The Comprehensive Guide To

RF & Microwave Engineering

For Passive Components

Richard Wallace

Krister Andreasson

/ 4 / 4 / 4

The Comprehensive Guide to RF & Microwave Engineering for Passive Components

2014 Richard Wallace and Krister Andreasson

Printed at Författares Bokmaskin

Stockholm 2014

ISBN 978-91-981996-0-4

Preface

Access to information has never been so easily available for all people around the

world. The demand for increased bandwidth and faster communication channels is

growing on a daily basis. The high technology used today in an ultra-modern product

is tomorrow’s standard low cost appliance.

Electronics has been driven previously by the stationary computer market in the early

80s for nearly twenty years. Each new generation had a faster computer with faster

peripherals that could send more and more data to each other. Mobile access devices

have replaced many of the stationary computers and the requirement for greater

bandwidth for each new mobile device has dominated the recent developments in

electronics. The latest development trends require direct access to distant positioned

electronic devices via the internet and cloud services.

Regardless of the platform being a stationary PC, mobile device or access to a distant

unit via a cloud service; one common platform for all these devices is the need for

greater bandwidth and faster operating speeds. To be able to meet the increasing

requirements in the mass market it has been necessary to operate at higher

frequencies for greater bandwidth.

To meet the bandwidth requirements, traditional communication systems have moved

from the radio frequency region (LF, MF, HF and UHF) to the RF, microwave and

mm-wave region. To ease developments in RF, microwave and mm-wave regions,

there are a variety of modular components which can be purchased of the shelf.

These components are designed as separate units with matched custom input and

output stages. Microwave design can be made from readymade component modules

and the complete system design can be analysed by understanding the usage of each

specific component block.

System designers need a descriptive explanation of the function, in order to make

best use of the components. An overview of all the components enables evaluation of

alternative system solutions. By selecting the best combination will provide the

optimum product for the available cost budget.

Component design engineers should have a broad overview of all the available

components to obtain new ideas for circuit solutions. The knowledge of experienced

engineers should always be utilized as much as possible. As well as usage of

computer simulations to design and optimize the components which simplifies the

mathematical workload considerably, but it is still vital to correctly choose the

appropriate circuit solution.

Technicians and test engineers need a descriptive explanation of the complete

system, which is not burdened with mathematical models. A technician needs to be

able to quickly understand complete circuit diagrams or special test setups. Sales

representatives and purchasers require a general understanding of the microwave

components since they must understand requirements for price negotiations.

Thus, there are now many roles who work with RF, microwave and mm-wave

technology requiring a broad knowledge of high frequency components, as well as an

understanding of the special characteristics exploited in microwave and high

frequency design.

The goal of the book is to provide an overview and introduction working with RF,

microwave and high frequency components. With over 700 figures to illustrate the

practical and comprehensive descriptions of high frequency components with the

mathematics kept to the minimum.

Contents

Introduction................................................................................... 1

Microwave Frequency Band .............................................................. 1 Electromagnetic Spectrum Divisions .............................................................. 2 Advantages with Microwaves ......................................................................... 3 Radio Frequency Region ................................................................................ 4

2 GHz Threshold ................................................................................. 4

Applications ......................................................................................... 5 Radar ............................................................................................................... 5 Radio Link ...................................................................................................... 6 Satellite TV ..................................................................................................... 6 Wireless Data Networks ................................................................................. 6 Mobile Telephones ......................................................................................... 7 Heating and Drying ......................................................................................... 7 RFID ............................................................................................................... 8 Car Tolls ......................................................................................................... 8 GPS ................................................................................................................. 8 Navigation for Cars ......................................................................................... 9 Police Radar .................................................................................................... 9 Fixed Wireless Access .................................................................................... 9 Motion Detector ............................................................................................ 10 Material Measurement .................................................................................. 10 ISM-bands ..................................................................................................... 10

Transmission Lines ..................................................................... 11

Introduction ....................................................................................... 11

Reflection ........................................................................................... 11 Transmission Lines Equivalent Circuit ........................................................ 11 DC Voltage ................................................................................................... 12 High Frequency AC Voltage ........................................................................ 14 Transmission Line Characteristic Impedance ............................................... 16 Matching ....................................................................................................... 16 Reflection ...................................................................................................... 17

Reflection Factor .......................................................................................... 17 Voltage Standing Wave Ratio (VSWR) ....................................................... 18 Return Loss ................................................................................................... 18 Insertion Loss ................................................................................................ 19 Typical Component Reflection Values ......................................................... 20 Reflection Factor Expressed as Impedances ................................................. 21 Standing Wave Ratio Expressed as Impedances .......................................... 22 Total Reflection ............................................................................................ 22 Impedance Transformation ........................................................................... 27 Multiple Reflections ..................................................................................... 28

Smith Diagram .................................................................................. 30 Reflection Factor .......................................................................................... 30 Resistance ..................................................................................................... 30 Impedance ..................................................................................................... 31 Varying Reactance ........................................................................................ 32 Varying Frequency ....................................................................................... 33 Movement along a Transmission Line .......................................................... 34 Admittance .................................................................................................... 36 Matching ....................................................................................................... 37

Waveguides ........................................................................................ 37 General .......................................................................................................... 37 Electromagnetic Wave .................................................................................. 37 Reflection Against a Metal Plane ................................................................. 38 Boundary Conditions .................................................................................... 39 Field at the Metal Plane ................................................................................ 39 Rectangular Waveguide ................................................................................ 42 Waveguide Dimensioning ............................................................................. 43 Wave Nomenclature Classification .............................................................. 44 Current in the Waveguide Structure ............................................................. 45 Double Ridge Waveguide ............................................................................. 45 Transition between Waveguide and Coaxial ................................................ 46 Flanges .......................................................................................................... 47 Horn .............................................................................................................. 48 Reactance ...................................................................................................... 49 Attenuators and Phase Shifters ..................................................................... 49 Reactive Attenuator ...................................................................................... 50 Terminator .................................................................................................... 51 Magic – T ...................................................................................................... 53

