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X-Parameters

Book Description

This is the definitive guide to X-parameters, written by the original inventors and developers of this powerful new paradigm for nonlinear RF and microwave components and systems. Learn how to use X-parameters to overcome intricate problems in nonlinear RF and microwave engineering. The general theory behind X-parameters is carefully and intuitively introduced, and then simplified down to specific, practical cases, providing you with useful approximations that will greatly reduce the complexity of measuring, modeling and designing for nonlinear regimes of operation. Containing real-world case studies, definitions of standard symbols and notation, detailed derivations within the appendices, and exercises with solutions, this is the definitive stand-alone reference for researchers, engineers, scientists and students looking to remain on the cutting-edge of RF and microwave engineering.

Table of Contents

  1. Coverpage
  2. X-Parameters
  3. The Cambridge RF and Microwave Engineering Series
  4. Title page
  5. Copyright page
  6. Dedication
  7. Epigraph
  8. Contents
  9. Preface
  10. Acknowledgments
  11. 1 S-parameters – a concise review
    1. 1.1 Introduction
    2. 1.2 S-parameters
    3. 1.3 Wave variables
    4. 1.4 S-parameter measurement
    5. 1.5 S-parameters as a spectral map
    6. 1.6 Superposition
    7. 1.7 Time invariance of components described by S-parameters
    8. 1.8 Cascadability
    9. 1.9 DC operating point
    10. 1.10 S-parameters of a nonlinear device
    11. 1.11 Additional benefits of S-parameters
      1. 1.11.1 S-parameters are applicable to distributed components at high frequencies
      2. 1.11.2 S-parameters are easy to measure at high frequencies
      3. 1.11.3 Interpretation of two-port S-parameters
      4. 1.11.4 Hierarchical behavioral design with S-parameters
    12. 1.12 Limitations of S-parameters
    13. 1.13 Summary
    14. Exercises
    15. References
    16. Additional reading
  12. 2 X-parameters – fundamental concepts
    1. 2.1 Overview
    2. 2.2 Nonlinear behavior and nonlinear spectral mapping
    3. 2.3 Multi-harmonic spectral maps
    4. 2.4 Load- and source-mismatch effects
    5. 2.5 Cascading DUTs
    6. 2.6 Example: cascading two RF power amplifiers with independent bias
    7. 2.7 Relationship to harmonic balance
    8. 2.8 Cross-frequency phase
      1. 2.8.1 Commensurate signals
      2. 2.8.2 Definition of cross-frequency phase
    9. 2.9 Basic X-parameters for multi-harmonic multi-port stimulus
      1. 2.9.1 Time invariance and related properties of Fp,k(.) functions
      2. 2.9.2 Definition of X-parameters and X-parameter behavioral model
      3. 2.9.3 Example: a set of X-parameters
    10. 2.10 Physical meaning of the basic X-parameters
      1. 2.10.1 Reference stimulus and response
      2. 2.10.2 Physical interpretation
    11. 2.11 Using the X-parameter behavioral model
      1. 2.11.1 Example: amplifier with source and load mismatch
    12. 2.12 Summary
    13. Exercises
    14. References
    15. Additional reading
  13. 3 Spectral linearization approximation
    1. 3.1 Simplification of basic X-parameters for small mismatch
      1. 3.1.1 Non-analytic maps
      2. 3.1.2 Large-signal operating point
    2. 3.2 Adding small-signal stimuli (linearized nonlinear spectral mapping)
      1. 3.2.1 Small-signal interactions: the RF terms
      2. 3.2.2 Small-signal interactions: the DC terms
    3. 3.3 Physical meaning of the small-signal interaction terms
    4. 3.4 Discussion: X-parameters and the spectral Jacobian
    5. 3.5 X-parameters as a superset of S-parameters
    6. 3.6 Two-stage amplifier design
    7. 3.7 Amplifier matching under large-signal stimulus
      1. 3.7.1 Output matching and hot-S22
      2. 3.7.2 Input matching
    8. 3.8 Practical application – a GSM amplifier
    9. 3.9 Summary
    10. Exercise
    11. References
    12. Additional reading
  14. 4 X-parameter measurement
    1. 4.1 Measurement hardware
      1. 4.1.1 Hardware requirements
      2. 4.1.2 Mixer-based systems
      3. 4.1.3 Sampler-based systems
      4. 4.1.4 Stimulus requirements
    2. 4.2 Calibration
      1. 4.2.1 Scalar-loss correction
      2. 4.2.2 S-parameter calibration
      3. 4.2.3 NVNA calibration
    3. 4.3 Phase references
