Electrical Circuits with Variable Parameters

Preface

Introduction

I. The Forced Current Component in an Oscillatory Circuit with a Periodically Varying Inductance

II. Free Oscillations in Circuits with Variable Parameters

III. Operational Admittances and System Functions of Circuits with Variable Parameters


1. Circuit with a Single Periodically Varying Parameter

IV. Calculation of Transients by the Fourier-Series Method


1. Theoretical Principles


2. Calculations Based on the Fourier-Series Method in Practice


3. The Choice of the Parameters


4. The Determination of the Complex Amplitudes of the Applied e.m.f

V. Methods for the Analysis of Pulse Circuits and Problems of the Theory of Pulse and Digital Automatic Controllers


1. General Considerations


2. The Use of the Laplace Transformation for Impulse Functions


3. The z-Transformation


4. Frequency Characteristics of Impulse Functions


5. System Functions of Pulse Circuits

(a) System Functions of a Simple Circuit

(b) System Functions of Complex Impulse Circuits


6. Determination of the Value of the System Response to an Impulse Disturbance at Instants of Time Between Impulses


7. The Passage through a Pulse Circuit of a Signal Displaced in Time with Respect to the Instants of Application of the Impulses


8. Correspondence theorem for z-Transforms


9. Functions that Begin with the k-th Impulse and Functions having k Additional Impulses


10. Derivatives and Integrals of Impulse Functions


11. The Choice of the Parameters of Pulse (Digital) Correcting Equipment

VI. Stability of Circuits with Variable Parameters and Stability of Periodic Modes of Operation in Non-Linear Circuits


1. General Considerations


2. Approximate Method for Investigating the Stability of Periodic Modes of Operation

(a) The Equation of Small Deviations, and Reduction of the Problem to Investigating a Characteristic Equation of Infinite Degree

(b) The Filter Conditions and the Reduction of the Degree of the Characteristic Equation


3. Calculation of the Complete Spectrum


4. Remarks on the Investigation of the Stability of Circuits with Feedback, Containing Parameters Varying Periodically (or Exponentially)


5. Analysis of the Stability of Pulse Circuits with Feedback

(a) The Construction of Nyquist's Diagram in the p-Plane

(b) The Construction of Nyquist's Diagram on the Basis of the z-Transformation

References

Index