《ENGINEERING DESIGN HANDBOOK SERVOMECHANISMS SECTION 3 AMPLIFICATION》

CHAPTER 13AMPLIFIERS USED IN CONTROLLERS1

13-1ELECTRONIC AMPLIFIERS1

13-1．1 VACUUM TUBES1

13-1．2 Diodes1

13-1．3 Control of electron flow2

13-1．4 Diodes as rectifiers2

13-1．5 Triodes3

13-1．6 Plate characteristics3

13-1．7 Graphical analysis3

13-1．8 Linear approximations4

13-1．9 Region of operation4

13-1．10 Linear equivalent circuits4

13-1．11 Alternate linear equivalent circuit5

13-1．12 Quiescent operating point5

13-1．13 Phase shift5

13-1．14 Pentodes and Beam-Power Tubes5

13-1．15 Plate characteristics6

13-1．16 Linear equivalent circuits6

13-1．17 Graphical analysis6

13-1．18 Interelectrode Capacitance6

13-1．19 Tube Specifications7

13-1．20 LINEAR ANALYSIS OF SINGLE-STAGE VACUUM-TUBE VOLTAGE AMPLIFIERS7

13-1．21 Characteristics of Tubes Used7

13-1．22 Simple Amplifier7

13-1．23 Series Tube Triode Amplifier8

13-1．24 Cascode Amplifier8

13-1．25 Cathode Followers9

13-1．26 Simple Feedback Amplifier11

13-1．27 Differential Amplifiers12

13-1．28 Use of Pentodes13

13-1．29 POWER AMPLIFIERS13

13-1．30 Tubes Used in Power Amplifiers13

13-1．31 Push-Pull Power Amplifiers14

13-1．32 Analysis of push-pull power amplifiers15

13-1．33 Push-pull amplifier with a-c supply15

13-1．34 Efficiency15

13-1．35 CASCADING AMPLIFIER STAGES15

13-1．36 Direct-Coupled Amplifiers15

13-1．37 Problems encountered in direct-coupled amplifiers18

13-1．38 Drift-compensated direct-coupled amplifier19

13-1．39 Bridge circuits19

13-1．40 A-C Coupled Amplifiers21

13-1．41 Two-stage a-c coupled amplifier21

13-1．42 FEEDBACK AMPLIFIERS23

13-1．43 Advantages23

13-1．44 Disadvantages25

13-1．45 PROBLEMS ENCOUNTERED IN USE OF ELEC-TRONIC AMPLIFIERS AS SERVO COMPONENTS26

13-1．46 Reliability26

13-1．47 Construction27

13-1．48 Maintenance27

13-1．49 Quadrature Signals27

13-1．50 Complete Amplifier27

13-1．51 Details of a Typical Servo Amplifier28

13-1．52 THYRATRON AMPLIFIERS28

13-1．53 Description of Thyratron28

13-1．54 Thyratron Characteristics30

13-1．55 Thyratron Amplifier with Resistive Load30

13-1．56 Control of Load Voltage31

13-1．57 Thyratron-Amplifier Loads32

13-1．58 Resistive loads33

13-1．59 Inductive loads33

13-1．60 Battery,capacitive,and separately excited d-c motor loads34

13-1．61 Dynamic Performance35

13-1．62 Exception to time-constant rule35

13-1．63 D-C POWER SUPPLIES FOR ELECTRONIC AM-PLIFIERS35

13-1．64 Types of Rectifiers35

13-1．65 Power-Supply Circuits35

13-1．66 Design of D-C Power Supplies36

13-1．67 Typical electronic regulator37

13-2TRANSISTOR AMPLIFIERS38

13-2．1 BASIC PRINCIPLES38

13-2．2 Operating Characteristics of Temperature-Limited Vacuum Diode38

13-2．3 Transistor Operation39

13-2．4 Advantages and disadvantages of transistors39

13-2．5 High-frequency operation39

13-2．6 Medium-frequency operation39

13-2．7 High-power applications40

13-2．8 Switching applications40

13-2．9 Summary40

13-2．10 BASIC THEORY OF JUNCTION DIODES AND TRANSISTORS40

13-2．11 Electron Current40

13-2．12 Hole Current40

13-2．13 Material Types41

13-2．14 Junctions41

13-2．15 Junction Diodes41

13-2．16 Junction Transistors42

13-2．17 Special transistor types42

13-2．18 Characteristics of transistor materials42

13-2．19 ANALYSIS OF TRANSISTOR CHARACTERISTICS43

