Chapter 1. Fundamental Electrical Concepts

Transcription

1 Chapter 1 Fundamental Electrical Concepts Charge, current, voltage, power circuits, nodes, branches Branch and node voltages, Kirchhoff Laws Basic circuit elements, combinations 01 fundamental 1

2 1.3 Electrical Charge Relates to electrical forces between particles Bipolar: positive or negative charge Electrical effects due to movement and separation of charge Is measured in coulomb [C] Symbol Q (static) or q (time varying) Discrete: electron has charge e = x C Coulomb s law: F Q Q = ε rˆ 2 12 r12 (charge = lading) r Q 1 1 r Q fundamental 2

3 Electrical Current (current = stroom) Moving electrical charge Controlled movement and separation of charges determines function of circuit or system Current can be: Function of time: alternating current (ac) Constant: direct current (dc) Symbol I (dc) or i (ac) Unit: ampere (A) Migration of electrons ampere = wire coulomb/second Conducting source with excess electrons Conducting target depleted of electrons 01 fundamental 3

4 Electrical Current pole Positive current shortage of electrons excess electrons pole battery Electron flow Conducting source with excess electrons Migration of electrons wire Conducting target depleted of electrons 01 fundamental 4

5 (stroomsterkte) Electrical Current Current: amount of charge being transferred per unit time: ampere = coulomb/second. q q q q A q t q I = q t q i = dq dt t t 01 fundamental 5

6 Electrical Current Current follows a path has a direction: arrow and sign and magnitude 2 ma 2 ma 2 ma 2 ma Four identical cases of 2x10 3 C/s flowing to the left 01 fundamental 6

7 Voltage or Potential Difference Relates to the energy associated with charge transfer (current) unit: volt [V] symbol: V (dc) or v (ac) One volt is the amount of work (energy) it costs to transfer one coulomb of charge v ab = w q ab a v ab b 01 fundamental 7

8 Hydraulic Analogy Pressure Difference Potential Difference Water Flow Current Flow 01 fundamental 8

9 Voltage and Current a v ab b i Voltage is an acrossquantity Current is a throughquantity Voltage across terminals a and b Current through a wire 01 fundamental 9

10 Power Power = Rate of Work = amount of work divided by time it takes p = work second = work charge x charge second voltage current p = voltage x current = v x i unit watt [W] = joule/second [J/s] symbols: P, p fundamental 10

11 Reference Directions v i v i Associated: into plus terminal, leaving minus terminal v i v i Unassociated 01 fundamental 11

12 Reference direction Power Direction vi product associated p > 0 associated p < 0 unassociated p > 0 unassociated p < 0 Condition absorbing releasing releasing absorbing I 1 = I V = 3V I = 20mA = 0.02A Assocociated! Lamp power: I? V = (0.02)(3) = 0.06 >0 absorbing Battery power: I 1? V = (0.02)(3) = 0.06 <0 releasing Note: total power = 0! 01 fundamental 12

13 Circuit Diagram Way of visual communication of electrical model of circuit / system / product 1.5 Example circuit diagram of battery charger 01 fundamental 13

14 Bierthermometer LM3914N 01 fundamental 14

15 Circuit Diagram Only gives connectivity Form or shape is not important Synonym: schematic (schema), schematic diagram All different schematics but identical circuits 01 fundamental 15

16 Node Elements are connected together Connections are called nodes (knooppunten) Nodes are drawn as line segments in circuit diagram Connected line segments form a node One node connects two or more elements Node has unique potential (Circuit behavior follows from potential (voltage) difference between nodes!) How many nodes? fundamental 16

17 Circuit Diagram dot jump gap cross shift connection dot jump x gap x cross x shift # nodes not prefered 2 01 fundamental 17

18 Node Names Nodes often have a unique identifier or name or number or label or... Idem elements a e1 b e2 c e3 e4 e5 INPUT AMP OUTPUT d COMMON Other annotations: Whatever is useful Element values and type numbers, voltage, current, power, noise and any other relevant signal property, etc. 01 fundamental 18

19 Path and Branch Path (pad): trace of adjoining twoterminal elements Branch (tak): a path that connects two nodes (and no more) a e1 b e2 c e3 e4 e5 d What are some paths? What are some branches? a e1 b e2 c a e3 d e4 b a e1 b b e2 c 01 fundamental 19

20 Branch Voltages and Currents Voltage across a branch (voltage is acrossquantity) Current through a branch (current is throughquantity) a V ab b c e V e d 1.6 Can use two node names or element name to specify a branch and branch voltage 01 fundamental 20

21 Node Voltages Do they exist? NO Only potential differences are important Voltage = potential difference Node voltage can not be defined unambiguously 10V 30V 20V 110V 130V 120V 5V 15V 5V 15V 115V 0V same branch voltages imply same behavior See next slide for YES answer 01 fundamental 21

22 Node Voltages Do they exist? YES Only when one arbitrary but specific node is chosen as reference node with a potential of 0V Identical branch voltages Identical currents Identical behavior a b d c 0V V c V x V xreference reference node = ground node = common node symbols: 01 fundamental 22

23 a a Reference Node is Arbitrary d 3V b 5V b c c 2V 2V May choose one arbitrary node as reference (0V) One choice may be much more convenient for calculation than other V c? V b? a d 3V b c V b? V d? d 2V 01 fundamental 23