Wire Pairs .......................................................................................... 54

Coaxial Cables ................................................................................... 55 Inner Conductor ............................................................................................ 56

Dielectric ....................................................................................................... 56 Outer Conductor ........................................................................................... 57 Impedance ..................................................................................................... 57 Higher Modes ............................................................................................... 58 Delay ............................................................................................................. 59 Isolation ........................................................................................................ 59 Attenuation ................................................................................................... 60

Coaxial Connectors ........................................................................... 61 Components and Systems ............................................................................. 61 SMA Clamp Connectors ............................................................................... 61 Performance .................................................................................................. 61 Measurements ............................................................................................... 62 7/16 Connector .............................................................................................. 62 Mm-Waves .................................................................................................... 62 Combining Various Connectors.................................................................... 62

Planar Transmission Lines ............................................................... 63 Microstrip ..................................................................................................... 63 Aluminium Oxide ......................................................................................... 63 Teflon ............................................................................................................ 64 Conductors and Ground Planes .................................................................... 64 High Power ................................................................................................... 65 Field Patterns ................................................................................................ 65 Radiation ....................................................................................................... 66 Impedance ..................................................................................................... 67 Advantages .................................................................................................... 68 Stripline ......................................................................................................... 69 Field Pattern .................................................................................................. 69 Comparison ................................................................................................... 69 LTCC ............................................................................................................ 70

Summary ............................................................................................ 71

Antennas ...................................................................................... 73

Introduction ....................................................................................... 73

Theory ................................................................................................ 73 Power Density ............................................................................................... 75 Spherical Propagation ................................................................................... 75 Directional Radiation .................................................................................... 75

Antenna Radiator .............................................................................. 76 Half-Wave Dipole ......................................................................................... 76 Dipole as a Resonator ................................................................................... 77

Thick Dipole ................................................................................................. 78 Folded Dipole ............................................................................................... 78 Near Field ..................................................................................................... 78 Polarisation ................................................................................................... 80 Linear Polarisation ........................................................................................ 80 45 Polarisation ............................................................................................. 81 Circular Polarization ..................................................................................... 82 Radiation Diagram ........................................................................................ 82 Omni-Directional Antennas .......................................................................... 83 Yagi-Uda Antenna ........................................................................................ 84 Ground Plane Dipole (Monopole) ................................................................ 86 End Capacitance ........................................................................................... 88

Patch Antenna ................................................................................... 89 Microstrip Antenna ....................................................................................... 89 Aperture Coupling ........................................................................................ 90 Patches in Several Layers ............................................................................. 91

Array .................................................................................................. 93 Two Antennas Fed In-Phase, Distance /2 ................................................... 93 Two Antennas Fed in Anti-Phase, Distance /2 ........................................... 94 Two Antennas Fed in 90 Out-of-Phase, Distance /4 ................................. 94 Multiple Antenna Combined In-Phase.......................................................... 95 Array with Reflector ..................................................................................... 97 Endfire Beam Array ...................................................................................... 97 Quadratic Array ............................................................................................ 98 Elements with High Directivity .................................................................... 99 Amplitude Weighting ................................................................................. 100

Feeding Network ............................................................................. 101 Corporate Feeding....................................................................................... 101 Series Feeding ............................................................................................. 101 Travelling Wave Array ............................................................................... 102 Combined Feeding ...................................................................................... 102 Doppler Navigator ...................................................................................... 103 Speedometer ................................................................................................ 104

Broadband Antennas ...................................................................... 105 Log Periodic Dipole Antenna ..................................................................... 105 Coplanar LPD ............................................................................................. 107 Pyramidal LPD............................................................................................ 107 Planar LPD .................................................................................................. 108 Right Angle Coplanar LPD ......................................................................... 109 Spiral Antenna ............................................................................................ 110 Reflecting Cavity ........................................................................................ 111

Impedance ................................................................................................... 111 Archimedean Spiral .................................................................................... 112 Equiangular Spiral ...................................................................................... 112 Conical Spiral ............................................................................................. 112

Reflector Antennas .......................................................................... 113 Antenna Diagram ........................................................................................ 114 Various Antenna Feeding Placements ........................................................ 115 Size of the Reflector ................................................................................... 117 Illumination ................................................................................................. 117 Beamwidth and Gain Correlation ............................................................... 118 Gain and Beamwidth for a Normal Parabolic Antenna .............................. 120 Various Parabolic Antennas ....................................................................... 121 Double Curved ............................................................................................ 121 Single Curved ............................................................................................. 121 Cosecant ...................................................................................................... 121 Sub-Reflector .............................................................................................. 122 Partial Section of a Parabolic Reflector ...................................................... 122 Horn Reflector ............................................................................................ 123

Comparison...................................................................................... 123 Sum / Difference Coupling ......................................................................... 124

Millimeter Waves ...................................................................... 125

Mm-Wave Region ........................................................................... 125 Attenuation in the Atmosphere ................................................................... 125 Noise ........................................................................................................... 126 Waveguide Bands ....................................................................................... 127

Applications ..................................................................................... 128 Small Antennas - Narrow Lobes ................................................................. 128 Large Bandwidth ......................................................................................... 129 Doppler ....................................................................................................... 130 Radiometry .................................................................................................. 130 Homing Missiles ......................................................................................... 131 TV Distribution ........................................................................................... 131 38 GHz Link ............................................................................................... 132 Short Distance Communication .................................................................. 132 WLAN ........................................................................................................ 132 Distance Measurement ................................................................................ 132 Speedometer ................................................................................................ 133 Car Radar .................................................................................................... 133