      1. 4.3.1 Phase-reference signals
      2. 4.3.2 Measurement considerations
      3. 4.3.3 Practical phase references
    4. 4.4 Measurement techniques
      1. 4.4.1 Large-signal response measurements
      2. 4.4.2 Small-signal response measurements
      3. 4.4.3 Practical measurement considerations
      4. 4.4.4 Simulation-based extraction
    5. 4.5 X-parameter files
      1. 4.5.1 Structure
      2. 4.5.2 Naming conventions
      3. 4.5.3 Example file
    6. 4.6 Summary
    7. References
    8. Additional reading
  15. 5 Multi-tone and multi-port cases
    1. 5.1 Introduction
    2. 5.2 Commensurate signals – large A1,1 and large A2,1: load-dependent X-parameters
      1. 5.2.1 Time invariance, phase normalization, and commensurate two-tone LSOP
      2. 5.2.2 Spectral linearization
    3. 5.3 Establishing the LSOP using a load tuner: passive load pull
    4. 5.4 Additional considerations for commensurate signals
      1. 5.4.1 Extraction of X-parameter functions under controlled loads
      2. 5.4.2 Harmonic superposition
      3. 5.4.3 Limitations of passive load pull for load-dependent X-parameters
      4. 5.4.4 Sampling of the three-RF-variable space defining the refLSOPS
      5. 5.4.5 Hardware setup for load-dependent X-parameters
      6. 5.4.6 Calibrating out uncontrolled harmonic impedances
    5. 5.5 Arbitrary load-dependent X-parameters of a GaAs FET
      1. 5.5.1 Load-dependent X-parameter model of a GaN HEMT: estimating the effect of independent harmonic impedance tuning
    6. 5.6 Design example: Doherty power amplifier design and validation
      1. 5.6.1 Doherty power amplifier
      2. 5.6.2 X-parameter characterization of the transistors
      3. 5.6.3 X-parameter model validation
      4. 5.6.4 Doherty power amplifier design using X-parameters
      5. 5.6.5 Results
    7. 5.7 Incommensurate signals
      1. 5.7.1 Notation for incommensurate two-tone X-parameters
      2. 5.7.2 Time invariance for incommensurate two-tone X-parameters
      3. 5.7.3 Reference LSOP
      4. 5.7.4 Spectral linearization
      5. 5.7.5 Discussion
      6. 5.7.6 When intermodulation frequencies are negative
      7. 5.7.7 X-parameter models of mixers
    8. 5.8 Summary
    9. Exercises
    10. References
    11. Additional reading
  16. 6 Memory
    1. 6.1 Introduction
    2. 6.2 Modulated signals: the envelope domain
    3. 6.3 Quasi-static X-parameter evaluation in the envelope domain
      1. 6.3.1 Quasi-static two-tone intermodulation distortion from a static one-tone X-parameter model
      2. 6.3.2 ACPR estimations using quasi-static approach
      3. 6.3.3 Limitations of quasi-static approach
      4. 6.3.4 Advantages of quasi-static X-parameters for digital modulation
    4. 6.4 Manifestations of memory
    5. 6.5 Causes of memory
      1. 6.5.1 Self-heating
      2. 6.5.2 Bias modulation
    6. 6.6 Importance of memory
      1. 6.6.1 Modulation-induced baseband memory and carrier memory
      2. 6.6.2 Dynamic X-parameters
      3. 6.6.3 Identification of the memory kernel: conceptual motivation
      4. 6.6.4 Step response of the memory kernel
      5. 6.6.5 Application to real amplifier
      6. 6.6.6 Validation of memory model
      7. 6.6.7 Interpretation of dynamic X-parameters
      8. 6.6.8 Wide-band X-parameters (XWB)
    7. References
    8. Additional reading
  17. Appendix A: Notations and general definitions
    1. A.1 Sets
    2. A.2 Vectors and matrices
    3. A.3 Signal representations
      1. A.3.1 Time-domain representation (real signal)
      2. A.3.2 Complex representation (complex envelope signal)
    4. A.4 Fourier analysis
    5. A.5 Wave definitions
      1. A.5.1 Generalized power waves
      2. A.5.2 Voltage waves
    6. A.6 Linear network matrix descriptions
      1. A.6.1 S-parameters
      2. A.6.2 Z-parameters
      3. A.6.3 Y-parameters
    7. References
  18. Appendix B: X-parameters and Volterra theory
    1. B.1 Introduction
    2. B.2 Mathematical notation and problem definition
    3. B.3 Application of the Volterra theory
    4. B.4 Derivation of the McLaurin series
    5. B.5 McLaurin series for the DC output
    6. B.6 Conclusions
    7. References
  19. Appendix C: Parallel Hammerstein symmetry
    1. References
  20. Appendix D: Wide-band memory approximation
  21. Appendix E: Solutions to exercises
  22. Index