an introduction to electronics

An introduction to electronics

Contents

1 Introduction 11.1 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Branches of Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Electronic devices and components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.3 History of electronic components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.4 Types of circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.5 Heat dissipation and thermal management . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.6 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.7 Electronics theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.8 Electronics lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.9 Computer aided design (CAD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.10 Construction methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.11 Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.12 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.14 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.15 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Hydraulic analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 Measuring instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.5 Typical voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.6 Galvani potential versus electrochemical potential . . . . . . . . . . . . . . . . . . . . . . 71.2.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Electric current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.1 Symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.2 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.3 Ohms law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.4 AC and DC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

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1.3.5 Occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.6 Current measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.7 Resistive heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.8 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.9 Conduction mechanisms in various media . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.10 Current density and Ohms law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.3.11 Drift speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.12 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.14 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4.1 Denitions and units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.4.3 Frequency of waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4.5 Period versus frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.4.6 Other types of frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.4.7 Frequency ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.4.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.4.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.5 Direct current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.5.1 Various denitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.5.2 Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.5.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.5.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.5.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.6 Alternating current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.6.1 Transmission, distribution, and domestic power supply . . . . . . . . . . . . . . . . . . . . 211.6.2 AC power supply frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221.6.3 Eects at high frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.6.4 Mathematics of AC voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241.6.5 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.6.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.6.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.6.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.6.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Electrical Components 302.1 Passivity (engineering) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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2.1.1 Thermodynamic passivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.2 Incremental passivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.3 Other denitions of passivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.5 Passive lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.1.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 Resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.1 Electronic symbols and notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2.2 Theory of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2.3 Nonideal properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.2.4 Fixed resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.2.5 Variable resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.6 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.7 Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.8 Resistor marking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.9 Electrical and thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2.10 Failure modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2.11 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.2.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.2.13 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.3 Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.3.2 Theory of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.3.3 Non-ideal behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.3.4 Capacitor types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522.3.5 Capacitor markings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.3.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542.3.7 Hazards and safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.3.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.3.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3.10 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.4 Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592.4.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602.4.3 Inductor construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.4.4 Types of inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.4.5 Circuit theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662.4.6 Q factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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2.4.7 Inductance formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.4.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.4.9 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 682.4.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.4.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

2.5 Electrical impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692.5.1 Complex impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.5.2 Ohms law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.5.3 Complex voltage and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702.5.4 Device examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712.5.5 Generalised s-plane impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.5.6 Resistance vs reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.5.7 Combining impedances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742.5.8 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.5.9 Variable impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.5.10 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.5.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.5.12 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

2.6 Voltage source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762.6.1 Ideal voltage sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762.6.2 Comparison between voltage and current sources . . . . . . . . . . . . . . . . . . . . . . 762.6.3 References and notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772.6.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

2.7 Current source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772.7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772.7.2 Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772.7.3 Current and voltage source comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 822.7.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832.7.5 References and notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832.7.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 832.7.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3 Basic circuit laws 843.1 Kirchhos circuit laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.1.1 Kirchhos current law (KCL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.1.2 Kirchhos voltage law (KVL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.1.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.1.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.1.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.2 Nortons theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.2.1 Example of a Norton equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

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3.2.2 Conversion to a Thvenin equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.2.3 Queueing theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.2.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.2.5 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.2.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.3 Thvenins theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.3.1 Calculating the Thvenin equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.3.2 Conversion to a Norton equivalent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.3 Practical limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.4 A proof of the theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.7 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913.3.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4 AC analysis 924.1 Phasor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.1.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.1.2 Phasor arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924.1.3 Phasor diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.1.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.1.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954.1.6 Footnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.1.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.1.8 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.1.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.2 Electric power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.2.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 964.2.2 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.2.3 Electric power supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.3 RLC circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.3.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1004.3.2 Series RLC circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.3.3 Parallel RLC circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.3.4 Other congurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.3.5 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.3.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.3.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

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4.3.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.3.9 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.4 Low-pass lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.4.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.4.2 Ideal and real lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.4.3 Continuous-time low-pass lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.4.4 Electronic low-pass lters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.4.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.4.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.4.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.5 High-pass lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.5.1 First-order continuous-time implementation . . . . . . . . . . . . . . . . . . . . . . . . . 1154.5.2 Discrete-time realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1154.5.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164.5.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.5.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.5.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.6 Band-pass lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.6.2 Q-factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.6.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.6.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.6.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1194.6.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5 Basic devices 1205.1 Pn junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.1.1 Properties of a pn junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.1.2 Equilibrium (zero bias) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.1.3 Forward bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1215.1.4 Reverse bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.1.5 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.1.7 Non-rectifying junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.1.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.1.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1235.1.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.1.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.2 Bipolar junction transistor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1245.2.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.2.3 Regions of operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

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5.2.4 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.2.5 Theory and modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1305.2.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.2.7 Vulnerabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.2.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.2.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.2.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.3 Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.3.1 Figures of merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1355.3.2 Amplier types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1365.3.3 Classication of amplier stages and systems . . . . . . . . . . . . . . . . . . . . . . . . 1395.3.4 Power amplier classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1425.3.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1495.3.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1505.3.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.3.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.4 Operational amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.4.1 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1525.4.2 Op-amp characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1535.4.3 Internal circuitry of 741-type op-amp . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1565.4.4 Classication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1595.4.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1605.4.6 Historical timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1625.4.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645.4.8 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1645.4.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1655.4.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1655.4.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6 Digital circuits 1676.1 Boolean algebra (logic) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1676.1.2 Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1676.1.3 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1686.1.4 Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1686.1.5 Diagrammatic representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1706.1.6 Boolean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1716.1.7 Axiomatizing Boolean algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1736.1.8 Propositional logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1746.1.9 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1756.1.10 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1776.1.11 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

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6.1.12 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.1.13 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.2 Logic gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.2.1 Electronic gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1786.2.2 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1796.2.3 Universal logic gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1806.2.4 De Morgan equivalent symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1806.2.5 Data storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1806.2.6 Three-state logic gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816.2.7 History and development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816.2.8 Implementations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816.2.9 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816.2.10 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1826.2.11 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.3 Karnaugh map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1826.3.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1836.3.2 Race hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1856.3.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1866.3.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1866.3.5 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1866.3.6 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

