DC Network Analysis

Thevenin's Theorem

Thevenin's theorem is a method of circuit analysis that involves reducing a complex circuit to a simple equivalent circuit. Thevenin's theorem is frequently used to make circuit analysis simpler.

Thevenin's theorem is especially useful in analyzing circuits where only one particular resistor in the circuit (called the load) is subject to change. Example:

Thevenin's theorem states: Any linear electrical circuit can be replaced at terminals A and B by a simple series circuit consisting of an equivalent voltage source V_th and an equivalent resistance R_th.

Note: A linear circuit is an electronic circuit in which the electronic components' values (such as resistance, conductance, capacitance, inductance, gain, etc.) do not change with the level of voltage or current in the circuit.

The equivalent series circuit will provide the same current through a load as would the original circuit. The equivalent voltage V_th is the voltage "seen" between the two terminals (A and B) being considered in the original network with the load resistance removed. The equivalent resistance R_th is the resistance "seen" between the terminals of the original network when all voltage sources of the original circuit are replaced by a short circuit (wire) and all current sources are replaced by an open circuit (break).

The figure below shows the application of Thevenin's theorem to a simple network. When Thevenin's theorem is applied, the current through R_L of the figure below (view A) is the same as the current in R_L of the figure below (view D).

It must be pointed out that Thevenin's theorem establishes equivalency for R_L only. The current, voltage, and power of R_L in the figure above (view D) are therefore the same as in the figure above (view A). The power supplied to the circuit of figure above (view D) by V_th is not the same as the power supplied to the circuit of figure above (view A) by V.

Thevenin's theorem has the effect of removing a portion of a circuit to make the remaining circuitry easier to analyze. Use of Thevenin's theorem is further demonstrated by the following examples.

Example 1:
Find the Thevenin-equivalent circuit of the circuit shown in the figure below.

Solution:

Calculating the equivalent voltage V_th

Use Kirchhoff's voltage law and Ohm's law to calculate the current I through elements in series (see the figure above):

The voltage between the points A and B can be figured from the voltages V₂ and V_R2. This is our equivalent voltage V_th in the equivalent circuit:

Calculating the equivalent resistance R_th

Replace the voltage sources V₁ and V₂ with a wire:

The resistance between the points A and B is equal to R₁ and R₂ in parallel: 0.8 Ω. This is our equivalent resistance R_th in the equivalent circuit:

Example 2:
Find the Thevenin-equivalent circuit of the circuit shown in the figure below.

Solution:

Calculating the equivalent voltage V_th

The current I through elements in series is equal to I₁.

The voltage between the points A and B can be figured from the voltages V₂ and V_R2. This is our equivalent voltage V_th in the equivalent circuit:

Calculating the equivalent resistance R_th

Replace the current source I₁ with a break and the voltage source V₂ with a wire:

The resistance between the points A and B is equal to R₂: 1 Ω. This is our equivalent resistance R_th in the equivalent circuit: