Frequency of Self-Oscillations

1st Edition - January 1, 1964
Author: Janusz Groszkowski
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 8 0 3 0 - 1

Frequency of Self-Oscillations covers the realm of electric oscillations that plays an important role both in the scientific and technical aspects. This book is composed of nine… Read more

Purchase options

LIMITED OFFER

Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

Institutional subscription on ScienceDirect

Request a sales quote

Frequency of Self-Oscillations covers the realm of electric oscillations that plays an important role both in the scientific and technical aspects. This book is composed of nine chapters, and begins with the introduction to the alternating currents and oscillation. The succeeding chapters deal with the free oscillations in linear isolated systems. These topics are followed by discussions on self-oscillations in linear systems. Other chapters describe the self-oscillations in non-linear systems, the influence of linear elements on frequency of oscillations, and the electro mechanical oscillators. The final chapters consider the oscillations in a system with reactances in RC and LR circuits. This book will prove useful to electrical engineering students, teachers, researchers.

1. Introduction

1.1. Alternating Currents and Oscillations

1.2. Sinusoidal and Distorted Currents

1.3. Damped, De-Damped and Undamped Currents

1.4. Frequency

1.5. Complex Frequency

1.6. Unit of Time and Standard of Time

1.7. Comparison of Two Slightly Differing Frequencies

1.8. Oscillations, Oscillatory Systems and Modes of Oscillations

1.9. Oscillation Generators

2. Free Oscillations in Linear Isolated Systems

2.1. Free Oscillations in Isolated Systems

2.2. Mechanical Oscillation in Linear Conservative Systems

2.3. Differential Equation, Integral Curve, Phase Plane and Phase Portrait of Oscillation

2.4. Electric Oscillation in Linear Conservative Systems

2.4.1. Energy Relations and Period of Oscillation

2.5. Oscillation in Linear Non-Conservative Systems

2.5.1. Energy Relations, Amplitudes, and Frequency

2.5.2. Frequency Spectrum and Phase Portrait of Damped Oscillation

2.6. Generation of Damped Oscillations

2.7. Solution of Linear Oscillation Equations in the Plane of a Complex Variable

3. Negative Resistors

3.1. Negative Resistors and Their Characteristics

3.2. Electric Arc

3.3. Glow Discharge Tube

3.4. Dynatron

3.5. Semiconductor Devices

3.5.1. Tunnel Diode

3.5.2. Transistor

3.6. Negative Resistors Based on Emission Current Distribution

3.7. Magnetron

3.8. Negative Resistors Based on Phase Inversion

3.8.1. Artificial Electric Arc

3.8.2. Artificial Dynatron

3.8.3. Push-Pull Symmetric Circuit

3.8.4. Series Symmetric Circuit

3.9. Negative Resistors Based on Feed-Back

3.9.1. Triode With Feed-Back

4. Self-Oscillations in Linear Systems

4.1. Mechanism of Producing Undamped Oscillations

4.1.1. Uniform and Non-Uniform Excitation

4.1.2. Uniform Excitation in Linear Systems

4.2. Oscillations in Systems With Negative Resistance

4.2.1. Series Circuit

4.2.2. Parallel Circuit

4.2.3. Oscillations in Series System

4.2.4. Oscillations in Parallel System

4.2.5. Resonant Circuit Excited By Negative Impedance

4.2.6. General Expression For Frequency

4.3. Oscillations in Systems With Two Coupled Circuits

4.4. Oscillations in Polyphase Systems

4.5. Oscillations in Feed-Back Systems

4.5.1. Oscillator With Triode as Negative Resistor

4.5.2. Triode with Feed-Back as Self-Maintained Generator

4.5.3. General Solution of Oscillation Equation

4.5.4. Real Feed-Back Factor

4.5.5. Push-Pull Feed-Back Oscillator

4.5.6. Feed-Back Amplifier

4.6. Feed-Back Circuits

4.6.1. Inductive Divider Oscillator

4.6.2. Capacitive Divider Oscillator

4.6.3. Transformer Oscillator

4.6.4. Grid Resonant Circuit Oscillator

4.6.5. Transformer-Capacitance Oscillator

4.6.6. Interelectrode Coupling Oscillator

4.6.7. Push-Pull Oscillators

4.6.8. Resonance Amplifier With Feed-Back

4.7. Transistor Oscillators

4.8. Building-Up and Decaying of Oscillations

4.9. Satisfying the Amplitude Condition

5. Self-Oscillations in Non-Linear Systems

5.1. Oscillations in Negative Resistor Circuits

5.1.1. Processes in Negative Resistor Oscillators

5.1.2. Negative Resistor Oscillator Equation

5.1.3. Amplitude Condition

5.2. Oscillators in Feed-Back Systems

5.2.1. Exciting Device Characteristic and Feed-Back Straight Line

5.2.2. Power Relations

5.2.3. Self-Maintenance and Self-Excitation of Oscillations

5.2.4. Building-Up of Oscillations

5.2.5. Grid Current Influence

5.2.6. Grid Current Limitation

5.2.7. No-Grid-Current Work

5.3. Mathematical Methods of Investigating Non-Linear Oscillations

5.3.1. Non-Linear Oscillation Equation and its Discussion

5.3.2. Dimensionless Non-Linear Equation

5.3.3. Method of Small Parameters

5.3.4. Method of Slowly Variable Parameters

