Thevenin's and Norton's Theorem

Thevenin’s theorem simplifies calculations and explanations of complex circuit operations.

• Thevenin voltage VTH is defined as the voltage across the load terminals when the load resistor is open. Because of this, the Thevenin voltage is sometimes called the open-circuit voltage (VTH= VOC).
• Thevenin resistance is defined as the resistance that an ohmmeter measures across the load terminals of the figure above when all sources are reduced to zero and the load resistor is open (RTH = ROC).
• The box in the figure above can contain any circuit with dc sources and linear resistances. (A linear resistance does not change with increasing voltage.) Thevenin was able to prove that no matter how complicated the circuit inside the black box of the figure above it would produce exactly the same load current as the simple circuit. Can be derived by using the following equation: IL=VTH/(RTH+RL)

• Norton current IN is defined as the load current when the load resistor is shorted. Because of this, the Norton current is sometimes called the short-current (IN = Isc).
• Norton resistance is the resistance that an ohmmeter measures across the load terminals when all sources are reduced to zero and the load resistor is open (RN = Roc).
• Since Thevenin resistance equals Roc, than: RN = RTH. This makes Norton resistance equal to Thevenin resistance. But there is a difference in the location of the resistors: Thevenin resistance is always in series with a voltage source; Norton resistance is always in parallel with a current source.
• In the figure above the box can contain any circuit with dc sources and linear resistances. Norton proves that the circuit inside the black box would produce exactly the same load voltage as the simple circuit.
• Norton's theorem looks like this: VL = IN (RN II RL). Which means the load voltage equals the Norton current times the Norton resistance in parallel with the load resistance.

Norton's theorem can be derived from the duality principle. It states that for any theorem in electrical circuit analysis there is a dual (opposite) theorem in which one replaces the original quantities with dual quantities. The figure below summarizes the duality principle as it applies to Thevenin and Norton circuits. It means that we can use either circuit in our calculations. Both equivalent circuits are useful and sometimes it is easier to use Thevenin, at other times we use Norton. It depends on the specific problem.

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