ENG1030 - Electrical Systems Summary Notes
ENG1030 - Electrical Systems Summary Notes Contents Basic Quantities................................................................................................................ 3 Sign convention for power: .................................................................................................... 3 Electric Circuit: ....................................................................................................................... 4 Tellegen’s Theorem ................................................................................................................ 4 Circuit Elements ..................................................................................................................... 4 Dependent/Independent Sources ..................................................................................... 5 Ohm’s Law ....................................................................................................................... 5 Conductance........................................................................................................................... 5 Sort/Open circuit .............................................................................................................. 5 Lumped-Parameter Model ................................................................................................ 6 Nodes, Branches and Loops .............................................................................................. 6 Kirchhoff’s Current Law (KCL)............................................................................................ 6 Kirchhoff’s Voltage Law (KVL) ........................................................................................... 7 Voltage Division ...................................................................................................................... 7 Current Division ...................................................................................................................... 7 Worked Examples................................................................................................................... 8 Operational Amplifiers (Op-Amps) .................................................................................... 9 Methods of Power Supply to Op-Amp ................................................................................... 9 Dual-Rail power supply: ......................................................................................................... 9 Model of an Op-Amp............................................................................................................ 10 Unity-Gain Buffer ................................................................................................................. 10 Idealised Op-Amp Model ..................................................................................................... 10 Inverting/Non-Inverting Op-Amps ....................................................................................... 11 Differential Op-Amps ........................................................................................................... 12 Instrumentation Amplifier ................................................................................................... 12 Worked Examples:................................................................................................................ 13 Summing Amplifier ............................................................................................................... 14 Digital Electronics ........................................................................................................... 14 Digital words and transmission ............................................................................................ 15 Grey code ............................................................................................................................. 15 Finn Andersen, 2011
1
Complement (negative) arithmetic ...................................................................................... 15 Logic Gates ........................................................................................................................... 16 Sum of Products (SOP) ......................................................................................................... 17 Product of Sums (POS) ......................................................................................................... 17 Karnaugh Maps. ................................................................................................................... 18 Advanced Circuit Analysis ............................................................................................... 19 Nodal Analysis with Super Nodes ........................................................................................ 19 Loop Analysis with Super Meshes ........................................................................................ 20 Superposition ....................................................................................................................... 21 Thevenin Equivalence .......................................................................................................... 22 Norton Equivalence .............................................................................................................. 23 Capacitors and Inductors ................................................................................................ 23 First Order Transients........................................................................................................... 24 Differential Equation Approach ........................................................................................... 24 Step by Step approach ......................................................................................................... 26 RC Circuit .............................................................................................................................. 27 RL Circuit............................................................................................................................... 27 Unit Step Function................................................................................................................ 27 Sinusoidal Circuits .......................................................................................................... 28 Complex Numbers and Relationships .................................................................................. 28
Finn Andersen, 2011
2
Basic Quantities Current: Flow of electric charge per unit time. There is only current when the charge changes. Current = gradient of q vs t graph.
• •
The total resistance of the circuit determines the amount of current that flows The current in a series circuit is constant. …
•
Current is divided/split when the circuit branches e.g. parallel circuit. Power: Change in energy over time
A voltage or force causes current to flow
!
" ! # ! !
Voltage is consumed by resistors in a series circuit so there is a voltage drop over components.
Energy is supplied and absorbed in a circuit. Total change in energy: &'
∆ % " # ! &(
Sign convention for power: If current is flowing from high to low (+ to -) across an element, then Power is positive (element is absorbing power) If current flowing from low to high across element (- to +), Power is negative (element is supplying power)
Finn Andersen, 2011
3
Kirchhoff’s Voltage Law (KVL) The algebraic sum of the voltages in a loop is zero. OR The sum of the emf’s in any closed loop is equivalent to the sum of the potential drops in that loop. Going around a circuit loops, increases and decreases in energy are encountered; • •
Decrease in energy considered positive Increase in energy considered negative " " " ": 0 Signs for voltage are negative or positive depending on whether current flows from positive to negative across element or vice versa.