24 Loops Loop (lus): closed path, begin node same as end node a b c How many loops? e a b d a d b c d b c b a d c fundamental 24

25 Voltage Drops Voltage drop (spanningsval): difference in potential between two nodes along a path Take care of positive and negative sign reference 3V 2V 4V a b c d V ab = V ac = V ad = 3V 5V 1V 01 fundamental 25

26 Voltage Drops Voltage drop (spanningsval): difference in potential between two nodes along a path Take care of positive and negative sign reference voltage drop node potential V V 1 V 2 3 a b c d V ab = V ac = V ad = V a V b =V 1 V a V c = (V a V b )(V b V c ) = V 1 V 2 V a V d = (V a V b ) (V b V c ) (V c V d ) = V 1 V 2 V 3! 01 fundamental 26

27 Kirchhoff s Voltage Law (Spanningswet) KVL: The algebraic sum of the branch voltage drops around any loop (= closed path) is zero v 1 v 2 KVL: v 4 v 5 v 2 = 0 v a v b v c v 3 v 4 v 5 v 4 v 5 v 2 = (v b v d ) (v c v d ) (v b v c ) = v b v b v d v d v c v c 1.7 v d = 0 01 fundamental 27

28 Kirchhoff s Current Law (Stroomwet) KCL: The sum of the currents entering a node is equal to the sum of the currents leaving the node 5µA 3µA Analogy: Flow of water in pipes Cars at highway junction 2µA 01 fundamental 28

29 Circuit Elements Transistors, switches, resistors, capacitors and many more At least two terminals fundamental 29

30 Constitutive Relation (Constitutieve Relatie) Terminal is connection point Current can flow into or out of terminal (and element) Potential difference can exist between terminals: branch voltage Relation between branch voltage and terminal current defines function of element v = f(i), i = f 1 (v) v Note: functions of more than 1 variable in case of multiterminal elements i 01 fundamental 30

31 Voltage Source (Spanningsbron) v Voltage v is defined Current may have any value Idealized component In practice, voltage will to some extend depend on current (and temperature, age,...) v ISO Symbol 01 fundamental 31

32 Current Source (Stroombron) i Current i is defined Voltage arbitrary In practice... i ISO symbol 01 fundamental 32

33 Resistance (Resistantie) Resistance: The property of materials to impede the flow of electric charge Linear resistance: voltage proportional to current Ohm s Law (wet van Ohm) v = i R R is resistance, unit: Ω (Ohm) = V/A v ISO symbol i R R 01 fundamental 33

34 Resistor (Weerstand) An actual circuit element having resistance as it s main characteristic Resistance means merely the electrical model of an ideal resistor In practice, v = i Ris only approximately or accurately valid in limited range of operating conditions (i.e. voltage, current, frequency, temperature) 01 fundamental 34

35 Resistivity (Resistiviteit) Resistance depends on Material shape of element l Consider rectangular resistive wire Resistance R proportional to l length of resistor 1/A R inverse of crosssectional area ρ specific resistivity of material l R = ρ A R i A R =hxw w h 01 fundamental 35

36 Current through Resistance i v R i = f (v,r) = v/r Constitutive relation (constitutieve relatie) 01 fundamental 36

37 Resistors in Series (serieschakeling) v v i i = f (v, R 1, R 2 ) =? R v KVL: v 1 v 2 v = v = v 1 v 2 = ir R 2 v 1 ir 2 2 = (R 1 R 2 ) i v = R eq i i R eq = R k Q: Did we use KCL? Equivalent resistance of series resistors equal to the sum of individual resistances 01 fundamental 37

38 Resistors in Series: Example V=6V I 1kΩ 2kΩ v 1 v 2 Determine I v = i R eq (Ohms Law) V = I R eq (Also in DC case) V = 6V R eq = 3kΩ 6V = I x 3kΩ I = 6V/3kΩ = A = 2 ma V v=ir TIP! equivalent V v=ir Ω A kω ma See 1.2 for units and prefixes 01 fundamental 38

39 Bierthermometer Example (Voltage Divider) i TUE/EE 5CC00 netwerk analyse 04/05 NvdM LM3914N 01 fundamental 14 LM3914N v R 1 R 2 v 1 v 2 R 3 v 3 01 fundamental 39

40 Example (Voltage Divider) V I R 1 R 2 V out Calculate V out V I = R 1 R 2 Note (KCL): all current flows from source through R 1 and R 2, no current flows into output terminals (it can t go anywhere there) R V out = IR 2 2 = V R1 R2 You will need this for first programming assignment of the course computation 01 fundamental 40

41 Potentiometers Potentiometer = adjustable voltage divider R (1 α)r αr 0 α 1 Depending on knob angle 01 fundamental 41

42 Potentiometers Potentiometer Typical audio amplifier: Preamplifier 2. adjustable level reduction 3. power amplifier V R V out Compute V out as a function of α. Does V out depend on R? (0 α 1 function of knob angle) 01 fundamental 42

43 Summary Charge, current, voltage Power Circuits, Nodes, Branches, Loops Branch vs Node Voltages KVL and KCL Ideal Voltage and Current Sources Resistance: Ohms Law, series connection Voltage division Next: capacitor, inductor, combining ckt elements 01 fundamental 43