1. ## 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

2. 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