6.4 Finite-state machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.4.1 Example: a turnstile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.4.2 Concepts and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1886.4.3 Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1886.4.4 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1896.4.5 Classication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1896.4.6 Alternative semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.4.7 FSM logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.4.8 Mathematical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1916.4.9 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.4.10 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.4.11 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.4.12 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1936.4.13 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1936.4.14 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

6.5 555 timer IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1956.5.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1956.5.2 Specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1986.5.3 Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1986.5.4 Example applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

CONTENTS ix

6.5.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1986.5.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1996.5.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1996.5.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

6.6 Schmitt trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006.6.1 Invention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006.6.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2006.6.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2056.6.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.6.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.6.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.6.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.7 Shift register . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2066.7.1 Serial-in and serial-out (SISO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.7.2 Serial-in, parallel-out (SIPO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.7.3 Parallel-in, Serial-out (PISO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.7.4 Uses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2076.7.5 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.7.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.7.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.7.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6.8 Flip-op (electronics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2086.8.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.8.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096.8.3 Flip-op types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2106.8.4 Metastability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2156.8.5 Timing considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2156.8.6 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2166.8.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2166.8.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2166.8.9 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

7 Text and image sources, contributors, and licenses 2187.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2187.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2307.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

Chapter 1

Introduction

1.1 ElectronicsThis article is about the technical eld of electronics. Forpersonal-use electronic devices, see consumer electron-ics. For the scientic magazine, see Electronics (maga-zine).

Electronics deals with electrical circuits that in-

Surface mount electronic components

volve active electrical components such as vacuum tubes,transistors, diodes and integrated circuits, and asso-ciated passive electrical components and interconnec-tion technologies. Commonly, electronic devices con-tain circuitry consisting primarily or exclusively of ac-tive semiconductors supplemented with passive elements;such a circuit is described as an electronic circuit.The nonlinear behaviour of active components and theirability to control electron ows makes amplication ofweak signals possible, and electronics is widely used ininformation processing, telecommunication, and signalprocessing. The ability of electronic devices to act asswitches makes digital information processing possible.Interconnection technologies such as circuit boards, elec-tronics packaging technology, and other varied forms ofcommunication infrastructure complete circuit function-ality and transform the mixed components into a regularworking system.Electronics is distinct from electrical and electro-mechanical science and technology, which deal with the

generation, distribution, switching, storage, and conver-sion of electrical energy to and from other energy formsusing wires, motors, generators, batteries, switches,relays, transformers, resistors, and other passive com-ponents. This distinction started around 1906 with theinvention by Lee De Forest of the triode, which madeelectrical amplication of weak radio signals and audiosignals possible with a non-mechanical device. Until1950 this eld was called radio technology because itsprincipal application was the design and theory of radiotransmitters, receivers, and vacuum tubes.Today, most electronic devices use semiconductor com-ponents to perform electron control. The study of semi-conductor devices and related technology is considered abranch of solid-state physics, whereas the design and con-struction of electronic circuits to solve practical problemscome under electronics engineering. This article focuseson engineering aspects of electronics.

1.1.1 Branches of Electronics

Electronics has branches as follows:1.Digital electronics2.Analogue electronics3.Microelectronics4.Fuzzy electronics5.Circuit Design6.Integrated circuit7.Optoelectronics8.Semiconductor9.Semiconductor device [1]

1.1.2 Electronic devices and components

Main article: Electronic component

An electronic component is any physical entity in an elec-tronic system used to aect the electrons or their associ-ated elds in a manner consistent with the intended func-

1

2 CHAPTER 1. INTRODUCTION

Electronics Technician performing a voltage check on a powercircuit card in the air navigation equipment room aboard the air-craft carrier USS Abraham Lincoln (CVN 72).

tion of the electronic system. Components are gener-ally intended to be connected together, usually by be-ing soldered to a printed circuit board (PCB), to createan electronic circuit with a particular function (for ex-ample an amplier, radio receiver, or oscillator). Com-ponents may be packaged singly, or in more complexgroups as integrated circuits. Some common electroniccomponents are capacitors, inductors, resistors, diodes,transistors, etc. Components are often categorized as ac-tive (e.g. transistors and thyristors) or passive (e.g. resis-tors, diodes, inductors and capacitors).

1.1.3 History of electronic componentsFurther information: Timeline of electrical and elec-tronic engineering

Vacuum tubes (Thermionic valves) were one of the ear-liest electronic components. They were almost solely re-sponsible for the electronics revolution of the rst half ofthe Twentieth Century. They took electronics from parlortricks and gave us radio, television, phonographs, radar,long distance telephony and much more. They playeda leading role in the eld of microwave and high powertransmission as well as television receivers until the mid-dle of the 1980s.[2] Since that time, solid state deviceshave all but completely taken over. Vacuum tubes are stillused in some specialist applications such as high powerRF ampliers, cathode ray tubes, specialist audio equip-ment, guitar ampliers and some microwave devices.In April 1955 the IBM 608 was the rst IBM productto use transistor circuits without any vacuum tubes and isbelieved to be the worlds rst all-transistorized calculatorto be manufactured for the commercial market.[3][4] The608 contained more than 3,000 germanium transistors.Thomas J. Watson Jr. ordered all future IBM products touse transistors in their design. From that time on transis-tors were almost exclusively used for computer logic andperipherals.

1.1.4 Types of circuitsCircuits and components can be divided into two groups:analog and digital. A particular device may consist of cir-cuitry that has one or the other or a mix of the two types.

Analog circuits

Main article: Analog electronicsMost analog electronic appliances, such as radio re-

Hitachi J100 adjustable frequency drive chassis

ceivers, are constructed from combinations of a few typesof basic circuits. Analog circuits use a continuous rangeof voltage or current as opposed to discrete levels as indigital circuits.The number of dierent analog circuits so far devisedis huge, especially because a 'circuit' can be dened asanything from a single component, to systems containingthousands of components.Analog circuits are sometimes called linear circuits al-though many non-linear eects are used in analog circuitssuch as mixers, modulators, etc. Good examples of ana-log circuits include vacuum tube and transistor ampliers,operational ampliers and oscillators.One rarely nds modern circuits that are entirely analog.These days analog circuitry may use digital or even mi-croprocessor techniques to improve performance. Thistype of circuit is usually called mixed signal rather thananalog or digital.Sometimes it may be dicult to dierentiate betweenanalog and digital circuits as they have elements of bothlinear and non-linear operation. An example is the com-parator which takes in a continuous range of voltage but

1.1. ELECTRONICS 3

only outputs one of two levels as in a digital circuit. Sim-ilarly, an overdriven transistor amplier can take on thecharacteristics of a controlled switch having essentiallytwo levels of output. In fact, many digital circuits are ac-tually implemented as variations of analog circuits similarto this exampleafter all, all aspects of the real physicalworld are essentially analog, so digital eects are only re-alized by constraining analog behavior.

