Practical RF System Design

From the Preface:

This book is about RF system analysis and design at the level that requires an understanding of the interaction between the modules of a system so the ultimate performance can be predicted. It describes concepts that are advanced, that is, beyond those that are more commonly taught, because these are necessary to the understanding of effects encountered in practice. It is about answering questions such as:

* How will the gain of a cascade (a group of modules in series) be affected by the SWR specifications of its modules?

* How will noise on a local oscillator affect receiver noise figure and desensitization?

* How is the effective noise figure of a mixer affected by the filtering that precedes it?

* How can we determine the linearity of a cascade from specifications on its modules?

* How do we expect intermodulation products (IMs) to change with signal amplitude and why do they sometimes change differently?

* How can modules be combined in a way that reduces certain IMs or turn bad impedance matches into good matches?

* How can the spurious response in a frequency conversion be visualized and how can the magnitudes of the spurs be determined? How can this picture be used to determine filter requirements?

* How does phase noise affect system performance; what are its sources and how can the effects be predicted?

 

Table of Contents:

Chapter 1 Introduction

Chapter 2 Gain

Chapter 3 Noise Figure

Chapter 4 Nonlinearity in the Signal Path

Chapter 5 Noise and Nonlinearities

Chapter 6 Architectures That Improve Linearity

Chapter 7 Frequency Conversion

Chapter 8 Contaminating Signals in Severe Nonlinearities

Chapter 9 Phase Noise

Note: there are approximately 64 examples in these 9 chapters.

Appendixes

 

 

Preface
Glossary and Symbols


1 Introduction
1.1 System Design Process
1.2 Organization of the Book
1.3 Appendixes
1.4 Spreadsheets
1.5 Test and Simulation
1.6 Practical Skepticism
1.7 References

2 Gain
2.1 Simple Cases
2.2 General Case
2.2.1 S Parameters
2.2.2 Normalized Waves
2.2.3 T Parameters
2.2.4 Relationship Between S and T Parameters
2.2.5 Restriction on T Parameters
2.2.6 Cascade Response
2.3 Simplification, Unilateral Modules
2.3.1 Module Gain
2.3.2 Transmission Line Interconnections
2.3.2.1 Effective Power Gain
2.3.2.2 Power Delivered to the Load
2.3.2.3 Phase Variation due to Reflection
2.3.2.4 Generalization to Bilateral Modules
2.3.3 Overall Response, Standard Cascade
2.3.3.1 Gain
2.3.3.2 End Elements in the Cascade
2.3.3.3 Phase
3.3.3.4 Cascade Calculations
2.3.4 Combined with Bilateral Modules
2.3.5 Lossy Interconnections
2.3.6 Additional Considerations
2.3.6.1 Variations in SWRs
2.3.6.2 Reflections at Interconnects
2.3.6.3 Parameters in Composite Modules
2.4 Non-Standard Impedances
2.5 The Use of Sensitivities to Find Variations
2.6 Summary

3 Noise Figure
3.1 Noise Factor and Noise Figure
3.2 Modules in Cascade
3.3 Applicable Gains and Noise Factors
3.4 Noise Figure of an Attenuator
3.5 Noise Figure of an Interconnect
3.6 Cascade Example
3.7 Expected Value and Variance of Noise Figure
3.8 Impedance-dependent Noise Factors
3.8.1 Representation
3.8.2 Constant Noise Circles
3.8.3 Relation to Standard Noise Factor
3.8.4 Using the Theoretical Noise Factor
3.8.5 Summary
3.9 Image Noise, Mixers
3.9.1 Effective Noise Figure of the Mixer
3.9.2 Verification for Simple Cases
3.9.3 Examples of Image Noise
3.10 Extreme Mismatch, Voltage Amplifiers
3.10.1 Module Noise Factor
3.10.2 Cascade Noise Factor
3.10.3 Combined with Unilateral Modules
3.10.4 Equivalent Noise Factor
3.11 Using Noise-Figure Sensitivities
3.12 Mixed Cascade Example
3.12.1 Effect of Some Resistor Changes
3.12.2 Accounting for Other Reflections
3.12.3 Using Sensitivities
3.13 Gain Controls
3.13.1 Automatic Gain Control
3.13.2 Level Control
3.14 Summary

