Guide to Noise in Microwave Circuits

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, Germany.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 xiiiPreface xv1 Introduction 1Preliminary Remarks 1History 6References 72 Basic Terms 9Average Values 9Amplitude Distribution 10Autocorrelation 12Cross-Correlation 15Noise Spectra 18Autocorrelation Function and Spectral Power Density 19Band-Limited Noise on the Spectrum Analyzer 20References 223 Noise Sources 23Thermal Noise 23Nyquist Formula and Thermal Radiation 24Validity and Experimental Confirmation of the Nyquist Formula 27Thermal Noise Under Extreme Conditions 28Shot Noise 29Plasma Noise 33Current Noise of Resistors and Contacts 34Technical Resistors 34Resistors Consisting of Semiconductor Material 36Contact Noise 37Generation–Recombination Noise 38LF Noise from Transistors 40References 424 Noise and Linear Networks 45Narrowband Noise 45Calculating with Phasors 45Noise Source with Complex Internal Resistance 51The Equivalent Noise Bandwidth 52Network Components at Different Temperatures 54Noise Generator and Attenuator 58References 585 Nonlinear Networks 59Mixing 59Band-Limited RF Noise at Input 59Amplitude Clipping 62The Detector as a Nonlinear Network 63The Noise Spectrum Behind a Quadratic Detector 65The Noise Spectrum Behind a Linear Detector 69The Sensitivity Limit 70Noise with Signal 73The Phase Sensitive Rectifier 74Trace Averaging 76References 786 The Noise Factor 79Amplifier and Noise Power 79The Noise Factor F 80Cascaded Amplifiers 83The Noise measure m 85Definitions of Gain 85Source and Load 89Broadband and Spot Noise Factor 91Noise Factor of a Passive Network 92Antenna Temperature 93The Reference Temperature T 0 = 290 K 98Noise Factor and Detection Limit 99References 1007 Noise of Linear Two-Ports 101Representation of Two-Ports 101Noise Modeling Using the Chain Matrix 102References 1088 Calculation Methods for Noise Quantities 109Noise Voltages, Currents, and Spectra 109Calculating with Current, Voltage, and Noise Waves 112The Noise Correlation Matrix 115The Correlation Matrix of Passive Components 117The Noise of Simple Passive Networks 119Transformation of Noise Sources in Different Network Representations 128Correlation Matrix and IEEE Elements 131FET-Like Network with the Y-Correlation Matrix 134Noise Sources at Input with ABCD Correlation Matrix 138References 1429 Diodes and Bipolar Transistors 143Semiconductor Diode 143Bipolar Transistor 145Small-Signal Equivalent Circuit 147Hawkins BJT Noise Model 148Two Approaches for the Collector Noise Current Source 155BJT Noise Model with Correlation Matrices 157The Π-Model 157The T-Model with Correlation Matrices 161Transformation of the Y-Sources to the Input 165Modeling of a Microwave Transistor with Correlation Matrices 168Simplest Π-Model 174Contour Diagram 177Transistor in the Circuit 179Using the Contour Diagram 183References 18510 Operational Amplifier 187Operational Amplifier as Circuit Element 187Noise Sources of the Operational Amplifier 188Consideration of 1/f Noise 193Operational Amplifier as an Active Low-Pass Filter 195References 19811 Field Effect Transistors 201Jfet 201Mode of Operation of the FET 201The Channel Noise 204NoiseSourcesattheGate 205The Correlation 206Transformation to the Input 206Simple Approximations 211Field Effect Transistors for the Microwave Range (MESFET, HFET) 214The Pucel Model 215The Pospieszalski model 218Discussion of the Results 225Criteria for Noise Data 225References 22912 Theory of Noise Measurement 231Measurements of Two-Ports 231The Equivalent Noise Resistance 234Voltage and Current Source 235Voltage and Current Source with Correlation 2373 dB and Y-Method 241References 24313 Basics of Measuring Technique 245Principles of the RF-Receiver 245The Detection Limit 245Diode as RF Receiver (Video Detector) 249RF and Microwave Range Receiver 254Dicke Radiometer 258Correlation Radiometer in the Microwave Range 261Network Analyzer as a Noise Measurement Device 263References 26514 Equipment and Measurement Methods 267Noise Measurement Receiver 267Spectrum Analyzer 269The