WILLIAM F. EGAN is an instructor at Santa Clara University, California, and formerly a Principle Engineer at TRW ESD and a Senior Technologist at GTE Government Systems. He received his PhD in electrical engineering from Stanford University and is the author of two previous books related to RF technology.

• Preface xviiGetting Files From the Wiley Ftp and Internet Sites xixSymbols List and Glossary xxi1 Introduction 11.1 System Design Process 11.2 Organization of the Book 21.3 Appendixes 31.4 Spreadsheets 31.5 Test and Simulation 31.6 Practical Skepticism 41.7 References 52 Gain 72.1 Simple Cases 82.2 General Case 92.2.1 S Parameters 92.2.2 Normalized Waves 112.2.3 T Parameters 122.2.4 Relationships Between S and T Parameters 132.2.5 Restrictions on T Parameters 142.2.6 Cascade Response 142.3 Simplification: Unilateral Modules 152.3.1 Module Gain 152.3.2 Transmission Line Interconnections 162.3.3 Overall Response, Standard Cascade 252.3.4 Combined with Bilateral Modules 282.3.5 Lossy Interconnections 322.3.6 Additional Considerations 382.4 Nonstandard Impedances 402.5 Use of Sensitivities to Find Variations 402.6 Summary 43Endnotes 453 Noise Figure 473.1 Noise Factor and Noise Figure 473.2 Modules in Cascade 493.3 Applicable Gains and Noise Factors 543.4 Noise Figure of an Attenuator 553.5 Noise Figure of an Interconnect 563.6 Cascade Noise Figure 563.7 Expected Value and Variance of Noise Figure 583.8 Impedance-Dependent Noise Factors 593.8.1 Representation 603.8.2 Constant-Noise Circles 613.8.3 Relation to Standard Noise Factor 623.8.4 Using the Theoretical Noise Factor 643.8.5 Summary 653.9 Image Noise, Mixers 653.9.1 Effective Noise Figure of the Mixer 663.9.2 Verification for Simple Cases 693.9.3 Examples of Image Noise 693.10 Extreme Mismatch, Voltage Amplifiers 743.10.1 Module Noise Factor 763.10.2 Cascade Noise Factor 783.10.3 Combined with Unilateral Modules 793.10.4 Equivalent Noise Factor 793.11 Using Noise Figure Sensitivities 793.12 Mixed Cascade Example 803.12.1 Effects of Some Resistor Changes 813.12.2 Accounting for Other Reflections 823.12.3 Using Sensitivities 823.13 Gain Controls 843.13.1 Automatic Gain Control 843.13.2 Level Control 863.14 Summary 88Endnotes 904 Nonlinearity In the Signal Path 914.1 Representing Nonlinear Responses 914.2 Second-Order Terms 924.2.1 Intercept Points 934.2.2 Mathematical Representations 954.2.3 Other Even-Order Terms 974.3 Third-Order Terms 974.3.1 Intercept Points 994.3.2 Mathematical Representations 1004.3.3 Other Odd-Order Terms 1014.4 Frequency Dependence and Relationship Between Products 1024.5 Nonlinear Products in the Cascades 1034.5.1 Two-Module Cascade 1044.5.2 General Cascade 1054.5.3 IMs Adding Coherently 1064.5.4 IMs Adding Randomly 1084.5.5 IMs That Do Not Add 1094.5.6 Effect of Mismatch on IPs 1104.6 Examples: Spreadsheets for IMs in a Cascade 1114.7 Anomalous IMs 1154.8 Measuring IMs 1164.9 Compression in the Cascade 1194.10 Other Nonideal Effects 1214.11 Summary 121Endnote 