Noise in high-frequency circuits and oscillators

This book examines noise phenomena in linear and nonlinear high-frequency circuits from both qualitative and quantitative perspectives. The authors explore important noise mechanisms using equivalent sources and analytical and numerical methods. Readers learn how to manage electrical noise to improve the sensitivity and resolution of communication, navigation, measurement, and other electronic systems.

Noise in High-Frequency Circuits and Oscillators has its origins in a university course taught by the authors. As a result, it is thoroughly classroom-tested and carefully structured to facilitate learning. Readers are given a solid foundation in the basics that allows them to proceed to more advanced and sophisticated themes such as computer-aided noise simulation of high-frequency circuits.

Following a discussion of mathematical and system-oriented fundamentals, the book covers:

Noise of linear one- and two-ports Measurement of noise parameters Noise of diodes and transistors Parametric circuits Noise in nonlinear circuits Noise in oscillators Quantization noise

Each chapter contains a set of numerical and analytical problems that enable readers to apply their newfound knowledge to real-world problems. Solutions are provided in the appendices.

With their many years of classroom experience, the authors have designed a book that is ideal for graduate students in engineering and physics. It also addresses key issues and points to solutions for engineers working in the burgeoning satellite and wireless communications industries.

Author Notes

Burkhard Schiek, PhD, is Professor in the Electrical Engineering Department of Ruhr-Universitat Bochum
Ilona Rolfes, PhD, is Professor in the Electrical Engineering Department of Universitat Hannover
Heinz-Jurgen Siweris, PhD, is Professor in the Electrical Engineering Department of the University of Applied Science in Regensburg