Digital circuits

Main article: Digital electronics

Digital circuits are electric circuits based on a number ofdiscrete voltage levels. Digital circuits are the most com-mon physical representation of Boolean algebra, and arethe basis of all digital computers. To most engineers, theterms digital circuit, digital system and logic are in-terchangeable in the context of digital circuits. Most dig-ital circuits use a binary system with two voltage levelslabeled 0 and 1. Often logic 0 will be a lower volt-age and referred to as Low while logic 1 is referred toas High. However, some systems use the reverse def-inition (0 is High) or are current based. Quite oftenthe logic designer may reverse these denitions from onecircuit to the next as he sees t to facilitate his design.The denition of the levels as 0 or 1 is arbitrary.Ternary (with three states) logic has been studied, andsome prototype computers made.Computers, electronic clocks, and programmable logiccontrollers (used to control industrial processes) are con-structed of digital circuits. Digital signal processors areanother example.Building blocks:

Logic gates Adders Flip-ops Counters Registers Multiplexers Schmitt triggers

Highly integrated devices:

Microprocessors Microcontrollers Application-specic integrated circuit (ASIC) Digital signal processor (DSP) Field-programmable gate array (FPGA)

1.1.5 Heat dissipation and thermal man-agement

Main article: Thermal management of electronic devicesand systems

Heat generated by electronic circuitry must be dissipatedto prevent immediate failure and improve long term re-liability. Techniques for heat dissipation can includeheat sinks and fans for air cooling, and other forms ofcomputer cooling such as water cooling. These tech-niques use convection, conduction, & radiation of heatenergy.

1.1.6 Noise

Main article: Electronic noise

Electronic noise is dened[5] as unwanted disturbancessuperposed on a useful signal that tend to obscure its in-formation content. Noise is not the same as signal dis-tortion caused by a circuit. Noise is associated with allelectronic circuits. Noise may be electromagnetically orthermally generated, which can be decreased by loweringthe operating temperature of the circuit. Other types ofnoise, such as shot noise cannot be removed as they aredue to limitations in physical properties.

1.1.7 Electronics theory

Main article: Mathematical methods in electronics

Mathematical methods are integral to the study of elec-tronics. To become procient in electronics it is also nec-essary to become procient in the mathematics of circuitanalysis.Circuit analysis is the study of methods of solving gen-erally linear systems for unknown variables such as thevoltage at a certain node or the current through a certainbranch of a network. A common analytical tool for thisis the SPICE circuit simulator.Also important to electronics is the study and understand-ing of electromagnetic eld theory.

1.1.8 Electronics lab

Main article: Electronic circuit simulation

Due to the complex nature of electronics theory, labora-tory experimentation is an important part of the develop-ment of electronic devices. These experiments are usedto test or verify the engineers theory and detect design er-rors. Historically, electronics labs have consisted of elec-


tronics devices and equipment located in a physical space,although in more recent years the trend has been towardselectronics lab simulation software, such as CircuitLogix,Multisim, and PSpice.

1.1.9 Computer aided design (CAD)Main article: Electronic design automation

Todays electronics engineers have the ability to designcircuits using premanufactured building blocks such aspower supplies, semiconductors (i.e. semiconductordevices, such as transistors), and integrated circuits.Electronic design automation software programs includeschematic capture programs and printed circuit board de-sign programs. Popular names in the EDA software worldare NI Multisim, Cadence (ORCAD), EAGLE PCB andSchematic, Mentor (PADS PCB and LOGIC Schematic),Altium (Protel), LabCentre Electronics (Proteus), gEDA,KiCad and many others.

1.1.10 Construction methodsMain article: Electronic packaging

Many dierent methods of connecting components havebeen used over the years. For instance, early elec-tronics often used point to point wiring with compo-nents attached to wooden breadboards to construct cir-cuits. Cordwood construction and wire wraps were othermethods used. Most modern day electronics now useprinted circuit boards made of materials such as FR4,or the cheaper (and less hard-wearing) Synthetic ResinBonded Paper (SRBP, also known as Paxoline/Paxolin(trade marks) and FR2) - characterised by its light yellow-to-brown colour. Health and environmental concerns as-sociated with electronics assembly have gained increasedattention in recent years, especially for products destinedto the European Union, with its Restriction of HazardousSubstances Directive (RoHS) and Waste Electrical andElectronic Equipment Directive (WEEE), which wentinto force in July 2006.

1.1.11 DegradationRasberry crazy ants have been known to consume the in-sides of electrical wiring, and nest inside of electronics;they prefer DC to AC currents. This behavior is not wellunderstood by scientists. [6]

1.1.12 See also Atomtronics Audio engineering

Broadcast engineering Computer engineering Electronic engineering Electronics engineering technology Index of electronics articles List of mechanical, electrical and electronic equip-

ment manufacturing companies by revenue

Marine electronics Power electronics Robotics

1.1.13 References[1] http://technofreck.wordpress.com/2009/06/26/

branches-of-electronics/

[2] Sgo Okamura (1994). History of Electron Tubes. IOSPress. p. 5. ISBN 978-90-5199-145-1. Retrieved 5 De-cember 2012.

[3] Bashe, Charles J.; et al. (1986). IBMs Early Computers.MIT. p. 386.

[4] Pugh, Emerson W.; Johnson, Lyle R.; Palmer, John H.(1991). IBMs 360 and early 370 systems. MIT Press. p.34. ISBN 0-262-16123-0.

[5] IEEE Dictionary of Electrical and Electronics TermsISBN 978-0-471-42806-0

[6] Andrew R Hickey (May 15, 2008). "'Crazy' Ant InvasionFrying Computer Equipment.

1.1.14 Further reading The Art of Electronics ISBN 978-0-521-37095-0 Online course on Computational Electronics on

Nanohub.org

1.1.15 External links Electronics at DMOZ Navy 1998 Navy Electricity and Electronics Train-

ing Series (NEETS)

DOE 1998 Electrical Science, Fundamentals Hand-book, 4 vols.