Voltage Division Travelling around a circuit, voltage is absorbed by elements in ratios determined by their resistance (current constant). If there are too many unknowns in a circuit, Ohm’s Law can be used to produce: )* n ,#,!*, # ,#- -**. /#/0#!: 3 2 3 ! 4 6 . . 3
98< 400 4 367
183.5 6 200
Current Division When elements are in parallel, current is split amongst them based on their resistances (voltage constant). )* -7!, # .---: &&89 &&89 Find ‘effective resistance’ of multiple resistors if there are more than two.
Finn Andersen, 2011
7
Worked Examples 1. Calculate total effective resistance and therefore current (It) 2. Calculate effective resistance of the left side (New RC) E
& F
Will be negative because current flowing from positive terminal. 1. Use KVL around circuit G 2H H 0 H ,*
H
2. V1 and R’s are given, so solve for V0 1. Chose top or bottom node, do KCL. 2. Make current flow through all resistors in one direction G
( G G G ' G 8 I
1
Complement (negative) arithmetic ...................................................................................... 15 Logic Gates ........................................................................................................................... 16 Sum of Products (SOP) ......................................................................................................... 17 Product of Sums (POS) ......................................................................................................... 17 Karnaugh Maps. ................................................................................................................... 18 Advanced Circuit Analysis ............................................................................................... 19 Nodal Analysis with Super Nodes ........................................................................................ 19 Loop Analysis with Super Meshes ........................................................................................ 20 Superposition ....................................................................................................................... 21 Thevenin Equivalence .......................................................................................................... 22 Norton Equivalence .............................................................................................................. 23 Capacitors and Inductors ................................................................................................ 23 First Order Transients........................................................................................................... 24 Differential Equation Approach ........................................................................................... 24 Step by Step approach ......................................................................................................... 26 RC Circuit .............................................................................................................................. 27 RL Circuit............................................................................................................................... 27 Unit Step Function................................................................................................................ 27 Sinusoidal Circuits .......................................................................................................... 28 Complex Numbers and Relationships .................................................................................. 28
Finn Andersen, 2011
2
Basic Quantities Current: Flow of electric charge per unit time. There is only current when the charge changes. Current = gradient of q vs t graph.
• •
The total resistance of the circuit determines the amount of current that flows The current in a series circuit is constant. …
•
Current is divided/split when the circuit branches e.g. parallel circuit. Power: Change in energy over time
A voltage or force causes current to flow
!
" ! # ! !
Voltage is consumed by resistors in a series circuit so there is a voltage drop over components.
Energy is supplied and absorbed in a circuit. Total change in energy: &'
∆ % " # ! &(
Sign convention for power: If current is flowing from high to low (+ to -) across an element, then Power is positive (element is absorbing power) If current flowing from low to high across element (- to +), Power is negative (element is supplying power)
Finn Andersen, 2011
3
Kirchhoff’s Voltage Law (KVL) The algebraic sum of the voltages in a loop is zero. OR The sum of the emf’s in any closed loop is equivalent to the sum of the potential drops in that loop. Going around a circuit loops, increases and decreases in energy are encountered; • •
Decrease in energy considered positive Increase in energy considered negative " " " ": 0 Signs for voltage are negative or positive depending on whether current flows from positive to negative across element or vice versa.
Voltage Division Travelling around a circuit, voltage is absorbed by elements in ratios determined by their resistance (current constant). If there are too many unknowns in a circuit, Ohm’s Law can be used to produce: )* n ,#,!*, # ,#- -**. /#/0#!: 3 2 3 ! 4 6 . . 3
98< 400 4 367
183.5 6 200
Current Division When elements are in parallel, current is split amongst them based on their resistances (voltage constant). )* -7!, # .---: &&89 &&89 Find ‘effective resistance’ of multiple resistors if there are more than two.
Finn Andersen, 2011
7
Worked Examples 1. Calculate total effective resistance and therefore current (It) 2. Calculate effective resistance of the left side (New RC) E
& F
Will be negative because current flowing from positive terminal. 1. Use KVL around circuit G 2H H 0 H ,*
H
2. V1 and R’s are given, so solve for V0 1. Chose top or bottom node, do KCL. 2. Make current flow through all resistors in one direction G
( G G G ' G 8 I