1225 Noise and Nonlinearity 1235.1 Intermodulation of Noise 1235.1.1 Preview 1245.1.2 Flat Bandpass Noise 1255.1.3 Second-Order Products 1255.1.4 Third-Order Products 1305.2 Composite Distortion 1335.2.1 Second-Order IMs (CSO) 1345.2.2 Third-Order IMs (CTB) 1365.2.3 CSO and CTB Example 1365.3 Dynamic Range 1375.3.1 Spurious-Free Dynamic Range 1375.3.2 Other Range Limitations 1395.4 Optimizing Cascades 1395.4.1 Combining Parameters on One Spreadsheet 1395.4.2 Optimization Example 1435.5 Spreadsheet Enhancements 1465.5.1 Lookup Tables 1465.5.2 Using Controls 1475.6 Summary 147Endnotes 1476 Architectures That Improve Linearity 1496.1 Parallel Combining 1496.1.1 90◦ Hybrid 1506.1.2 180◦ Hybrid 1526.1.3 Simple Push–Pull 1546.1.4 Gain 1556.1.5 Noise Figure 1566.1.6 Combiner Trees 1566.1.7 Cascade Analysis of a Combiner Tree 1576.2 Feedback 1586.3 Feedforward 1596.3.1 Intermods and Harmonics 1606.3.2 Bandwidth 1616.3.3 Noise Figure 1616.4 Nonideal Performance 1626.5 Summary 163Endnotes 1637 Frequency Conversion 1657.1 Basics 1657.1.1 The Mixer 1657.1.2 Conversion in Receivers 1677.1.3 Spurs 1687.1.4 Conversion in Synthesizers and Exciters 1707.1.5 Calculators 1707.1.6 Design Methods 1707.1.7 Example 1717.2 Spurious Levels 1717.2.1 Dependence on Signal Strength 1717.2.2 Estimating Levels 1737.2.3 Strategy for Using Levels 1757.3 Two-Signal IMs 1767.4 Power Range for Predictable Levels 1777.5 Spur Plot, LO Reference 1807.5.1 Spreadsheet Plot Description 1807.5.2 Example of a Band Conversion 1827.5.3 Other Information on the Plot 1847.6 Spur Plot, IF Reference 1867.7 Shape Factors 1967.7.1 Definitions 1977.7.2 RF Filter Requirements 1977.7.3 IF Filter Requirements 2007.8 Double Conversion 2027.9 Operating Regions 2037.9.1 Advantageous Regions 2037.9.2 Limitation on Downconversion, Two-by-Twos 2067.9.3 Higher Values of m 2097.10 Examples 2117.11 Note on Spur Plots Used in This Chapter 2167.12 Summary 216Endnotes 2178 Contaminating Signals In Severe Nonlinearities 2198.1 Decomposition 2208.2 Hard Limiting 2238.3 Soft Limiting 2238.4 Mixers, Through the LO Port 2258.4.1 AM Suppression 2258.4.2 FM Transfer 2268.4.3 Single-Sideband Transfer 2268.4.4 Mixing Between LO Components 2288.4.5 Troublesome Frequency Ranges in the LO 2288.4.6 Summary of Ranges 2358.4.7 Effect on Noise Figure 2368.5 Frequency Dividers 2408.5.1 Sideband Reduction 2408.5.2 Sampling 2418.5.3 Internal Noise 2428.6 Frequency Multipliers 2428.7 Summary 243Endnotes 2449 Phase Noise 2459.1 Describing Phase Noise 2459.2 Adverse Effects of Phase Noise 2479.2.1 Data Errors 2479.2.2 Jitter 2489.2.3 Receiver Desensitization 2499.3 Sources of Phase Noise 2509.3.1 Oscillator Phase Noise Spectrums 2509.3.2 Integration Limits 2529.3.3 Relationship Between Oscillator Sϕ and Lϕ 2529.4 Processing Phase Noise in a Cascade 2529.4.1 Filtering by Phase-Locked Loops 2539.4.2 Filtering by Ordinary Filters 2549.4.3 Implication of Noise Figure 2559.4.4 Transfer from Local Oscillators 2559.4.5 Transfer from Data