Y-Method 273Measurements in the Microwave Range 275Selection Criteria of the Mixer 278Image Rejection 279Complete Noise Characterization 282Analysis of Multi-impedance Measurements 283Cold Source Method 285The 7-State Method 287On-Wafer Measurement of Cold Source 288On-Wafer with Noise Generator According to the Y-method 293References 29615 Noise Generators 299Vacuum Diode 299Gas Discharge 300Semiconductor Diodes 302Excess Noise Ratio (ENR) 303Hot–Cold Sources 305References 30716 Impedance Tuners 309Impedance Transformation with Simple Methods 309Mechanical Components for the Microwave Range 311Electronic Components 313Precision Automatic Tuner 315Attenuation of the Tuner 317References 31817 Examples of Measurement Problems 319Transistor in a Test Fixture 319The Low Noise Block (LNB) of Satellite Television 322Verification of a Noise Measurement 325References 32718 Measurement and Modeling of Low-Frequency Noise 329Correlation Radiometer for Low Frequencies (f < 10 MHz) 329The Low-Frequency Noise of Transistors 333Measurement Setup for LF Noise 334Examples of LF Noise Measurements on GaAs-HBT 336Modeling of LF Noise 337The Noise of the Microphone 337References 34219 Measurement Accuracy and Sources of Error 345Accuracy of Measured Data 345Error of Measurements 345Inaccuracies of the Noise Measurement 346Uncertainty of the ENR Calibration 349Noise Source Mismatch 350T0 = 290 K Is not TOFF 352Mismatch in the System 353Linearity of the Receiver 356References 35720 Phase Noise 359Basics 359Reciprocal Mixing 361Description of Phase Noise 363Spectral Power Density of Phase Fluctuations Sφ (f) 364The Single Sideband Phase Noise L(f) 365Spectral Power Density of Frequency Fluctuations SΔf (f) 365Excursus on Frequency and Phase Modulation 366The Allan Variance σ2Y (τ) 368Residual FM 370Multiplication and Division 371Amplitude Noise 371Phase Noise and Jitter 372References 37421 Physics of the Oscillator 377Oscillation Condition [1] 377Simple Model of the Phase Disturbance [2] 378Phase Slope, Resonator Quality, and Frequency Stability [3] 379The Formula of Leeson [4] 382Components of Oscillators 384Influence of the Varactor Diode 386Upward Mixing of LF Noise 390The Influence of Microwave Noise on Phase Noise 393References 39622 Phase Noise Measurement 399Basic Parameters 399Spectrum Analyzer 399Phase Detector Method 406The Sensitivity of the Phase Detector 407Example Calibration and Measurement 409Keeping the Quadrature by a PLL 410Delay Line as Frequency Discriminator 412The Sensitivity of the Delay-Line Method 414Configuration and Calibration 418Resonator as Frequency Discriminator 420Detection Limit 421Comparison of Measurement Systems 422Cross-Correlation Technique 423Amplitude Noise 425Problems with On-Wafer Measurement 429Residual Phase Noise 430References 432Appendix 435Noise Signals and Deterministic Signals 435Random Signals 436Characteristic Values 437The Probability Density Function 438Example Sine Function 439Example Sawtooth Voltage 440Example White Noise 440Example Sinusoidal Signal with Noise 441Example Narrowband Noise 441The Autocorrelation Function 444Example Sine 444Example Sawtooth 444Example Noisy Sine 445Example White Noise 446Example Low-Pass Noise 447Example Bandpass Noise 449Fourier Series 451Sine–Cosine Spectrum 452Amplitude–Phase Spectrum 452Complex Fourier Series 452The Fourier Integral 453Energy and Power Signals 456Example Transient Time Function 457The Parseval Equation 459Example Voltage Pulse 460Fourier Transform and Power Spectral Density 462Example Rectangular Pulse 463Time-Limited Noise Signal 465Example of a Time-Limited Wave Train 466The Wiener–Khinchin Theorem 468Cross Correlation 470Example of Two Sine Functions 471Example of Two White Noise Signals 472Example of Two Bandpass Noise Signals 472Example White Noise and Bandpass Noise 474Cross-Correlation After Splitting into Two Branches 474Power Spectral Density Real and Complex 477The Cross-Spectral Density 478Complex Representation of the Cross-Spectral Density 479Transmission of Noise by Networks 479References 485Glossary of Symbols 487Index 491