Transmission Guides ...................................................................... 133 Waveguides ................................................................................................. 133

Dielectric Waveguide ................................................................................. 134 Image Guide ................................................................................................ 134 Insular Guide ............................................................................................... 135 Non-Radiative Dielectric (NRD) Guide ..................................................... 135 Insert Dielectric Guide (IDG) ..................................................................... 135 Microstrip ................................................................................................... 136 Suspended Substrate Stripline .................................................................... 138 Coplanar Lines ............................................................................................ 138 Slot-line ....................................................................................................... 139 Fin-line ........................................................................................................ 139 E-plane Circuits .......................................................................................... 140 Summary ..................................................................................................... 141

Diode Connection ............................................................................ 142 Whisker ....................................................................................................... 142 Beam-lead ................................................................................................... 143 Comparison ................................................................................................. 144

Semiconductors ......................................................................... 145

Introduction ..................................................................................... 145

Basic Principles ............................................................................... 146 Energy Band Model .................................................................................... 146 Self-Conduction .......................................................................................... 147 Semiconductor - Isolator - Metal ................................................................ 147 Recombination ............................................................................................ 148 Disturbance Conductance ........................................................................... 148 Total Current ............................................................................................... 149 The p-n Junction ......................................................................................... 150 Fermi Level ................................................................................................. 152 Energy Band Model of a p-n Junction ........................................................ 152 Reverse Biased (Blocked) ........................................................................... 153 Forward Biased (Conducting) ..................................................................... 154 Injection of Charge Carriers ....................................................................... 155 Electrical Breakdown .................................................................................. 155 Avalanche Effect (Impact Ionization) ......................................................... 155 Tunnel Effect .............................................................................................. 156

Tunnel Diode ................................................................................... 156 Function ...................................................................................................... 157 Comparison with a Normal p-n Diode ........................................................ 159

Back Diode ....................................................................................... 160

Schottky-Barrier ............................................................................. 161

Function ...................................................................................................... 162 Forward Bias ............................................................................................... 163 Reverse Bias ............................................................................................... 164 Switch Characteristics ................................................................................ 164 Hole Current ............................................................................................... 165 Other Transitions Between Metal and Semiconductor ............................... 165 Metal Connections of Semiconductor Components ................................... 166 Low Barrier Schottky .................................................................................. 167 Zero-Bias Schottky ..................................................................................... 167 Physical Design ........................................................................................... 168 Advantages .................................................................................................. 169 Application Areas ....................................................................................... 169

Planar Doped Barrier (PDB) Diode............................................... 169

PIN Diode ......................................................................................... 170 Control ........................................................................................................ 171 Microwave .................................................................................................. 172 Variable Resistance .................................................................................... 172 Frequency Limit .......................................................................................... 172 Mathematical Description ........................................................................... 173 Switching .................................................................................................... 174 Delay ........................................................................................................... 174 Switching Time ........................................................................................... 174 Faster Switching ......................................................................................... 175 Maximum Power ......................................................................................... 176 Distortion .................................................................................................... 176 Limiting ...................................................................................................... 177

Varactor ........................................................................................... 177 Depletion Layer Capacitance ...................................................................... 177 Diffusions Capacitance ............................................................................... 178 Doping Profile............................................................................................. 179 Abrupt Transition........................................................................................ 180 Hyper Abrupt Transition ............................................................................. 180 Step Recovery Transition ........................................................................... 181 Losses, Q-Value .......................................................................................... 182 Output Power .............................................................................................. 183

Step Recovery .................................................................................. 184 Mode of Operation ...................................................................................... 185 Application Areas ....................................................................................... 187

Gunn ................................................................................................. 187 Description .................................................................................................. 187

Impatt ............................................................................................... 189 Output Power at Different Frequencies ...................................................... 190

Diode Summary ............................................................................... 191

Bipolar Transistor ........................................................................... 192 Construction ................................................................................................ 194 Effective Emitter Area ................................................................................ 194 Emitter Resistance ...................................................................................... 195 Cut-off Frequency ....................................................................................... 195 Matching ..................................................................................................... 196 Balanced Transistors ................................................................................... 196

Hetero Junction Bipolar Transistor (HBT) .................................. 197 Power .......................................................................................................... 198 Input Impedance .......................................................................................... 199 Intermodulation ........................................................................................... 199

FET Transistor ................................................................................ 199 FET for Microwaves ................................................................................... 200 Dimensions ................................................................................................. 201 Short Channel ............................................................................................. 201 Higher Current ............................................................................................ 202 Higher Breakdown Voltage ........................................................................ 202 Heavily Doped Source and Drain ............................................................... 203 Multi Chip ................................................................................................... 203 Cooling ........................................................................................................ 203 Dual Gate FET ............................................................................................ 203

Hetero Junction FET ...................................................................... 204 Spacer.......................................................................................................... 206 Advantages .................................................................................................. 206 Disadvantages ............................................................................................. 206 Performance ................................................................................................ 207

Pseudomorfic HFET ....................................................................... 207 Double Channels ......................................................................................... 208

Pulse Doping .................................................................................... 209 Pulse Doped PFET ...................................................................................... 210

Metamorphic HFET ....................................................................... 211

Summary of Transistors ................................................................. 212

Ferrites ....................................................................................... 215

Introduction ..................................................................................... 215