13-2．20 Transistor Model43

13-2．21 Piecewise linear model44

13-2．22 Incremental model44

13-2．23 Hybrid Parameters46

13-2．24 Frequency Dependence46

13-2．25 Temperature Sensitivity47

13-2．26 Nonuniformity47

13-2．27 Noise Factor50

13-2．28 Microphonics and Vibration Effects50

13-2．29 Maximum Collector Voltage50

13-2．30 Maximum Power Dissipation50

13-2．31 TRANSISTOR AMPLIFIER CIRCUITS50

13-2．32 Grounded-Emitter Amplifier50

13-2．33 Grounded-Base Amplifier50

13-2．34 Grounded-Collector Amplifier51

13-2．35 Phase-Inverter and Difference-Amplifier Circuits51

13-2．36 High Power Amplifiers51

13-2．37 Maximum power output52

13-2．38 Biasing52

13-2．39 Typical Two-Stage Transistor Amplifier54

13-2．40 Direct-Coupled Amplifiers54

13-2．41 State of the Art55

13-2．42 A-C POWER AMPLIFIER DESIGN55

13-3MAGNETIC AMPLIFIERS58

13-3．1 BASIC CONSIDERATIONS58

13-3．2 Functions of Magnetic Amplifiers in Servo Systems58

13-3．3 Features of Magnetic Amplifiers58

13-3．4 Application Problems of Magnetic Amplifiers58

13-3．5 Temperature Limitations58

13-3．6 Design Difficulties58

13-3．7 PRINCIPLES OF OPERATION59

13-3．8 Single-Core,Single-Rectifier Circuit59

13-3．9 Operating cycle of a single-core circuit59

13-3．10 Exciting and conducting periods60

13-3．11 Reset period60

13-3．12 Control limits60

13-3．13 Control characteristics61

13-3．14 Analysis limitations61

13-3．15 Analysis extension62

13-3．16 TYPICAL CIRCUITS62

13-3．17 Half-Cycle(Ramey)Circuit62

13-3．18 Single-Ended,Two-Core Circuits62

13-3．19 Operation of two-core circuits63

13-3．20 Reversible-Polarity and Reversible-Phase Circuits63

13-3．21 Example of reversible-phase amplifier63

13-3．22 ANALYTICAL REPRESENTATION OF MAGNETIC AMPLIFIERS64

13-3．23 Dynamic Performance64

13-3．24 Dynamic response65

13-3．25 Accuracy of prediction65

13-3．26 Analytical Representation65

13-3．27 Effectivecontrol-circuit resistance65

13-3．28 Limitations in analytical representation66

13-3．29 Conclusions66

13-3．30 PERFORMANCE OF MAGNETIC AMPLIFIERS66

13-3．31 Ranges of Input and Output Power66

13-3．32 Control Characteristics66

13-3．33 Figure of Merit66

13-3．34 Typical values of Figure of Merit68

13-3．35 Expression for Figure of Merit69

13-3．36 Largest factor70

13-3．37 Effects of dimensions70

13-3．38 Leakage effects70

13-3．39 Temperature effects70

13-3．40 CONSTRUCTION OF MAGNETIC AMPLIFIERS70

13-3．41 Methods of Core Construction70

13-3．42 Relative merits71

13-3．43 Core Materials71

13-3．44 Applications71

13-3．45 Rectifiers72

13-3．46 Characteristics of selenium rectifiers72

13-3．47 Characteristics of germanium rectifiers72

13-3．48 Characteristics of silicon rectifiers72

13-3．49 Factors governing choice of rectifier type72

13-3．50 SPECIFICATIONS AND DESIGN72

13-3．51 Specifications72

13-3．52 Approach to Design73

13-4ROTARY ELECTRIC AMPLIFIERS73

13-4．1 TYPES OF ROTARY ELECTRIC AMPLIFIERS73

13-4．2 Basic Principles73

13-4．3 Power-Handling and Time-Constant Characteristics73

13-4．4 Basic Features74

13-4．5 Types of Rotary Electric Amplifiers74

13-4．6 Excitation74

13-4．7 Single-shunt-winding machine76

13-4．8 Armature reaction76

13-4．9 Cross-field machine76

13-4．10 Other multistage machines76

13-4．11 CHARACTERISTICS OF ROTARY ELECTRIC AM-PLIFIERS77

