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Math Help - Pre-reading for the book "Equations of Phase-Locked Loops"

  1. #1
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    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

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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ignoramus View Post
    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
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