Isolator ........................................................................................................ 215 Circulator .................................................................................................... 215 Transmitter and Receiver Switch ................................................................ 216 Phase Shifter ............................................................................................... 216 Ferrite Switch .............................................................................................. 217 YIG Filter .................................................................................................... 217

Theory .............................................................................................. 217 An Atoms Magnetic Moment ..................................................................... 217 Different Magnetic Materials ..................................................................... 218 Dia-Magnetic .............................................................................................. 218 Para-Magnetic ............................................................................................. 218 Ferro-Magnetic ........................................................................................... 218 Anti-Ferro-Magnetic ................................................................................... 219 Ferri-Magnetic ............................................................................................ 219 Ferrite Crystals ............................................................................................ 219 Gyro Magnetic Resonance .......................................................................... 219 Electromagnetic Wave in Ferrite ................................................................ 220 Low Field Loss ........................................................................................... 221 Resonance Loss........................................................................................... 221 Electromagnetic Wave in Ferrite with Strong DC Magnetic Field ............ 221 Resonance Peak .......................................................................................... 223 Below Resonance ........................................................................................ 223 Above Resonance ....................................................................................... 223 Faraday Rotation ......................................................................................... 224

Isolator ............................................................................................. 225 Faraday Isolator .......................................................................................... 225 Resonance Isolator ...................................................................................... 226 Field Displacement Isolator ........................................................................ 227

Circulator ......................................................................................... 228 Y-Circulator ................................................................................................ 228 Discrete Miniature Circulator ..................................................................... 230 Y-Circulator in a Waveguide ...................................................................... 231 Circulator with Fixed Phase Shifter ............................................................ 232 Comparison ................................................................................................. 233

Ferrite Switch .................................................................................. 234

Phase Shifter .................................................................................... 234

YIG Filter ......................................................................................... 235 Function ...................................................................................................... 236 Q-value and Bandwidth .............................................................................. 237 Frequency Region ....................................................................................... 237

mm-wave ..................................................................................................... 238 Temperature Dependence ........................................................................... 239 Settling Time............................................................................................... 239 FM-Coil ...................................................................................................... 239 Balanced Loop ............................................................................................ 240 Selectivity ................................................................................................... 240 Closed-Loop Adjustment ............................................................................ 241 Notch Filter ................................................................................................. 242

Hybrids ...................................................................................... 245

Rat Race ........................................................................................... 246 Power Division ........................................................................................... 247 Bandwidth ................................................................................................... 248 Slot-Line Ring ............................................................................................. 249

Branch Line ..................................................................................... 251 Phase Relation ............................................................................................ 251 Coupling ...................................................................................................... 252 Impedance Transformation ......................................................................... 252 Coupler with Several Sections .................................................................... 253 Double Centre Line ..................................................................................... 253 Larger Bandwidth ....................................................................................... 254 Extremely Wide Lines ................................................................................ 254 Extremely Narrow Lines ............................................................................. 255

Backward Coupler .......................................................................... 255 Phase Shifting ............................................................................................. 256 Amplitude Variation ................................................................................... 257

Wide Band Directional Coupler .................................................... 258 In-line .......................................................................................................... 258 Tandem ....................................................................................................... 259 Comparison between In-Line and Tandem ................................................. 259 Asymmetrical Coupler ................................................................................ 260 Non-Uniform Directional Coupler .............................................................. 260

Compensation of Phase Velocities ................................................. 262 Odd and Even Modes .................................................................................. 262 Dielectric Sheet ........................................................................................... 263 Compensating with Double Substrate......................................................... 263 Capacitance in the Ground Plane ................................................................ 263 Podell Coupler ............................................................................................ 264 Capacitive Compensation ........................................................................... 264 Meander Coupling ...................................................................................... 265

Microstrip with 3 dB coupling ....................................................... 265 Broadside Coupling .................................................................................... 266 Vertical Laminate ....................................................................................... 266 Lange Coupler ............................................................................................. 267 Tandem-Coupler ......................................................................................... 268 Strip/Slot Coupler ....................................................................................... 269 Re-Entrant ................................................................................................... 269 Slot Coupling Through Intermediate Ground Plane ................................... 270

Hybrid for Crossing Lines.............................................................. 272

Comparison...................................................................................... 273 Partial Over-Lapped Lines .......................................................................... 273 Comparison between Different Couplers ................................................... 274

180 Hybrid ..................................................................................... 274 Schiffman .................................................................................................... 275 Cascading .................................................................................................... 276 Asymmetric Non-Uniform Coupler ............................................................ 276 Reflection from 90 Hybrid & 180 Hybrid ............................................... 277

Reduced Line Lengths .................................................................... 278 Branch-Line ................................................................................................ 278 Rat-Race ...................................................................................................... 279 Open Stubs .................................................................................................. 279

Discrete Components ...................................................................... 280 Branch-Line ................................................................................................ 280 Rat-Race ...................................................................................................... 281 Back Wave Coupler .................................................................................... 281 Phase Shifting Net ...................................................................................... 282

RF Hybrids ...................................................................................... 283 Wire-Line .................................................................................................... 283 Transformer as a 180 Hybrid .................................................................... 283 Directional Coupler with Transformers ...................................................... 284

Specifications ................................................................................... 284 Coupling ...................................................................................................... 284 Directivity ................................................................................................... 285 Isolation ...................................................................................................... 285 Losses.......................................................................................................... 285 Coupling Loss ............................................................................................. 285 Directional Coupler .................................................................................... 286 Hybrid ......................................................................................................... 286 Power Divider ............................................................................................. 286