Clocks 2569.4.6 Integration of Phase Noise 2589.5 Determining the Effect on Data 2589.5.1 Error Probability 2589.5.2 Computing Phase Variance, Limits of Integration 2599.5.3 Effect of the Carrier-Recovery Loop on Phase Noise 2609.5.4 Effect of the Loop on Additive Noise 2629.5.5 Contribution of Phase Noise to Data Errors 2639.5.6 Effects of the Low-Frequency Phase Noise 2689.6 Other Measures of Phase Noise 2699.6.1 Jitter 2699.6.2 Allan Variance 2719.7 Summary 271Endnote 272Appendix A OP AMP Noise Factor Calculations 273A.1 Invariance When Input Resistor Is Redistributed 273A.2 Effect of Change in Source Resistances 274A.3 Model 276Appendix B Representations of Frequency Bands, If Normalization 279B.1 Passbands 279B.2 Acceptance Bands 279B.3 Filter Asymmetry 286Appendix C Conversion Arithmetic 289C.1 Receiver Calculator 289C.2 Synthesis Calculator 291Appendix E Example of Frequency Conversion 293Appendix F Some Relevant Formulas 303F.1 Decibels 303F.2 Reflection Coefficient and SWR 304F.3 Combining SWRs 306F.3.1 Summary of Results 306F.3.2 Development 307F.3.3 Maximum SWR 308F.3.4 Minimum SWR 309F.3.5 Relaxing Restrictions 309F.4 Impedance Transformations in Cables 310F.5 Smith Chart 310Appendix G Types of Power Gain 313G.1 Available Gain 313G.2 Maximum Available Gain 313G.3 Transducer Gain 314G.4 Insertion Gain 315G.5 Actual Gain 315Appendix H Formulas Relating to IMs and Harmonics 317H.1 Second Harmonics 317H.2 Second-Order IMs 318H.3 Third Harmonics 318H.4 Third-Order IMs 319H.5 Definitions of Terms 320Appendix I Changing the Standard Impedance 321I.1 General Case 321I.2 Unilateral Module 323Appendix L Power Delivered to the Load 325Appendix M Matrix Multiplication 327Appendix N Noise Factors—Standard and Theoretical 329N.1 Theoretical Noise Factor 329N.2 Standard Noise Factor 331N.3 Standard Modules and Standard Noise Factor 332N.4 Module Noise Factor in a Standard Cascade 333N.5 How Can This Be? 334N.6 Noise Factor of an Interconnect 334N.6.1 Noise Factor with Mismatch 335N.6.2 In More Usable Terms 336N.6.3 Verification 338N.6.4 Comparison with Theoretical Value 340N.7 Effect of Source Impedance 341N.8 Ratio of Power Gains 342Endnote 343Appendix P IM Products In Mixers 345Appendix S Composite S Parameters 349Appendix T Third-Order Terms at Input Frequency 353Appendix V Sensitivities and Variance of Noise Figure 355Appendix X Crossover Spurs 359Appendix Z Nonstandard Modules 363Z.1 Gain of Cascade of Modules Relative to Tested Gain 363Z.2 Finding Maximum Available Gain of a Module 366Z.3 Interconnects 367Z.4 Equivalent S Parameters 367Z.5 S Parameters for Cascade of Nonstandard Modules 368Endnote 369References 371Endnote 377Index 379

WILLIAM F. EGAN is an instructor at Santa Clara University, California, and formerly a Principle Engineer at TRW ESD and a Senior Technologist at GTE Government Systems. He received his PhD in electrical engineering from Stanford University and is the author of two previous books related to RF technology.

