ENSC2003 - Lecture 7

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ENSC2003 - Lecture 6
Equivalent Circuits - Slides

Equivalent Circuits

If we are interested with only one part of the network, the remainder of the network may be replaced by a simple equivalent network

• Aim: Take a complex circuit and replace it with a similar equivalent

We can replace our complex circuit with either:

1. Thevenin: Voltage source with resistor in series
2. Norton: Current source with resistor in parallel

These two simple networks are the same as our practical sources!

Thevenin Theorem

• Thevenin Theorem $-$ replace network with voltage source $V_{Th}$ and resistor $R_{Th}$ in series
  • Network must be linear
  • Network only contains voltage/current sources + resistors

• Theorem can be expanded to fit other linear elements
  e.g. capacitors and inductors

Find $V_{Th}$ → equivalent voltage is the voltage difference across the open terminals with the load removed
$V_{Th}=V_{oc}$

Find $R_{th}$ → replace voltage sources with short circuits + current sources with open circuits, calculate $R_{eq}$ between open terminals with load removed
$R_{eq}=R_{Th}$
Remember, a chain of resistors connected to the same node at both ends of the chain with no source (as we have removed them) do not contribute to $R_{eq}$ → look for resistors that are connected in chain with the open part of the circuit

The new circuit is known as the Thevenin equivalent circuit

Norton’s Theorem

• Norton’s Theorem $-$ replace network with current source $I_N$ in parallel with resistor $R_N$
  • Network must be linear

Find $I_N$ → replace load with short-circuit, the current flowing through short-circuit is $I_{sc}$
$I_N=I_{sc}$
Find $R_N$ → replace load with open terminals & turn off all independent sources, calculate $R_{eq}$ between open terminals with load removed
$R_{eq}=R_N$

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ENSC2003 - Lecture 8