13-4．12 Steady-State and Transient Characteristics77

13-4．13 Deriving input-output characteristics77

13-4．14 Simplifying characteristic derivation77

13-4．15 Effects of saturation and variable speed78

13-4．16 Results of saturation79

13-4．17 Results of speed variations79

13-4．18 Linear operation79

13-4．19 Derivation of dynamic characteristics79

13-4．20 PARAMETERS OF D-C ROTARY AMPLIFIERS80

13-4．21 Fundamental Requirements80

13-4．22 Stored energy82

13-4．23 Resistance of field winding82

13-4．24 Dissipated power82

13-4．25 Basic information for field-system design82

13-4．26 Power amplification83

13-4．27 PROBLEMS ENCOUNTERED IN THE USE OF ROTARY ELECTRIC AMPLIFIERS IN SERVO APPLICATIONS83

13-4．28 Design Factors83

13-4．29 SELECTION OF ROTARY ELECTRIC AMPLIFIERS FOR CONTROL PURPOSES85

13-4．30 Controlling Factors85

13-4．31 TYPICAL CHARACTERISTICS AND DESIGN DATA OF SOME ROTARY ELECTRIC AMPLIFIERS86

13-4．32 Information Available from Manufacturers86

13-4．33 Dynamic Performance87

13-5RELAY AMPLIFIERS87

13-5．1 DEFINITION87

13-5．2 ADVANTAGES AND DISADVANTAGES87

13-5．3 RELAY CHARACTERISTICS88

13-5．4 Description of Operation88

13-5．5 Usage of Relays88

13-5．6 SINGLE-SIDED RELAY AMPLIFIERS FOR SPEED CONTROL88

13-5．7 Typical Amplifiers88

13-5．8 Operation89

13-5．9 REVERSIBLE MOTOR-SHAFT ROTATION90

13-5．10 Servomechanism Applications90

13-5．11 Relay-Amplifier Operation for Positional Control90

13-5．12 Basic operation90

13-5．13 Phase-Sensitive Relay Amplifiers90

13-5．14 Typical types90

13-5．15 Operation of single-stage phase-sensitive relay amplifier90

13-5．16 Choice of circuit components91

13-5．17 POLARIZED RELAYS93

13-5．18 Purpose93

13-5．19 Advantages and Disadvantages98

13-5．20 STATIC CHARACTERISTICS OF RELAYS98

13-5．21 Idealized Relay98

13-5．22 Sensitivity98

13-5．23 Contact Rating99

13-5．24 DYNAMIC CHARACTERISTICS OF RELAYS100

13-5．25 Response Time100

13-5．26 Nature of time delay100

13-5．27 General Considerations100

13-5．28 PARAMETER MEASUREMENT101

13-5．29 Relay Operating Time101

13-5．30 PROBLEMS ENCOUNTERED WITH RELAY AMPLIFIERS102

13-5．31 R/δ,A Figure of Merit102

13-5．32 Relay Life102

13-5．33 False Operation103

13-6HYDRAULIC AMPLIFIERS105

13-6．1 INTRODUCTION105

13-6．2 Description and Usage105

13-6．3 Characteristics109

13-6．4 TRANSLATIONAL HYDRAULIC AMPLIFIERS110

13-6．5 Spool-Valve Type110

13-6．6 Equivalent source representation of four-way spool valve110

13-6．7 Flow equations of underlapped four-way spool valve110

13-6．8 Dimensionalizing flow-gain and conductance plots of underlapped four-way spool valve119

13-6．9 Small-signal gain and conductance parameters of underlapped four-way spool valve119

13-6．10 Balanced-load steady-state characteristics of un-derlapped four-way spool valve121

13-6．11 Flow equations of four-way spool valve with radial clearance122

13-6．12 Dimensionalizing flow-gain and conductanee plots of four-way spool valve with radial clearance124

13-6．13 Plate-Valve Type128

13-6．14 Double Nozzle-Baffle-Valve Type129

13-6．15 Flow equations of double nozzle-bafile valve130

13-6．16 Double nozzle-baffle amplifier with balanced load131

13-6．17 Dimensionalizing pressure-gain and resistance plots of double nozzle-baffle amplifier132

