Hi all,
I recently picked up the book titled "Equations of Phase-Locked Loops - Dynamics on Circle, Torus and Cylinder" Its Table of Contents can be found here. My math background is very little that is necessary for engineering and that was a while ago. I learned things like differential equations and their solutions, vector algebra and calculus etc but most of them forgotten as I don't have any need for them in my daily work.
I am having a hard time understanding the above book. Can you guys kindly suggest some easy going pre-reading books to understand the math used in the book. I am pasting a short-version of the table of contents below. The longer version is available in the link above. Thank You for your time.
- Introduction:
- What Is Phase-Locked Loop?
- PLL and Differential or Recurrence Equations
- Averaging Method
- Organization of the Book
- The First Order Continuous-Time Phase-Locked Loops:
- Equations of the System
- The Averaged Equation
- Solutions of the Basic Frequency
- Differential Equation on the Torus
- Fractional Synchronization
- The System with Rectangular Waveform Signals
- The Mapping (f(p)=p+2πμ+a sin(p)
- The Second Order Continuous-Time Phase-Locked Loops:
- The System with a Low-Pass Filter
- Phase-Plane Portrait of the Averaged System
- Perturbation of the Phase Difference φ(wt)
- Stable Integral Manifold
- The PLL System Reducible to the First Order One
- Homoclinic Structures
- Boundaries of Attractive Domains
- The Smale Horseshoe, Transient Chaos
- Higher Order Systems Reducible to the Second Order Ones
- One-Dimensional Discrete-Time Phase-Locked Loop:
- Recurrence Equations of the System
- Periodic Output Signals
- Rotation Interval and Frequency Locking Regions
- Stable Orbits, Hold-In Regions
- The Number of Stable Orbits
- Bifurcations of Periodic Orbits
- Bifurcation of the Rotation Interval
- Two-Dimensional Discrete-Time Phase-Locked Loop:
- Description of the DPLL System by a Two-Dimensional Map
- Stable Periodic Orbits
- Reduction to a One-Dimensional System
- Strange Attractors and Chaotic Steady-States