• Preface xviiGetting Files From the Wiley Ftp and Internet Sites xixSymbols List and Glossary xxi1 Introduction 11.1 System Design Process 11.2 Organization of the Book 21.3 Appendixes 31.4 Spreadsheets 31.5 Test and Simulation 31.6 Practical Skepticism 41.7 References 52 Gain 72.1 Simple Cases 82.2 General Case 92.2.1 S Parameters 92.2.2 Normalized Waves 112.2.3 T Parameters 122.2.4 Relationships Between S and T Parameters 132.2.5 Restrictions on T Parameters 142.2.6 Cascade Response 142.3 Simplification: Unilateral Modules 152.3.1 Module Gain 152.3.2 Transmission Line Interconnections 162.3.3 Overall Response, Standard Cascade 252.3.4 Combined with Bilateral Modules 282.3.5 Lossy Interconnections 322.3.6 Additional Considerations 382.4 Nonstandard Impedances 402.5 Use of Sensitivities to Find Variations 402.6 Summary 43Endnotes 453 Noise Figure 473.1 Noise Factor and Noise Figure 473.2 Modules in Cascade 493.3 Applicable Gains and Noise Factors 543.4 Noise Figure of an Attenuator 553.5 Noise Figure of an Interconnect 563.6 Cascade Noise Figure 563.7 Expected Value and Variance of Noise Figure 583.8 Impedance-Dependent Noise Factors 593.8.1 Representation 603.8.2 Constant-Noise Circles 613.8.3 Relation to Standard Noise Factor 623.8.4 Using the Theoretical Noise Factor 643.8.5 Summary 653.9 Image Noise, Mixers 653.9.1 Effective Noise Figure of the Mixer 663.9.2 Verification for Simple Cases 693.9.3 Examples of Image Noise 693.10 Extreme Mismatch, Voltage Amplifiers 743.10.1 Module Noise Factor 763.10.2 Cascade Noise Factor 783.10.3 Combined with Unilateral Modules 793.10.4 Equivalent Noise Factor 793.11 Using Noise Figure Sensitivities 793.12 Mixed Cascade Example 803.12.1 Effects of Some Resistor Changes 813.12.2 Accounting for Other Reflections 823.12.3 Using Sensitivities 823.13 Gain Controls 843.13.1 Automatic Gain Control 843.13.2 Level Control 863.14 Summary 88Endnotes 904 Nonlinearity In the Signal Path 914.1 Representing Nonlinear Responses 914.2 Second-Order Terms 924.2.1 Intercept Points 934.2.2 Mathematical Representations 954.2.3 Other Even-Order Terms 974.3 Third-Order Terms 974.3.1 Intercept Points 994.3.2 Mathematical Representations 1004.3.3 Other Odd-Order Terms 1014.4 Frequency Dependence and Relationship Between Products 1024.5 Nonlinear Products in the Cascades 1034.5.1 Two-Module Cascade 1044.5.2 General Cascade 1054.5.3 IMs Adding Coherently 1064.5.4 IMs Adding Randomly 1084.5.5 IMs That Do Not Add 1094.5.6 Effect of Mismatch on IPs 1104.6 Examples: Spreadsheets for IMs in a Cascade 1114.7 Anomalous IMs 1154.8 Measuring IMs 1164.9 Compression in the Cascade 1194.10 Other Nonideal Effects 1214.11 Summary 121Endnote 1225 Noise and Nonlinearity 1235.1 Intermodulation of Noise 1235.1.1 Preview 1245.1.2 Flat Bandpass Noise 1255.1.3 Second-Order Products 1255.1.4 Third-Order Products 1305.2 Composite Distortion 1335.2.1 Second-Order IMs (CSO) 1345.2.2 Third-Order IMs (CTB) 1365.2.3 CSO and CTB Example 1365.3 Dynamic Range 1375.3.1 Spurious-Free Dynamic Range 1375.3.2 Other Range Limitations 1395.4 Optimizing Cascades 1395.4.1 Combining Parameters on One Spreadsheet 1395.4.2 Optimization Example 1435.5 Spreadsheet Enhancements 1465.5.1 Lookup Tables 1465.5.2 Using Controls 1475.6 Summary 147Endnotes 1476 Architectures That Improve Linearity 1496.1 Parallel Combining 1496.1.1 90◦ Hybrid 1506.1.2 180◦ Hybrid 1526.1.3 Simple Push–Pull 