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Thevenin's Theorem (Thevenin Equivalent)

Thevenin theorem (also known as the Helmholtz–Thévenin theorem) states that any linear circuit containing only voltage sources, current sources, and resistances can be replaced by an equivalent combination of a voltage source (VTh) in series with a single resistance (RTh) connected across the load. This simplified circuit is known as the Thevenin Equivalent Circuit.

Thevenin’s theorem was invented by a French engineer Léon Charles Thévenin (hence the name).

Thevenin theorem is used to convert a complex electrical circuit to a simple two-terminal Thevenin equivalent circuit. A Thevenin equivalent circuit contains one Thevenin resistance and Thevenin voltage source connected with a load, as shown in the figure below.

Thevenin resistance (Rth) is also known as equivalent resistance. And Thevenin voltage (Vth) is an open-circuit voltage across load terminals.

This theorem is suited with only linear circuits. If the circuit has elements like semiconductor components or gas-discharging components, you can not apply Thevenin’s Theorem

Thevenin Equivalent Formula

Thevenin equivalent circuit contains an equivalent voltage source, equivalent resistance, and load as shown in above figure-1(b).

Thevenin equivalent circuit has a single loop. If we apply a KVL (Kirchhoff’s Voltage Law) to this loop, we can find the current passing through the load.

According to the KVL,

How to Find The Thevenin Equivalent Circuit

The Thevenin equivalent circuit contains Thevenin resistance and Thevenin voltage source. therefore, we have to find these two values for Thevenin equivalent circuit.

Thevenin Equivalent Resistance

To calculate the Thevenin equivalent resistance, remove all power sources from the original circuit. And voltage sources are short-circuited and current sources are opened.

Hence, the remaining circuit has only resistances. Now, calculate the total resistance between the open connection points across load terminals.

The equivalent resistance is calculated by making series and parallel connection of resistances. And find a value of equivalent resistance. This resistance is also known as Thevenin resistance (Rth).

Thevenin Equivalent Voltage

To calculate the Thevenin equivalent voltage, the load impedance is open-circuited. And find an open-circuit voltage across the load terminals.

Thevenin equivalent voltage (Veq) is equal to the open-circuit voltage measured across two terminals of load. This value of the ideal voltage source is used in Thevenin equivalent circuit.

Thevenin Equivalent Dependent Source

If a circuit network consists of some dependent sources, the Thevenin resistance is calculated by a different method. In this condition, the dependent sources kept as it is. You cannot remove (open or short circuit) the voltage or current sources.

There are two methods to find Thevenin resistance in the case of dependent sources.

Method 1

In this method, we have to find Thevenin voltage (Vth) and short-circuit current (Isc). Put these values in the below equation to find the Thevenin resistance.