1. technology and computing
2. electronic components

The Comprehensive Guide To
RF & Microwave Engineering
For Passive Components
 /4
 /4
Richard Wallace
Krister Andreasson
 /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
Designation
Frequency
(GHz)
UHF
L
S
C
X
Ku
0.5 - 1
1-2
2-4
4-8
8 - 12
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
Wavelength
100
km
Frequency
3
10
30
1
300
100
3
m
30
1
300
cm
1
LF
MF
Radio
MHz
HF
10
10
kHz
3
UHF
TV
GHz
Microwave
30
Radar &
Communication
mm-wave
1
mm
300
100
µm
3
sub-mm
THz
10
IR
1
Visible light
1000
Å
Electro optics
UV
100
10
X-Ray
1
0.1
Gamma
1 Å (Ångström) = 10-10 m
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.
frequency
3
MHz
wavelength
100
m
2
km
5
30
MHz
10
200
m
50
300
MHz
1
20
m
500
3
GHz
10
30
GHz
1
cm
2
m
20
cm
antenna diameter
to achieve 3.5°
lobe width
2 000
2
50 000
25
200 000
100
telephone
channels
TV
channels
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
Gal
100 K
Atmosphere
attenuation
c
acti
50 K
ise
No
20 K
10 K
5 K
2 K
frequency
0.1
0.2
0.5
1
5
2
10
20
50 100 GHz
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
Radar video
Baseband
RF
µ-wave
mm-wave
frequency
DC
10 MHz
100 MHz
Bipolar
1
2
18
300 GHz
FET
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 Semiconductor) 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.