Coaxial Electrical Circuits for Interference-Free Measurements

351 Pages·2011·2.342 MB·English

by  Shakil Awan, Bryan Kibble, Jurgen Schurr

IETELECTRICALMEASUREMENT SERIES 13
Coaxial Electrical
Circuits for
Interference-Free
Measurements
Othervolumesinthisseries:
Volume4 ThecurrentcomparatorW.J.M.MooreandP.N.Miljanic
Volume5 PrinciplesofmicrowavemeasurementsG.H.Bryant
Volume7 RadiofrequencyandmicrowavepowermeasurementA.E.Fantom
Volume8 AhandbookforEMCtestingandmeasurementD.Morgan
Volume9 Microwavecircuittheoryandfoundationsofmicrowavemetrology
G.Engen
Volume11 Digitalandanalogueinstrumentation:testingandmeasurement
N.Kularatna
Volume12 Microwavemeasurements,3rdeditionR.CollierandD.Skinner(Editors)
Coaxial Electrical
Circuits for
Interference-Free
Measurements
Shakil Awan, Bryan Kibble
and Ju¨rgen Schurr
The Institution ofEngineeringand Technology
PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom
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†2011TheInstitutionofEngineeringandTechnology
Firstpublished2011
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Contents
Listoffigures xiii
Abstract xxiii
Preface xxv
Acknowledgements xxvii
1 Introduction 1
1.1 Interactionsbetween circuits – eliminating electrical interference 1
1.1.1 Basic principles 2
1.1.2 Anillustrative example –usinga phase-sensitive detector 11
1.1.3 Diagnostic equipment 12
1.1.4 Isolation 17
1.1.5 Totallyisolatingtransformersand power supplies 18
1.1.6 Isolating a noisyinstrument 20
1.1.7 The available methods for isolatingoutputs 22
1.1.8 Balancing 24
1.1.9 Minimising the effects of insufficiently isolated
commercial instruments 24
1.1.10 The ‘traditional’ approach to DCand low-frequency
circuitry versusthe current-balanced conductor-pair
coaxial approach 26
1.1.11 Thermoelectric emfs 27
1.1.12 Designing temperature-controlled enclosures 28
1.1.13 Ionising radiation (cosmic rays, etc.) 30
1.1.14 Final remarks 31
References 31
2 Sources, detectors,cables andconnectors 33
2.1 General principles 33
2.1.1 The output impedance of a network affects
detector sensitivity 33
2.1.2 The sensitivity of detectorsto harmonic content 34
2.1.3 Noise and noise matching a detector to a network 37
2.1.4 The concept of a noise figure 39
2.2 Attributes of sources 41
vi Coaxial electrical circuits for interference-freemeasurements
2.3 Properties of different detectors 42
2.3.1 Preamplifiers 42
2.3.2 Wideband (untuned) detectors 43
2.3.3 Narrowband (tuned)detectors 44
2.3.4 Phase-sensitive detectors that employ a
switching technique 44
2.3.5 Phase-sensitive detectors employing a
modulating technique 44
2.4 Cables and connectors 45
References 46
3 The conceptof a low-frequency coaxial network 47
3.1 The coaxial conductor 49
3.1.1 Achieving current equalisation 49
3.1.2 The concept of a coaxial network 53
3.2 Construction and properties of coaxial networks 54
3.2.1 Equalisers in bridge or other measuring networks 54
3.2.2 Assessingthe efficiency of current equalisers 57
3.2.3 Single conductors added to an equalised network 59
3.2.4 Other conductor systems having similar properties 61
3.2.5 DCnetworks 63
3.2.6 The effect of a length of cable on a measured value 63
3.2.7 Tri-axial cable 67
References 68
4 Impedance measurement 69
4.1 Improvements in defining what isto be observed or measured 69
4.1.1 Ratio devices 70
4.1.2 Impedance standards 70
4.1.3 Formal representation of circuit diagrams and components 73
5 General principles of accurate impedance measurement 79
5.1 The evolution of a coaxial bridge 79
5.1.1 Asimple coaxial bridge as an example of a coaxial
network 82
5.2 The validity of lumped component representations 84
5.3 General principles applying to all impedance standards 85
5.3.1 The physical definition of a standard 85
5.3.2 The electrical definitionof a standard impedance 86
5.3.3 Two-terminal definition 87
5.3.4 Four-terminal definition 88
5.3.5 Four-terminal coaxial definition 88
5.3.6 Two-terminal-pair definition 88
5.3.7 Three-terminal definition 89
5.3.8 Four-terminal-pair definition 90
Contents vii
5.3.9 Measuringfour-terminal-pair admittances in a
two-terminal-pair bridge by extrapolation 92
5.3.10 Adaptors to convert a two- or four-terminal
definition to a four-terminal-pair definition 94
5.4 The effect of cables connected tothe ports of impedance standards 95
5.4.1 The effect of cables ona two-terminal component 96
5.4.2 The effect of cables ona four-terminal coaxial component 96
5.4.3 The effect of cables ona two-terminal-pair component 99
5.4.4 The effect of cables ona four-terminal-pair component 100
5.5 Ananalysisof conductor-pair bridges to showhowthe effect
of shunt admittances can be eliminated 102
5.5.1 Comparing direct admittances usingvoltage sources 103
5.6 Combining networksto eliminate the effect of unwanted
potential differences 104