Applications ..................................................................................... 287 Transmitter Testing ..................................................................................... 287 Receiver Testing ......................................................................................... 288 Reflection Coupling with a 90 Hybrid ...................................................... 288 Balanced Detector ....................................................................................... 289 Reflection Amplifier ................................................................................... 289 Phase Shifter ............................................................................................... 289 Attenuator ................................................................................................... 290 Parallel Coupling with Two 90 Hybrids ................................................... 290 Balanced Amplifier ..................................................................................... 290 Balanced Mixer ........................................................................................... 291 Double Balanced Mixer .............................................................................. 291

Summary .......................................................................................... 292

Power Dividers .......................................................................... 293

Various Circuit Designs .................................................................. 293 Resistive Power Divider ............................................................................. 293 T-Junction ................................................................................................... 294 Reactive Power Divider .............................................................................. 294 Wilkinson Power Divider ........................................................................... 295 Several Combined Sections of the Wilkinson Power Divider .................... 296 Wilkinson with Different Power Divisions ................................................ 297 Continuously Decreasing Wilkinson .......................................................... 297 Comparison between Wilkinson and a 90 hybrid ..................................... 298 Division with Different Phase .................................................................... 299 Three Outputs ............................................................................................. 300 Several Outputs ........................................................................................... 300 Millimeter Wave ......................................................................................... 301 Division to Lines in Parallel Respective Series .......................................... 303

Discrete Components ...................................................................... 304 RF Power Divider ....................................................................................... 305

Power Combiner ............................................................................. 305

Power Splitter .................................................................................. 307

Summary .......................................................................................... 309

Filters ......................................................................................... 311

Basics ................................................................................................ 311 Lumped Components .................................................................................. 312 Distributed Components ............................................................................. 313 Resonator .................................................................................................... 314

Filter Dimensioning .................................................................................... 316

Low-Pass Filter ................................................................................ 317 Coplanar Line ............................................................................................. 318 Suspended Substrate Stripline .................................................................... 320 Waveguide .................................................................................................. 321

High-Pass Filter ............................................................................... 322

Band-Pass Filter .............................................................................. 323 End Coupled ............................................................................................... 323 Side Coupled ............................................................................................... 324 Overtones with Side Coupling .................................................................... 325 Compact Side Coupling .............................................................................. 326 Open Loop Resonator ................................................................................. 327 Direct Coupled Stub Filter .......................................................................... 328 Combination of Low-Pass and High-Pass .................................................. 331 Interdigital Filter ......................................................................................... 331 Comb-Line Filter ........................................................................................ 332 Design ......................................................................................................... 333 Connections ................................................................................................ 333 Tuning ......................................................................................................... 335 Aperture Coupling ...................................................................................... 336 Suspended Substrate Stripline (SSS) .......................................................... 337 Semi-Discrete Resonators ........................................................................... 337 Multi-Layer Board ...................................................................................... 338 Coplanar Line ............................................................................................. 339 Size Reduction from /2 to /4................................................................... 340 Direct Connection to Coplanar Line ........................................................... 341 Connection with Stepped Impedance ......................................................... 341 Stepped Impedance Resonator (SIR) .......................................................... 342 Extremely Large Bandwidths ..................................................................... 344

Waveguide Filter ............................................................................. 345 Cavity in the Waveguide ............................................................................. 345 Coupling between Cavities ......................................................................... 347 Combination of Low-Pass and High-Pass .................................................. 351 Substrate Integrated Waveguide Cavity (SIW) ........................................... 352

Evanescent Mode............................................................................. 353

Tubular Filter .................................................................................. 356

Helix Filter ....................................................................................... 357 /2 Resonator .............................................................................................. 358

Comparison...................................................................................... 358

Symmetry .................................................................................................... 360 Q-Value ....................................................................................................... 361

Coupling Factor............................................................................... 362 Coupling Factor Size .................................................................................. 365 Coupling Factor Sign .................................................................................. 365 Coupling at the Input, Qe ............................................................................ 366

Notch Filter ...................................................................................... 367 Tandem Coupled Stubs ............................................................................... 370 Spur-Line Filter........................................................................................... 371 Coplanar Line with Shorted Series Stub ..................................................... 372 Coplanar Line with Open Series Stub ........................................................ 372 Coplanar Line with Series Stub in the Ground Plane ................................. 373 Waveguide .................................................................................................. 373

Transmission Zeros ......................................................................... 375 Low-Pass Filter with Transmission Zero .................................................... 375 Band-Pass Filter with External Zeros ......................................................... 381 Several External Zeros ................................................................................ 383 Transmission Zero from Direct Connection ............................................... 385 External Zero Resonator in a Waveguide ................................................... 387

Cross Coupling ................................................................................ 387 Triplet Cross Coupling ............................................................................... 388 Quadruple Cross Coupling.......................................................................... 390 Linear Phase ................................................................................................ 390 6-pole Filter................................................................................................. 391 Canonical Cross Coupling .......................................................................... 392 Cascaded Cross Couplings.......................................................................... 393 Cross Coupling in Microstrip ..................................................................... 393 Reactance in Series with the Resonators .................................................... 394 Waveguide .................................................................................................. 395 Doublet........................................................................................................ 396 Doublet with Higher Mode ......................................................................... 397

Dual Behaviour Filter ..................................................................... 398

Dielectric Filter ................................................................................ 400

Dual Mode Filter ............................................................................. 404

Multiplexer ...................................................................................... 406 Diplexer ...................................................................................................... 407 Comb-Line Diplexer ................................................................................... 408 Fin-Line Diplexer ....................................................................................... 408 Bifurcated Diplexer .................................................................................... 409

Cascade Coupling ....................................................................................... 409 Common Division Point ............................................................................. 410 Combined Division ..................................................................................... 411 Manifold ..................................................................................................... 411 Multi-Coupler (Combiner) .......................................................................... 413 Circulator Coupling .................................................................................... 414 Hybrid Coupled Filters ............................................................................... 415 Ring Filter ................................................................................................... 417

