1.2 THEVENIN AND NORTON EQUIVALENTS

 

• A sometimes useful transformation is based on the equivalence of certain circuit elements,

 

 

• We can use this to test an unknown circuit for open circuit voltage, and short circuit current, and then replace it with an equivalent circuit.

1. Measure open circuit voltage Vs

2. Measure short circuit current Is

3.a) If using a Thevenin equivalent calculate, Rs = Vs/Is

3.b) If using a Norton equivalent calculate, Rs = Vs/Is

4. Draw the appropriate circuit.

* note the resistor values are the same for both circuits.

 

• We can also use the Thevenin/Norton transformation to simplify circuits. Consider example 4.13 from [Nilsson].

 

 

 

 

 

 

 

1.2.1 Superposition

 

• This is a simple technique that can be used when there are multiple sources in a circuit. The basic technique is,

1. Select one source in a circuit.

2. Make all other current sources open circuit.

3. Make all other voltage sources short circuits.

4. Analyze as normal.

5. Pick the next voltage/current source and go back to 2.

6. Add together the results for each source.

 

• Consider an example below, 4.19 from [Nilsson],

 

 

 

 

 

1.2.2 Maximum Power Transfer

 

• When we will add a load to a network, we may want to try and maximize the amount of power delivered to it.

 

• Consider the simple case below,

 

 

• For practice try proving this theorem for the Norton equivalent circuit.

 

 

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