4 Nonlinearity in the Signal Path
4.1 Representing Nonlinear Responses
4.2 Second-Order Terms
4.2.1 Intercept Points
4.2.2 Mathematical Representations
4.2.3 Other Even-Order Terms
4.3 Third-Order Terms
4.3.1 Intercept Points
4.3.2 Mathematical Representations
4.3.3 Other Odd-Order Terms
4.4 Frequency Dependence and Relationship Between Products
4.5 Nonlinear Products in Cascades
4.5.1 Two-Module Cascade
4.5.2 General Cascade
4.5.3 IMs Adding Coherently
4.5.4 IMs Adding Randomly
4.5.5 IMs That Do Not Add
4.5.6 Effect of Mismatch on IPs
4.6 Examples, Spreadsheets for IMs in a Cascade
4.7 Anomalous IMs
4.8 Measuring IMs
4.9 Compression in the Cascade
4.10 Other Nonideal Effects
4.11 Summary

5 Noise and Nonlinearity
5.1 Intermodulation of Noise
5.1.1 Preview
5.1.2 Flat Bandpass Noise
5.1.3 Second-Order Products
5.1.3.1 DC Term
5.1.3.2 Density
5.1.3.3 Effect of a Signal with the Noise
5.1.3.4 Crystal Video Receiver with Preamplification
5.1.4 Third-Order Products
5.1.4.1 Density Spectrum
5.1.4.2 Third-Order Terms an Input Frequencies
5.1.4.3 NPR Measurement
5.2 Composite Distortion
5.2.1 Second-Order IMs (CSO)
5.2.2 Third-Order IMs (CTB)
5.2.3 Example, CSO and CTB
5.3 Dynamic Range
5.3.1 Spurious-Free Dynamic Range
5.3.2 Other Range Limitations
5.4 Optimizing Cascades
5.4.1 Combining Parameters on One Spreadsheet
5.4.2 Optimization
5.5 Spreadsheet Enhancements
5.5.1 Look-up Tables
5.5.2 Using Controls
5.6 Summary

6 Architectures that Improve Linearity
6.1 Parallel Combining
6.1.1 90° Hybrid
6.1.1.1 Combining Amplifiers
6.1.1.2 Impedance Matching
6.1.1.3 Intermods and Harmonics
6.1.1.4 Summary
6.1.2 180° Hybrid
6.1.2.1 Combining Amplifiers
6.1.2.2 Impedance Matching
6.1.2.3 Intermods and Harmonics
6.1.2.4 Summary
6.1.3 Simple Push-Pull
6.1.4 Gain
6.1.5 Noise Figure
6.1.6 Combiner Trees
6.1.7 Cascade Analysis of a Combiner Tree
6.2 Feedback
6.3 Feedforward
6.3.1 Intermods and Harmonics
6.3.2 Bandwidth
6.3.3 Noise Figure
6.4 Nonideal Performance
6.5 Summary

7 Frequency Conversion
7.1 Basics
7.1.1 The Mixer
7.1.2 Conversion in Receivers
7.1.3 Spurs
7.1.4 Conversion in Synthesizers and Exciters
7.1.5 Calculators
7.1.6 Design Methods
7.1.7 Example
7.2 Spurious Levels
7.2.1 Dependence on Signal Strength
7.2.2 Estimating Levels
7.2.3 Strategy for Using Levels
7.3 Two-Signal IMs
7.4 Power Range for Predictable Levels
7.5 Spur Plot, LO Reference
7.5.1 Spreadsheet Plot Description
7.5.2 Example of a Band Conversion
7.5.3 Other Information on the Plot
7.6 Spur Plot, IF Reference
7.7 Shape Factors
7.7.1 Definitions
7.7.2 RF Filter Requirements
7.7.3 IF Filter Requirements
7.8 Double Conversion
7.9 Operating Regions
7.9.1 Advantageous Regions
7.9.1.1 Region 1, fLO > fRF, fIF
7.9.1.2 Region 2, fLO, fRF >> fIF
7.9.1.3 Region 3, fLOfIF > fRF
7.9.2 Limitation on Down Converters, Two-by-Twos
7.9.3 Higher Values of m
7.10 Examples
7.11 Note on the Spur Plots Used in this Chapter
7.12 Summary

8 Contaminating Signals in Severe Nonlinearities
8.1 Decomposition
8.2 Hard Limiting
8.3 Soft Limiting
8.4 Mixers, Through the LO Port
8.4.1 AM Suppression
8.4.2 FM Transfer
8.4.3 Single Sideband Transfer
8.4.4 Mixing Between LO Components
8.4.5 Troublesome Frequency Ranges in the LO
8.4.5.1 Range 1
8.4.5.2 Range 2
8.4.5.3 Range 3
8.4.5.4 Range 4
8.4.6 Summary of Ranges
8.4.7 Effect on Noise Figure
8.4.7.1 Computing the Increase
8.4.7.2 Filtering the Noise
8.4.7.3 Oscillator Noise Sidebands
8.5 Frequency Dividers
8.5.1 Sideband Reduction
8.5.2 Sampling
8.5.3 Internal Noise
8.6 Frequency Multipliers
8.7 Summary

