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A fulsome exploration of critical considerations in microwave circuit noise
In A Guide to Noise in Microwave Circuits: Devices, Circuits, and Measurement, a team of distinguished researchers deliver a comprehensive introduction to noise in microwave circuits, with a strong focus on noise characterization of devices and circuits. The book describes fluctuations beginning with their physical origin and touches on the general description of noise in linear and non-linear circuits.
Several chapters are devoted to the description of noise measurement techniques and the interpretation of measured data. A full chapter is dedicated to noise sources as well, including thermal, shot, plasma, and current.
A Guide to Noise in Microwave Circuits offers examples of measurement problems—like low noise block (LNB) of satellite television – and explores equipment and measurement methods, like the Y, cold source, and 7-state method. This book also includes:
Perfect for graduate students specializing in microwave and wireless electronics, A Guide to Noise in Microwave Circuits: Devices, Circuits, and Measurement will also earn a place in the libraries of professional engineers working in microwave or wireless circuits and system design.
Dr. Peter Heymann, retired, was the head of the microwave measurement laboratory at the Ferdinand-Braun-Institut (FBH), Leibniz-Institute for High Frequency Technology in Berlin.
Dr. Matthias Rudolph, is Ulrich L. Rohde Professor for RF and Microwave Techniques at Brandenburg University of Technology in Cottbus, Germany. He heads the low-noise components laboratory at the FBH.
Author Biographies xiii
Preface xv
1 Introduction 1
Preliminary Remarks 1
History 6
References 7
2 Basic Terms 9
Average Values 9
Amplitude Distribution 10
Autocorrelation 12
Cross-Correlation 15
Noise Spectra 18
Autocorrelation Function and Spectral Power Density 19
Band-Limited Noise on the Spectrum Analyzer 20
References 22
3 Noise Sources 23
Thermal Noise 23
Nyquist Formula and Thermal Radiation 24
Validity and Experimental Confirmation of the Nyquist Formula 27
Thermal Noise Under Extreme Conditions 28
Shot Noise 29
Plasma Noise 33
Current Noise of Resistors and Contacts 34
Technical Resistors 34
Resistors Consisting of Semiconductor Material 36
Contact Noise 37
Generation–Recombination Noise 38
LF Noise from Transistors 40
References 42
4 Noise and Linear Networks 45
Narrowband Noise 45
Calculating with Phasors 45
Noise Source with Complex Internal Resistance 51
The Equivalent Noise Bandwidth 52
Network Components at Different Temperatures 54
Noise Generator and Attenuator 58
References 58
5 Nonlinear Networks 59
Mixing 59
Band-Limited RF Noise at Input 59
Amplitude Clipping 62
The Detector as a Nonlinear Network 63
The Noise Spectrum Behind a Quadratic Detector 65
The Noise Spectrum Behind a Linear Detector 69
The Sensitivity Limit 70
Noise with Signal 73
The Phase Sensitive Rectifier 74
Trace Averaging 76
References 78
6 The Noise Factor 79
Amplifier and Noise Power 79
The Noise FactorF 80
Cascaded Amplifiers 83
The Noise MeasureM 85
Definitions of Gain 85
Source and Load 89
Broadband and Spot Noise Factor 91
Noise Factor of a Passive Network 92
Antenna Temperature 93
The Reference Temperature T0 = 290 K 98
Noise Factor and Detection Limit 99
References 100
7 Noise of Linear Two-Ports 101
Representation of Two-Ports 101
Noise Modeling Using the Chain Matrix 102
References 108
8 Calculation Methods for Noise Quantities 109
Noise Voltages, Currents, and Spectra 109
Calculating with Current, Voltage, and Noise Waves 112
The Noise Correlation Matrix 115
The Correlation Matrix of Passive Components 117
The Noise of Simple Passive Networks 119
Transformation of Noise Sources in Different Network
Representations 128
Correlation Matrix and IEEE Elements 131
FET-Like Network with the Y-Correlation Matrix 134
Noise Sources at Input with ABCD Correlation Matrix 138
References 142
9 Diodes and Bipolar Transistors 143
Semiconductor Diode 143
Bipolar Transistor 145
Small-Signal Equivalent Circuit 147
Hawkins BJT Noise Model 148
Two Approaches for the Collector Noise Current Source 155
BJT Noise Model with Correlation Matrices 157
The Π-Model 157
The T-Model with Correlation Matrices 161
Transformation of the Y-Sources to the Input 165
Modeling of a Microwave Transistor with Correlation Matrices 168
Simplest Π-Model 174
Contour Diagram 177
Transistor in the Circuit 179
Using the Contour Diagram 183
References 185
10 Operational Amplifier 187
Operational Amplifier as Circuit Element 187
Noise Sources of the Operational Amplifier 188
Consideration of 1/f Noise 193
Operational Amplifier as an Active Low-Pass Filter 195
References 198
11 Field Effect Transistors 201
JFET 201
Mode of Operation of the FET 201
The Channel Noise 204
Noise Sources at the Gate 205
The Correlation 206
Transformation to the Input 206
Simple Approximations 211
Field Effect Transistors for the Microwave Range (MESFET, HFET) 214
