.9

40.2

35.8

30.3

25.8

3.0365

0.0613

3.1073

3.1681

3.2515

1.3042

3.3842

3.4638

3.5924

3.7331

1.479

1.447

1.389

1.318

1.227

173

1.098

1.029

0.9309

0.8386

4.3068

3.3569

2.5897

2.1248

1.8005

1.6741

1.5398

1.4474

1.3466

1.2753

1.795

1.742

1.649

1.535

1.398

,322

1.219

1.132

1.016

0.9195

3.0843

2.4244

1.9051

1.5877

1.3782

1.2995

1.2191

1.1664

1.1126

1.0777

1.274

1.272

1.268

1.263

1.256

1.251

1.243

1.236

1.224

1.211

0.0597

0.101

0.1775

0.2854

0.4401

0.5440

0.7133

0.8969

1.233

1.665

1.760

1.684

1.553

1.390

1.196

1.088

0.9434

0.8195

0.6553

0.5172

FILTERS, MODERN-NETWORK-THEORY DESIGN

9-9

(dB)

85.2

72.0

60.8

51.0

45.0

40.7

35.3

31.3

26.1

21.0

86.3

72.4

60.6

50.1

45.4

40.5

35.3

30.2

25.0

21.1

86.0

73.1

60.5

50.6

45.3

40.0

36.2

31.1

25.8

20.4

101

86.6

73.2

60.2

50.9

45.7

40.6

35.4

30.0

25.7

(dB)

TABLE

CAUER-PARAMETER

LOW-PASS,

DEGREE=7

0.6054 0.031t

0.5919 0.049(

0.5749 0.071:

0.5537 0.0992

0.5369 0.1221

0.5225 0.1421

0.5006 0.1725

0.4818 0.199i

0.4527 0.2425

0.4178 0.2984

0.7776 0.0364

0.7607 0.0578

0.7387 0.085s

0.7107 0.1226

0.6963 0.1417

0.6744 0.1712

0.6488 0.2068

0.6183 0.2505

0.5813 0.3065

0.5478 0.3613

0.9740 0.0435

0.9551 0.0667

0.9270 0.1021

0.8951 0.1431

0.8728 0.1725

0.8466 0.2076

0.8238 0.2391

0.7879 0.2905

0.7433 0.3584

0.6856 0.4564

1.456 0.0377

1.437 0.0597

1.409 0.0932

1.367 0.1449

1.323 0.2000

1.292 0.2402

1.256 0.2897

1.210 0.3530

1.153 0.4387

1.098 0.5291

2.28115

.88708

1,62425

1.43956

1.34563

1.28676

1.22078

1.17918

1.13255

1.09464

2.06266

1.70130

1.46628

1.30541

1.25214

19236

L.14335

L.10338

1.071 14

1.05146

1.88708

1.58902

,36733

,23607

17918

L.13257

L.10338

1.07114

1.04569

1.02630

1.464

1.405

1.334

1.252

1.191

1.141

1.071

1.016

0.9374

0.8556

1.609

1.530

1.435

1.324

1.271

1.197

1.117

1.032

0.9419

0.8719

1.752

1.661

1.536

1.409

1.329

1.243

1.174

1.079

0.9763

0.8684

L.06266

1.70130

1.43956

1.25214

15470

11260

1.07853

1.05146

,03061

l.01872

0.1331 1.379

0.2100 1.281

0.3130 1.163

0.4523 1.029

0.5745 0.929:

0.6882 0.8504

0.8829 0.7385

1.077 0.6505

1.444 0.5275

2.045 0.4003

0.1603 1.403

0.2589 1.281

0.3945 1.136

0.5859 0.9699

0.6935 0.8925

0.8734 0.7840

1.116 0.6696

1.464 0.5500

2.012 0.4260

2.692 0.3314

0.1983 1.356

0.3090 1.232

0.4856 1.064

0.7085 0.8972

0.8827 0.7938

1.112 0.6852

1.340 0.6006

1.771 0.4840

2.481 0.3639

3.875 0.2428

2.3339

1.9282

1.6571

1.4660

1.3685

1.3072

1.2383

1.1946

1.1455

1.1052

2.1090

1.7366

1.4936

1.3266

1.2711

1.2085

1.1569

1.1145

1.0800

1.0587

1.9282

1.6206

1.3910

1.2543

1.1946

1.1455

1.1145

1.0800

1.0524

1.0310

Z.1090

1.7366

1.4660

1.2711

1.1689

1.1243

1.0880

1.0587

1.0358

1.0225

1.247

1.228

1.204

1.174

1.151

1.131

1.100

1.073

1.030

0.9761

1.424 0.1075 1.137 2.8596 0.5358

1.348 0.1717 1.063 2.3410 0.4851

1.259 0.2597 0.9729 1.9895 0.4215

1.161 0.3820 0.8674 1.7371 0.3430

1.092 0.4919 0.7887 1.6056 0.2807

1.040 0.5957 0.7253 1.5213 0.2278

0.9708 0.7758 0.6352 1.4245 0.1472

0.9214 0.9567 0.5638 1.3616 0.7749

0.8623 1.299 0.4639 1.2883 -.0319

0.8182 1.851 0.3598 1.2253 -.1677

1.558 0.1227 1.231 2.5729 0.6988

1.454 0.2000 1.141 2.0933 0.6379

1.332 0.3081 1.031 1.7741 0.5612

1.195 0.4628 0.9015 1.5482 0.4657

1.133 0.5505 0.8396 1.4709 0.4180

1.049 0.6973 0.7512 1.3817 0.3467

0.9643 0.8942 0.6561 1.3056 0.2647

0.8819 1.173 0.5543 1.2402 0.1690

0.8059 1.599 0.4462 1.1838 0.0540

0.7575 2.103 0.3616 1.1467 -.0505

1.684 0.1459 1.251 2.3410 0.8812

1.564 0.2286 1.160 1.9418 0.8165

1.402 0.3614 1.034 1.6362 0.7236

1.243 0.5293 0.9020 1.4473 0.6230

1.146 0.6596 0.8177 1.3616 0.5557

1.046 0.8291 0.7267 1.2883 0.4795

0.9707 0.9946 0.6537 1.2402 0.4153

0.8701 1.297 0.5500 1.1838 0.3176

0.7732 1.769 0.4386 1.1352 0.2008

0.6866 2.618 0.3195 1.0933 0.0540

2.137 0.1242 1.216 2.5729 1.375

2.005 0.1989 1.147 2.0933 1.312

1.822 0.3158 1.050 1.7371 1.223

1.579 0.5055 0.9143 1.4709 1.096

1.366 0.7233 0.7893 1.3235 0.9741

1.237 0.8942 0.7093 1.2556 0.8937

1.102 1.121 0.6225 1.1972 0.8031

0.9634 1.440 0.5280 1.1467 0.6996

0.8226 1.934 0.4248 1.1032 0.5779

0.7168 2.543 0.3404 1.0747 0.4689

1.353

1.328

1.296

1.255

1.234

1.202

1.165

1.120

1.063

1.010

1.386

1.359

1.319

1.273

1.242

1.205

1.173

1.122

1.058

1.9706

1.306

1.285

1.254

1.207

158

1.124

1.084

.034

1.9705

1.9081

5.0385

4.0756

3.4121

2.9248

2.6645

2.4945

2.2946

2.1606

1.999c

1.853C

4.5080

3.6093

2.9970

2.5494

2.3913

2.2039

2.0378

1.8883

1.7515

1.6553

4.0756

3.3209

2.7259

2.3422

2.1606

1.9990

1.8883

1.7515

1.6241

1.5025

1.265

1.167

1.033

0.8560

0.7013

0.6071

0.5090

0.4074

0.3031

0.2237

9-10

(dB)

