Thread: Pre-reading for the book "Equations of Phase-Locked Loops"

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
  
  

Originally Posted by ignoramus

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.

I would have thought that at least you should be familiar with the contents of a standard text on Engineering Maths, lets say Kreysig.

CB