Ali M. Niknejad

114 Pages·2015·49.33 MB·English

ELECTRONICS
Ali M. Niknejad
Copyright c 2015AliNiknejad
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Thirdprinting,September25,2015
Contents
1 Current and Voltage ........................................... 7
1.1 Charge and Current 7
1.1.1 CountingCharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.2 MotionofRealCharges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.3 CurrentFlowThroughaComponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 DCversusACCurrents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Voltage 10
1.2.1 VoltageAcrossaComponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 TheConceptofGround . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Voltage Sources and Batteries 13
1.3.1 AnIdealVoltageSource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.3 WaterPumpAnalogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4 Current Source 14
1.4.1 BatteryCharger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Dependent Sources 15
2 KCL/KVL and Energy and Power ............................... 17
2.1 KVL and KCL 17
2.1.1 KCL:Kirchhoff’sCurrentLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 KVL:Kirchhoff’sVoltageLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3 KVLImplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.4 YourTasteforOpensandShorts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Power and Energy 20
2.2.1 EnergySignConvention. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Conductance and Resistance ................................. 23
3.1 Conductors 23
3.1.1 IdealConductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.3 CalculatingResistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.4 ConductanceandConductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Power Loss in Resistors 26
3.3 Resistors versus Resistance 26
3.3.1 WhyPowerIsDeliveredwithHighVoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Series Resistors 29
3.4.1 ResistanceofWires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 Parallel Resistors 30
3.6 Internal Resistance of Battery 32
3.7 An Ideal Switch 33
3.8 Is Ohm’s Law Strange? 34
4 Voltage and Current Dividers .................................. 35
4.1 Voltage Dividers 35
4.1.1 Potentiometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Current Dividers 36
4.2.1 GeneralizationofDividers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 (Bad) Application: Light Dimmer 37
4.3.1 DimmerwithPotentiometer? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Resistive Touch Screen 39
4.5 The Wheatstone Bridge 43
5 Analyzing a Complex Network ................................ 45
5.0.1 IdentifyingtheReferenceNode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1 Nodal Analysis 46
5.1.1 NodeEquationsforResistiveBranches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.1.2 Dealingwith“Floating"VoltageSources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.3 KCLata“SuperNode" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.4 EliminationofTrivialNodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 Nodal Analysis with Dependent Sources 49
5.3 Nodal Analysis Summary 51
5.4 Systematic Nodal Analysis 52
5.4.1 BranchIncidenceMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.4.2 BranchVoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.4.3 NodalVoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 Network Theorems and Equivalence ........................... 57
6.1 Non-Linear Components and Dependent Sources 57
6.1.1 LinearResistororConductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Superposition 58
6.3 Thevenin Equivalent Circuit 60
6.3.1 TheveninDerivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.3.2 TheveninSourceResistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3.3 CalculatingR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
th
6.4 Norton Equivalent Circuit 65
6.4.1 SourceTransformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.5 Maximum Power Transfer 67
7 Capacitance and Capacitors ................................. 69
7.1 Thought Experiment 69
7.1.1 CapacitorCharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.1.2 CapacitorVoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.2 Definition of Capacitance 71
7.2.1 CapacitorAnalogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.2.2 CapacitorEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.2.3 FieldLines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.3 Parallel Plate Capacitor 73
7.3.1 DielectricConstant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.3.2 PracticalCapacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.4 Capacitor I-V Relations 75
7.4.1 CapacitorCurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.4.2 CapacitorVoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.4.3 SinusoidalDrive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.5 Circuits with Capacitors 78
7.5.1 ShuntConnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.5.2 SeriesConnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.6 KCL with Capacitors 80
7.7 Application: Capacitive Touch Screen 80
7.7.1 SelfCapacitanceTouchSensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.7.2 MutualCapacitanceTouchScreen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.7.3 CapacitiveTouchSensorDetection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.8 Capacitors Everywhere! 83
7.8.1 CanCapacitorsReplaceBatteries? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.9 Non-Linear Capacitors 84
8 Amplifiers and Circuit Interfaces ............................... 85
8.1 Amplifiers 85
8.1.1 UnilateralGain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.1.2 AmplifierPackaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.1.3 AmplifierModules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Ideal Amplifiers 87
8.2.1 IdealVoltageAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2.2 IdealCurrentAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.2.3 IdealTransconductanceAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.2.4 IdealTransresistanceAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3 Real Amplifiers 89
8.3.1 RealVoltageAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3.2 EquivalentCircuitModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
8.3.3 CascadeofAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.3.4 LoadingwithOtherAmplifierTopologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.4 Amplifiers Non-Idealities 93
8.4.1 Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.4.2 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
9 Operational Amplifiers ........................................ 95
9.1 Operational Amplifiers 95
9.1.1 Classic741Schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
9.2 Equivalent Circuit Model 96
9.2.1 Op-AmpInvertingAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9.2.2 DifferentialratherthanDifferenceAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
9.2.3 DynamicRangeofAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
9.3 Feedback System 100
9.4 Ideal Op-Amp: Golden Rules 101
9.5 Op-Amp Circuits 101
9.5.1 InvertingAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
9.5.2 VoltageFollower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.5.3 Non-InvertingAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.5.4 CurrentSummingAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.5.5 VoltageSummingAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.5.6 ACurrentSource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.6 Application: Instrumentation Amplifiers 105
9.6.1 Common-ModeandDifferential-ModeGain . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.6.2 Don’tDoThis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.6.3 DifferenceAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.6.4 InstrumentationAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
9.6.5 ImprovedInstrumentationAmplifier(Subtle) . . . . . . . . . . . . . . . . . . . . . . . . . . 108
9.7 Digital Signal Processing 109
9.7.1 Comparator/ZeroCrossingDetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.7.2 Op-AmpBasedDAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.7.3 ComparatorAnalog-to-DigitalConverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.8 Positive Feedback 111
9.8.1 SchmittTrigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
1. Current and Voltage
1.1 Charge and Current
Currentischargeinmotion. Aconductorisamaterialwherechargersarefreetomoveabout. Even
in“rest",thechargecarriersareinrapidmotionduetothethermalenergy. Typicalcarriersinclude
electrons,ions,and“holes"(insemiconductors)1
Netchargecrossingsurfaceintime∆t
I= (1.1)
∆t
Whenpositivechargesmoveinthepositivedirection(sayright),wesaythecurrentispositive. If
negativechargesmoveinthesamedirection,wesaythecurrentisnegative. Likewise,ifapositive
chargemovesinthenegativedirection(sayleft),wealsosaythecurrentisnegative.
Whenbothpositiveandnegativechargearemoving(Fig.1.1),thenetchargemotiondetermines
theoverallcurrent.
1.1.1 Counting Charges
Supposethatthechargecarrierseachhaveachargeofq. Let’scountthenumberofcharges(n)
crossingasurfaceintime∆t andmultiplybytheelectricalcharge(Fig.1.2)
n
I=q (1.2)
∆t
To find n, let’s make the simple assumption that all the charges are moving at a speed of v to
theright. Thenthedistancetraversedbythechargesintime∆t issimplyv∆t,orinotherwords
if we move back from the surface this distance, all the charges in the volumeV formed by the
cross-sectionalsurfaceAandthedistancev∆t willcrossthesurfaceintime∆t. Thismeansthat
V =v∆tA (1.3)
1Holes are vacancies in a crystal, or the absence of an electron (positive charge), which can move around like
bubbles,buttheyhavemassandactlikechargedparticles.Afullunderstandingofholesrequiresknowledgeofquantum
mechanics.
8 Chapter 1. Current and Voltage
i i
q 1 q 1
1 + v 1 + v
1 1
_ _
v2 q2 q2 v2
i i
2 2
(a) (b)
Figure 1.1: Net current is determined by the net positive charge moving to the right. (a) Since
thechargeq isnegativeandmovingtotheleft, itcontributestocurrentpositively, Q =q
2 net 1
−
( q )=q +q . (b)Nowq isalsomovingtotheright,andduetoitsnegativecharge,itsubtracts,
2 1 2 2
−| |
Q =q q .
net 1 2
−| |
+ +
+
+ A
+
+ +
v∆t
Figure1.2: ThenumberofchargescrossingthecrosssectionalareaAisgivenbythenumberof
chargesdefinedbythevolumeofAmultipliedbyv∆t,orthedistancetraveledbythechargesina
timeinternalof∆t.