c, c2

2 33 1.89679 86.6 0.5447 0.0724

2 40 1.60249 72.2 0.5116 0.1113

2 46 1.42779 61.4 0.4761 0.1549

2 53 1.28108

50.0

0.4245 0.2221

2 56 1.23189 45.3 0.3982 0.2582

2 59 1.18924 40.8 0.3688 0.3001

2 62 1.15228 36.3 0.3357 0.3496

2 66 1.11071 30.5 0.2845 0.4316

2 69 1.08464 26.1 0.2392 0.5107

2 73 1.05591 20.1 0.1658 0.6551

5 37 1.71384 86.1 0.6891 0.0834

1,48002 72.9 0.6538 0.1236

5 51 1.31802 61.1 0.6094 0.1764

1.20279 50.3 0.5534 0.2474

5 61 1.16402 45.8 0.5249 0.2856

5 64 1.13047 41.4 0.4928 0.3304

68 1.09287 35.5 0.4433 0.4039

5 71 1.06945 31.1 0.3995 0.4739

5 75 1.04394 25.0 0.3287 0.5999

78 1.02877 20.2 0.2615 0.7379

40 1.60249 86.2 0.8520 0.0934

48 1.38060 72.0 0.8075 0.1420

1.24752 60.9 0.7582 0.1987

62 1.15228 50.4 0.6959 0.2751

65 1.12034 46.0 0.6639 0.3167

69 1.08464 40.1 0.6146 0.3844

72 1.06248 35.6 0.5714 0.4483

75 1,04394 31.0 0.5206 0.5292

78 1.02877 26.2 0.4591 0.6380

1.01681 21.0 0.3813 0.7981

5 37 1.71384

100

1.255 0.0776

5 45 1.45323 85.3 1.211 0.1197

53 1.28108

72.2 1.155 0.1757

61 1.16402 60.0

1.082 0.2519

67 1.10156 51.2 1.013 0.3297

5 71 1.06945 45.3 0.9576 0.3976

74 1.04974 40.8

0.9084 0.4616

5 77 1.03346 36.0

0.8507 0.5430

1.02044

31.0 0.7801 0.6534

83 1.01057 25.4

0.6892 0.8209

)

fl,

(dB)

TABLE

CAUER-PARAMETER LOW-PASS,

DEGREE=^

fl2 c3

1.205 3.3870 1.397 0.1969 1.364

1.157 2.7865 1.310 0.3075 1.226

1.107 2.4152 1.223 0.4367 1.091

1.036 2.0853 1.106 0.6510 0.9125

1.000

1.9680

1.051

0.7755 0.830C

0.9613 1.8617 0.9938 0.9303 0.7438

0.9184 1.7648 0.9335 1.129 0.6542

0.8536 1.6475 0.8485 1.504 0.5295

0.7976 1.5668 0.7815 1.931 0.4335

0.7095 1.4668 0.6880 2.921 0.3034

1.318 3.0164 1.479 0.2376 1.386

1.266 2.5280 1.381 0.3577 1.239

1.203 2.1707 1.267 0.5242 1.070

1.125 1.8960 1.137 0.7680 0.8803

1.085 1.7962 1.077 0.9115 0.7932

1.042 1.7046 1.013 1.092 0.7034

0.9755 1.5931 0.9231 1.425 0.5785

0.9182 1.5159 0.8517 1.791 0.4815

0.8274 1.4194 0.7512 2.600 0.3493

0.7432 1.3503 0.6718 3.764 0.2496

1.380 2.7865 1.542 0.2723 1.386

1.318 2.3115 1.418 0.4227 1.207

1.251 2.0058 1.292 0.6099 1.029

1.167 1.7648 1.149 0,8888 0.8309

1.125 1.6757 1.082 1.057 0.7408

1.060 1.5668 0.9874 1.360 0.6159

1.003

1.4911 0.9121 1.686 0.5189

0.9379 1.4194 0.8326 2.167 0.4192

0.8597 1.3503 0.7483 2.953 0.3174

0.7617 1.2825 0.6588 4.480 0.2147

1.417 3.0164 1.756 0.2208 1.492

1.369 2.4704 1.631 0.3461 1.329

1.309 2.0853 1.484 0.5223 1.138

1.230 1.7962 1.313 0.7850 0.9213

1.155 1.6200 1.168 1.090 0.7436

1.094 1.5159 1.062 1.396 0.6181

1.041 1.4429 0.9777 1.724 0.5204

0.9768 1.3732 0.8874 2.211 0.4198

0.8985 1.3051 0.7901 3.017 0.3162

0.7963 1.2369 0.6835 4.639 0.2102

1.9298

1.6281

1.4486

1.2973

1.2464

1.2022

1.1637

1.1202

1.0927

1.0622

1.7423

1.5023

1.3355

1.2162

1.1759

1.1409

1.1014

1.0766

1.0493

1.0329

1.6281

1.4000

1.2626

1.1637

1.1303

1.0927

1.0493

1.0329

1.0197

1.7423

1.4748

1.2973

1.1759

1.1105

1.0766

1.0556

1.0380

1.0238

1.0127

1.0692

1.416

1.303

1.193

1.050

0.984:

0.9175

0.8505

0.761:

0.6965

0.6198

1.446

1.322

1.181

1.023

0.951;

0.8777

0.7775

0.7025

0.6046

0.5365

1.451

1.299

1.146

0.9771

0.9002

0.7942

0.6303

0.5482

0.4691

1.545

1.405

1.239

1.049

0.8922

0.7803

0.6929

0.6024

0.5091

0.4133

0.7125

0.1458

0.2270

0.3208

0.4728

0.5590

0.6634

0.7934

1.027

1.275

1.797

0.1711

0.2566

0.3732

0.5387

0.6330

0.7484

0.9510

1.162

1.588

2.135

0.1901

0.2936

0.4196

0.6004

0.7050

0.8860

1.070

1.325

1.708

2.367

0.1432

0.2243

0.3369

0.5002

0.6813

0.8529

1.028

1.271

1.641

2.297

1.358

1.251

1.141

0.9928

0.922;

0.847L

0.7675

0.654:

0.5635

0.4338

1.435

1.317

1.177

1.015

0.9376

0.8555

0.739:

0.645C

0.509C

0.3994

1.493

1.345

1.192

1.015

0.9305

0.81

0.7142

0.6107

0.4992

0.3778

1.715

1.569

1.393

1.187

1.009

0.8785

0.7730

0.6597

0.5368

0.4007

2.2472

1.8769

1.6528

1.4595

3.3928

1.3337

1.2812

1.2199

1.1796

1.1325

2.0178

1.7203

1.5088

1.3526

1.2980

1.2494

1.1926

1.1552

1.1115

1.0828

1.8769

1.5913

1.4141

1.2812

1.2344

1.1796

1.1436

1.1115

1.0829

1.0575

2.0178

1.6858

1.4595

1.2980

1.2060

1.1552

1.1218

1.0920

1.0656

1.0423

1.183 0.613

1.125 0.615

1.065 0.617

0.9798 0.618

0.9377 0.619

0.8918 0.619

0.8409 0.620

0.7641 0.620

0.6975 0.620

0.5919 0.618

1.294 0.768

1.234 0.768

1.161 0.768

1.074 0.768

1.031 0.767

0.9843 0.766

0.9146 0.765

0.8547..0.763

0.7616 0.759

0.6767 0.755

1.355 0.940

1.285 0.938

1.211 0.936

1.123 0.932

1.080 0.930

1.017 0.926

0.9628 0.922

0.9021 0.917

0.8320 0.911

0.7473 0.902

1.398 1.330

1.343 1.324

1.277 1.315

1.197 1.303

1.126 1.291

1.072 1.281

1.026 1.271

0.9747 1.259

0.9158 1.244

0.8443 1.223

FILTERS, MODERN-NETWORK-THEORY DESIGN

(dB)

c5 C6

2 34 1.78829

101

0.6236 0.0332 1.289

4.8248 1.498 0.1723 1.423 2.0198 1.479 0.2254 1.353

1.8111

1.413 0.1236 1.162 2.6394 0.541

2 40 1.55573 87.0 0.6123 0.0476 1.273

4.0634 1.438 0.2489 1.324 1.7423 1.368 0.3280 1.231 1.5740 1.325 0.1805 1.096 2.2480 0.496

2 47 1.36733 72.9 0.5955 0.0689 1.249

3.4103 1.355 0.3674

1.188

1.5135 1.219 0.4907 1.068 1.3815 1.207 0.2707 1.002 1.9200 0.430

2 54 1.23607 60.2 0.5736 0.0968 1.217

2.9140 1.257 0.5320 1.032 1.3498 1.053 0.7263

0.8855

1.2469 1.075 0.3999 0.8896 1.6766 0.346

2 60 1.15470

50.0

0.5493 0.1282 1.182

2.5690 1.159 0.7331 0.8806 1.2446 0.8987 1.032 0.7158 1.1632 0.9530 0.5632 0.7753 1.5133 0.255

2 63

12233 45.0 0.5345 0.1476 1.160

2.4161

1.105

0.8673 0.7990 1.2013 0.8192 1.250 0.6269 1.1297 0.8902 0.6752 0.7111 1.4432

0.201

2 66 1.09464 40.0 0.5172 0.1704 1.135

2.2732 1.046 1.037 0.7131 1.1631 0.7389 1.540 0.5358 1.1009 0.8270 0.8193 0.6415 1.3793 0.138