Vol. 1, Basic Electrical Theory, Basic DCTheory

Vol. 2, DC Circuits, Batteries, Generators,Motors

1.2. VOLTAGE 5

Vol. 3, Basic AC Theory, Basic AC Reac-tive Components, Basic AC Power, Basic ACGenerators

Vol. 4, AC Motors, Transformers, Test Instru-ments & Measuring Devices, Electrical Distri-bution Systems

1.2 VoltagePotential dierence redirects here. For other uses, seePotential.

Voltage or electric potential tension (denoted V orU and measured in units of electric potential: volts, orjoules per coulomb) is the electric energy charge dier-ence of electric potential energy transported between twopoints.[1] Voltage is equal to the work done per unit ofcharge against a static electric eld to move the chargebetween two points. A voltage may represent either asource of energy (electromotive force), or lost, used, orstored energy (potential drop). A voltmeter can be usedto measure the voltage (or potential dierence) betweentwo points in a system; often a common reference poten-tial such as the ground of the system is used as one of thepoints. Voltage can be caused by static electric elds, byelectric current through a magnetic eld, by time-varyingmagnetic elds, or some combination of these three.[2][3]

The electric eld around the rod exerts a force on the chargedpith ball, in an electroscope

1.2.1 DenitionGiven two points in the space, called A and B, voltageis the dierence of electric potentials between those twopoints. From the denition of electric potential it followsthat:

A

B

In a static eld, the work is independent of the path

VBA = VB VA = R Br0

~E d~l R A

r0~E d~l

=

Z r0B

~E d~l +Z Ar0

~E d~l =Z AB

~E d~l

Voltage is electric potential energy per unit charge, mea-sured in joules per coulomb ( = volts). It is often re-ferred to as electric potential, which then must be dis-tinguished from electric potential energy by noting thatthe potential is a per-unit-charge quantity. Like me-chanical potential energy, the zero of potential can bechosen at any point, so the dierence in voltage is thequantity which is physically meaningful. The dierencein voltage measured when moving from point A to pointB is equal to the work which would have to be done, perunit charge, against the electric eld to move the chargefrom A to B. The voltage between the two ends of a pathis the total energy required to move a small electric chargealong that path, divided by the magnitude of the charge.Mathematically this is expressed as the line integral ofthe electric eld and the time rate of change of magneticeld along that path. In the general case, both a static(unchanging) electric eld and a dynamic (time-varying)electromagnetic eld must be included in determining thevoltage between two points.Historically this quantity has also been called tension[4]and pressure. Pressure is now obsolete but tensionis still used, for example within the phrase "high ten-sion" (HT) which is commonly used in thermionic valve(vacuum tube) based electronics.Voltage is dened so that negatively charged objects arepulled towards higher voltages, while positively chargedobjects are pulled towards lower voltages. Therefore, theconventional current in a wire or resistor always ows


from higher voltage to lower voltage. Current can owfrom lower voltage to higher voltage, but only when asource of energy is present to push it against the oppos-ing electric eld. For example, inside a battery, chemicalreactions provide the energy needed for current to owfrom the negative to the positive terminal.Technically, in a material the electric eld is not the onlyfactor determining charge ow, and dierent materialsnaturally develop electric potential dierences at equilib-rium (Galvani potentials). The electric potential of a ma-terial is not even a well dened quantity, since it varieson the subatomic scale. A more convenient denition of'voltage' can be found instead in the concept of Fermilevel. In this case the voltage between two bodies is thethermodynamic work required to move a unit of chargebetween them. This denition is practical since a realvoltmeter actually measures this work, not dierences inelectric potential.

1.2.2 Hydraulic analogy

Main article: Hydraulic analogy

A simple analogy for an electric circuit is water owingin a closed circuit of pipework, driven by a mechanicalpump. This can be called a water circuit. Potential dif-ference between two points corresponds to the pressuredierence between two points. If the pump creates apressure dierence between two points, then water ow-ing from one point to the other will be able to do work,such as driving a turbine. Similarly, work can be doneby an electric current driven by the potential dierenceprovided by a battery. For example, the voltage providedby a suciently-charged automobile battery can pusha large current through the windings of an automobilesstarter motor. If the pump isn't working, it produces nopressure dierence, and the turbine will not rotate. Like-wise, if the automobiles battery is very weak or dead(or at), then it will not turn the starter motor.The hydraulic analogy is a useful way of understandingmany electrical concepts. In such a system, the work doneto move water is equal to the pressure multiplied by thevolume of water moved. Similarly, in an electrical circuit,the work done to move electrons or other charge-carriersis equal to electrical pressure multiplied by the quan-tity of electrical charges moved. In relation to ow,the larger the pressure dierence between two points(potential dierence or water pressure dierence), thegreater the ow between them (electric current or waterow). (See "Electric power".)

1.2.3 Applications

Specifying a voltage measurement requires explicit or im-plicit specication of the points across which the voltage

Working on high voltage power lines

is measured. When using a voltmeter to measure poten-tial dierence, one electrical lead of the voltmeter mustbe connected to the rst point, one to the second point.A common use of the term voltage is in describing thevoltage dropped across an electrical device (such as a re-sistor). The voltage drop across the device can be under-stood as the dierence between measurements at eachterminal of the device with respect to a common refer-ence point (or ground). The voltage drop is the dier-ence between the two readings. Two points in an electriccircuit that are connected by an ideal conductor withoutresistance and not within a changing magnetic eld havea voltage of zero. Any two points with the same potentialmay be connected by a conductor and no current will owbetween them.

Addition of voltages

The voltage between A and C is the sum of the volt-age between A and B and the voltage between B and C.The various voltages in a circuit can be computed usingKirchhos circuit laws.When talking about alternating current (AC) there isa dierence between instantaneous voltage and averagevoltage. Instantaneous voltages can be added for directcurrent (DC) and AC, but average voltages can be mean-ingfully added only when they apply to signals that all have

1.2. VOLTAGE 7

the same frequency and phase.

1.2.4 Measuring instruments

Multimeter set to measure voltage

Instruments for measuring voltages include the voltmeter,the potentiometer, and the oscilloscope. The voltmeterworks by measuring the current through a xed resistor,which, according to Ohms Law, is proportional to thevoltage across the resistor. The potentiometer works bybalancing the unknown voltage against a known voltage ina bridge circuit. The cathode-ray oscilloscope works byamplifying the voltage and using it to deect an electronbeam from a straight path, so that the deection of thebeam is proportional to the voltage.

1.2.5 Typical voltagesA common voltage for ashlight batteries is 1.5 volts(DC). A common voltage for automobile batteries is 12volts (DC).Common voltages supplied by power companies to con-sumers are 110 to 120 volts (AC) and 220 to 240 volts(AC). The voltage in electric power transmission linesused to distribute electricity from power stations can beseveral hundred times greater than consumer voltages,typically 110 to 1200 kV (AC).The voltage used in overhead lines to power railway loco-motives is between 12 kV and 50 kV (AC).