The Pucel Model 215
The Pospieszalski model 218
Discussion of the Results 225
Criteria for Noise Data 225
References 229
12 Theory of Noise Measurement 231
Measurements of Two-Ports 231
The Equivalent Noise Resistance 234
Voltage and Current Source 235
Voltage and Current Source with Correlation 237
3 dB and Y-Method 241
References 243
13 Basics of Measuring Technique 245
Principles of the RF-Receiver 245
The Detection Limit 245
Diode as RF Receiver (Video Detector) 249
RF and Microwave Range Receiver 254
Dicke Radiometer 258
Correlation Radiometer in the Microwave Range 261
Network Analyzer as a Noise Measurement Device 263
References 265
14 Equipment and Measurement Methods 267
Noise Measurement Receiver 267
Spectrum Analyzer 269
The Y-Method 273
Measurements in the Microwave Range 275
Selection Criteria of the Mixer 278
Image Rejection 279
Complete Noise Characterization 282
Analysis of Multi-impedance Measurements 283
Cold Source Method 285
The 7-State Method 287
On-Wafer Measurement of Cold Source 288
On-Wafer with Noise Generator According to the Y-method 293
References 296
15 Noise Generators 299
Vacuum Diode 299
Gas Discharge 300
Semiconductor Diodes 302
Excess Noise Ratio (ENR) 303
Hot–Cold Sources 305
References 307
16 Impedance Tuners 309
Impedance Transformation with Simple Methods 309
Mechanical Components for the Microwave Range 311
Electronic Components 313
Precision Automatic Tuner 315
Attenuation of the Tuner 317
References 318
17 Examples of Measurement Problems 319
Transistor in a Test Fixture 319
The Low Noise Block (LNB) of Satellite Television 322
Verification of a Noise Measurement 325
References 327
18 Measurement and Modeling of Low-Frequency Noise 329
Correlation Radiometer for Low Frequencies (f <10 MHz) 329
The Low-Frequency Noise of Transistors 333
Measurement Setup for LF Noise 334
Examples of LF Noise Measurements on GaAs-HBT 336
Modeling of LF Noise 337
The Noise of the Microphone 337
References 342
19 Measurement Accuracy and Sources of Error 345
Accuracy of Measured Data 345
Error of Measurements 345
Inaccuracies of the Noise Measurement 346
Uncertainty of the ENR Calibration 349
Noise Source Mismatch 350
T0 = 290 K Is not TOFF 352
Mismatch in the System 353
Linearity of the Receiver 356
References 357
20 Phase Noise 359
Basics 359
Reciprocal Mixing 361
Description of Phase Noise 363
Spectral Power Density of Phase Fluctuations S𝜙(f ) 364
The Single Sideband Phase Noise L(f ) 365
Spectral Power Density of Frequency Fluctuations S𝛥f (f ) 365
Excursus on Frequency and Phase Modulation 366
The Allan Variance 368
Residual FM 370
Multiplication and Division 371
Amplitude Noise 371
Phase Noise and Jitter 372
References 374
21 Physics of the Oscillator 377
Oscillation Condition [1] 377
Simple Model of the Phase Disturbance [2] 378
Phase Slope, Resonator Quality, and Frequency Stability [3] 379
The Formula of Leeson [4] 382
Components of Oscillators 384
Influence of the Varactor Diode 386
Upward Mixing of LF Noise 390
The Influence of Microwave Noise on Phase Noise 393
References 396
22 Phase Noise Measurement 399
Basic Parameters 399
Spectrum Analyzer 399
Phase Detector Method 406
The Sensitivity of the Phase Detector 407
Example Calibration and Measurement 409
Keeping the Quadrature by a PLL 410
Delay Line as Frequency Discriminator 412
The Sensitivity of the Delay-Line Method 414
Configuration and Calibration 418
Resonator as Frequency Discriminator 420
Detection Limit 421
Comparison of Measurement Systems 422
Cross-Correlation Technique 423
Amplitude Noise 425
Problems with On-Wafer Measurement 429
Residual Phase Noise 430
References 432
Appendix 435
Noise Signals and Deterministic Signals 435
Random Signals 436
Characteristic Values 437
The Probability Density Function 438
Example Sine Function 439
Example Sawtooth Voltage 440
Example White Noise 440
Example Sinusoidal Signal with Noise 441
Example Narrowband Noise 441
The Autocorrelation Function 444
Example Sine 444
Example Sawtooth 444
Example Noisy Sine 445
Example White Noise 446
Example Low-Pass Noise 447
Example Bandpass Noise 449
Fourier Series 451
Sine–Cosine Spectrum 452
Amplitude–Phase Spectrum 452
Complex Fourier Series 452
The Fourier Integral 453
Energy and Power Signals 456
Example Transient Time Function 457
The Parseval Equation 459
Example Voltage Pulse 460
Fourier Transform and Power Spectral Density 462
Example Rectangular Pulse 463
Time-Limited Noise Signal 465
Example of a Time-LimitedWave Train 466
TheWiener–Khinchin Theorem 468
Cross Correlation 470
Example of Two Sine Functions 471
Example of Two White Noise Signals 472
Example of Two Bandpass Noise Signals 472
Example White Noise and Bandpass Noise 474
Cross-Correlation After Splitting into Two Branches 474
Power Spectral Density Real and Complex 477
The Cross-Spectral Density 478
Complex Representation of the Cross-Spectral Density 479
Transmission of Noise by Networks 479
References 485
Glossary of Symbols 487
Index 491
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