13-6．18 Pressure-Control and Flow-Control Valve Amplifiers134

13-6．19 ROTARY HYDRAULIC AMPLIFIERS136

13-6．20 Characteristies136

13-6．21 INTERACTION OF LOAD AND VALVE137

13-6．22 Equivalent Hydraulic Circuit of Amplifier138

13-6．23 Block Diagram148

13-6．24 DYNAMIC RESPONSE OF ROTARY PUMP AND LOAD149

13-6．25 DYNAMIC RESPONSE OF TRANSLATIONAL AM-PLIFIER AND LOAD150

13-6．26 PROBLEMS ENCOUNTERED IN USE OF HY-DRAULIC AMPLIFIERS150

13-6．27 HYDRAULIC-CIRCUIT ELEMENTS155

13-6．28 ILLUSTRATIVE EXAMPLE158

13-6．29 List of Pertinent Equations and Parameters158

13-6．30 Calculation of Valve Constants158

13-6．31 Calculation of Other Constants159

13-6．32 Calculation of Coefficients a and b159

13-6．33 Results,Simplification,and Significance160

13-7PNEUMATIC AMPLIFIERS160

13-7．1 INTRODUCTION162

13-7．2 PNEUMATIC VALVES163

13-7．3 STATIC CHARACTERISTICS OF PNEUMATIC VALVES163

13-7．4 Orifice Flow163

13-7．5 Nondimensional Flow165

13-7．6 Equivalent Source168

13-7．7 Plate-Valve Static Characteristics169

13-7．8 Conical-Plug Valve Static Characteristics170

13-7．9 Nozzle-Baffle Valve Static Characteristics170

13-7．10 DYNAMIC BEHAVIOR OF PNEUMATIC AMPLI-FIERS173

13-7．11 Equivalent-Circuit Elements for Pneumatic Systems173

13-7．12 Resistance173

13-7．13 Capacitance175

13-7．14 Inertance175

13-7．15 Time constant176

13-7．16 Pneumatic Equivalents for Dashpots,Springs,and Masses176

13-7．17 Dynamic Behavior of Four-Way Valves176

13-7．18 Dynamic Behavior of Three-Way Valves177

13-7．19 Typical Performance of Low-Pressure Three-Way Valves178

13-7．20 ADVANTAGES AND DISADVANTAGES OF PNEU-MATIC SYSTEMS180

13-7．21 Advantages180

13-7．22 Disadvantages180

13-8MECHANICAL AMPLIFIERS181

13-8．1 BASIC TYPES181

13-8．2 Variable-Speed-Output Mechanical Amplifier181

13-8．3 Ball-disc integrator182

13-8．4 Cone-and-disc-amplifier182

13-8．5 Variable-Torque-Output Mechanical Amplifier182

13-8．6 STATIC CHARACTERISTICS OF MECHANICAL AMPLIFIERS184

13-8．7 Ideal and Actual Characteristics184

13-8．8 Static Characteristics of Integrator Type Mechanical Amplifiers185

13-8．9 Static Characteristics of Capstan Type Amplifier187

13-8．10 DYNAMIC BEHAVIOR OF MECHANICAL AMPLI-FIERS187

13-8．11 Capstan Amplifier187

13-8．12 Integrator Amplifier191

13-8．13 OTHER MECHANICAL AMPLIFIERS191

13-8．14 Clutch-Type Amplifiers191

13-8．15 PROBLEMS ENCOUNTERED WITH MECHANICAL AMPLIFIERS195

13-8．16 Capstan Amplifiers195

13-8．17 Integrator Amplifiers195

13-8．18 Clutch Amplifiers196

LIST OF ILLUSTRATIONS1

13-1Symbolic representation of a diode1

13-2 Volt-ampere curve of a diode cathode temperature constant2

13-3 Diode used as a rectifier2

13-4 Symbolic representation of a triode3

13-5 Plate characteristics of a triode3

13-6 Triode amplifier3

13-7 Graphical analysis of a triode amplifier4

13-8 Linear equivalent circuit of a triode4

13-9 Alternate equivalentcircuit of a triode5

13-10 Symbolic representation of a beam-power tube and a pen-tode6

13-11 Plate characteristics of a beam-power tube with constant screen voltage6

13-12 Plate characteristics of a pentode with constant suppressor and screen voltages6

