Resistor Theory and Technology

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1 Resistor Theory and Technology Felix Zandman Chairman, Scientific Director, and CEO, Vishay Intertechnology, Inc. Paul-Rene Simon Consultant Joseph Szwarc Chief Engineer, Vishay Israel Ltd SciTECH PUBLISHING; INC. Distributed by SciTech Publishing, Inc.

2 Contents Preface Introduction 1 Part I: Theory 5 1 Ohm's Law Resistance 5 1. Introduction ' 5 2. Electrokinetics Solids, Magnitude of Electric Current, Charge Conservation, 8 3. Steady-State Ohm's Law Conductivity, Electrostatic Equilibrium of a Conductor, Conductors in a Steady-State Environment, Integral Form of Ohm's Law Elementary Theory of Conductivity (P. K. Drude Model) Conduction in a Sinusoidal Environment, Skin Effect, Joule's Law The Limits of Validity of Ohm's Law Electrodynamics of Steady-State Environments Conclusion 21 xi iii

3 iv Contents 2 Reversible Phenomena Associated with Ohm's Law Introduction Matthiessen's Rule Reversibility Associated with Changes in Temperature Reversibility Associated with Changes in Electric Field Reversibility Associated with the Magnetic Field Reversibility Associated with Mechanical Forces and Deformations Conclusion 31 3 Irreversible Phenomena Associated with Ohm's Law Introduction Time-Temperature Effects Kinetics and Diffusion Phenomena, Nature of the Transport Force, Study and Determination of the Diffusion Coefficient, 36 ^ 2.4 Diffusion Mechanisms, Permanent Changes in Resistivity, Oxidation of a Metal or Alloy, 46 4 Resistive Materials Introduction Metals and Solid Alloys Copper-Nickel and Copper-Manganese- Nickel Alloys, Nickel-Chrome Alloys, Conduction Mechanism in Magnetic Alloys, Thin Films Thin Films in Use: Description and Electronic Properties, Conduction Mechanisms in Thin Films and the Origins of Nonreversible Drift, Substrates, Thick-and Thin-Film Cermets Conductivity Mechanism, Thick-Film Glass-Metal Cermets, 66

4 Contents 4.3 Thick-Film Organic Cermets, Thin-Film Cermets, Conclusion 74 Noise Phenomena Introduction Origins of Noise Thermal Noise, Excess Noise, Current Fluctuations, Noise Measurements, Conclusion 84 Heat Transfer Introduction Description of Heat Transfer Mechanisms Conduction, Convection, Radiation, Heat Exchange through Phase Changes, General Equations for Conduction Energy Balance, Analytical Expressions for the Heat Equation, Heating in Resistors Heating in a Cylindrical Resistor, Heating in Flat Resistors, Components as Shown in Fig. 3, Components as Shown in Fig. 4, Transfer at the Interfaces and Contact Resistances, Conclusion 106 Part II: Technology 107 Introduction Overview of Fixed and Variable Resistors Fundamental Parameters Ohmic Value, Nominal Ohmic Value of a Resistor, Dissipation and Nominal Temperature, HI

5 ri Contents 1.4 Critical Resistance, Temperature Coefficient, Voltage Coefficient, Resistors General, Wirewound Resistors, Potentiometer Characteristics Taper and Conformity, Total Mechanical and Electrical Travel, Contact Resistance, Setting Stability, Precision Resistors Resistive Circuits Introduction Parasitic Resistance, Insulation, and Connections Influence on Ohmic Values, Resistor Assemblies (Ratio, Dividers, Bridges, etc.) Ratio, Voltage Divider (Potentiometer, Half-bridge, etc.), Wheatstone Bridge, Frequency Response of Resistors 130 Power and Wirewound Resistors 135 l Introduction Low-Power Resistors 2.1 Electrical and Mechanical Characteristics, 140 High-Power Resistors Low-Ohmic Value Power Resistors High-Power Surface-Mount Resistors Measurement of Heat Dissipation during Operation Conclusion Precision Resistors and Resistor Networks Introduction Precision Wirewound Resistors Foil Resistors Physical Principles of TCR Control and Adjustment, 160

6 Contents vii 4. Thick-Film Precision Resistors Thin-Film Precision Resistors High Precision Low-Ohmic Value Resistors Thermoelectric Effect Comparison of the Different Technologies Conclusion Potentiometers and Potentiometric Position Sensors Introduction Potentiometers and Trimmers Track Materials and Characteristics, Wipers: Characteristics and Materials, Displacement Transducers and Precision Potentiometers Practical Results Nature and Structure of the Tracks, Wipers, Adjustment, Nonlinear Laws, Conclusion Magnetoresistance and Its Applications: Anisotropic Magnetoresistance in Ferromagnetic Alloys Introduction Definitions Structure and Operating Principles Hysteresis Cycles, Material Selection Sensor Design Applications Incremental Magnetic Encoders, Absolute Magnetic Encoders, Conclusion V, Nonlinear Resistors Introduction Conductivity Mechanisms in Ceramics and Oxides Electrical Conductivity of Ceramics, Ionic Conductivity in Ceramics, 228

7 viii Contents Negative Temperature Coefficient Thermistors 3.1 Production Techniques for Ceramic and for Electrode Deposition, Thermistor Types, Typical Applications, Current-Voltage Characteristics, Temperature Sensors (Low Heat Dissipation), Applications Based on the Nonlinear b-c Region, Applications Based on Current-Time Relations, 239 Positive Temperature Coefficient Thermistors 4.1 Chemical Composition and Electrical Properties, 240 PTC Thermistor Types Applications Varistors 7.1 Varistor Effects, Varistor Structure and Fabrication, Equivalent Circuit, Applications, Varistor Types, Areas of Application, 253 Gas Sensors Time Constants for Temperature Measurement Conclusion Appendix I: A Precision Film Resistor Exhibiting Bulk Properties 259 A.I A.2 A.3 A.4 A.5 A.6 A.7 A.8 Introduction Design Concepts Principles Used in the Resistor Construction and Manufacture Some Strain Considerations Limitations Other Applications Conclusion References / Appendix II: Quality Assurance 275 Appendix III: Model for Accelerated Lifetime Testing 277 A. 1 Exponential Distribution 277 A.2 Normal and Log-Normal Distributions 279

8 Contents ix A.3 The Weibull Distribution 280 A.4 Accelerated Aging and the Arrhenius Model 284 A.5 Other Degradation Models 290 Appendix IV: The Resistance Strain Gage 291 A.I Introduction 291 A.2 Strain Gage Construction and Configurations 292 A.3 Significant Characteristics and Parameters 295 A.4 Calibration of Strain Gages 298 A.5 Applications 300 Index 303

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