Precision Measurement of Microwave Thermal Noise

Comprehensive resource covering the foundations and analysis of precision noise measurements with a detailed treatment of their uncertainties

Precision Measurement of Microwave Thermal Noise presents the basics of precise measurements of thermal noise at microwave frequencies and guides readers through how to evaluate the uncertainties in such measurement. The focus is on measurement methods used at the U.S. National Institute of Standards and Technology (NIST), but the general principles and methods are useful in a wide range of applications. Readers will learn how to perform accurate microwave noise measurements using the respected author’s expertise of calculations to aid understanding of the challenges and solutions.

The text covers the background required for the analysis of the measurements and the standards employed to calibrate radiofrequency and microwave radiometers. It also covers measurements of noise temperature (power) and the noise characteristics of amplifiers and transistors. In addition to the usual room-temperature two-port devices, cryogenic devices and multiport amplifiers are also discussed. Finally, the connection of these lab-based measurements to remote-sensing measurement (especially from space) is considered, and possible contributions of the lab-based measurements to remote-sensing applications are discussed.

Specific topics and concepts covered in the text include:

• Noise-temperature standards, covering ambient standards, hot (oven) standards, cryogenic standards, and other standards and noise sources
• Amplifier noise, covering definition of noise parameters, measurement of noise parameters, uncertainty analysis for noise-parameter measurements, and simulations and strategies
• On-wafer noise measurements, covering on-wafer microwave formalism, noise temperature, on-wafer noise-parameter measurements, and uncertainties
• Multiport amplifiers, covering formalism and noise matrix, definition of noise figure for multiports, and degradation of signal-to-noise ratio

Containing some introductory material, Precision Measurement of Microwave Thermal Noise is an invaluable resource on the subject for advanced students and all professionals working in (or entering) the field of microwave noise measurements, be it in a standards lab, a commercial lab, or academic research.

James Randa received the Ph.D. degree in Theoretical Physics from the University of Illinois at Urbana-Champaign, USA. After a series of postdoctoral and temporary faculty positions, he joined NIST, where he worked for about 25 years, leading the Noise Project for much of that time. Since his retirement he has continued to work on topics in noise on a part-time basis, as a contractor and/or a guest researcher at NIST. He is a Senior Member of the IEEE.