1546.1.4 Gain 1556.1.5 Noise Figure 1566.1.6 Combiner Trees 1566.1.7 Cascade Analysis of a Combiner Tree 1576.2 Feedback 1586.3 Feedforward 1596.3.1 Intermods and Harmonics 1606.3.2 Bandwidth 1616.3.3 Noise Figure 1616.4 Nonideal Performance 1626.5 Summary 163Endnotes 1637 Frequency Conversion 1657.1 Basics 1657.1.1 The Mixer 1657.1.2 Conversion in Receivers 1677.1.3 Spurs 1687.1.4 Conversion in Synthesizers and Exciters 1707.1.5 Calculators 1707.1.6 Design Methods 1707.1.7 Example 1717.2 Spurious Levels 1717.2.1 Dependence on Signal Strength 1717.2.2 Estimating Levels 1737.2.3 Strategy for Using Levels 1757.3 Two-Signal IMs 1767.4 Power Range for Predictable Levels 1777.5 Spur Plot, LO Reference 1807.5.1 Spreadsheet Plot Description 1807.5.2 Example of a Band Conversion 1827.5.3 Other Information on the Plot 1847.6 Spur Plot, IF Reference 1867.7 Shape Factors 1967.7.1 Definitions 1977.7.2 RF Filter Requirements 1977.7.3 IF Filter Requirements 2007.8 Double Conversion 2027.9 Operating Regions 2037.9.1 Advantageous Regions 2037.9.2 Limitation on Downconversion, Two-by-Twos 2067.9.3 Higher Values of m 2097.10 Examples 2117.11 Note on Spur Plots Used in This Chapter 2167.12 Summary 216Endnotes 2178 Contaminating Signals In Severe Nonlinearities 2198.1 Decomposition 2208.2 Hard Limiting 2238.3 Soft Limiting 2238.4 Mixers, Through the LO Port 2258.4.1 AM Suppression 2258.4.2 FM Transfer 2268.4.3 Single-Sideband Transfer 2268.4.4 Mixing Between LO Components 2288.4.5 Troublesome Frequency Ranges in the LO 2288.4.6 Summary of Ranges 2358.4.7 Effect on Noise Figure 2368.5 Frequency Dividers 2408.5.1 Sideband Reduction 2408.5.2 Sampling 2418.5.3 Internal Noise 2428.6 Frequency Multipliers 2428.7 Summary 243Endnotes 2449 Phase Noise 2459.1 Describing Phase Noise 2459.2 Adverse Effects of Phase Noise 2479.2.1 Data Errors 2479.2.2 Jitter 2489.2.3 Receiver Desensitization 2499.3 Sources of Phase Noise 2509.3.1 Oscillator Phase Noise Spectrums 2509.3.2 Integration Limits 2529.3.3 Relationship Between Oscillator Sϕ and Lϕ 2529.4 Processing Phase Noise in a Cascade 2529.4.1 Filtering by Phase-Locked Loops 2539.4.2 Filtering by Ordinary Filters 2549.4.3 Implication of Noise Figure 2559.4.4 Transfer from Local Oscillators 2559.4.5 Transfer from Data Clocks 2569.4.6 Integration of Phase Noise 2589.5 Determining the Effect on Data 2589.5.1 Error Probability 2589.5.2 Computing Phase Variance, Limits of Integration 2599.5.3 Effect of the Carrier-Recovery Loop on Phase Noise 2609.5.4 Effect of the Loop on Additive Noise 2629.5.5 Contribution of Phase Noise to Data Errors 2639.5.6 Effects of the Low-Frequency Phase Noise 2689.6 Other Measures of Phase Noise 2699.6.1 Jitter 2699.6.2 Allan Variance 2719.7 Summary 271Endnote 272Appendix A OP AMP Noise Factor Calculations 273A.1 Invariance When Input Resistor Is Redistributed 273A.2 Effect of Change in Source Resistances 274A.3 Model 276Appendix B Representations of Frequency Bands, If Normalization 279B.1 Passbands 279B.2 Acceptance Bands 279B.3 Filter Asymmetry 286Appendix C Conversion Arithmetic 289C.1 Receiver Calculator 289C.2 Synthesis Calculator 291Appendix E Example of Frequency Conversion 293Appendix F Some Relevant Formulas 303F.1 Decibels 303F.2 Reflection Coefficient and SWR 304F.3 Combining SWRs 306F.3.1 Summary of Results 306F.3.2 Development 307F.3.3 Maximum SWR 308F.3.4 Minimum SWR 309F.3.5 Relaxing Restrictions 