Voltage Controlled Filter ................................................................ 418 Control Voltage .......................................................................................... 419 Intermodulation and Power Level ............................................................... 419 Tuning Speed .............................................................................................. 419 Linearity ...................................................................................................... 419 Bandwidth ................................................................................................... 420 Losses.......................................................................................................... 420 Stop Band .................................................................................................... 420 Digital Control ............................................................................................ 420 Digital Control Filter Bank ......................................................................... 420

Summary .......................................................................................... 421

Introduction - 1

Introduction

Microwave Frequency Band

Microwaves are electromagnetic waves with a wavelength shorter than radio/TV but

longer than light waves. Microwave wavelength is between 1 cm and 1 m which

means that with practical dimensions; components can be designed utilizing the

wavelength characteristics.

Normally, the frequency is specified instead of the wavelength. Frequency range is

approximately from 0.5 GHz to 20 GHz. Microwave frequency band is usually

divided into several smaller frequency bands. A common sub division uses the octave

bands.

Frequency Band Frequency

Designation (GHz)

UHF 0.5 - 1

L 1 - 2

S 2 - 4

C 4 - 8

X 8 - 12

Ku 12 - 18

The letter designations can vary since there are several different designations for

reserved frequency bands. The same letter designation can have different frequency

bands so it is wise to specify the frequency limits as well. Frequency band

designations should only be used when it is clearly understood which frequency band

will be used.

Frequency band for radar and communication are significantly narrower. Working

with radar in the X-band usually is a narrow frequency area around 9 GHz. There are

components and measurement equipment which can handle a decade frequency range

which will cover the whole microwave frequency band.

2 - RF & Microwave Engineering Comprehensive Guide: Passive Components

Electromagnetic Spectrum Divisions

km100

10

1

100

10

1

10

1

1

100

10

1

100

10

1

0.1

m

cm

mm

µm

Å1000

3

30

300

3

30

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3

30

300

3

kHz

MHz

GHz

THz

Wavelength Frequency

LF

MF

HF

UHF

Microwave

mm-wave

sub-mm

IR

Visible light

UV

X-Ray

Gamma

Radio

TV

Radar &Communication

Electro optics

1 Å (Ångström) = 10 m-10

Figure 1 – Electromagnetic spectrum

Microwave is well established definition for approximately 1 to 18 GHz. Each band

is basically sorted according to the wavelength in either cm or dm. Frequency region

for mm-waves corresponds to the wavelengths in mm; mm-waves have shorter

wavelength than microwaves.

Introduction - 3

Advantages with Microwaves

Main advantages of microwaves are the large information capabilities and the small

antenna size with good directivity.

100

10

1

10

1

m

cm

3

30

300

3

30

MHz

GHz

wavelength

MHz

MHz

GHz

frequency

2

200

20

km

cm

m

20 m

2 m

5

50

500

2 000

50 000

200 000

2

25

100

antenna diameterto achieve 3.5°lobe width

telephonechannels

TVchannels

1 % bandwidth

Figure 2 – Frequency, wavelength and bandwidth

Sometimes a directional antenna is required for positioning towards a specific object.

Directivity of an antenna is proportional to the antennas size in wavelengths. With

microwaves, a good directional antenna with reasonable dimensions is obtainable.

Different frequencies are affected individually with wave propagation effects and

when passing through components. To avoid that the signal information is distorted

the percentage of occupied bandwidth should remain small. Within microwaves it is

possible to fit a large amount of information in 1% of bandwidth. The number of

channels that can be fitted in the bandwidth depends on the method of modulation.

Figure 2 illustrates an average number of channels that can be employed at a given

frequency. At the lower frequencies it can be seen that the amount of information

bandwidth is not practical compared to the higher frequencies.

4 - RF & Microwave Engineering Comprehensive Guide: Passive Components

Radio Frequency Region

Noise temperature

500 K

200 K

100 K

50 K

20 K

10 K

5 K

2 K

0.1 5 100.2 10050

frequency

GHz20210.5

Galactic N

oise

Atmosphere

attenuation

Figure 3 – Noise across the radio transmission region

Electron noise decreases with increased frequency; therefore, the frequency should

be increased as much as possible. To avoid that the signal is attenuated too much

through the atmosphere, the frequency should be kept below approx. 20 GHz. This

region between approx. 1 - 20 GHz is known as microwave.

2 GHz Threshold

300

frequency

GHz110 MHzDC 100 MHz 2 18

Radar video

Baseband RF µ-wave mm-wave

BipolarFET

Figure 4 – Frequency spectrum divided according to design principles

One method to divide the frequency spectrum is according to the design principles

employed and existing broadband systems. Traditional circuit design with discrete

components has worked well up to about 2 GHz; the bandwidth is typically from 10

Introduction - 5

MHz to 2 GHz. Distributed components are common with the wavelength

determining the components function for frequencies higher than 2 GHz. Up to 2

GHz, it is common with the bipolar transistor. Around 2 GHz threshold, the most

common FET is the MOSFET in Silicon CMOS (Complementary Metal Oxide Semi-

conductor) processes. For frequencies much greater than 2 GHz then the FET

transistor uses a gallium-arsenide (GaAs) process.

Video is the detected radar pulse which can go down to DC. The video signal has

normally a bandwidth of approx. 1 - 10 MHz. Very short pulses contain higher

frequency contents up to 1 GHz. Within communication the detected signal is known

as baseband. Audio sound has a small bandwidth; TV/Video has approx. 6 MHz

bandwidth. Digital signals have normally a speed up to 140 Mb/s but there are also

systems for Gb/s data transfer.