13-13 Equivalent circuit of a simple plate-loaded amplifier7

13-14 Series tube amplifier8

13-15 Cascode amplifier circuit9

13-16 Cathode follower9

13-17 Equivalent circuit of a cathode follower and its manipula-tion10

13-18 White cathode follower11

13-19 Thevenin equivalent circuit of White cathode follower11

13-20 Two-tube cathode follower11

13-21 Plate-and-cathode-loaded amplifier13

13-22 Differential amplifier13

13-23 Push-pull amplifier14

13-24 Graphical analysis of a push-pull amplifier16

13-25 Power amplifier with a-c supply17

13-26 Waveforms of power amplifier in Fig．13-2517

13-27 Voltage-divider-coupled d-c amplifier17

13-28 Battery-coupled,d-c amplifier18

13-29 D-c amplifier with single supply voltage18

13-30 D-c amplifier with gas-discharge tube coupling19

13-31 Drift-compensated d-c amplifier20

13-32 Drift-compensated d-c amplifier20

13-33 Drift-compensated d-c amplifier20

13-34 Use of a-c amplifier to replace d-c amplifier21

13-35 Two-stage a-c amplifier(resistance-capacitance coupled)21

13-36 Equivalent circuit of two-stage a-c amplifier in Fig．13-3522

13-37 Simplified equivalent circuits of first stage of Fig．13-3522

13-38 Frequency response of single-stage a-c coupled amplifier using resistance-capacitance coupling24

13-39 Single-stage a-c coupled amplifier with voltage feedback25

13-40 A-c servo amplifier29

13-41 Typical thyratron control characteristics30

13-42 Half-wave thyratron amplifier31

13-43 Waveforms of circuit in Fig．13-4232

13-44 Control of a thyratron by means of a phase-variable a-c sig-hal33

13-45 Plate and load connections of typical thyratron amplifiers33

13-46 Load voltage and current supplied by a single-phase full-wave thyratron amplifier to a highly inductive load34

13-47 Full-wave rectifier with typical L-C filter35

13-48 Bridge rectifier with typical L-C filter35

13-49 Block diagram of regulated power supply36

13-50 Circuit schematic of series regulator37

13-51 Temperature-limited diode amplifier38

13-52 Typical characteristics of Type 1N137B silicon junction diode41

13-53 Types of junction transistors43

13-54 Typical collector characteristics44

13-55 Approximate junction transistor model45

13-56 Incremental transistor models45

13-57 Models of h-parameter transistor47

13-58 Ico temperature dependence48

13-59 Variation of h-parameter with bias and temperature48

13-60 Basic transistor amplifier configurations51

13-61 Typical amplifier circuits52

13-62 Push-pull Class B power-amplifier circuits53

13-63 Typical biasing circuits54

13-64 Two-stage transistor feedback amplifier55

13-65 Collector characteristics of typical power transistor57

13-66 Simple single-core magnetic amplifier59

13-67 Simplified B-H characteristic of core material59

13-68 Waveforms of source voltage,flux density,and load current over one cycle60

13-69 Curves showing relationship between average load current I1,firing angle α,and control voltage Ec61

13-70 Ramey circuit62

13-71 Doubler circuit63

13-72 Half-wave magnetic servo amplifier bridge circuit64

13-73 Waveforms of load current during a transient change in output from minimum to maximum output(resistive load)65

13-74 (Left)Power output vs total weight of 60-cycle standard self-saturating magnetic amplifiers．(Right)Comparison of power output vs rcactor weight at 60 cps and 400 cps68

13-75 Control characteristics for N2/R=1．0 zero bias current69

13-76 Power gain per cycle for self-saturating magnetic amplifiers with several core materials in single and three-phase bridge circuits;with d-c output and 60-cycle supply69

13-77 A rotary electric amplifier74

13-78 Types of excitation in d-c rotary amplifiers75

13-79 Block diagram representation of multifield d-c rotary am-plifier78

13-80 Types of control circuits used in rotary electric amplifiers86

13-81 Typical saturation curves for a rotary electric amplifier86

13-82 Speed control using single-sided single-stage relay amplifier88

13-83 Speed control using single-sided cascade relay amplifier89

13-84 Position control illustrating use of double-sided single-stage phase-sensitive relay amplifier90

13-85 Position control with single-stage relay amplifier showing rate compensation or anticipation91

13-86 Position control illustrating use of single-stage phase-sensi-tire relay amplifier93

13-87 Position control illustrating use of two-stage phase-sensi-tive relay amplifier98