1.2.6 Galvani potential versus electro-chemical potential

Main articles: Galvani potential, Electrochemical poten-tial and Fermi level

Inside a conductive material, the energy of an electronis aected not only by the average electric potential, but

also by the specic thermal and atomic environment thatit is in. When a voltmeter is connected between two dif-ferent types of metal, it measures not the electrostatic po-tential dierence, but instead something else that is af-fected by thermodynamics.[5] The quantity measured by avoltmeter is the negative of dierence of electrochemicalpotential of electrons (Fermi level) divided by electroncharge, while the pure unadjusted electrostatic poten-tial (not measurable with voltmeter) is sometimes calledGalvani potential. The terms voltage and electric po-tential are a bit ambiguous in that, in practice, they canrefer to either of these in dierent contexts.

1.2.7 See also

Alternating current (AC)

Direct current (DC)

Electric potential

Electric shock

Electrical measurements

Electrochemical potential

Fermi level

High voltage

Mains electricity (an article about domestic powersupply voltages)

Mains electricity by country (list of countries withmains voltage and frequency)

Ohms law

Open-circuit voltage

Phantom voltage

1.2.8 References

[1] Voltage, Electrochemistry Encyclopedia

[2] Demetrius T. Paris and F. Kenneth Hurd, Basic Electro-magnetic Theory, McGraw-Hill, New York 1969, ISBN0-07-048470-8, pp. 512, 546

[3] P. Hammond, Electromagnetism for Engineers, p. 135,Pergamon Press 1969 OCLC 854336.

[4] Tension. CollinsLanguage.

[5] Bagotskii, Vladimir Sergeevich (2006). Fundamentals ofelectrochemistry. p. 22. ISBN 978-0-471-70058-6.


1.2.9 External links

Electrical voltage V, amperage I, resistivity R,impedance Z, wattage P

Elementary explanation of voltage at NDT ResourceCenter

1.3 Electric current

A simple electric circuit, where current is represented by the letteri. The relationship between the voltage (V), resistance (R), andcurrent (I) is V=IR; this is known as Ohms Law.

An electric current is a ow of electric charge. In electriccircuits this charge is often carried by moving electrons ina wire. It can also be carried by ions in an electrolyte, orby both ions and electrons such as in a plasma.[1]

The SI unit for measuring an electric current is theampere, which is the ow of electric charge across a sur-face at the rate of one coulomb per second. Electric cur-rent is measured using a device called an ammeter.[2]

Electric currents can have many eects, notably heating,but they also create magnetic elds, which are used inmotors, inductors and generators.

1.3.1 Symbol

The conventional symbol for current is I, which originatesfrom the French phrase intensit de courant, or in En-glish current intensity.[3][4] This phrase is frequently usedwhen discussing the value of an electric current, but mod-ern practice often shortens this to simply current. The Isymbol was used by Andr-Marie Ampre, after whomthe unit of electric current is named, in formulating theeponymous Ampres force law which he discovered in1820.[5] The notation travelled from France to Britain,where it became standard, although at least one journaldid not change from using C to I until 1896.[6]

Flow of positive charge Flow of electrons

The electrons, the charge carriers in an electrical circuit, ow inthe opposite direction of the conventional electric current.

The symbol for a battery in a circuit diagram.

1.3.2 Conventions

In metals, which make up the wires and other conductorsin most electrical circuits, the positively charged atomicnuclei are held in a xed position, and the electrons arefree to move, carrying their charge from one place to an-other. In other materials, notably the semiconductors, thecharge carriers can be positive or negative, depending onwhat dopant is used. It is even possible for both posi-tive and negative charge carriers to be present at the same

1.3. ELECTRIC CURRENT 9

time, as happens in an electrochemical cell.A ow of positive charges gives the same electric current,and has the same eect in a circuit, as an equal ow ofnegative charges in the opposite direction. Since currentcan be the ow of either positive or negative charges, orboth, a convention is needed for the direction of currentthat is independent of the type of charge carriers. Thedirection of conventional current is arbitrarily dened sothat a positive current ows in the same direction as pos-itive charges and vice versa.The consequence of this convention is that electrons, be-ing negatively charged, ow in the opposite direction tothe direction of conventional current ow in an electricalcircuit.

Reference direction

Since the current in a wire or component can ow in eitherdirection, when a variable I is dened to represent thatcurrent, the direction representing positive current mustbe specied, usually by an arrow on the circuit schematicdiagram. This is called the reference direction of currentI. If the current is owing in the opposite direction, thevariable I will have a negative value.When analyzing electrical circuits, the actual direction ofcurrent through a specic circuit element is usually un-known. Consequently, the reference directions of cur-rents are often assigned arbitrarily. When the circuit issolved, a negative value for the variable means that theactual direction of current through that circuit element isopposite that of the chosen reference direction. In elec-tronic circuits, the reference current directions are oftenchosen so that all currents are toward ground. This of-ten corresponds to the actual current direction, becausein many circuits the power supply voltage is positive withrespect to ground.

1.3.3 Ohms lawMain article: Ohms law

Ohms law states that the current through a conduc-tor between two points is directly proportional to thepotential dierence across the two points. Introducingthe constant of proportionality, the resistance,[7] one ar-rives at the usual mathematical equation that describesthis relationship:[8]

I =V

R

where I is the current through the conductor in units ofamperes, V is the potential dierence measured acrossthe conductor in units of volts, and R is the resistance ofthe conductor in units of ohms. More specically, Ohms

law states that the R in this relation is constant, indepen-dent of the current.[9]

1.3.4 AC and DCThe abbreviations AC and DC are often used to meansimply alternating and direct, as when they modify cur-rent or voltage.[10][11]

Direct current

Main article: Direct current

Direct current (DC) is the unidirectional ow of electriccharge. Direct current is produced by sources such asbatteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct cur-rent may ow in a conductor such as a wire, but can alsoow through semiconductors, insulators, or even througha vacuum as in electron or ion beams. The electriccharge ows in a constant direction, distinguishing it fromalternating current (AC). A term formerly used for directcurrent was galvanic current.[12]

Alternating current

Main article: Alternating current

In alternating current (AC, also ac), the movement ofelectric charge periodically reverses direction. In directcurrent (DC, also dc), the ow of electric charge is onlyin one direction.AC is the form in which electric power is delivered tobusinesses and residences. The usual waveform of an ACpower circuit is a sine wave. In certain applications, dif-ferent waveforms are used, such as triangular or squarewaves. Audio and radio signals carried on electrical wiresare also examples of alternating current. In these appli-cations, an important goal is often the recovery of infor-mation encoded (or modulated) onto the AC signal.

