A 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 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 GenerationRecombination 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 Factor F 80 Cascaded Amplifiers 83 The Noise measure m 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 T 0 = 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 -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 -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 NoiseSourcesattheGate 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-Receive