DC circuits and methods of circuits analysis

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DC circuits and methods of circuits analysis

• Circuits elements
• Voltage source
• Current source
• Resistors
• Capacitors
• Inductors

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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

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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)

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Resistance - R ?

• Coductance G1/R S
• Ideal resistorlinear R const.V I . R
• Real resistornon-linear(electric bulb, PN
  junction)

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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)

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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

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Resistors

• Feature resistivity
• r R const.
• nonreversible el. energy transfer to heat
• Data R ?, P W
• Description ? ? J, R 4,7 ? ?
  4R7
• k? ? k 68 k? ? 68k
• M? ? M 2.2 M? ? 2M2
• 0,15 M? ? M15
• 47k/0,125W 3R3/ 5W

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Resistors
Resistors color codings
color color number tolerance
      Blacká 0  
  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 Meaning
Strip 4 strips 5strips
1 first digit first digit
2 second digit second digit
3 exponent 10x third digit
4 tolerance exponent 10x
5   tolerance
First strip is near to edge than last If
tolerance is 20 , the 4. strip miss
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Resistors

• Material
• Carbon non stable, temperature dependent
• Metalised - stable, precise
• Wired more power dissipation gt 5W

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Resistors

• Potentiometer variable resistor

Potentiometr adjustable by hand
Potentiometer adjustable by tool
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Resistors
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Capacitors

• Part Capacitor, condenser
• Feature capacity

Accumulator of the energy in electrostatic field
symbol
dynamic definition
c C const.
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Capacitors
static definition
power definition
For calculation should be used SI system only!
unit 1 F (Farrad) dimension
A.s/V
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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

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Capacitors
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Inductors

• Part Inductor, coil
• Feature inductivity

Accumulator of the energy in electrostatic field
dynamic definition l L konst.
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Inductors
static definition
power definition
For calculation should be used SI system only!
unit 1 H (Henry) dimension
V.s/A
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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
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Ohms and Kirchhoffs laws

• Ohms law I U / R
• 1st Kirchhoffs 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 Kirchhoffs law (KVL) ? U 0 The algebraic
  sum of the voltages across all the components
  around any loop of circuits is zero

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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

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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

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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.

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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.

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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.

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Example
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Methods of electrical circuits analysis

• Node Voltage Method Sii 0 , SIi 0
• Mesh Current Method Svi 0 , SVi 0
• Thevenin and Norton Eq. Cirtuits
• Principle of Superposition
• --- and other 15 methods

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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

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• 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

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Node Voltage Analysis Method

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

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Mesh Current Analysis Method

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

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