1.3.5 OccurrencesNatural observable examples of electrical current includelightning, static electricity, and the solar wind, the sourceof the polar auroras.Man-made occurrences of electric current include theow of conduction electrons in metal wires such as theoverhead power lines that deliver electrical energy acrosslong distances and the smaller wires within electrical andelectronic equipment. Eddy currents are electric currentsthat occur in conductors exposed to changing magneticelds. Similarly, electric currents occur, particularly inthe surface, of conductors exposed to electromagnetic


waves. When oscillating electric currents ow at the cor-rect voltages within radio antennas, radio waves are gen-erated.In electronics, other forms of electric current include theow of electrons through resistors or through the vacuumin a vacuum tube, the ow of ions inside a battery or aneuron, and the ow of holes within a semiconductor.

1.3.6 Current measurementCurrent can be measured using an ammeter.At the circuit level, there are various techniques that canbe used to measure current:

Shunt resistors[13]

Hall eect current sensor transducers Transformers (however DC cannot be measured) Magnetoresistive eld sensors[14]

1.3.7 Resistive heatingMain article: Joule heating

Joule heating, also known as ohmic heating and resistiveheating, is the process by which the passage of an elec-tric current through a conductor releases heat. It was rststudied by James Prescott Joule in 1841. Joule immerseda length of wire in a xed mass of water and measuredthe temperature rise due to a known current through thewire for a 30 minute period. By varying the current andthe length of the wire he deduced that the heat producedwas proportional to the square of the current multipliedby the electrical resistance of the wire.

Q / I2RThis relationship is known as Joules First Law. TheSI unit of energy was subsequently named the joule andgiven the symbol J. The commonly known unit of power,the watt, is equivalent to one joule per second.

1.3.8 ElectromagnetismElectromagnet

Main article: ElectromagnetElectric current produces a magnetic eld. The magneticeld can be visualized as a pattern of circular eld linessurrounding the wire that persists as long as there is cur-rent.Magnetism can also produce electric currents. Whena changing magnetic eld is applied to a conductor, an

According to Ampres law, an electric current produces amagnetic eld.

Electromotive force (EMF) is produced, and when thereis a suitable path, this causes current.Electric current can be directly measured with agalvanometer, but this method involves breaking theelectrical circuit, which is sometimes inconvenient. Cur-rent can also be measured without breaking the circuit bydetecting the magnetic eld associated with the current.Devices used for this include Hall eect sensors, currentclamps, current transformers, and Rogowski coils.

Radio waves

Main article: Radio waves

When an electric current ows in a suitably shaped con-ductor at radio frequencies radio waves can be generated.These travel at the speed of light and can cause electriccurrents in distant conductors.

1.3.9 Conduction mechanisms in variousmedia

Main article: Electrical conductivity

In metallic solids, electric charge ows by means ofelectrons, from lower to higher electrical potential. Inother media, any stream of charged objects (ions, for ex-ample) may constitute an electric current. To provide adenition of current that is independent of the type ofcharge carriers owing, conventional current is dened tobe in the same direction as positive charges. So in metalswhere the charge carriers (electrons) are negative, con-


ventional current is in the opposite direction as the elec-trons. In conductors where the charge carriers are posi-tive, conventional current is in the same direction as thecharge carriers.In a vacuum, a beam of ions or electrons may be formed.In other conductive materials, the electric current is dueto the ow of both positively and negatively charged parti-cles at the same time. In still others, the current is entirelydue to positive charge ow. For example, the electric cur-rents in electrolytes are ows of positively and negativelycharged ions. In a common lead-acid electrochemicalcell, electric currents are composed of positive hydrogenions (protons) owing in one direction, and negative sul-fate ions owing in the other. Electric currents in sparksor plasma are ows of electrons as well as positive andnegative ions. In ice and in certain solid electrolytes, theelectric current is entirely composed of owing ions.

Metals

A solid conductive metal contains mobile, or free elec-trons, which function as conduction electrons. Theseelectrons are bound to the metal lattice but no longer toan individual atom. Metals are particularly conductivebecause there are a large number of these free electrons,typically one per atom in the lattice. Even with no ex-ternal electric eld applied, these electrons move aboutrandomly due to thermal energy but, on average, there iszero net current within the metal. At room temperature,the average speed of these random motions is 106 me-tres per second.[15] Given a surface through which a metalwire passes, electrons move in both directions across thesurface at an equal rate. As George Gamow wrote in hispopular science book, One, Two, Three...Innity (1947),The metallic substances dier from all other materialsby the fact that the outer shells of their atoms are boundrather loosely, and often let one of their electrons go free.Thus the interior of a metal is lled up with a large num-ber of unattached electrons that travel aimlessly aroundlike a crowd of displaced persons. When a metal wireis subjected to electric force applied on its opposite ends,these free electrons rush in the direction of the force, thusforming what we call an electric current.When a metal wire is connected across the two termi-nals of a DC voltage source such as a battery, the sourceplaces an electric eld across the conductor. The momentcontact is made, the free electrons of the conductor areforced to drift toward the positive terminal under the in-uence of this eld. The free electrons are therefore thecharge carrier in a typical solid conductor.For a steady ow of charge through a surface, the cur-rent I (in amperes) can be calculated with the followingequation:

I =Q

t;

where Q is the electric charge transferred through the sur-face over a time t. If Q and t are measured in coulombsand seconds respectively, I is in amperes.More generally, electric current can be represented as therate at which charge ows through a given surface as:

I =dQdt :

Electrolytes

Main article: Conductivity (electrolytic)

Electric currents in electrolytes are ows of electricallycharged particles (ions). For example, if an electric eldis placed across a solution of Na+ and Cl (and conditionsare right) the sodium ions move towards the negative elec-trode (cathode), while the chloride ions move towards thepositive electrode (anode). Reactions take place at bothelectrode surfaces, absorbing each ion.Water-ice and certain solid electrolytes called proton con-ductors contain positive hydrogen ions or "protons" whichare mobile. In these materials, electric currents are com-posed of moving protons, as opposed to the moving elec-trons found in metals.In certain electrolyte mixtures, brightly coloured ions arethe moving electric charges. The slow progress of thecolour makes the current visible.[16]

