《THE DESIGN AND USE OF ELECTRONIC ANALOGUE COMPUTERS》求取 ⇩

1．Introduction to Analogue Computers1

1．1．ANALOGUES1

1．1．1．Basic Ideas1

1．1．2．Analogous Systems-Scale Factors1

1．1．3．The Analogue Method4

1．1．4．Analogue Computers5

1．2．THE ELECTRONIC ANALOGUE COMPUTER6

1．2．1．General Requirements6

1．2．2．Passive Computing Circuits6

1．2．3．D．C．Amplifiers10

1．2．4．Active Computing Circuits11

1．2．5．The Virtual Earth Concept13

1．2．6．Feedback in Computing Circuits15

1．3．BASIC COMPUTING CIRCUITS16

1．3．1．Addition16

1．3．2．Integration17

1．3．3．Differentiation19

1．3．4．Operational Form20

1．4．EXAMPLE OF THE SOLUTION OF A DIFFERENTIAL EQUATION23

1．4．1．Linear Equation23

1．4．2．Use of the Analogue26

1．4．3．Non-linear and Time Varying Systems27

1．4．4．Time Scaling28

1．5．USES OF ANALOGUE COMPUTERS29

1．5．1．General29

1．5．2．Equations for which Analogue Computers can be Used31

1．5．3．Implicit Circuits32

1．6．DIGITAL COMPUTERS35

1．6．1．General Considerations35

1．6．2．General Comparison38

2．The Behaviour of Operational Computing Circuits40

2．1．FUNDAMENTAL APPROACH40

2．2．ERRORS DUE TO FINITE AMPLIFIER GAIN48

2．2．1．Adder48

2．2．2．Integrator50

2．2．3．Differentiator55

2．3．AMPLIFIER IMPERFECTIONS57

2．3．1．Amplifier Input Impedance57

2．3．2．Effect of Amplifier Output Impedance59

2．3．3．Effect of Amplifier Drift61

2．3．4．The Effect of a Current Injected at the Amplifier Input64

2．3．5．Amplifier Balancing69

2．4．COMPUTING UNIT STABILITY70

2．4．1．General70

2．4．2．Method of Representation72

2．4．3．Adder Frequency Response75

2．4．4．Integrator Frequency Response78

2．4．5．Frequency Response of a Differentiator81

2．5．OVERALL FREQUENCY RESPONSE81

2．6．HIGH FREQUENCY EFFECTS85

2．6．1．Amplifier Input Capacitance85

2．6．2．Load Capacitance90

3．Computing Amplifier Design94

3．1．D．C．AMPLIFIERs94

3．2．INPUT STAGE DESIGN CONSIDERATIONS98

3．2．1．Drift98

3．2．2．Reduction of Drift Due to Power Supply Fluctuations99

3．2．3．Unsymmetrical Input Stages102

3．2．4．Practical Considerations105

3．3．OUTPUT STAGE107

3．4．FREQUENCY RESPONSE OF COMPUTING AMPLIFIERS110

3．4．1．Introduction110

3．4．2．Pentode Amplifiers111

3．4．3．Triode Amplifiers113

3．4．4．The Cathode Follower,and Cathode Coupled Stages119

3．4．5．Frequency Response of Complete Computing Amplifiers120

3．4．6．Shaping the Overall Frequency Response125

3．4．7．Practical Considerations130

3．5．DRIFT CORRECTORS131

3．5．1．Carrier Amplifiers131

3．5．2．Relay＂Chopper＂Amplifier133

3．5．3．Relay Properties136

3．5．4．Sources of Drift139

3．5．5．Frequency Response of a Drift Corrected Amplifier143

3．5．6．Effect of Drift Correctors Upon Computation146

3．5．7．Use of Higher Carrier Frequencies147

3．6．PUSH-PULL AMPLIFIERS148

3．7．REGENERATION152

3．8．TRANSISTOR AMPLIFIERS154

3．9．ANALYSIS155

3．9．1．Cathode Coupled Amplifier155

3．9．2．Phase-reversing(Miller)Compensator157

3．9．3．Non-phase-reversing Compensator158

3．9．4．Effect of Grid-anode Capacitance on a Two-stage Ampli-fier159

4．The Solution of Differential Equations164

4．1．BASIC METHOD OF SOLUTION164

4．2．ELEMENTARY APPLICATIONS168

4．2．1．First Order Equation168

4．2．2．Second Order Equation172

