Thevenin Theorem

To develop Thevenin’s theorem, consider figure consisting of two two-terminal networks, N and N_L , joined at A and B. ‘N’ consist of only resistors and independent sources, whereas N_L contains arbitrary even non-linear elements. Suppose N_L undergoes various changes while N remains unchanged.

To simplify repeated calculations, N is replaced by a simple circuit called its Thevenin equivalent, as shown in fig. (b). The Thevenin’s equivalent consists of a single voltage source Voc in series with a single resistance R_Th.

Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source Vth in series with a resistor R_th, where Vth is the open-circuit voltage at the terminals and R_th is the input or equivalent resistance at the terminals when the independent sources are turned off.

Procedure to Calculate V_th :

Remove the defined load and measure its open circuit voltage as per polarity prescribed. Thus, V_th is the open-circuit voltage across the terminals as shown in fig. (c), i.e., V_th = V_oc

Note:

If a circuit contains dependent sources only, i.e. there is no independent source present in the network then its open-circuit voltage or Thevenin voltage will simply be zero.

Procedure to Calculate R_th :

To apply this idea in finding the Thevenin resistance R_th, we need to consider two cases :

Case-1: When only independent source, i.e., no dependent source in the circuit.

Nullify all the independent source, i.e., (voltage source by short circuit and current source by open circuit) by doing this obtain R_eq (or R_th) from the open circuit load using resistance reduction method.

Case-2: When both independent and dependent source are present in the circuit.

Nullify all independent source and keep the dependent source as it is then connect an independent voltage source V_α and current flow through it is I_α. Thevenin resistance is given as R_th = V_α/I_α

Note:

It often occurs that R_Th takes a negative value. In this case, the negative resistance implies that the circuit is supplying power.

 

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