2 69 1.07114 35.1 0.4970 0.1978 1.106

2.1381 0.9828 1.259 0.6225 1.1296 0.6592 1.948 0.4430 1.0764 0.7643 1.013 0.5661 1.3208 0.064

2 72 1.05146 30.1 0.4726 0.2315 1.070

2.0089 0.9141 1.569 0.5266 1.1002 0.5817 2.570 0.3490 1.0558 0.7039 1.287 0.4841 1.2669 -.024

2 74 1.04030 26.6 0.4534 0.2592 1.041

1.9249 0.8650 1.857 0.4594 1.0827 0.5326 3.204 0.2864 1.0440 0.6662 1.546 0.4253 1.2332 -.0951

37 1.66164 102 0.7940 0.0370 1.385

4.4144 1.625 0.2023 1.415 1.8692 1.548

0.2644 1.337 1.6820 1.521 0.1360 1.247 2.4282 0.704

44 1.43956 86.7 0.7798 0.0545 1.364

3.6664 1.546 0.3014 1.293 1.6018 1.402

0.3972 1.189 1.4554 1.404 0.2042 1.167 2.0480 0.650

1.28676 73.5 0.7614 0.0773 1.336 3.1119 1.453 0.4347

1.151

1.4137 1.236

0.5807 1.021 1.2990 1.270 0.2973 1.070 1.7727 0.582

58 1.17918 61.3 0.7374 0.1072 1.301 2.6775 1.343 0.6207 0.9884 1,2767

1.051

0.8480 0.8349 1.1884 1.120 0.4290 0.9531 1.5640 0.497

64 1.11260 51.3 0.7103 0.1416 1.260

2.3675 1.234 0.8514 0.8322

1.1880

0.8812 1.201 0.6641 1.1196 0.9810 0.5941 0.8334 1.4212 0.406

67 1.08636 46.3 0.6935 0.1631 1.235 2.2274 1.173

1.008

0.7480 1.1514 0.7931 1.457 0.5754 1.0923 0.9082 0.7071 0.7654 1.3592 0.351

70 1.06418 41.4 0.6737 0.1890 1.206 2.0945 1.107 1.210 0.6594 1.1193 0.7037

1.804 0.4849 1.0691 0.8339 0.8531 0.6911 1.3023 0.288

73 1.04567 36.3 0.6498 0.2208 1.171 1.9667 1.036 1.484 0.5658 1.0912 0.6141 2.309 0.3930 1.0497 0.7586

1.051

0.6092 1.2498 0.214

76 1,03061 31.1 0.6202 0.2616 1.127

1.8420 0.9578 1.884 0.4665 1.0668 0.5256 3.114 0.3005 1.0337 0,6835 1.338

0.5181

1.2011 0.124

79 1.01872

25.6 0.5821 0.3172 1.069 1.7175 0.8713 2.538 0.3601 1.0459 0.4412 4.597 0.2087 1.0209 0.6109 1.801 0.4159

1.1555

0.010

40 1.55573

101

0.9894 0.0430 1.410 4.0634 1.754 0.2443 1.348 1.7423 1.618 0.3195 1.264 1.5740 1.626 0.1567 1.262 2.2489 0.886

48 1.34563

85.0

0.9710 0.0651 1.383

3.3315 1.650 0.3753 1.205 1.4868 1.429 0.4957 1.092 1.3593 1.473 0.2419 1.168 1.8808 0.819

1.22078

72.5 0.9498 0.0909 1.353

2.8522 1.543 0.5334 1,059 1.3303 1.241 0.7152 0.9223 1.2312 1.319 0.3452 1.068 1.6470 0.746

62 1.13257

60.7 0.9218 0.1253 1.313

2.4659 1.417 0.7579 0.8936 1.2152 1.034 1.043 0.7376 1.1403 1.147 0.4917 0.9466 1.4658 0.654

68 1.07853

50.7 0.8894 0.1657 1.267

2.1824 1.292 1.046 0.7351 1.1403 0.8439 1.494 0.5694 1.0841 0.9870 0.6783 0.8214 1.3397