4．2．3．Typical Input Signals175

4．3．ALTERNATIVE METHODS OF CIRCUIT DESIGN179

4．4．COMPUTERS AND SIMULATORS183

4．4．1．Illustrative Example183

4．4．2．Comparison of Simulator and Computer Circuits188

4．4．3．Simplified Formulation190

4．5．TRANSFER FUNCTIONS192

4．5．1．Introduction192

4．5．2．Multiple and Combined Input Circuits．198

4．5．3．Suitability of Circuits199

4．5．4．Shunt Components200

4．5．5．Underdamped Second Order Transfer Functions205

4．5．6．Design of Second Order Transfer Function Circuits209

4．5．7．Multiple Input Second Order Transfer Function Circuits212

4．5．8．Transfer Functions Involving Differentiation215

4．5．9．Higher Order Transfer Functions216

4．6．AMPLITUDE SCALE FACTORS219

4．6．1．Basic Ideas219

4．6．2．Introductory Examples221

4．6．3．General Procedure228

4．6．4．Scaling of a Second Order Equation228

4．6．5．Discussion232

4．7．TIME SCALE FACTORS232

4．7．1．Introduction232

4．7．2．Range of CoefficientS237

4．7．3．Dimensional Time Scale Factor241

4．7．4．Summary245

4．8．DYNAMIC ACCURACY246

4．8．1．Introduction246

4．8．2．Dynamic Errors in a Damped Second Order Circuit252

4．8．3．General Conclusions257

5．Auxiliary Computing Equipment259

5．1．NON-LINEAR PHENOMENA259

5．2．NON-LINEAR CIRCUITS USING DIODES(CONTINUOUS FUNCTIONS)260

5．2．1．Diode Characteristics260

5．2．2．Series Diode Circuits261

5．2．3．Series Circuit Design264

5．2．4．Shunt Diode Circuits270

5．2．5．More Advanced Techniques275

5．2．6．Discussion of Methods279

5．3．DIODE CIRCUITS GIVING DISCONTINUOUS FUNCTIONS280

5．3．1．Simple Limiter280

5．3．2．Alternative Biasing Methods286

5．3．3．Idealised Diode Circuit290

5．3．4．Examples of Discontinuous Circuits291

5．3．5．Discussion on Discontinuous Circuits Using Biased Diodes294

5．3．6．Biased Diodes in Capacitive Circuits294

5．4．NON-LINEAR RESISTIVE MATERIALS297

5．5．COMPUTING CIRCUITS USING RELAYS301

5．5．1．Comparator Controlled Relays301

5．5．2．Mechanical Limits303

5．5．3．Non-linear Friction304

5．6．MISCELLANEOUS METHODS OF INTRODUCING NON-LINEAR EFFECTS306

5．6．1．Electromechanical Methods306

5．6．2．Curve Followers(＇Photoformers＇)309

5．7．MULTIPLIERS311

5．7．1．Multiplier Scaling311

5．7．2．Electrodynamic Multipliers312

5．7．3．Function Multipliers312

5．7．4．Variable Gain Multipliers314

5．7．5．Practical Features of Mark-Space Ratio Multipliers320

5．7．6．Application of Multipliers to Division323

5．7．7．Multiplier Examples326

5．7．8．Summary of Multiplier Properties328

5．8．TIME FUNCTION GENERATORS328

5．9．MISCELLANEOUS TOPICS331

5．9．1．Generalised Integration331

5．9．2．Functions of Two Variables333

5．9．3．Time Delays(Transportation Lags)336

6．Computer Construction348

6．1．INTRODUCTION348

6．2．COMPUTING COMPONENTS352

6．3．INTERCONNECTION SYSTEM357

6．3．1．Elementary Methods357

6．3．2．Mounting of Computing Components358

6．3．3．Interconnection by Patching360

6．3．4．Improved Direct Patching361

6．3．5．Discussion of Methods364

6．4．CONTROL SYSTEM364

6．4．1．Principal Requirements364

6．4．2．Reset or Balance365

6．4．3．Combined Reset Circuits368

6．4．4．Additional Modes of Operation369

6．4．5．Relay Operating Speed373

6．4．6．Relay Energising Circuits373