309F.4 Impedance Transformations in Cables 310F.5 Smith Chart 310Appendix G Types of Power Gain 313G.1 Available Gain 313G.2 Maximum Available Gain 313G.3 Transducer Gain 314G.4 Insertion Gain 315G.5 Actual Gain 315Appendix H Formulas Relating to IMs and Harmonics 317H.1 Second Harmonics 317H.2 Second-Order IMs 318H.3 Third Harmonics 318H.4 Third-Order IMs 319H.5 Definitions of Terms 320Appendix I Changing the Standard Impedance 321I.1 General Case 321I.2 Unilateral Module 323Appendix L Power Delivered to the Load 325Appendix M Matrix Multiplication 327Appendix N Noise Factors—Standard and Theoretical 329N.1 Theoretical Noise Factor 329N.2 Standard Noise Factor 331N.3 Standard Modules and Standard Noise Factor 332N.4 Module Noise Factor in a Standard Cascade 333N.5 How Can This Be? 334N.6 Noise Factor of an Interconnect 334N.6.1 Noise Factor with Mismatch 335N.6.2 In More Usable Terms 336N.6.3 Verification 338N.6.4 Comparison with Theoretical Value 340N.7 Effect of Source Impedance 341N.8 Ratio of Power Gains 342Endnote 343Appendix P IM Products In Mixers 345Appendix S Composite S Parameters 349Appendix T Third-Order Terms at Input Frequency 353Appendix V Sensitivities and Variance of Noise Figure 355Appendix X Crossover Spurs 359Appendix Z Nonstandard Modules 363Z.1 Gain of Cascade of Modules Relative to Tested Gain 363Z.2 Finding Maximum Available Gain of a Module 366Z.3 Interconnects 367Z.4 Equivalent S Parameters 367Z.5 S Parameters for Cascade of Nonstandard Modules 368Endnote 369References 371Endnote 377Index 379

WILLIAM F. EGAN is an instructor at Santa Clara University, California, and formerly a Principle Engineer at TRW ESD and a Senior Technologist at GTE Government Systems. He received his PhD in electrical engineering from Stanford University and is the author of two previous books related to RF technology.

• Preface xviiGetting Files From the Wiley Ftp and Internet Sites xixSymbols List and Glossary xxi1 Introduction 11.1 System Design Process 11.2 Organization of the Book 21.3 Appendixes 31.4 Spreadsheets 31.5 Test and Simulation 31.6 Practical Skepticism 41.7 References 52 Gain 72.1 Simple Cases 82.2 General Case 92.2.1 S Parameters 92.2.2 Normalized Waves 112.2.3 T Parameters 122.2.4 Relationships Between S and T Parameters 132.2.5 Restrictions on T Parameters 142.2.6 Cascade Response 142.3 Simplification: Unilateral Modules 152.3.1 Module Gain 152.3.2 Transmission Line Interconnections 162.3.3 Overall Response, Standard Cascade 252.3.4 Combined with Bilateral Modules 282.3.5 Lossy Interconnections 322.3.6 Additional Considerations 382.4 Nonstandard Impedances 402.5 Use of Sensitivities to Find Variations 402.6 Summary 43Endnotes 453 Noise Figure 473.1 Noise Factor and Noise Figure 473.2 Modules in Cascade 493.3 Applicable Gains and Noise Factors 543.4 Noise Figure of an Attenuator 553.5 Noise Figure of an Interconnect 563.6 Cascade Noise Figure 563.7 Expected Value and Variance of Noise Figure 583.8 Impedance-Dependent Noise Factors 593.8.1 Representation 603.8.2 Constant-Noise Circles 613.8.3 Relation to Standard Noise Factor 623.8.4 Using the Theoretical Noise Factor 643.8.5 Summary 653.9 Image Noise, Mixers 653.9.1 Effective Noise Figure of the Mixer 663.9.2 Verification for Simple Cases 693.9.3 Examples of Image Noise 693.10 Extreme Mismatch, Voltage Amplifiers 743.10.1 Module Noise Factor 763.10.2 Cascade Noise Factor 