Applications

Radar

Radar measures the time difference between the transmitted and received signal

which is a measure of the distance. Normally the RF signal is pulsed to obtain a high

power and simple time measurement. The frequency can also be swept (FMCW) to

distinguish the transmitted and received signal. This gives a high resolution when

measuring the distance. Radar systems use antennas with a high directivity. With

high directivity the environment surroundings can be established.

Radar is used to maintain surveillance and track airplanes in the environment. With

radar systems, the airplane can be tracked at great distances despite the time of day or

weather conditions. Radar is also used to navigate ships between islands and other

ships. Height radar has a fixed antenna directed towards the ground. Weather radar

keeps surveillance over traitorous weather conditions so these regions can be avoided

to give a safer flight conditions. Doppler radar can distinguish between different

speeds. Airplanes can then be distinguished from strong ground reflections. Impulse

radar (very short pulse) can be used to see objects underneath the ground or via a

drilled hole find cracks or air pockets in bedrock.

6 - RF & Microwave Engineering Comprehensive Guide: Passive Components

Radio Link

Radio links are used for data transport of a large number of telephone channels, or

transport of radio and TV programs. Data transfer is from ”Point to Point” (P-P) in a

long chain, or ”Point to Multi Point” (P-MP) where a central station has simultaneous

contact with several radio stations. P-MP is also the term for systems with a link

station sending radio and TV programs direct to homes.

Communication within 1 to 3 GHz band is used in several countries for mobile use

and to P-MP systems. Long distance links with high capacity normally use the 4 GHz

and 6 GHz band (3.4 to 4.2 GHz, 5.925 to 6.425 GHz and 6.430 to 7.11 GHz). This is

a good compromise between range distance, capacity, quality, wave propagation and

cost.

In cities, there is a need for higher data rates so the bands 15 GHz, 18 GHz and 23

GHz (14.3 - 15.35 GHz, 17.7 – 19.7 GHz & 21.2 – 23.6 GHz) are utilized. Generally,

2 Mb/s data rate is used but 8 Mb/s, 34 Mb/s and 140 Mb/s are available as well.

With Synchronous Digital Hierarchy (SDH) the data rate is 155 Mb/s. Future digital

systems have a capacity of 622 Mb/s and 2.5 Gb/s.

Satellite TV

Television programs sent from satellite direct to the home.

TVRO Television Receive Only in USA at 3.7 - 4.2 GHz.

DBS Direct Broadcast Satellite in Europe and Japan at 12 GHz band (10.7 –

12.75 GHz). Up-link operates at 12.75 – 13.25 GHz and 14.0 – 14.8

GHz.

HDTV High Definition TV concept is to send from a satellite at 17.3 – 17.8

GHz in America and 21.4 - 22 GHz for other regions in the world.

Wireless Data Networks

Wireless LAN, WLAN. Computer networks can be interconnected with microwaves

instead of using cables; this gives a simpler and quicker installation especially for

temporary or mobile applications. However, this is not a full replacement for cables

since the disadvantages are limited bandwidth (data rates), more disturbances and

higher costs.

IEEE 802.11 specifications are primarily for WLAN in the ISM band 2.4 GHz (2.400

- 2483 MHz). It is also possible to use the 5 GHz band (5150 - 5350 MHz and 5470 -

5725 MHz), IEEE 802.11ac standard and 60 GHz (IEEE 802.11ad). Finished

Introduction - 7

products which are tested and compliant are called Wi-Fi. The maximum data rate for

2.4 GHz (IEEE 802.11g) is up to 54 Mb/s and for 60 GHz up to 6.912 Gb/s.

Mobile Telephones

The majority of systems for mobile telephones have started with the frequency band

900 MHz. In order to handle the need of increased telephone channels, higher

frequency bandwidths have been introduced to compliment the demand. GSM system

is standard within Europe and is the most common system in the world. The exact

frequency bands can differ depending on the region.

1G First generation of mobile system based upon analogue non-encrypted

techniques with a channel bandwidth up to 30 kHz. The Nordic region

used NMT.

2G Second generation of mobile system based upon digital encrypted

techniques with a channel bandwidth up to 200 kHz. GSM is the most

common standard at the 900 MHz band and CDMA standard is

employed in the U.S. at the 800 MHz band. For higher capacity GSM is

also applied at the 1800 MHz band. In U.S. it is known as Personal

Communication Network (PCN) at the 1900 MHz band

3G Third generation of mobile system designed for mobile broadband data

which uses 1920-1980 MHz up-link and 2110-2170 MHz down-link.

4G Fourth generation mobile system uses a very flexible modulation at the

air interface and a network that can handle a user data rate of 100Mb/s.

It can be used in any frequency band that is intended for mobile

communication.

LEO Low Earth Orbit is a satellite system under development which targets

the rural areas which are not covered by the existing base stations. This

system is a viable option for developing countries which do not have an

existing mobile infrastructure.

Mobile telephones operate at 1610 - 1626.5 MHz or 2483.5 - 2500 MHz.

Globestar is a system which uses 48 satellites, each with 6 fixed antenna

lobes.

Heating and Drying

There are large microwave ovens for industrial use, up to 10 or 100 kW. Small

microwave ovens for households are at 300 - 1000 W. The frequency is typically 2.45

GHz.

8 - RF & Microwave Engineering Comprehensive Guide: Passive Components

RFID

RF Identification or commonly known as RF tags. Microwave can be used for

identification and automatic transfer of data. A fixed unit can transmit a query

request which can be answered by a simpler transponder tag when in the vicinity.