13-88 Static characteristics of idealized relay99

13-89 Error response of contactor servo with large input change100

13-90 Circuit for measuring relay pull-in and drop-out time101

13-91 Typical waveforms observed during relay test102

13-92 Arc suppression circuit103

13-93 Nomograph and equations for use in calculating the com-ponent values for an arc suppression circuit104

13-94 Three-way spool-valve amplifier107

13-95 Single nozzle-baffle amplifier108

13-96 Four-way spool-valve amplifier108

13-97 Four-way spool-valve amplifier with open center109

13-98 Nozzle-baffle amplifier with balanced load109

13-99 Sliding-plate valve amplifier109

13-100 Amplifier with position feedback by means of moving valve sleeve110

13-101 Amplifier with position feedback by means of linkage111

13-102 Amplifier with feedback by means of force-balance system111

13-103 Oil-gear rotary hydraulic amplifier with radial pistons112

13-104 Constant-speed rotary hydraulic amplifier with axial pis-tons113

13-105 Ball-and-piston type rotary hydraulic amplifier114

13-106 Four-way spool valve,all pressures measured above sump pressure115

13-107 Four-way spool valve,nondimensional plot of load pressure vs．spool displacement for zero load flow116

13-108 Four-way spool valve,nondimensional plot of load pressure vs．spool displacement for zero load flow117

13-109 Four-way spool valve,nondimensional plot of load flow vs．spool displacement for zero underlap and zero radial clear-ance(b=X0=0)117

13-110 Four-way spool valve,nondimensional plot of load flow vs．spool displacement for zero underlap(X0=0)and finite radial clearance(b≠0)118

13-111 Four-way spool valve,nondimensional plot of load flow vs．spool displacement for γ=0．5118

13-112 Four-way spool valve,equivalent hydraulic-source repre-sentation118

13-113 Four-way spool valve nondimensional plot of flow gain vs．load pressure for zero radial clearance(b=0)119

13-114 Four-way spool valve with negligible radial clearance,non-dimensional plot of internal conductance vs．load pressure120

13-115 Four-way spool valve,nondimensional plot of load flow vs．differential load pressure for balanced load121

13-116 Equivalent circuit of four-way spool-valve amplifier with balanced load121

13-117 Simplified equivalent circuits of four-way spool-valve ampli-fier with balanced load121

13-118 Geometry of spool valve with radial clearance and underlap122

13-119 Four-way spool valve,nondimensional plot of flow gain vs．load pressure for β=0．5122

13-120 Four-way spool valve,nondimensional plot of flow gain vs．load pressure for β=1．0124

13-121 Four-way spool valve,nondimensional plot of flow gain vs．load pressure for β=5124

13-122 Plot of ？ vs P/Ps with x/X0 as parameter with β=0．5,1．0,and 5．0125

13-123 Four-way spool valve with finite radial clearance,plot of load flow vs spool displacement for P5/P2=100(lb/in．2)/350(lb/in．2)=con-stant128

13-124 Geometry of orifice plate valve with underlap and clearance129

13-125 Double nozzle-baffle valve with balanced piston load130

13-126 Double nozzle-baffle valve,nondimensional plot of pressure gain vs load pressure132

13-127 Double nozzle-bafile valve,nondimensional plot of internal resistance vs load pressure133

13-128 Double nozzle-bafile valve,nondimensionl plot of load pres-sure vs baffle displacement for zero load flow134

13-129 Double nozzle-baffle valve with balanced piston load,non-dimensional plot of load flow vs differential load pressure135

13-130 Pressure-control valve amplifier(single-sided amplifier with pressure compensation)136

13-131 Pressure-control valve amplifier with balanced load,dimen-sional plot of differential load pressure vs load flow136

13-132 Rotary pump,typical dimensional plot of load flow vs load pressure137

13-133 Rotary hydraulic pump138

13-134 Four-way spool-valve amplifier and load;equivalent hydrau-lic-circuit representation139

13-135 Equivalent circuit representation of load having mass and opposing force146

13-136 Equivalent circuit representation of load having mass and spring and opposing force147

13-137 Equivalent circuit representation of load having mass,spring,viscous damping,and opposing force148

13-138 Piston with unequal working areas148

13-139 Equivalent circuit representation of load having mass,fric-tion,compliance,and opposing force148