783.10.3 Combined with Unilateral Modules 793.10.4 Equivalent Noise Factor 793.11 Using Noise Figure Sensitivities 793.12 Mixed Cascade Example 803.12.1 Effects of Some Resistor Changes 813.12.2 Accounting for Other Reflections 823.12.3 Using Sensitivities 823.13 Gain Controls 843.13.1 Automatic Gain Control 843.13.2 Level Control 863.14 Summary 88Endnotes 904 Nonlinearity In the Signal Path 914.1 Representing Nonlinear Responses 914.2 Second-Order Terms 924.2.1 Intercept Points 934.2.2 Mathematical Representations 954.2.3 Other Even-Order Terms 974.3 Third-Order Terms 974.3.1 Intercept Points 994.3.2 Mathematical Representations 1004.3.3 Other Odd-Order Terms 1014.4 Frequency Dependence and Relationship Between Products 1024.5 Nonlinear Products in the Cascades 1034.5.1 Two-Module Cascade 1044.5.2 General Cascade 1054.5.3 IMs Adding Coherently 1064.5.4 IMs Adding Randomly 1084.5.5 IMs That Do Not Add 1094.5.6 Effect of Mismatch on IPs 1104.6 Examples: Spreadsheets for IMs in a Cascade 1114.7 Anomalous IMs 1154.8 Measuring IMs 1164.9 Compression in the Cascade 1194.10 Other Nonideal Effects 1214.11 Summary 121Endnote 1225 Noise and Nonlinearity 1235.1 Intermodulation of Noise 1235.1.1 Preview 1245.1.2 Flat Bandpass Noise 1255.1.3 Second-Order Products 1255.1.4 Third-Order Products 1305.2 Composite Distortion 1335.2.1 Second-Order IMs (CSO) 1345.2.2 Third-Order IMs (CTB) 1365.2.3 CSO and CTB Example 1365.3 Dynamic Range 1375.3.1 Spurious-Free Dynamic Range 1375.3.2 Other Range Limitations 1395.4 Optimizing Cascades 1395.4.1 Combining Parameters on One Spreadsheet 1395.4.2 Optimization Example 1435.5 Spreadsheet Enhancements 1465.5.1 Lookup Tables 1465.5.2 Using Controls 1475.6 Summary 147Endnotes 1476 Architectures That Improve Linearity 1496.1 Parallel Combining 1496.1.1 90◦ Hybrid 1506.1.2 180◦ Hybrid 1526.1.3 Simple Push–Pull 1546.1.4 Gain 1556.1.5 Noise Figure 1566.1.6 Combiner Trees 1566.1.7 Cascade Analysis of a Combiner Tree 1576.2 Feedback 1586.3 Feedforward 1596.3.1 Intermods and Harmonics 1606.3.2 Bandwidth 1616.3.3 Noise Figure 1616.4 Nonideal Performance 1626.5 Summary 163Endnotes 1637 Frequency Conversion 1657.1 Basics 1657.1.1 The Mixer 1657.1.2 Conversion in Receivers 1677.1.3 Spurs 1687.1.4 Conversion in Synthesizers and Exciters 1707.1.5 Calculators 1707.1.6 Design Methods 1707.1.7 Example 1717.2 Spurious Levels 1717.2.1 Dependence on Signal Strength 1717.2.2 Estimating Levels 1737.2.3 Strategy for Using Levels 1757.3 Two-Signal IMs 1767.4 Power Range for Predictable Levels 1777.5 Spur Plot, LO Reference 1807.5.1 Spreadsheet Plot Description 1807.5.2 Example of a Band Conversion 1827.5.3 Other Information on the Plot 1847.6 Spur Plot, IF Reference 1867.7 Shape Factors 1967.7.1 Definitions 1977.7.2 RF Filter Requirements 1977.7.3 IF Filter Requirements 2007.8 Double Conversion 2027.9 Operating Regions 2037.9.1 Advantageous Regions 2037.9.2 Limitation on Downconversion, Two-by-Twos 2067.9.3 Higher Values of m 2097.10 Examples 2117.11 Note on Spur Plots Used in This Chapter 2167.12 Summary 216Endnotes 2178 Contaminating Signals In Severe Nonlinearities 2198.1 Decomposition 2208.2 Hard Limiting 2238.3 Soft Limiting 2238.4 Mixers, Through the LO Port 2258.4.1 AM Suppression 2258.4.2 FM Transfer 2268.4.3 Single-Sideband Transfer 2268.4.4 Mixing Between LO Components 2288.4.5 Troublesome Frequency Ranges in the LO 2288.4.6 Summary of