1.1 Charge and Current 9
1 1
v¯= v =0 v¯= v xˆv
N i N i≈ d
i i
! !
(a) (b)
Figure1.3: (a)Arandomdistributionofvelocitiesleadstoanetzerovelocity(onaverage). (b)A
smalldriftvelocityisnowaddedtotherandomdistribution,whichshowsthatonaveragecharges
movetotheright.
J⃗
ρ(t)
Figure 1.4: Conservation of charge is a fundamental physical fact. If the charge in a region is
changing,itmustbeduetocurrentflowintooroutofthatregion.
IfthevolumedensityofchargedcarriersinthisvolumeisgivenbyN,then
V N v∆tA N
I=q · =q · =q(NA)v (1.4)
∆t ∆t
Aside:ConservationofChargeWeknowfromfundamentalphysicsthatchargeisconserved.
R
Thatmeansthatifinagivenregionthechargeischangingintime,itmustbeduetothenet
flowofcurrentintothatregion(Fig.1.4). Thisisexpressedbythecurrentcontinuityrelation
inphysics(whichcanbederivedfromMaxwell’sequations)
∂ρ
∇ J=
· −∂t
Thedivergenceisanexpressionofspatialvariationofcurrentdensitywhereastheright-hand-
sideisthechangeinchargedensityatagivenpoint.
10 Chapter 1. Current and Voltage
Node
a
i i i
A B C
i
ab i
ba A B C
Branches
b
(a) (b)
Figure1.5: (a)Thedefinitionofthecurrentthroughacomponent. (b)Branchcurrentsaredefined
whencomponentsareconnectedinparallelthroughcommonnodes.
1.1.2 Motion of Real Charges
The above result emphasizes that current is associated with motion. In our simple example, we
assumedallcarriersmoveatavelocityv. Inreality,asyoumayknow,electronsmoveveryrapidly
in random directions due to thermal motion (mv2 kT) and v is the net drift velocity. This is
∼
showninFig.1.3,wherewehaveactuallyexaggeratedtheamountofdriftvelocityinmosttypical
situations. Electronsactuallymovereallyfastduetothermalenergy. Therandommotiongivesrise
to“noise"(thinkofstaticonaradioorsnowonaTVscreen),andsignalsarejustperturbationson
thisrandomjigglingabout.
1.1.3 Current Flow Through a Component
Whencurrentflowsintoacomponent(resistor,lamp,motor)fromnodeatob,asshowninFig.1.5a,
wecallthiscurrenti . Notethatthecurrenti isthesameas i . Whenseveralcomponentsare
ab ab ba
−
connectedinacircuit,wecallthecomponentsbranchesandassociateacurrentwitheachbranch,
asshowninFig.1.5b.
CurrentintoaComponent
Supposethatwenowconsiderthecurrentflowintoacomponent. Ifwecounttheamountofcharge
∆qflowingintothecomponentinatimeinterval∆t,theninthelimitas∆t 0,theratioisexactly
→
thecurrentflowingintothecomponent
∆q dq
I= lim =
∆t 0 ∆t dt
→
1.1.4 DC versus AC Currents
VariousexamplecurrentwaveformsareshowninFig.1.6. Aconstantcurrentiscalleda“Direct
Current" (DC). Otherwise it’s AC. Some AC typical waveforms are shown above. Sine waves
arethewaveformscomingoutofanelectricoutletandareverycommon. Asquarewaveisthe
clocksignalinadigitalcircuit,whichhasawelldefinededgewhichcanbeusedfortiming. Any
time-varyingcurrentisknownasanAC,oralternatingcurrent. Notethatthesignofthecurrent
does not necessarily have to change (the current does not have to alter direction), as the name
implies.
1.2 Voltage
Duetoboththeattractiveandrepulsivenatureofcharges,movingthemaroundmaytakeenergy,or
itmayreturnenergy. Forexample,ifwedesignacircuitthatmovesalotofchargesintoaregion