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Thevenin's Theorem

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					Introduction to Circuit Theory
Image Source: Wikipedia
   Charge is measured in Coulombs (C)
   1 C = 6.24 x 1018 electrons
   Conventional Current flows from positive to
    negative
   Electrons actually flow from negative to
    positive
   The measure of the rate of electron flow in a
    circuit
   Measured in Amperes (A)
     1 mA (milliamp) = 0.001 A
     1 µA (microamp)= 0.001 mA
   Direct Current (DC)
     Flow of electricity (current) in an unchanging
     direction
   Alternating Current (AC)
     Current flows in different directions
Image Source: Electronics Demystified
   Opposition that a component of device offers
    to the flow of an electric current
   Unit of resistance is Ohm Ω
     1 kilohm (k Ω) = 1000 Ω
     1 megohm (m Ω) = 1,000 k Ω or 1,000,000 Ω
     Good conductors have low resistance
     Good insulators have high resistance
     Assumption in circuit analysis: Resistance of an
     ideal resistor is constant and does not vary in time
   Standard unit of EMF is the volt (V)
   Voltage is the measure of work done to move
    a charge from one point to another in an
    electric field
     1 mV (millivolt) = 0.001 V
     1 µV (microvolt)= 0.001 mV
   Voltage is referred to as “electric potential” or
    “electric pressure”
   More voltage in a circuit means more
    potential for current
   V = IR               V
   I =V / R
   R =V / I         I       R


   V – Voltage
   I – Current
   R - Resistance
   DC is 10 V and potentiometer is 10 Ω. What is
    the current?
   Potentiometer is 100 Ω and current is 10 mA.
    What is voltage across the resistance?
    Potentiometer is uncalibrated. Voltmeter
    reads 24 V and Ammeter 3A. What is the
    resistance?
   Measure in Watts (W)
   P = IV                     V
   P = I 2R
   P = V2 / R             I       R
   Resistance in Series
     Values are added to get total resistance



   Resistance in Parallel
     Overall resistance decreases
     Conductance (S) siemens
      ▪ G= 1 / R
     Add conductances to get total resistance
   V1 = V2 = V3
   I = I1 + I2 + I3
   1 / Req = 1 /R1 + 1/R2 + 1/R3
   Current Law – Kirchoff’s First Rule
     The total current entering a junction in a circuit
      must equal the sum of the currents leaving that
      junction
     Principle of conservation of electric charge

                                   I1 = I2 + I3
                                   I2 = I1 – I3
                                   I3 = I1 – I2
   Voltage Law – Kirchoff’s Second Rule
     The directed sum of the emfs (potential
      differences) around any closed circuit it zero
     Principle of conservation of energy

                                -VB + V1 + V2 = 0
                                -V2 - V3 + V4 = 0
                                -VB + V1 - V3 + V4 = 0
 It is possible to simplify a linear circuit, no matter
  how complex to an equivalent circuit with just a
  single voltage source and series resistance
  connected to a load
 This is true for circuits with passive components
  (resistors, inductors and capacitors)
 Underlying equations are linear (no exponents or
  roots)
 Non-linear (opposition to current changes with
  voltage/current)
   Useful for analyzing circuits where one
    component is changing
   Tedious re-calculation does not need to occur
   Advantage of Thevenin Conversion is a
    simpler circuit which makes load voltage and
    current easier to solve
   Step 1
     The chosen load resistor is removed from the
     original circuit and replaced with a break (open
     circuit)
•Next, the voltage between the two points where the load resistor used
to be attached is determined
•Ohm’s and Kirchoff’s voltage law can be used
•The voltage between the two load connection points can be figured
from one of the battery’s voltage and one of the resistor’s voltage drops
   Step 2
     Find the Thevenin series resistance for the circuit
     Remove all power sources from the circuit and
     replace them with wires (current sources are
     replaced with breaks)
 Total resistance is R1 and R3 in parallel
= 0.8 Ω
   With the 2 load resistor attached between
    the points we can determine the voltage
    across it
   Just a simple series circuit
1.   Find Thevenin Voltage by removing load
     resistor from original circuit and calculate
     voltage across open connection points
2.   Find Thev. resistance be removing power
     sources from original circuit (voltage
     shorted and current sources open) and
     calculate total resistance between points
3.   Draw Thev Eq circuit with Thev voltage in
     series with Thev resistance and load resistor
   Possible to simplify linear circuit to a circuit
    with just a single current source and parallel
    resistance connected to a load
   Step 1
     Remove load resistor and place a short connection
      between load points
     Calculate total current between the load points
   Step 2 – Calculate Norton Resistance in the
    same manner as Thev Resistance
1.   Find Norton Current by removing load
     resistor from original circuit and calculate
     current across closed connection points
2.   Find Norton resistance be removing power
     sources from original circuit (voltage
     shorted and current sources open) and
     calculate total resistance between points
3.   Draw Norton Eq circuit with Norton Current
     Source in parallel with Thev resistance and
     load resistor
   RThevenin = RNorton
   EThevenin=INortonRNorton

				
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posted:11/27/2012
language:English
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