6．4．7．Elementary Forms of Automatic Control374

6．4．8．Automatic Programming377

6．4．9．Repetitive Computers378

6．5．OUTPUT ELEMENTS378

6．5．1．General Methods378

6．5．2．XY Recorders(Plotting Tables)379

6．5．3．＇High Speed＇Recorders380

6．6．OVERLOAD ALARM SYSTEMS381

6．6．1．Causes of Overloading381

6．6．2．Output Monitoring381

6．6．3．Input Monitoring385

6．6．4．Drift Monitoring385

6．7．OVERALL COMPUTER DESIGN385

7．General Techniques387

7．1．THE PROCESS OF SOLVING PROBLEMS387

7．2．PROBLEM AND CIRCUIT CHECKING388

7．2．1．Problem Checking388

7．2．2．Fault Investigation392

7．2．3．Common Types of Faults394

7．2．4．Use of Differentiators398

7．3．ANALYSIS OF RESULTS399

7．3．1．General Considerations399

7．3．2．First Order System400

7．3．3．Second Order Systems402

7．3．4．Higher Order Systems409

7．4．COMPUTER CIRCUITS FOR OUTPUT EVALUATION411

7．4．1．General Applications411

7．4．2．Integral-of-Product Circuit412

7．4．3．Phase Plane and Phase Measurements415

7．4．4．Nyquist Diagrams416

7．5．COMPUTER ACCURACY417

7．6．1．Types of Errors417

7．5．2．The Effect of Spurious Inputs418

7．5．3．Calibration Errors420

7．5．4．Measurement Errors423

7．6．DIRECT CALIBRATION TECHNIQUES-VOLTAGE MEASUREMENT423

7．6．1．Voltage Measurement423

7．6．2．Adder Calibration424

7．6．3．Reference Supply426

7．6．4．The＂Calibrator＂Circuit426

7．6．5．Adjustment of Adder gain428

7．6．6．Practical Features of Calibration Equipment431

7．7．DIRECT CALIBRATION TECHNIQUES-TIME MEASUREMENT433

7．7．1．Integrator Calibration433

7．7．2．Accurate Timing Methods435

7．7．3．Calibration Procedure437

7．7．4．Example on the Accuracy of Integrator Calibration437

7．7．5．Time Constant Adjustment440

7．7．6．Timing Equipment441

7．8．MISCELLANEOUS CALIBRATION TECHNIQUES443

7．8．1．Rate Testing of Integrators443

7．8．2．Difierentiator Calibration443

7．8．3．Calibration of other Transfer Functions445

8．Applications of Analogue Computers449

8．1．PARTIAL DIFFERENTIAL EQUATIONS449

8．2．ALGEBRAIC EQUATIONS AND RELATED TOPICS453

8．2．1．Simultaneous Equations453

8．2．2．Non-Linear Flow455

8．2．3．Eigenvalue Problems458

8．2．4．An Eigenvalue Problem Involving the Diffusion Equation460

8．3．PROBLEMS IN ECONOMICS,PROGRAMMING,ETC．462

8．3．1．Business Gaming462

8．3．2．Programming Methods466

8．4．BOUNCING SPRING471

8．5．A CHEMICAL ENGINEERING PROBLEM473

8．6．THE AUTOMATIC TEMPERATURE CONTROL OF A POWER PRODUCING NUCLEAR REACTOR475

8．6．1．General Description475

8．6．2．Neutron Kinetics476

8．6．3．Xenon Poisoning480

8．6．4．Heat Transfer480

8．6．5．Automatic Controller485

8．7．ELECTRICAL ENGINEERING PROBLEMS486

8．7．1．General486

8．7．2．Simulation of Rectifiers486

8．7．3．Switches and Circuit Breakers489

8．7．4．Simulation of a Three Phase Circuit491

8．7．5．Restriking495

9．Appendices498

9．1．LAPLACE TRANSFORMS498

9．1．1．General498

9．1．2．Solution of Equations498

9．1．3．Other Uses of the Laplace Transformation504

9．2．FACTORS OF HIGH ORDER POLYNOMIALS508

9．3．STABILITY510

9．3．1．Characteristic Equation510

9．3．2．System Stability511

9．3．3．Routh Criterion512

9．3．4．Nyquist Criterion513

9．3．5．Logarithmic Co-ordinates515

9．3．6．Use of Logarithmic Co-ordinates．(＇Bode＇Diagrams)518

Index521