9 Phase Noise
9.1 Describing Phase Noise
9.2 Adverse Effects of Phase Noise
9.2.1 Data Errors
9.2.2 Jitter
9.2.3 Receiver Desensitization
9.3 Sources of Phase Noise
9.3.1 Oscillator Phase Noise Spectrums
9.3.2 Integration Limits
9.3.3 Relationship between Oscillator S
j and Lj.
9.4 Processing Phase Noise in a Cascade
9.4.1 Filtering by Phase-Locked Loops
9.4.2 Filtering by Ordinary Filters
9.4.3 The Implication of Noise Figure
9.4.4 Transfer from Local Oscillators
9.4.5 Transfer from Data Clocks
9.4.6 Integration of Phase Noise
9.5 Determination of the Effect on Data
9.5.1 Error Probability
9.5.2 Computing Phase Variance, Limits of Integration
9.5.3 Effect of the Carrier-Recovery Loop on Phase Noise
9.5.4 Effect of the Loop on Additive Noise
9.5.5 Contribution of Phase Noise to Data Errors
9.5.6 Effects of Low-Frequency Phase Noise
9.6 Other Measures of Phase Noise
9.6.1 Jitter
9.6.2 Allan Variance
9.7 Summary

Appendices

Appendix A: Op Amp Noise Factor Calculations
A.1 Invariance When Input Resistor is Redistributed
A.2 Effect of Change in Source Resistance
A.3 Model

Appendix B: Representations of Frequency Bands, IF Normalization
B.1 Passbands
B.2 Acceptance Bands
B.3 Filter Asymmetry

Appendix C: Conversion Arithmetic
C.1 Receiver Calculator
C.2 Synthesis Calculator

Appendix E: Example of Frequency Conversion

Appendix F: Some Related Formulas
F.1 Decibels
F.2 Reflection Coefficient and SWR
F.3 Combining SWRs
F.3.1 Summary of Results
F.3.2 Development
F.3.3 Maximum SWR
F.3.4 Minimum SWR
F.3.5 Relaxing Restrictions
F.4 Impedance Transformations in Cables
F.5 Smith Chart

Appendix G: Types of Power Gain
G.1 Available Gain
G.2 Maximum Available Gain
G.3 Transducer Gain
G.4 Insertion Gain
G.5 Actual Gain


Appendix H: Formulas Relating to IMs and Harmonics
H.1 Second Harmonics
H.2 Second-Order IMs
H.3 Third Harmonics
H.4 Third-Order IMs
H.5 Definition of Terms

Appendix I: Changing the Standard Impedance
I.1 General Case
I.2 Unilateral Module

Appendix L: Power Delivered to the Load

Appendix M: Matrix Multiplications

Appendix N: Noise Factors, Standard and Theoretical
N.1 Theoretical Noise Factor
N.2 Standard Noise Factor
N.3 Standard Modules and Standard Noise Factor
N.4 Module Noise Factor In a Standard Cascade
N.5 How Can This Be?
N.6 Noise Factor of an Interconnect
N.6.1 Noise Factor with Mismatch
N.6.2 In More Usable Terms
N.6.3 Verification
N.6.4 Comparison with Theoretical Value
N.7 Effect of Source Impedance
N.8 Ratio of Power Gains

Appendix P: IM Products in a Mixer

Appendix R is not included in the book. It is available on the Wiley web site.
Appendix R: Reflections and Mismatches in Interconnects
R.1 Reflections
R.2 Mismatches
R.2.1 Procedure
R.2.2 Comments
R.2.3 Example
R.2.3.1 Eighth Wavelength Line
R.2.3.2 Unknown Interconnect Length

Appendix S: Composite S Parameters

Appendix T: Third-Order Terms at Input Frequency

Appendix V: Sensitivities and Variance of Noise Figure

Appendix X: Crossover Spurs

Appendix Z: Nonstandard Modules
Z.1 Gain of a Chain of Modules Relative to Tested Gain
Z.2 Finding the Maximum Available Gain of a Module
Z.3 Interconnects
Z.4 Equivalent S Parameters
Z.5 S Parameters for a Cascade of Nonstandard Modules

References
Index