Gases and plasmas

In air and other ordinary gases below the breakdown eld,the dominant source of electrical conduction is via rel-atively few mobile ions produced by radioactive gases,ultraviolet light, or cosmic rays. Since the electricalconductivity is low, gases are dielectrics or insulators.However, once the applied electric eld approaches thebreakdown value, free electrons become suciently ac-celerated by the electric eld to create additional freeelectrons by colliding, and ionizing, neutral gas atoms ormolecules in a process called avalanche breakdown. Thebreakdown process forms a plasma that contains enoughmobile electrons and positive ions to make it an electri-cal conductor. In the process, it forms a light emittingconductive path, such as a spark, arc or lightning.Plasma is the state of matter where some of the electronsin a gas are stripped or ionized from their molecules oratoms. A plasma can be formed by high temperature, orby application of a high electric or alternating magneticeld as noted above. Due to their lower mass, the elec-trons in a plasma accelerate more quickly in response toan electric eld than the heavier positive ions, and hencecarry the bulk of the current. The free ions recombineto create new chemical compounds (for example, break-


ing atmospheric oxygen into single oxygen [O2 2O],which then recombine creating ozone [O3]).[17]

Vacuum

Since a "perfect vacuum" contains no charged particles, itnormally behaves as a perfect insulator. However, metalelectrode surfaces can cause a region of the vacuum tobecome conductive by injecting free electrons or ionsthrough either eld electron emission or thermionic emis-sion. Thermionic emission occurs when the thermal en-ergy exceeds the metals work function, while eld elec-tron emission occurs when the electric eld at the surfaceof the metal is high enough to cause tunneling, whichresults in the ejection of free electrons from the metalinto the vacuum. Externally heated electrodes are oftenused to generate an electron cloud as in the lament orindirectly heated cathode of vacuum tubes. Cold elec-trodes can also spontaneously produce electron cloudsvia thermionic emission when small incandescent regions(called cathode spots or anode spots) are formed. Theseare incandescent regions of the electrode surface that arecreated by a localized high current. These regions maybe initiated by eld electron emission, but are then sus-tained by localized thermionic emission once a vacuumarc forms. These small electron-emitting regions canform quite rapidly, even explosively, on a metal surfacesubjected to a high electrical eld. Vacuum tubes andsprytrons are some of the electronic switching and am-plifying devices based on vacuum conductivity.

Superconductivity

Main article: Superconductivity

Superconductivity is a phenomenon of exactly zeroelectrical resistance and expulsion of magnetic elds oc-curring in certain materials when cooled below a charac-teristic critical temperature. It was discovered by HeikeKamerlingh Onnes on April 8, 1911 in Leiden. Likeferromagnetism and atomic spectral lines, superconduc-tivity is a quantum mechanical phenomenon. It is charac-terized by the Meissner eect, the complete ejection ofmagnetic eld lines from the interior of the superconduc-tor as it transitions into the superconducting state. Theoccurrence of the Meissner eect indicates that super-conductivity cannot be understood simply as the ideal-ization of perfect conductivity in classical physics.

Semiconductor

Main article: Semiconductor

In a semiconductor it is sometimes useful to think of thecurrent as due to the ow of positive "holes" (the mobile

positive charge carriers that are places where the semi-conductor crystal is missing a valence electron). This isthe case in a p-type semiconductor. A semiconductorhas electrical conductivity intermediate in magnitude be-tween that of a conductor and an insulator. This means aconductivity roughly in the range of 102 to 104 siemensper centimeter (Scm1).In the classic crystalline semiconductors, electrons canhave energies only within certain bands (i.e. ranges oflevels of energy). Energetically, these bands are locatedbetween the energy of the ground state, the state in whichelectrons are tightly bound to the atomic nuclei of the ma-terial, and the free electron energy, the latter describingthe energy required for an electron to escape entirely fromthe material. The energy bands each correspond to a largenumber of discrete quantum states of the electrons, andmost of the states with low energy (closer to the nucleus)are occupied, up to a particular band called the valenceband. Semiconductors and insulators are distinguishedfrom metals because the valence band in any given metalis nearly lled with electrons under usual operating con-ditions, while very few (semiconductor) or virtually none(insulator) of them are available in the conduction band,the band immediately above the valence band.The ease with which electrons in the semiconductor canbe excited from the valence band to the conduction banddepends on the band gap between the bands. The size ofthis energy bandgap serves as an arbitrary dividing line(roughly 4 eV) between semiconductors and insulators.With covalent bonds, an electron moves by hopping to aneighboring bond. The Pauli exclusion principle requiresthe electron to be lifted into the higher anti-bonding stateof that bond. For delocalized states, for example in onedimension that is in a nanowire, for every energy there isa state with electrons owing in one direction and anotherstate with the electrons owing in the other. For a netcurrent to ow, more states for one direction than for theother direction must be occupied. For this to occur, en-ergy is required, as in the semiconductor the next higherstates lie above the band gap. Often this is stated as:full bands do not contribute to the electrical conductiv-ity. However, as the temperature of a semiconductor risesabove absolute zero, there is more energy in the semi-conductor to spend on lattice vibration and on excitingelectrons into the conduction band. The current-carryingelectrons in the conduction band are known as free elec-trons, although they are often simply called electronsif context allows this usage to be clear.

1.3.10 Current density and Ohms lawMain article: Current density

Current density is a measure of the density of an electriccurrent. It is dened as a vector whose magnitude is theelectric current per cross-sectional area. In SI units, the


current density is measured in amperes per square metre.

I =

Z~J d ~A

where I is current in the conductor, ~J is the currentdensity, and d ~A is the dierential cross-sectional areavector.The current density (current per unit area) ~J in mate-rials with nite resistance is directly proportional to theelectric eld ~E in the medium. The proportionality con-stant is called the conductivity of the material, whosevalue depends on the material concerned and, in general,is dependent on the temperature of the material:

~J = ~E

The reciprocal of the conductivity of the material iscalled the resistivity of the material and the aboveequation, when written in terms of resistivity becomes:

~J =~E

~E = ~J

Conduction in semiconductor devices may occur by acombination of drift and diusion, which is proportionalto diusion constant D and charge density q . The cur-rent density is then:

J = E +Dqrn;with q being the elementary charge and n the electrondensity. The carriers move in the direction of decreasingconcentration, so for electrons a positive current resultsfor a positive density gradient. If the carriers are holes,replace electron density n by the negative of the hole den-sity p .In linear anisotropic materials, , and D are tensors.In linear materials such as metals, and under low frequen-cies, the current density across the conductor surface isuniform. In such conditions, Ohms law states that thecurrent is directly proportional to the potential dierencebetween two ends (across) of that metal (ideal) resistor(or other ohmic device):

I =V

R;

where I is the current, measured in amperes; V is thepotential dierence, measured in volts; and R is theresistance, measured in ohms. For alternating currents,especially at higher frequencies, skin eect causes thecurrent to spread unevenly across the conductor cross-section, with higher density near the surface, thus increas-ing the apparent resistance.

