Chapter 1 Linear SingleLoop Feedback System

1.1

Transmission and DrivingPoint Impedance


1.1.1

Definitions


1.1.2

Generic SingleLoop System


1.1.3

Inverse Block Diagram; TwoPoles' Connection


1.1.4

Return Ratio as a Function of the Load


1.1.5

Balanced Bridge


1.1.6

Examples and Exercises

1.2

Sensitivity


1.2.1

Sensitivity of Transmission Function


1.2.2

Sensitivity of DrivingPoint Impedance


1.2.3

Reflection Coefficients




1.2.4

Examples and Exercises

1.3

Nonlinear Distortions

1.4

Regulation


1.4.1

Introduction


1.4.2

Parameter Dependence of a Circuit Function


1.4.3

Symmetrical Regulation

1.5

Noise


1.5.1

Noise at the System's Output


1.5.2

Noise at the Input of the Plant


1.5.3

SignaltoNoise Ratio


1.5.4

Examples and Exercises


Chapter 2 Stability and Frequency Response Constraints
of Linear Systems

2.1

Nyquist Stability Criterion


2.1.1

Nyquist Diagram


2.1.2

Nyquist Diagram and Stability Margins for the Amplifier Return
Ratio


2.1.3

TwoPoles' Coupling


2.1.4

Reflection Coefficients


2.1.5

Examples and Exercises

2.2

Integral Constraints


2.2.1

Minimum Phase Functions


2.2.2

Integral of the Real Part


2.2.3

Integral of the Imaginary Part


2.2.4

Examples and Exercises

2.3

PhaseGain Relations


2.3.1

General Relation


2.3.2

Phase Response Calculation


2.3.3

PiecewiseConstant Real and Imaginary Components




2.3.4

Examples and Exercises

2.4

Feedback Maximization


2.4.1

Bode Optimal CutOff


2.4.2

More CutOffs


2.4.3

Asymptotic Losses, HighFrequency Bypass, Loop Gain Correction
in Feedback Amplifiers


2.4.4

Prediction and Feedback Maximization


2.4.5

Negative Resistance Sensitivity


2.4.5

Examples and Exercises

2.5

Nonminimum Phase Shift


2.5.1

Causes for the Nonminimum Phase Shift


2.5.2

Parallel Connection of Two Links


2.5.3

Effect of Loading


2.5.4

Noncascade Connection of Active TwoPorts


Chapter 3 Linear SingleLoop Feedback System

3.1

Absolute Stability Problem

3.2

Popov Criterion


3.2.1

Nonlinear Physical TwoPoles


3.2.2

Popov Criterion


3.2.3

Applications


3.2.3

Examples and Exercises

3.3

Periodical and NonPeriodical SelfOscillation

3.4

Multifrequency Oscillation in a Bandpass System with
Saturation


3.4.1

Goals for Analysis




3.4.2

Oscillation with Fundamental at which the Loop Gain is Large


3.4.3

Oscillation with Fundamental at which the Loop Gain is Small

3.5

Describing Function Approach

3.6

Describing Functions for the Basic Types of Nonlinear Links

3.7

Multivalued OutputInput Relations


3.7.1

TwoPole with Begative dc Resistance


3.7.2

TwoPort


Chapter 4 Forced Oscillation

4.1

Periodic Excitation

4.2

Absolute Stability of the Output Process

4.3

JumpResonance


4.3.1

Conditions for the Jumps


4.3.2

System with Dynamic Saturation


4.3.3

System with Nondynamic Linear Link


4.3.4

System with Nondynamic Saturation


4.3.5

Substantiation of DF Technique for the JumpResonance Analysis




4.3.6

System with DeadZone Element


4.3.7

System with Nonlinear Element Having PowerType DF


4.3.8

Examples and Exercises

4.4

Odd Subharmonics

4.5

Second Subharmonic


Chapter 5 Nonlinear Dynamic Compensator (NDC)

5.1

Loop Regulation


5.1.1

Variable Loop Gain


5.1.2

Switching in the Compensator


5.1.3

Quasilinear Variable Compensator


5.1.4

Nonlinear Dynamic Compensator

5.2

Describing Function Approach to NDC design


5.2.1

Generalities


5.2.2

Stability Conditions


5.2.3

Phase Stability Margin




5.2.4

Design Constraints


5.2.5

Amplitude Characteristics


5.2.6

Effect of Loop Gain Ignorance


5.2.7

Sufficient Stability Criterion

5.3

NDC in the Interstage Circuit of a Wideband Feedback Amplifier

5.4

Experiments

5.5

Special Applications


Chapter 6 Linear Multiloop System

6.1

Generalities

6.1

Stability Criteria


6.2.1

Generalization of the Nyquist Criterion


6.2.2

Examples and Exercises



6.3

FeedForward

6.4

System with Parallel Amplification Channels


6.4.1

Sensitivity


6.4.2

Stability


Chapter 7 Nonlinear Multiloop System: Describing Function
Approach

7.1

Local Feedback


7.1.1

Cascaded Links


7.1.2

Feedback Around the Ultimate Stage

7.2

Two Parallel Channels with Saturation


7.2.1

Frequency Responses of the Linear Part


7.2.2

Piecewise Analysis of the AAPC


7.2.3

JumpResonance


7.2.4

Frequency Response of the Main Channel Transmission Function


7.2.5

Modifications




7.2.6

Numerical Examples


7.2.7

Experiment

7.3

Two Parallel Channels with Saturation and Dead Zone


7.3.1

Frequency Responses of the Linear Part


7.3.2

JumpResonance


7.3.3

Nonlinear Dynamic Compensator


7.3.4

Experiment


Chapter 8 Nonlinear Multiloop System: Absolute Stability
Approach

8.1

System Reducible to SingleChannel


8.1.1

Block Diagrams


8.1.2

Integral Constraint and Stability margin


8.1.3

Plant with Saturation

8.2

DeadZone Element in the NDC Feedback Path

8.3

Positive and Negative Feedback in the NDC

8.4

Multifrequency Oscillation in a Bandpass System with
Saturation

8.5

DF versus AS Techniques



8.6

TwoChannel System with a Lowpass in the Plant


8.6.1

Block Diagram


8.6.2

Noise


8.6.3

Other Points of View


8.6.3

The Allowable Discrepancy of Nonlinear Link Characteristics


8.6.3

Experiment

8.7

NDC with Two Nonlinear Elements

8.8

Switching Regulation