Preface	p. xi
1 Mathematical and System-oriented Fundamentals	p. 1
1.1 Introduction	p. 2
1.1.1 Technical relevance of noise	p. 2
1.1.2 Physical origins of noise	p. 2
1.1.3 General characteristics of noise signals	p. 3
1.2 Mathematical basics for the description of noise signals	p. 4
1.2.1 Stochastic process and probability density	p. 4
1.2.2 Compound probability density and conditional probability	p. 7
1.2.3 Mean value and moments	p. 7
1.2.4 Auto- and cross-correlation function	p. 9
1.2.5 Description of noise signals in the frequency domain	p. 11
1.2.6 Characteristic function and the central limit theorem	p. 13
1.2.7 Interrelationship between moments of different orders	p. 19
1.3 Transfer of noise signals by linear networks	p. 20
1.3.1 Impulse response and transfer function	p. 20
1.3.2 Transformation of the autocorrelation function and the power spectrum	p. 22
1.3.3 Correlation between input and output noise signals	p. 23
1.3.4 Superposition of partly correlated noise signals	p. 25
2 Noise of Linear One- and Two-Ports	p. 29
2.1 Noise of one-ports	p. 30
2.1.1 Thermal noise of resistors	p. 30
2.1.2 Networks of resistors of identical temperature	p. 31
2.1.3 The RC-circuit	p. 32
2.1.4 Thermal noise of complex impedances	p. 33
2.1.5 Available noise power and equivalent noise temperature	p. 34
2.1.6 Networks with inhomogeneous temperature distribution	p. 36
2.1.7 Dissipation theorem	p. 37
2.2 Noise of two-ports	p. 39
2.2.1 Description of the internal noise by current and voltage sources	p. 39
2.2.2 Noise equivalent sources for two-ports at homogeneous temperature	p. 44
2.2.3 Noise description by waves	p. 46
2.2.4 Noise of circulators and isolators	p. 47
2.2.5 Noise waves for thermally noisy two-ports at a homogeneous temperature	p. 48
2.2.6 Equivalent noise waves for linear amplifiers	p. 53
2.3 Noise figure of linear two-ports	p. 54
2.3.1 Definition of the noise figure	p. 55
2.3.2 Calculation of the noise figure based on equivalent circuits	p. 57
2.3.3 Noise figure of two-ports with thermal noise	p. 60
2.3.4 Noise figure of cascaded two-ports	p. 62
2.3.5 Noise matching	p. 65
3 Measurement of Noise Parameters	p. 73
3.1 Measurement of noise power	p. 75
3.1.1 Power measurement on the basis of a thermocouple	p. 75
3.1.2 Thermistor bridge	p. 78
3.1.3 Power measurements with Schottky-diodes	p. 79
3.1.4 Power measurements with field effect transistors	p. 82
3.1.5 Power measurements with analog multipliers	p. 84
3.1.6 Power measurements with a digital detector	p. 84
3.1.7 Power measurements with a spectrum analyzer	p. 84
3.1.8 Errors in noise power measurements	p. 85
3.2 Measurement of the correlation function and the cross-spectrum	p. 88
3.3 Illustrative interpretation of the correlation	p. 92
3.4 Measurement of the equivalent noise temperature of a one-port	p. 93
3.5 Special radiometer circuits	p. 95
3.5.1 Dicke-Radiometer	p. 95
3.5.2 Problems with mismatched devices under test	p. 97
3.5.3 Compensation radiometers	p. 101
3.5.4 Correlation radiometer	p. 107
3.5.5 Fundamental errors of noise power or noise temperature measurements	p. 110
3.5.6 Principle errors of a correlation radiometer or correlator	p. 112
3.6 Measurement of the noise figure	p. 113
3.7 Measurement of minimum noise figure and optimum source impedance	p. 115
3.7.1 Hot-cold method or paired method	p. 116
3.7.2 Cold method or unpaired method	p. 117
3.7.3 The 7-state-method	p. 119
3.8 De-embedding of the noise parameters	p. 123
3.9 Alternative determination of the noise temperature of a one-port	p. 125
4 Noise of Diodes and Transistors	p. 127
4.1 Shot noise	p. 128
4.2 Shot noise of Schottky diodes	p. 133
4.3 Shot noise of pn-diodes	p. 137
4.4 Noise of PIN diodes	p. 137
4.5 Noise equivalent circuits of bipolar transistors	p. 140
4.6 Noise of field effect transistors	p. 146
4.6.1 Static characteristics and small signal behavior	p. 146
4.6.2 Thermal noise of the inner FET	p. 151
4.6.3 Noise figure of the complete FET	p. 158
5 Parametric Circuits	p. 163
5.1 Parametric theory	p. 163
5.2 Down converters with Schottky diodes	p. 166
5.3 Mixer circuits	p. 172
5.3.1 Single diode mixer	p. 172
5.3.2 Two-diode mixer or balanced mixer	p. 173
5.3.3 Four-diode double balanced mixer	p. 175
5.4 Noise equivalent circuit of pumped Schottky diodes	p. 177
5.5 Noise figure of down-converters with Schottky diodes	p. 184
5.6 Mixers with field effect transistors	p. 186
5.7 Noise figure of down converters with field effect transistors	p. 188
5.8 Harmonic mixers	p. 189
5.9 Noise figure of harmonic mixers	p. 194
5.10 Noise figure measurements of down converters	p. 196
5.11 Noise figure of a parametric amplifier	p. 196
5.11.1 Characteristics and parameters of depletion layer varactors	p. 197
5.11.2 Parametric operation of a varactor	p. 199
5.11.3 Parametric amplifier	p. 200
5.11.4 Noise figure of the parametric amplifier	p. 203
5.12 Up-converters with varactors	p. 205
6 Noise in Non-linear Circuits	p. 207
6.1 Introduction	p. 207
6.2 Problems with the noise characterization of non-linear two-ports	p. 208
6.3 1/f-noise	p. 209
6.4 Amplitude and phase noise	p. 211
6.4.1 Noise modulation	p. 211
6.4.2 Sinusoidal amplitude and phase modulation	p. 212
6.4.3 Spectra of the amplitude and phase noise	p. 214
6.5 Normalized single sideband noise power density	p. 216
6.6 Amplitude and phase noise of amplifiers	p. 218
6.7 Transformation of amplitude and phase noise in linear two-ports	p. 221
6.8 Amplitude and phase noise in non-linear two-ports	p. 223
6.8.1 Conversion matrix	p. 223
6.8.2 Large signal amplifiers	p. 226
6.8.3 Frequency multipliers and dividers	p. 228
6.8.4 Frequency converters or mixers	p. 230
6.9 Measurement of the phase noise	p. 230
7 Noise in Oscillators	p. 235
7.1 Two-port and one-port oscillators	p. 235
7.2 Oscillation condition	p. 236
7.3 Noise analysis	p. 238
7.4 Stability condition	p. 242
7.5 Examples	p. 243
7.5.1 Two-port oscillator with transmission resonator	p. 243
7.5.2 One-port oscillator with a series resonator	p. 248
7.5.3 Voltage controlled oscillator (VCO)	p. 255
7.6 Noise in phase-locked loop circuits	p. 256
7.7 Measurement of the oscillator noise	p. 262
7.7.1 Amplitude noise	p. 262
7.7.2 Phase noise	p. 264
7.7.3 Injection locking	p. 272
7.8 Disturbing effects of oscillator noise	p. 279
7.8.1 Heterodyne reception	p. 279
7.8.2 Sensitivity of a spectrum analyzer	p. 280
7.8.3 Distance measurements	p. 281
7.8.4 Velocity measurements	p. 282
7.8.5 Transmission of information by a frequency or phase modulated carrier signal	p. 284
7.8.6 Measurement system for the microwave gas spectroscopy	p. 285
8 Quantization Noise	p. 287
8.1 Quantization noise of analog-to-digital converters	p. 287
8.2 Quantization noise of fractional divider phase locked loops	p. 289
8.2.1 Application of the Sigma-Delta modulation	p. 291
8.2.2 Multiple integration	p. 292
8.2.3 Identity of the cascade and the chain circuit	p. 295
8.2.4 Chain circuit with weighting coefficients	p. 298
8.2.5 Transient behavior of a fractional logic circuit	p. 302
8.2.6 Fractional divider without a PLL	p. 303
Appendix A Solutions to the problems of Chapter 1	p. 305
Appendix B Solutions to the Problems of Chapter 2	p. 315
Appendix C Solutions to the Problems of Chapter 3	p. 335
Appendix D Solutions to the Problems of Chapter 4	p. 355
Appendix E Solutions to the Problems of Chapter 5	p. 365
Appendix F Solutions to the Problems of Chapter 6	p. 379
Appendix G Solutions to the Problems of Chapter 7	p. 389
Appendix H Solutions to the Problems of Chapter 8	p. 401
References	p. 405
Index	p. 408

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Author Notes

Table of Contents