13-140 Four-way spool-valve amplifier and load block diagram—hydraulic circuit shown in Fig．13-134—load has spring,mass,and dashpot149

13-141 Four-way spool-valve amplifier;simplified block diagram derived from Fig．13-140149

13-142 Equivalent hydraulic-circuit representation of rotary ampli-fier(pump)with load having hydraulic compressibility,leakage,and attached mass,spring,and viscous friction150

13-143 Commercially available electrohydraulic servo valves152

13-144 Block diagram of electric amplifier,torque motor,and first-and second-stage hydraulic amplifier154

13-145 Relative compressibility coefficient as a function of pressure and amount of entrained gas157

13-146 Simplified circuit diagram for illustrative example161

13-147 Simplified block diagram for illustrative example162

13-148 Schematic of sliding-plate valve164

13-149 Schematic of conical-plug type three-way valve165

13-150 Schematic of nozzle-baffle three-way valve166

13-151 Plot of restriction factor versus pressure ratio for flow of compressible fluid through an orifice166

13-152 Nondimensional plot of theoretical load flow versus load pressure for open-center(under-lapped)three-way valve168

13-153 Nondimensional plot of internal shunt conductance versus valve displacement for conical-plug valve170

13-154 Nondimensional plot of flow gain versus valve displacement for conical-plug valve170

13-155 Nondimensional plot of internal shunt conductance versus baffle opening for nozzle-baffle valve171

13-156 Nondimensional plot of gain versus baffle opening for nozzle-baffle valve171

13-157 Nondimensional plot of load pressure versus baffle opening for nozzle-baffle valve172

13-158 Plots of(1)discharge coefficient versus baffle opening;and(2)discharge coefficient-baffle opening product versus baffle opening for typical exhaust nozzle in nozzle-baffle valve172

13-159 Plot of pressure ratio versus exhaust-to-supply orifice area ratio for nozzle-baffle valve173

13-160 Equivalent-circuit representation for pneumatic amplifier(three-way valve)with spring-opposed ram load174

13-161 Frequency-response curve for a four-way pneumatic servo-mechanism with 1000 psi supply pressure(plate-valve and piston combination with position feedback by electrical means)176

13-162 Ball-disc integrator181

13-163 Cone-and-disc amplifier182

13-164 Two forms of double capstan amplifier183

13-165 Ideal and actual characteristics of mechanical amplifiers184

13-166 Typical speed-torque characteristics of variable-speed-out-put mechanical amplifier184

13-167 Schematic of working parts of integrator type mechanical amplifier185

13-168 Block diagram of capstan amplifier,with load inertia J and load torque TL187

13-169 Capstan amplifier with electrical input190

13-170 Block diagram of integrator-type amplifier with inertia load and external feedback192

13-171 Solenoid-operated clutch193

13-172 Solenoid-operated clutches194

LIST OF TABLES1

13-1Symbols1

13-2 Relations between incremental parameters46

13-3 Typical parameter variation for a low-power transistor49

13-4 Comparison of typical design information on silicon and germanium power transistors56

13-5 Typical characteristics of magnetic amplifiers67

13-6 Dynamic characteristics of some basic configurations of rotary electric amplifiers81

13-7 Inductances and sensitivities associated with the windings of rotary electric amplifiers84

13-8 Some typical values of parameters for rotary electric ampii-fiers87

13-9 Comparison of commercial relays94

13-10 Methods of increasing relay sensitivity99

13-11 Methods of increasing contact rating99

13-12 Methods of increasing relay response speed101

13-13 Methods of increasing R/δ105

13-14 Classification of hydraulic amplifiers106

13-15 Four-way spool valve with appreciable radial clearance—equivalent-source flow gain and conductance parameters123

13-16 Transfer functions of four-way spool-valve amplifier and load140

13-17 Transfer functions of rotary amplifier and load142

13-18 Circuit parameters for rotary hydraulic amplifier and load144

13-19 Dynamic and static characteristics of commercially avail-able electrohydraulic servo control valves151

13-20 Friction factors156

13-21 Elasticity factors for pipe157

13-22 Orifice area equations for pneumatic three-way valves167

13-23 Minimum tubing lengths for linear flow175

13-24 Calculated time constants for a three-way conical-plug valve179

13-25 Characteristics of VSD units188

13-26 Some typical values of mechanical amplifier parameters191

13-27 Characteristics of solenoid-operated clutch195