Preface xi

1 Background 1

1.1 Nyquist’s Theorem and Noise Temperature 1

1.1.1 Nyquist’s Theorem 1

1.1.2 Limits and Numbers 2

1.1.3 Definition of Noise Temperature 4

1.1.4 Excess Noise Ratio and T0 5

1.2 Microwave Networks 5

1.2.1 Notation 5

1.2.2 Noise Correlation Matrix and Bosma’s Theorem 6

1.2.3 Power Ratios 7

1.2.4 Noise-Temperature Translation Through a Passive Device 9

References 10

2 Noise-Temperature Standards 11

2.1 Introduction 11

2.2 Ambient Standards 12

2.3 Hot (Oven) Standards 13

2.4 Cryogenic Standards 13

2.4.1 Coaxial Standards 13

2.4.2 Waveguide Standards 15

2.5 Other Standards and Noise Sources 18

2.5.1 Tunable Primary Standards 18

2.5.2 “Equivalent Hot Standard” Based on RF Power 18

2.5.3 Secondary Standards 19

2.5.4 Synthetic Primary Standards 19

References 20

3 Noise-Temperature Measurement 23

3.1 Background 23

3.2 Total-Power Radiometer 24

3.2.1 Idealized Case 24

3.2.2 Nonideal Case 25

3.2.3 Radiometer Equation for Isolated Total-Power Radiometer 27

3.2.4 Total-Power Radiometer Design 29

3.2.5 Radiometer Testing 32

3.3 Total-Power Radiometer Uncertainties 34

3.3.1 Type-A Uncertainties 34

3.3.2 Type-B Uncertainties 36

3.3.3 Sample Results 40

3.4 Other Radiometer Designs 40

3.4.1 Switching or Dicke Radiometer 40

3.4.2 Digital Radiometer 41

3.5 Measurements through Adapters 42

3.6 Traceability and Inter-laboratory Comparisons 43

References 44

4 Amplifier Noise 47

4.1 Noise Figure, Effective Input Noise Temperature 47

4.2 Noise-Temperature Definition Revisited 48

4.3 Noise Figure Measurement, Simple Case 49

4.4 Definition of Noise Parameters 50

4.4.1 Circuit Treatment of Noisy Amplifier 50

4.4.2 Wave Representation of Noise Parameters 52

4.5 Measurement of Noise Parameters 55

4.5.1 General Measurement Setup 55

4.5.2 Fit to Noise-Figure Parameterization 59

4.5.3 Fit to Noise-Temperature or Power Parameterization 60

4.5.4 Possible Variations When Using theWave Formulation 62

4.5.5 Choice of Input Terminations 63

4.5.6 Commercial Systems, Source-Pull Measurements 66

4.5.7 Frequency–Variation Method 66

4.6 Uncertainty Analysis for Noise-Parameter Measurements 67

4.6.1 Simple Considerations 67

4.6.2 Full Analysis 70

4.6.3 Input Uncertainties 72

4.6.4 General Features and Sample Results 74

4.7 Simulations and Strategies 77

References 79

5 On-Wafer Noise Measurements 83

5.1 Introduction 83

5.2 On-Wafer Microwave Formalism 84

5.2.1 TravelingWaves vs. Pseudo Waves 84

5.2.2 On-Wafer Reference Planes 84

5.3 Noise-Temperature Measurements 85

5.4 On-Wafer Noise-Parameter Measurements 88

5.4.1 General 88

5.4.2 Radiometer-Based Systems 90

5.4.3 Commercial Systems and Reference-Plane Considerations 93

5.4.4 “Enhanced” or Model-Assisted Measurements 95

5.5 Uncertainties 101

5.5.1 Differences from Packaged Amplifiers 101

5.5.2 General Features and Properties 103

5.5.3 Measurement Strategies 104

References 105

6 Noise-Parameter Checks and Verification 109

6.1 Measurement of Passive or Previously Measured Devices 109

6.2 Physical Bounds and Model Predictions 111

6.3 Tandem or Hybrid Measurements 112

References 118

7 Cryogenic Amplifiers 121

7.1 Background 121

7.1.1 Introduction 121

7.1.2 Vacuum-Fluctuation Contribution 121

7.2 Measurement of the Matched Noise Figure 123

7.2.1 Cold-Attenuator Method 123

7.2.2 Internal Hot–Cold Method 124

7.2.3 Full-Characterization Measurements 125

7.3 Noise-Parameter Measurement 128

References 129

8 Multiport Amplifiers 133

8.1 Introduction 133

8.2 Formalism and Noise Matrix 134

8.3 Definition of Noise Figure for Multiports 136

8.4 Degradation of Signal-to-Noise Ratio 138

8.5 Three-Port Example – Differential Amplifier with Reflectionless Terminations 139

8.5.1 Motivation 139

8.5.2 Characteristic Noise Temperature, Gains, and Effective Input Noise Temperature 139

8.5.3 Noise Figure 142

8.5.4 Practical Applications 143

8.6 Four-Port Example with Reflectionless Terminations 143

References 145

9 Remote Sensing Connection 147

9.1 Introduction 147

9.2 Theory for Standard Radiometer 149

9.3 Standard-Radiometer Measurements 154

9.3.1 Determination of 𝛼154

9.3.2 Determination of Illumination Efficiency, 𝜂IE 154

9.3.2.1 Measurements of a Standard Target 155

9.4 Standard-Target Design 155

9.5 Target Reflectivity Effects 156

9.5.1 Effect of Target Reflectivity 156

9.5.2 Measurement of Target Reflectivity 157

References 157

Index 159

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