0.555

71 1.05762

45.8 0.8689 0.1920 1.238 2.0514 1.221 1.251 0.6496 1.1095 0.7454 1.837 0.4825 1.0622 0.9023 0.8091 0.7492 1.2844 0.495

74 1.04030

40.6 0.8440 0.2244 1.203

1,9249 1.145 1.525 0.5592 1.0827 0,6454 2.328 0.3941 1.0440

0.8140

0.9838 0.6683 1.2332 0.426

77 1.02630

35.3 0.8130 0.2661 1.159

1,8006 1.060 1.922 0.4634 1.0595 0.5447 3.093 0.3052 1.0291 0.7254 1.228 0.5793 1.1856 0.342,

79 1.01872

31.6 0.7873 0.3019 1.123

1.7175 0,9987 2.309 0.3958 1.0459 0.4781 3.903 0.2458 1.0209 0.6645 1.462 0.5124 1.1555 0.276

82 1.00983

25.6 0.7369 0.3771

1.050

1.5893 0.8954 3.290 0.2874 1.0284 0.3807 6.205 0.1576 1.0113 0.5730 2.029 0.3983 1.1124

0.150

25 44 143956

101

1.452 0.0572 1.301 3.6664 2.091 0.3414 1.141 1.6018 1.849 0.4468 1.057 1.4554 1.910 0.2068 1.153 2.0480 1.318

52 1.26902 85.9 1.428 0.0847 1.274 3.0437 1.958 0.5122

1.008

1.3914 1.610 0.6778 0.8994 1.2808 1.713 0.3101 1.066 1.7395 1.238

60 1.15470 72.2 1.397 0,1223 1.238 2.5690 1.800 0.7565 0.8534 1.2446 1.338 1.022 0.7235 1.1632 1.487 0.4562 0.9572 1.5133 1.137

25 67 1.08636 60.6 1.358 0 1686 1.196 2,2274 1.635 1.079 0.6991 1.1514 1.077

1.505

0.5570 1.0923 1.264 0.6444 0.8400 1.3592 1.024

25 73 1.04569 50.6 1.312 0.2258 1.145 1.9667 1.470 1.523 0.5514 1.0912 0.8373 2.230 0.4069 10497 1.052 0.8937 0.7163 1.2498 0.900.

76 1.03061 45.3 1281 0.2653

1.111

1.8420 1.375 1.865 0.4712 1.0668 0.7127 2.836 0.3299 1.0337 0.9388 1.078 0.6431 1.2011 0.824

25 78 1.02234 41.7 1.256 0.2982 1.084 1.7592 1.306 2.176 0.4149 1.0525 0.6282 3.423 0.2781 1.0248 0.8596 1.240 0.5887 1.1704 0.766

25 81 1.01247 35.8 1.209 0.3637

1.031

1.6328 1.190 2.878 0.3251 1.0339 0,4995 4.859 0,2001 1.0142 0,7350 1.590 0.4956

1265 0.661

25 83 1.00751 31.5 1.166 0.4258 0.9844 1.5447 1.102 3.665 0.2606 1.0233 0.4128 6.637 0.1481 1.0087 0.6467 1.959 0.4230 10985 0.574'

85 1.00382 26.7 1.108 0.5174 0.9194 1.4499 0.9994 5.088 0.1911 1.0143 0.3257 10.24 0.0968 1.0045

0.5537

2.578 0.3381 1.0711 0.4641

(dB)

C* 04

16 C6

TABLE

CAUER-PARAMETER LOW-PASS, DEGREE=9

9-11

9-12

REFERENCE

DATA

FOR ENGINEERS

Fig.

Selecting the degree for a Cauer-parameter low-pass. (Example

is drawn in to illustrate use

the chart.)

FILTERS, MODERN-NETWORK-THEORY DESIGN

9-13

Fig.

10.

Selecting the degree for

Cauer-parameter low-pass-expanded.

9-14

REFERENCE DATA FOR ENGINEERS

beyond that intersection specifies the necessary degree.

Example

in the section headed “Numerical Exam-

ples” demonstrates this application.

CH EBYSHEV LOW- PASS

FILTERS

If the passband requirement is for a variation of

attenuation between zero and a maximum and the stop

requirement is only

increase monotonically to infini-

ty, a Chebyshev (sometimes spelled “Tchebyscheff

’)

filter can be used. Fig.

shows this performance

characteristic and the circuit configurations for both

odd- and even-degree filters.