Transponders can be active. SART (Search and Rescue Transponder) is an

emergency transmitter for lifeboats which give a clear indication on radar. They can

also be passive and very simple. Shoplifting protection devices are normally small

patches that contain an antenna and a diode which radiate overtones when they are in

the vicinity of the transponders placed at the shop entrance. Same principle is also

used in ski equipment to search for skiers after an avalanche.

Transponder can contain a memory for more precise identification and information.

Car factories use transponders to inform about the assembly. To simplify logistics for

transport storage containers when located in large harbour ports. Railway carriages

and locomotives use RFID to keep track of their location. Their location can still be

read even when passing at 320 km/hr.

There are systems at very low frequencies (<500 kHz) and at mid-high frequencies

(1.7 - 28 MHz). Microwaves mostly use 908 - 920 MHz, 1812 - 1830 MHz and 2.45

GHz. Compared with bar-code readers, RFID works at longer distances and does not

need to be visible; data can be read whilst passing, insensitive for dirt, rain and heat.

Car Tolls

RFID is also used in car tolls for use of roads which are chargeable. Payment occurs

automatically when passing by without the need to stop. Digital transfer of

information occurs with FSK, PSK or ASK. Data speed is in the region of 1 - 3 Mb/s.

Frequency range which is used is 2400 – 2483.5 MHz and 5850 - 5925 MHz. In

Europe (CEPT-91) 5795 - 5805 MHz which possibly shall be expanded to 5815

MHz.

GPS

Global Positioning System (GPS) is a system for navigation which is based around

24 satellites. Each satellite sends a coded signal at 1575.42 MHz. The satellite

contains an atom clock which deviates maximum a second every 300 000 years. The

transmitted signal is therefore well defined with respect to time. A receiver measures

the time when the transmitted signal is received and a calculation can be made to

determine the distance to the satellite. By measuring the distance to three satellites,

the position including height can be determined. By using a fourth satellite, the error

can be compensated for in the receiver since this is only based on a quartz oscillator.

Introduction - 9

The civilian available code (SPS) has an accuracy of approx. 100 m. Differential

GPS contains a fixed receiver of a known position which sends out correction data to

the nearby GPS users which improves the SPS accuracy so that a few meters can be

achieved. SPS broadcasts at a single frequency and the military version (PPS) uses

two frequencies. The accuracy of both the civilian system and military system are

similar but the security and susceptibility to interference is greater for the military

system.

Navigation for Cars

Navigation equipment determines your locational position and indicates how to

navigate to arrive at a specific destination. The system can contain a calculation of

movement with help of the wheel revolutions, together with a gyro compass (dead

reckoning). The accuracy is 2 % of the distance travelled. To determine the position,

then the map has to be matched to the position. i.e. only a probable position is

indicated. The most common systems today use GPS navigator with stored digital

maps.

Traffic, local maps and the "yellow pages" (restaurants, shops, companies, etc.) can

be transmitted by FM radio to get wide coverage or with the nearest base station for

mobile phone for better adaptation locally. It is also likely to use local radio beacons

in the mm-wave band for correcting the position and transmission of information.

Police Radar

Police radar is used to measure the vehicle speed. It uses the Doppler displacement

when something moves. The wavelength is compressed when the car approaches and

stretched out when leaving. Doppler frequency is a measure of the velocity. Many

systems have used a signal at X-band, such as 9.41 or 10.525 GHz. Newer systems

use e.g. 34.3 or 24.15 GHz.

Fixed Wireless Access

Fixed Wireless Access (FWA) is a system which sends to several receivers

simultaneously. It is similar to satellite TV but with the transmitter station on the

ground. The main function is based upon a 2-way system which can be utilized for

internet and interactive TV. Up-link is at 3410 - 3494 MHz and down-link at 3510 -

3594 MHz. Systems for FWA is using specifications such as WiMAX.

10 - RF & Microwave Engineering Comprehensive Guide: Passive Components

Motion Detector

The motion detector utilizes Doppler shift during movement. Doppler modules are

used for automatic door openers, elevator control, intrusion alarm, traffic light and

measurement of vibration on large machines.

Material Measurement

A materials dielectric value, dimension or displacement can be calculated by

measuring the relative change in frequency, phase or amplitude. Measurement takes

place without contact at a distance. Unfortunately, the measurement result is affected

by several variables, such as temperature, density and moisture. Therefore

measurements must use several parameters, such as resonance frequency and Q-value

or phase and amplitude, or several frequencies, or a combination with other

measurement techniques.

The resonance is measured (i.e. frequency and Q-value) so that the dielectric value

(r) can be determined. By measuring the dielectric value in a blended composition,

the proportions of the composition can be determined. The dielectric value for a

material is humidity dependent; therefore the humidity in a material can be measured

and controlled. This is critical for materials where the price is based on weight such

as paper, wood, soap and food.

Phase measurement can be used to read a very small movement. A metal sheet (1-10

mm) can be measured with an accuracy of 0.03 mm. The measurement time is only

20 ms. The measurement can therefore be used to automatically maintain the correct

thickness during manufacture.

FMCW (Frequency Modulated Continuous Wave) radar can be used to measure the

level of a tanker, with a precision of a few mm.

Some systems measure the phase and amplitude between the two antennas used in a

transmission system. Alternatively, the amplitude and phase of the reflection from

only one antenna can be measured. A typical sensor is a coaxial wire which is held

against the object.

ISM-bands

ISM: Industrial, Scientific, Medical. Frequency bands which can be used without a

license providing that the regulations are followed. When using spread spectrum

techniques, a maximum of 1W can be transmitted.

The most common ISM bands are 433-435 MHz, 862-869 MHz, 902-928 MHz,

2400-2484 MHz, 5250-5350 MHz, 5725-5850 MHz and 24-24.25 GHz.