5.6.1 The concept of a combining network 104
5.6.2 Ageneral purpose AC combining network and
current source 105
5.7 Connecting two-terminal-pair impedances in parallel 107
References 107
6 Impedance standards 109
6.1 The history of impedance standards 110
6.2 The Thompson–Lampard theorem 111
6.3 Primary standards of phase angle 114
6.4 Impedance components in general 115
6.4.1 Capacitors 115
6.4.2 Parallel-plate capacitance standard 117
6.4.3 Two-terminal capacitors 122
6.4.4 Three-terminal capacitors 122
6.4.5 Two- and four-terminal-pair capacitors 123
6.4.6 The mechanical construction and properties of various
types of capacitors 123
6.4.7 Capacitance standards of greater than 1 mF 126
6.4.8 Voltage dependence of capacitors 129
6.4.9 Resistors 130
6.4.10 T-networks 132
6.4.11 Adding auxiliary components to resistors to reduce
their reactive component 133
6.4.12 Mutual inductors: Campbell’s calculable mutual
inductance standard 135
6.4.13 Self-inductors 139
6.5 Resistors,capacitors and inductors of calculable frequency
dependence 140
6.5.1 Resistance standards 140
6.5.2 Haddad coaxial resistance standard 140
viii Coaxial electrical circuits for interference-free measurements
6.5.3 Anearly ideal HFcalculable coaxial resistance standard 144
6.5.4 Abifilarresistance standard 146
6.5.5 Gibbings quadrifilar resistance standard 147
6.5.6 Boha´cˇek and Wood octofilar resistance standard 149
6.5.7 HFsecondary resistance standards 150
6.5.8 HFparallel-plate capacitance standard 152
6.5.9 HFcalculable coaxial capacitance standard 153
6.5.10 HFcalculable coaxial inductance standard 155
6.5.11 Afrequency-independent standard of impedance 156
6.5.12 Anideal standard of impedance of calculable frequency
dependence 157
6.6 Quantum Hall resistance 162
6.6.1 Properties of the quantum Hall effect (QHE) and its
use as a DCresistance standard 162
6.6.2 The properties and the equivalent circuit
of a quantum Hall device 166
6.6.3 Device handling 171
6.7 QHE measured with AC 171
6.7.1 Multiple-series connection scheme 173
6.7.2 Adevice holder and coaxial leads 176
6.7.3 Active equalisers 179
6.7.4 Capacitive model of ungated and split-gated
quantum Hall devices 180
6.7.5 Ungated quantum Hall devices 181
6.7.6 Split-gated quantum Hall devices 182
6.7.7 Double-shielded device 183
References 184
7 Transformers 187
7.1 General considerations 188
7.1.1 The causes of departure from an ideal transformer 188
7.1.2 The magnetic core 189
7.1.3 The windings;the effect of leakage inductances,
capacitances and resistances 192
7.1.4 Representation of a non-ideal transformer: the effect
of loading onits ratio windings 195
7.1.5 The two-stage principle 197
7.1.6 Electrical screens between windings 199
7.2 Constructional techniques 200
7.2.1 Design of transformer windings 200
7.2.2 Techniques for minimising the effect of leakage
inductance, winding resistance and the capacitances
of ratio windings 203
7.2.3 Bifilar winding 204
7.2.4 Rope winding having randomly arranged strands 205
Contents ix
7.2.5 Ordered rope winding 206
7.2.6 Magnetic and electric screens 207
7.2.7 Testingthe attainment of a nearly toroidal field 208
7.2.8 Connections to the output ports 209
7.3 Types of transformers 210
7.3.1 Inductive voltage dividers 210
7.3.2 Two-staged IVDs 216
7.3.3 Injectionand detection transformers 218
7.3.4 Useof an injection transformer as a small voltage source 220
7.3.5 Useofaninjectiontransformerasadetectorofzerocurrent 222
7.3.6 Calibration of injectiontransformersand their associated
phase change circuits 222
7.3.7 Voltage ratio transformers 224
7.3.8 Two-stage construction 225
7.3.9 Matching transformers 226
7.3.10 Current ratio transformers 226
7.3.11 High-frequency construction 227
7.4 Calibration of transformers 228
7.4.1 Calibrating an IVDin terms of a fixed-ratio transformer 228
7.4.2 Calibrating voltage ratio transformersusinga calibration
transformer with a single output voltage 229
7.4.3 Calibration witha 1:(cid:1)1ratio transformer 232
7.4.4 The bridge circuit and details of the shielding 236
7.4.5 The balancingprocedure 238
7.4.6 Calibrating voltage transformers by permuting
capacitorsin a bridge 240
7.4.7 Calibration of current transformers 242
7.4.8 Assessingthe effectiveness of current equalisers 243
References 243
8 General considerationsaboutimpedance comparison networks 245
8.1 Designing bridge networks 245
8.1.1 Applying coaxial techniques toclassical
single-conductor bridges 245
8.1.2 Placement of current equalisers 246
8.1.3 Wagner circuit (andwhen it is applicable) 246
8.1.4 Convergence 247
8.1.5 Moving a detector to other ports in a bridge network 249
8.1.6 T-connecting shuntimpedances for balance
adjustment 249
8.1.7 Role of electronics in bridge design 250
8.1.8 Automating bridge networks 250
8.1.9 Higher-frequency networks 250
8.1.10 Tests of the accuracy of bridges 251
References 253