Network Theorems

1
Chapter 9

• Network Theorems

2
Superposition Theorem

• The total current through or voltage across a
  resistor or branch may be determined by summing
  the effects due to each independent source.
• Replace a voltage source with a short.
• Replace a current source with an open.
• Find the results of using each source
  independently, and then combine the results.

3
Superposition Theorem

• Power is not a linear quantity it is found by
  squaring the voltage or current.
• The superposition theorem does not apply to
  power.
• To find power using superposition, first
  determine the voltage or current, then calculate
  power.

4
Thévenins Theorem

• Allows us to make calculations on a complicated
  circuit where one of the components may have
  different values.
• Any linear bilateral network may be reduced to a
  simplified two-terminal circuit consisting of a
  single voltage source with a single resistor.

5
Thévenins Theorem

• To convert to a Thévenin circuit, first remove
  the load from the circuit.
• Label the resulting terminals.
• Set all sources to zero. Replace voltage sources
  with shorts, current sources with opens.
• Determine Thévenin resistance as seen by the open
  circuit.

6
Thévenins Theorem

• Replace the sources and calculate the voltage
  across the open.
• If there is more than one source, use
  superposition.
• The resulting open-circuit voltage is the
  Thévenin voltage.
• Draw the Thévenin equivalent circuit, including
  the load.

7
Nortons Theorem

• Similar to Thévenin circuit.
• Any linear bilateral network may be reduced to a
  simplified two-terminal circuit consisting of a
  single current source and a single shunt resistor.

8
Nortons Theorem

• To convert to a Norton circuit, first remove the
  load from the circuit.
• Label the resulting two terminals.
• Set all sources to zero.
• Determine the open circuit resistance. This is
  the Norton resistance.

9
Nortons Theorem

• Replace the sources and determine the current
  which would occur in a short between the two
  terminals.
• For multiple sources, use superposition.
• Draw the Norton equivalent circuit. Return the
  load to the circuit.

10
Nortons Theorem

• The Norton equivalent circuit may be determined
  directly from a Thévenin circuit.

11
Maximum Power Transfer

• It is often desired that the load receives the
  maximum amount of power from the source.
• The maximum power transfer theorem states that a
  load resistor will receive maximum power from a
  circuit when the resistance of the load is
  exactly the same as the Thévenin (Norton)
  resistance looking at the circuit.

12
Maximum Power Transfer

• To calculate the maximum power to the load, we
  use P V2/R.
• The voltage across the load is one half the
  Thévenin voltage.

13
Maximum Power Transfer

• We can see how power across a load changes as the
  load changes.

14
Maximum Power Transfer
15
Efficiency

• To calculate efficiency