Ranges 2358.4.7 Effect on Noise Figure 2368.5 Frequency Dividers 2408.5.1 Sideband Reduction 2408.5.2 Sampling 2418.5.3 Internal Noise 2428.6 Frequency Multipliers 2428.7 Summary 243Endnotes 2449 Phase Noise 2459.1 Describing Phase Noise 2459.2 Adverse Effects of Phase Noise 2479.2.1 Data Errors 2479.2.2 Jitter 2489.2.3 Receiver Desensitization 2499.3 Sources of Phase Noise 2509.3.1 Oscillator Phase Noise Spectrums 2509.3.2 Integration Limits 2529.3.3 Relationship Between Oscillator Sϕ and Lϕ 2529.4 Processing Phase Noise in a Cascade 2529.4.1 Filtering by Phase-Locked Loops 2539.4.2 Filtering by Ordinary Filters 2549.4.3 Implication of Noise Figure 2559.4.4 Transfer from Local Oscillators 2559.4.5 Transfer from Data Clocks 2569.4.6 Integration of Phase Noise 2589.5 Determining the Effect on Data 2589.5.1 Error Probability 2589.5.2 Computing Phase Variance, Limits of Integration 2599.5.3 Effect of the Carrier-Recovery Loop on Phase Noise 2609.5.4 Effect of the Loop on Additive Noise 2629.5.5 Contribution of Phase Noise to Data Errors 2639.5.6 Effects of the Low-Frequency Phase Noise 2689.6 Other Measures of Phase Noise 2699.6.1 Jitter 2699.6.2 Allan Variance 2719.7 Summary 271Endnote 272Appendix A OP AMP Noise Factor Calculations 273A.1 Invariance When Input Resistor Is Redistributed 273A.2 Effect of Change in Source Resistances 274A.3 Model 276Appendix B Representations of Frequency Bands, If Normalization 279B.1 Passbands 279B.2 Acceptance Bands 279B.3 Filter Asymmetry 286Appendix C Conversion Arithmetic 289C.1 Receiver Calculator 289C.2 Synthesis Calculator 291Appendix E Example of Frequency Conversion 293Appendix F Some Relevant Formulas 303F.1 Decibels 303F.2 Reflection Coefficient and SWR 304F.3 Combining SWRs 306F.3.1 Summary of Results 306F.3.2 Development 307F.3.3 Maximum SWR 308F.3.4 Minimum SWR 309F.3.5 Relaxing Restrictions 309F.4 Impedance Transformations in Cables 310F.5 Smith Chart 310Appendix G Types of Power Gain 313G.1 Available Gain 313G.2 Maximum Available Gain 313G.3 Transducer Gain 314G.4 Insertion Gain 315G.5 Actual Gain 315Appendix H Formulas Relating to IMs and Harmonics 317H.1 Second Harmonics 317H.2 Second-Order IMs 318H.3 Third Harmonics 318H.4 Third-Order IMs 319H.5 Definitions of Terms 320Appendix I Changing the Standard Impedance 321I.1 General Case 321I.2 Unilateral Module 323Appendix L Power Delivered to the Load 325Appendix M Matrix Multiplication 327Appendix N Noise Factors—Standard and Theoretical 329N.1 Theoretical Noise Factor 329N.2 Standard Noise Factor 331N.3 Standard Modules and Standard Noise Factor 332N.4 Module Noise Factor in a Standard Cascade 333N.5 How Can This Be? 334N.6 Noise Factor of an Interconnect 334N.6.1 Noise Factor with Mismatch 335N.6.2 In More Usable Terms 336N.6.3 Verification 338N.6.4 Comparison with Theoretical Value 340N.7 Effect of Source Impedance 341N.8 Ratio of Power Gains 342Endnote 343Appendix P IM Products In Mixers 345Appendix S Composite S Parameters 349Appendix T Third-Order Terms at Input Frequency 353Appendix V Sensitivities and Variance of Noise Figure 355Appendix X Crossover Spurs 359Appendix Z Nonstandard Modules 363Z.1 Gain of Cascade of Modules Relative to Tested Gain 363Z.2 Finding Maximum Available Gain of a Module 366Z.3 Interconnects 367Z.4 Equivalent S Parameters 367Z.5 S Parameters for Cascade of Nonstandard Modules 368Endnote 369References 371Endnote 377Index 379