The discussion of impedance variation in the preced-

ing section also applies for this network type.

Table

contains data for a number of normalized

Chebyshev low-pass filters for degree

through

For

each degree, one network is tabulated for reflection

coefficients of

2,5,

10,

and

percent. Since stopband

attenuation increases monotonically, there is only one

circuit for a given

A,.

Figs.

and

are used in the same way as described

for Cauer-parameter filters to ascertain the order of

low-pass required.

BUTTERWORTH LOW-PASS

LTE RS

Whenever a filter performance is desired with mono-

tonically increasing attenuation from frequency equal to

zero to infinity, Butterworth filters may be applicable.

Fig.

shows the performance characteristic and circuit

configurations for Butterworth low-pass filters of odd

and even degree.

Table

contains data for a number of normalized

Butterworth low-pass filters of degree

through

For each degree, circuit elements are tabulated for at-

tenuation maxima at

fief

0.011,

0.044,

0.28,

and

3.0

dB.

Figs.

and

are used in the same way as described

for Cauer-parameter filters to determine the degree of

the low-pass to satisfy the requirements.

LOW-PASS TO HIGH-PASS

TRANSFORMATION

The frequency performance of a low-pass filter can

be transformed into high-pass performance by the

frequency transformation

a,,

1/RLP

The transformation of normalized circuit-element val-

ues is shown

Fig.

17.

LOW-PASS TO BANDPASS

TRANSFORMATION

FREQUENCY

(A)

Odd-degree

performance

FREQUENCY

(E)

Even-degree performance

----?

(C)

0dd.degree

configurntion

----_lbbdl_r,

(DI

Euewdegree configuration

Fig.

11.

Chebyshev low-pass

filters.

a(11

1/11)

the frequency characteristic of a low-pass filter is

converted into that of a bandpass filter. Two normalized

bandpass frequencies,

f+,/frref

and

Q-~

l/vP

f-,/frref,

correspond to the normalized low-pass

R,.

Similarly, the geometrically symmetrical stopband lim-

its,

fs/fref

and

v-,

f-,/fref

are defined as shown

in Fig.

and:

411-,

11+,)

411-,

11,)

The relation between stopband limits and passband

limits

By the transformation

FILTERS, MODERN-NETWORK-THEORY DESIGN

9-15

TABLE

CHEBYSHEV LOW-PASS, DEGREE

2-9

0.2746

0.4151

0.5455

0.6928

0.9608

0.9048

0.8182

0.6000

0.7838

0.9789

1.104

1.141

0.4520

0.6396

0.8534

1.345

1.000

.ooo

1.000

1.041

1.207

1.292

1.260

1.084

1.334

1.580

2.100

0.5168

0.6543

0.7636

0.8519

0.9608

0.9048

0.8182

,6000

1.169

1.310

1.372

1.307

1.369

1.588

1.803

2.283

1.169

1.310

1.372

1.307

0.5849

0.7664

0.9732

1.456

1.000

0.9608

0.9048

0.8182

0.6000

0.6301 1

.ooo

0.8068 1.000

1.010

.ooo

1.488

1.000

1.363

0.6167 0.9608

1.566 0.7392

0.9048

1.774

0.8336 0.8182

2.252

0.8977 0.6000

1.652 1.328

0.6501 1.000

1.813 1.431

0.8242 1.000

1.985 1.462

1.025

1.000

2.420

1.357

1.502 1.000

1.240

1.365

1.413

1.330

1.505

1.700

1.895

2.353

1.446

1.538

1.550

1.412

1.290

1.508

1.727

2.216

0.5885

0.7159

0.8147

0.8855

1.579

1.757

1.941

2.388

1.575

1.634

1.622

1.45 1

1.579

1.757

1.941

2.388

1.282

1.400

1.437

1.343

1.560

1.621

1.610

1.444

1.684

1.712

1.677

1.481

1.282

1.400

1.437

1.343

1.309

1.417

1.452

1.351

1.643

1.684

1.657

1.470

1.684

1.712

1.677

1.481

1.710

1.861

2.025

2.450

1.779

1.913

2.066

2.480

1.623

1.791

1.968

2.407

1.652

1.813

1.985

2.420

2 0.6501

0.8242

10 1.025

25 1.502

1.328

1.43 1

1.462

1.357