1. DC circuits and methods of circuits analysis
Circuits elements:
Voltage source
Current source
Resistors
Capacitors
Inductors

2. Voltage source - V [V]
Ideal source Constant output voltage, internal resistance equals to zero
Real source Output voltage depends on various conditions. Dependence may be linear (battery) on non-linear

3. Current source - I [A]
Ideal source Constant output current, internal resistance equals to infinity
Real source Output current depends on various conditions. Dependence may be linear on non-linear (Usually electronic sources)

4. Resistance - R [] Coductance G=1/R [S]
Ideal resistor linear R = const. V= I . R
Real resistor non-linear (electric bulb, PN junction)

5. Resistance (2) Resistors in series R = R1 + R2
Resistors in parallel R = R1 // R2 = (R1 . R2) / (R1 + R2)
Voltage divider U2 = U . R2 /(R1 + R2) potential divider (‘pot’)

6. Passive electronic parts
Resistors feature electrical resistivity R
dimensioning according maximal dissipation power (loses) Pmax
Capacitors feature capacity C
dimensioning according maximal granted voltage Vmax
Inductors feature inductivity L
dimensioning according maximal granted current Imax

7. Resistors Feature: resistivity r = R = const.
nonreversible el. energy transfer to heat
Data: R [Ω], P [W]
Description: Ω → J, R ,7 Ω → 4R7
kΩ → k kΩ → 68k
MΩ → M MΩ → 2M2
0,15 MΩ → M15
47k/0,125W 3R3/ 5W

8. Resistors Resistors color codings color number tolerance Blacká Brown
     
Blacká
Brown 1
± 1 %
Red 2
± 2 %
Orange 3
Yelow 4
Green 5
± 0,5 %
Blue 6
± 0,25 %
violet 7
± 0,1 %
grey 8
white 9
gold -1
± 5 %
silver -2
± 10 %
no color
± 20 %
Meaning
Strip
4 strips
5strips 1
first digit 2
second digit 3
exponent 10x
third digit 4
tolerance 5
First strip is near to edge than last
If tolerance is ±20 %, the 4. strip miss

9. Resistors Material Carbon – non stable, temperature dependent
Metalised - stable, precise
Wired more power dissipation > 5W

10. Resistors Potentiometer variable resistor
Potentiometr adjustable by hand
Potentiometer adjustable by tool

11. Resistors

12. Capacitors Part: Capacitor, condenser Feature: capacity symbol
Accumulator of the energy in electrostatic field
symbol
dynamic definition
c = C = const.

13. Capacitors static definition power definition
For calculation should be used SI system only! :
unit: F (Farrad) dimension: [A.s/V]

14. Capacitors Description: pF → J, R 4,7 pF → 4R7
103 pF → k , n pF → 68k
106 pF → M 3,3 µF → 3M3
109 pF → G 200 µF → 200M
Number code: number, number, exponent in pF
eg. : 474 → pF → 470k → M47 ±20%

15. Capacitors

16. Inductors Part: Inductor, coil Feature: inductivity dynamic definition
Accumulator of the energy in electrostatic field
dynamic definition
l = L = konst.

17. Inductors static definition power definition
For calculation should be used SI system only! :
unit: H (Henry) dimension: [V.s/A]

18. Details for instalation and ordering
Inductors
Details for instalation and ordering
L [H], IMAX [A]
Lower units 1 µH = 10-3 mH = 10-6 H
It use in electronic not very often.
See next semestr

19. Ohm’s and Kirchhoff’s laws
Ohm’s law I = U / R
1st Kirchhoff’s law (KCL)  I = 0 At any node of a network, at every instant of time, the algebraic sum of the currents at the node is zero
2nd Kirchhoff’s law (KVL)  U = 0 The algebraic sum of the voltages across all the components around any loop of circuits is zero

20. Nodal analysis (for most circuits the best way)
Uses 1st K. law
Chose reference node
Label all other voltage nodes
Eliminate nodes with fixed voltage by source of emf
At each node apply 1st K. law
Solve the equations

21. Mesh analysis Uses 2nd K. law Find independent meshs
Eliminate meshs with fixed current source
Across each mesh apply 2nd K. law
Solve the equations

22. Thevenin equialent circuit for linear circuit
As far as any load connected across its output terminals is concerned, a linear circuits consisting of voltage sources, current sources and resistances is equivalent to an ideal voltage source VT in series with a resistance RT. The value of the voltage source is equal to the open circuit voltage of the linear circuit. The resistance which would be measured between the output terminals if the load were removed and all sources were replaced by their internal resistances.

23. Norton equialent circuit for linear circuit
As far as any load connected across its output terminals is concerned, a linear circuits consisting of voltage sources, current sources and resistances is equivalent to an ideal current source IN in parallel with a resistance RN. The value of the current source is equal to the short circuit voltage of the linear circuit. The value of the resistance is equal to the resistance measured between the output terminals if the load were removed and all sources were replaced by their internal resistances.

24. Principle of superposition
The principle of superposition is that, in a linear network, the contribution of each source to the output voltage or current can be worked out independently of all other sources, and the various contribution then added together to give the net output voltage or current.

25. Example

26. Methods of electrical circuits analysis:
Node Voltage Method Σii = 0 , ΣIi = 0
Mesh Current Method Σvi = 0 , ΣVi = 0
Thevenin and Norton Eq. Cirtuits
Principle of Superposition
--- and other 15 methods

27. Topology and Number of Lineary Independent Equations
No. of elements p No. of voltage sources zv
No. of nodes u No. of current sources zi

28. No of elements p = 5 No of voltage sources zv = 2
No. of nodes u = No of current sources zi = 0
No of independent nodes Xi = u – 1 - zu = 4 – = 1
No of independent meshes Xi = p – u + 1 – zi = 5 – = 2

29. Node Voltage Analysis Method
Select a reference node (usually ground). All other node voltages will be referenced to this node.
Define remaining n-1 node voltages as the independent variables.
Apply KCL at each of the n-1 nodes, expressing each current in terms of the adjacent node voltages
Solve the linear system of n-1 equations in n-1 unknowns

31. Mesh Current Analysis Method
Define each mesh current consistently. We shall define each current clockwise, for convenience
Apply KVL around each mesh, expressing each voltage in terms of one or more mesh currents
Solve the resulting linear system of equations with mesh currents as the independent variables

32. ________________