Thevenin's theorem

• Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source V_th in series connection with an equivalent resistance R_th.
• This equivalent voltage V_th is the voltage obtained at terminals A-B of the network with terminals A-Bopen circuited.
• This equivalent resistance R_th is the resistance obtained at terminals A-B of the network with all its independent current sources open circuited and all its independent voltage sources short circuited.

                                                

Any black box containing resistances only and voltage and current sources can be replaced to a Thévenin equivalent circuit consisting of an equivalent voltage source in series connection with an equivalent resistance.

To calculate the equivalent circuit:

1. Calculate the output voltage, V_AB, when in open circuit condition (no load resistor—meaning infinite resistance). This is V_Th.
2. Calculate the output current, I_AB, when the output terminals are short circuited (load resistance is 0). R_Th equals V_Th divided by this I_AB.

The equivalent circuit is a voltage source with voltage V_Th in series with a resistance R_Th.

Step 2 could also be thought of as:

a. Replace the independent voltage sources with short circuits, and independent current sources with open circuits.

b. Calculate the resistance between terminals A and B. This is R_Th.