5.3.5. Transient State of Operation

5.3.6. Oscillations in a Non-Linear Conservative System

5.4. Graphical Methods of Investigating the Non-Linear Oscillation Equation

5.4.1. Short Arcs Method

5.4.2. Isocline Method

5.5. Technical Methods

5.5.1. Oscillator in Steady State of Operation

5.5.2. Oscillator in Transient State of Oscillation

5.5.3. Oscillations in Non-Linear Conservative System

5.6. Method of Reactive Power Balance of Harmonics

5.6.1. Difficulties of Mathematical and Graphical Methods

5.6.2. Principles of the Method

5.6.3. Oscillation Frequency

5.7. Application of the Method to Negative Resistance Oscillators

5.7.1. Series Circuit

5.7.2. Parallel Circuit

5.7.3. Physical Interpretation of Frequency Variations

5.7.4. Combined Resonant Circuits

5.8. Application of the Method to Feed-Back Oscillators

5.8.1. Condition of Reactive Power Balance

5.8.2. Oscillator With Grid Current

5.9. Frequency of Self-Oscillations in Circuits With Non-Linear Reactance Excited By Non-Linear Negative Resistor

6. Influence of Linear Elements on Frequency of Oscillations

6.1. Frequency of Oscillations in Linear Systems

6.2. Influence of Reactive Elements

6.3. Inductors

6.3.1. Influences of Geometric Character

6.3.2. Influences of Electric Character

6.3.3. Maintaining Constant Inductance

6.3.4. Temperature Compensated Coils

6.4. Capacitors

6.4.1. Influences of Geometrical Character

6.4.2. Influences of Electrical Character

6.4.3. Maintenance of Constant Capacitance

6.4.4. Temperature Compensated Condensers

6.5. Maintaining Constant Frequency of Circuits

6.6. Oscillator Tube

6.6.1. Linear Influences

6.6.2. Interelectrode Capacitances

6.6.3. Influence of Cgk as Function of the Feed-Back Factor

6.6.4. Influence of Cgk as a Function of Oscillatory Circuit Capacitance

6.6.5. Oscillators With Reduced Influence of Cgk

6.6.6. Influence of Cathode Interface Layer

6.7. Power Output Influence

6.7.1. Power Output

6.7.2. Indirect Deriving of Power

6.7.3. Power Derivation By Electron Coupling

6.8. Thermostats

6.8.1. Non-Continuous Control Thermostat

6.8.2. Continuous-Control Thermostat

7. Influence of Non-Linear Factors on Oscillation Frequency

7.1. Oscillation Frequency in Non-Linear Systems

7.2. Frequency Stabilization With Respect to Non-Linear Factors

7.3. Operation Without Harmonics

7.3.1. Limit State Operation

7.3.2. Use of Filters

7.3.3. Use of Additional Resistances

7.4. Constant Harmonic Spectrum Operation

7.5. Reactive Power Compensation

7.5.1. Quarter-Wave-Length Line Oscillator

7.5.2. Positive and Negative Feed-Back Oscillators

7.6. High-Q-Circuit Oscillator

7.6.1. High-Q Resonant Circuits

7.6.2. Quarter-Wave-Length Line as High-Q Circuit

7.6.3. Toroidal Circuit

7.7. Constant Harmonic Content Operation

7.7.1. Influence of Supply Voltages

7.7.2. Combined Circuit Oscillators

7.7.3. Hartley and Colpitts Oscillators

7.7.4. Kusunose Circuit

7.7.5. Electron-Coupled Oscillator

7.7.6. Transitron Oscillator

7.8. Grid Current Influence

7.8.1. Oscillator With Automatic Bias

7.9. Influence of the Supply Voltage on the Frequency of Self-Oscillators

7.10. Numerical Example

8. Electromechanical Oscillators

8.1. Piezoelectric Element

8.1.1. Quartz Crystal Axes and Kinds of Cuts

8.1.2. Modes of Vibrations

8.1.3. Natural Frequency

8.1.4. Mechanical Properties of Quartz

8.1.5. Electric Properties

8.1.6. Thermal Expansion of Quartz

8.1.7. Temperature Coefficient of Frequency

8.2. A Piezoelectric Element as Oscillatory Circuit

8.2.1. Vibration Equation and Equivalent Parameters

8.2.2. Equivalent Circuit Impedance

8.3. Piezoelectric Oscillator Circuits

8.3.1. Basic Single-Stage Circuits

8.3.2. gk Oscillator

8.3.3. ga Oscillator

8.3.4. Numerical Example

8.3.5. Influence of Various Factors on Frequency

8.3.6. Negative Resistance Piezoelectric Oscillators

8.3.7. Piezoelectric Element as Feed-Back Coupler

8.3.8. Electron Coupled Oscillators

8.4. Tuning Fork Oscillators

8.4.1. Tuning Fork as Resonant Circuit and Coupling Element

8.4.2. Tuning Fork Feed-Back Oscillator

8.5. Magnetostrictive Oscillators

9. Oscillations in a System With Reactances of Either Sign

9.1. Possibility of Generating Oscillations in RC and LR Circuits

9.2. Bridge RC Oscillators

9.2.1. Sinusoidal Oscillations

9.2.2. Quasi-Sinusoidal Oscillations

9.3. Phase Shift RC Oscillators

9.3.1. RC Oscillator

9.3.2. CR Oscillator

9.3.3. Example

9.4. Relaxation Oscillations

9.4.1. Transition from Sinusoidal to Relaxation Oscillation

9.4.2. Amplitude and Frequency of Relaxation Oscillations

9.4.3. Basic Types of Relaxation Oscillators

9.4.4. Frequency of Relaxation Oscillation in Single Reactive Element Systems

9.4.5. Voltages and Currents in a Relaxation Oscillator

9.4.6. Limit Cycle

9.5. Relaxation Oscillators

9.5.1. Negative Resistance Relaxation Oscillators

9.5.2. Feed-Back Relaxation Oscillators

Bibliography

Subject Index