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

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

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)

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

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’)

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

Resistors Feature: resistivity r = R = const. nonreversible el. 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

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

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

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

Resistors

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

Capacitors static definition power definition For calculation should be used SI system only! : unit: 1 F (Farrad) dimension: [A.s/V]

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%

Capacitors

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

Inductors static definition power definition For calculation should be used SI system only! : unit: 1 H (Henry) dimension: [V.s/A]

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

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

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

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

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.

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.

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.

Example

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

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

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

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

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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