1.3.11 Drift speedThe mobile charged particles within a conductor moveconstantly in random directions, like the particles of agas. In order for there to be a net ow of charge, theparticles must also move together with an average driftrate. Electrons are the charge carriers in metals and theyfollow an erratic path, bouncing from atom to atom, butgenerally drifting in the opposite direction of the electriceld. The speed at which they drift can be calculated fromthe equation:

I = nAvQ ;

where

I is the electric currentn is number of charged particles per unit vol-ume (or charge carrier density)A is the cross-sectional area of the conductorv is the drift velocity, andQ is the charge on each particle.

Typically, electric charges in solids ow slowly. For ex-ample, in a copper wire of cross-section 0.5 mm2, carry-ing a current of 5 A, the drift velocity of the electrons ison the order of a millimetre per second. To take a dif-ferent example, in the near-vacuum inside a cathode raytube, the electrons travel in near-straight lines at about atenth of the speed of light.Any accelerating electric charge, and therefore anychanging electric current, gives rise to an electromagneticwave that propagates at very high speed outside the sur-face of the conductor. This speed is usually a signicantfraction of the speed of light, as can be deduced fromMaxwells Equations, and is therefore many times fasterthan the drift velocity of the electrons. For example,in AC power lines, the waves of electromagnetic energypropagate through the space between the wires, movingfrom a source to a distant load, even though the electronsin the wires only move back and forth over a tiny distance.The ratio of the speed of the electromagnetic wave to thespeed of light in free space is called the velocity factor,and depends on the electromagnetic properties of the con-ductor and the insulating materials surrounding it, and ontheir shape and size.The magnitudes (but, not the natures) of these three ve-locities can be illustrated by an analogy with the threesimilar velocities associated with gases.

The low drift velocity of charge carriers is analogousto air motion; in other words, winds.

The high speed of electromagnetic waves is roughlyanalogous to the speed of sound in a gas (these waves


move through the medium much faster than any in-dividual particles do)

The random motion of charges is analogous to heat the thermal velocity of randomly vibrating gas par-ticles.

1.3.12 See also Current 3-vector Direct current Electric shock Electrical measurements History of electrical engineering Hydraulic analogy International System of Quantities SI electromagnetism units

1.3.13 References[1] Anthony C. Fischer-Cripps (2004). The electronics com-

panion. CRC Press. p. 13. ISBN 978-0-7503-1012-3.

[2] Lakatos, John; Oenoki, Keiji; Judez, Hector; Oenoki,Kazushi; Hyun Kyu Cho (March 1998). Learn PhysicsToday!". Lima, Peru: Colegio Dr. Franklin D. Roosevelt.Retrieved 2009-03-10.

[3] T. L. Lowe, John Rounce, Calculations for A-level Physics,p. 2, Nelson Thornes, 2002 ISBN 0-7487-6748-7.

[4] Howard M. Berlin, Frank C. Getz, Principles of ElectronicInstrumentation and Measurement, p. 37, Merrill Pub.Co., 1988 ISBN 0-675-20449-6.

[5] A-M Ampre, Recuil d'Observations lectro-dynamiques,p. 56, Paris: Chez Crochard Libraire 1822 (in French).

[6] Electric Power, vol. 6, p. 411, 1894.

[7] Consoliver, Earl L., and Mitchell, Grover I. (1920).Automotive ignition systems. McGraw-Hill. p. 4.

[8] Robert A. Millikan and E. S. Bishop (1917). Elements ofElectricity. American Technical Society. p. 54.

[9] Oliver Heaviside (1894). Electrical papers 1. Macmillanand Co. p. 283. ISBN 0-8218-2840-1.

[10] N. N. Bhargava and D. C. Kulshreshtha (1983). BasicElectronics & Linear Circuits. Tata McGraw-Hill Educa-tion. p. 90. ISBN 978-0-07-451965-3.

[11] National Electric Light Association (1915). Electrical me-termans handbook. Trow Press. p. 81.

[12] Andrew J. Robinson, Lynn Snyder-Mackler (2007).Clinical Electrophysiology: Electrotherapy and Electro-physiologic Testing (3rd ed.). Lippincott Williams &Wilkins. p. 10. ISBN 978-0-7817-4484-3.

[13] What is a Current Sensor and How is it Used?. Fo-cus.ti.com. Retrieved on 2011-12-22.

[14] Andreas P. Friedrich, Helmuth Lemme The UniversalCurrent Sensor. Sensorsmag.com (2000-05-01). Re-trieved on 2011-12-22.

[15] The Mechanism Of Conduction In Metals, Think Quest.

[16] Rudolf Holze, Experimental Electrochemistry: A Labora-tory Textbook, page 44, John Wiley & Sons, 2009 ISBN3527310983.

[17] Lab Note #106 Environmental Impact of Arc Suppres-sion". Arc Suppression Technologies. April 2011. Re-trieved March 15, 2012.

1.3.14 External links Allaboutcircuits.com, a useful site introducing elec-

tricity and electronics

1.4 FrequencyFor other uses, see Frequency (disambiguation).Frequency is the number of occurrences of a repeat-

ing event per unit time. It is also referred to as temporalfrequency, which emphasizes the contrast to spatial fre-quency and angular frequency. The period is the dura-tion of one cycle in a repeating event, so the period is thereciprocal of the frequency. For example, if a newbornbabys heart beats at a frequency of 120 times a minute,its period the interval between beats is half a second(60 seconds (i.e. a minute) divided by 120 beats). Fre-quency is an important parameter used in science and en-gineering to specify the rate of oscillatory and vibratoryphenomena, such as mechanical vibrations, audio (sound)signals, radio waves, and light.

1.4.1 Denitions and units

For cyclical processes, such as rotation, oscillations, orwaves, frequency is dened as a number of cycles perunit time. In physics and engineering disciplines, such asoptics, acoustics, and radio, frequency is usually denotedby a Latin letter f or by the Greek letter (nu). Note, therelated

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