DC circuits and methods of circuits analysis

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

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

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

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

5. Resistance (2) • Resistors in seriesR = R1 + R2 • Resistors in parallelR = R1 // R2 = (R1 . R2) / (R1 + R2) • Voltage dividerU2 = 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. • nonreversibleel. energy transfer to heat • Data: R [Ω], P [W] • Description: Ω → J, R 4,7 Ω → 4R7 • kΩ → k 68 kΩ → 68k • MΩ → M 2.2 MΩ → 2M2 • 0,15 MΩ → M15 • 47k/0,125W 3R3/ 5W

8. Resistors Resistors color codings First strip is near to edgethan last If tolerance is ±20 %, the 4. strip miss

9. Resistors Material • Carbon – non stable, temperature dependent • Metalised - stable, precise • Wiredmore 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 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: 1 F (Farrad) dimension: [A.s/V]

14. Capacitors Description: • pF → J, R 4,7 pF → 4R7 • 103 pF → k , n 68 000 pF → 68k • 106 pF → M 3,3 µF → 3M3 • 109 pF → G 200 µF→ 200M Number code: number, number, exponent in pF eg. : 474 → 470 000pF → 470k → M47±20%

15. Capacitors

16. Inductors Part: Inductor, coil Feature: inductivity 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: 1 H (Henry) dimension: [V.s/A]

18. 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 = 0At 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 = 0The 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 circuitfor 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 circuitfor 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 MethodΣvi = 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 = 4 No of current sources zi = 0 • No of independent nodes Xi = u – 1- zu= 4 – 1 - 2 = 1 • No of independent meshes Xi = p – u + 1– zi= 5 – 4 + 1 = 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

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