Key Takeaways

• Learn about Thevenin’s theorem and how it can be useful

• How to calculate a Thevenin equivalent circuit

• Limitations of Thevenin’s theorem 

Thevenin’s theorem is a valuable circuit concept and analytical method used to convert a complex circuit into a simpler equivalent circuit. The theorem states: 

In other words, any electrical circuit consisting of purely passive components (resistors, capacitors, and inductors) can be simplified to an equivalent two-terminal circuit connected to a load resistor.

More About Thevenin’s Theorem

Thevenin’s theorem is especially useful for completing circuit analysis of battery or power systems in addition to other interconnected resistive circuits that will have an impact on the adjoining part of the circuit. This adjoining part can be a load resistor or other circuit network.

Thevenin’s circuits can be calculated across any two nodes of a circuit. The circuit consists of a Thevenin voltage source V_TH and equivalent Thevenin resistance R_TH (or Z_TH in the case of capacitors + inductors present). V_TH is obtained at the open-circuited terminals A–B and R_TH is obtained with all voltage sources replaced by shorts.

Calculating a Thevenin Equivalent Circuit

In a Thevenin equivalent circuit, between nodes A and B, any complex “single-port” network consisting of passive elements can be replaced by a single equivalent resistance R_TH and voltage V_TH. R_TH is the source resistance looking back into the circuit while V_TH is the open circuit voltage at the terminals. Calculating a Thevenin circuit is done as follows:

1. If it exists, remove the load resistor from the circuit, across the terminals of interest.

2. Determine the voltage across the terminals; this is V_TH. You can do this through any circuit analysis method (series circuits laws, Ohm’s law, or Kirchhoff’s voltage law). 

3. Find the Thevenin equivalent resistance R_TH by shorting all voltage sources and open-circuiting all current sources. Use laws for resistors in series and parallel to achieve a single equivalent resistance. 

   1. In the case of reactive components (inductors and capacitors), utilize simplification techniques for these elements to ultimately achieve a single complex impedance (resistance and reactance).

4. Create a circuit with your Thevenin voltage source V_TH in series with your Thevenin equivalent resistance R_TH. This is your Thevenin equivalent circuit. 

It is important to note that the voltage and resistance figures for the Thevenin source and resistor do not correspond to any actual component from the original circuit. Thevenin’s theorem is useful for determining what happens to a single resistor in the network – across terminals A and B. Depending on which two nodes are chosen in the circuit, the Thevenin equivalent circuit will be different. In other words, there is one Thevenin equivalent circuit (values of V_TH and R_TH) for a complex circuit given two specific nodes, not just the circuit as a whole. 

Advantages of Thevenin's Theorem 

Thevenin’s theorem is especially useful for analyzing circuits by removing the load resistance from the original circuit and simplifying. After reconnecting the load resistance, any later calculations can be carried out as if the whole network were the simplified circuit.

If correctly derived, the Thevenin circuit will behave the exact same as the original circuit. The load across the two specified ports will not be able to tell the difference between the original network and the Thevenin equivalent circuit.

In analyzing power systems and other circuits where the load resistor is subject to change, knowing the Thevenin equivalent voltage and resistance makes it easy to calculate the current through the load, simplifying further analysis.

Limitations of Thevenin’s Theorem

Thevenin’s theorem is only applicable in specific situations, given a couple of limitations.

• Thevenin’s theorem is applicable only to linear circuits, e.g., only passive resistors, inductors, and capacitors. Thevenin’s theorem is not applicable to nonlinear devices such as diodes and transistors.

• The Thevenin equivalent only has I-V characteristics from the point of view of the load (specified nodes A–B).

• Power dissipation for the Thevenin circuit is not necessarily the same as that of the real system. That being said, the power dissipated by the external resistor between terminals A–B is the same regardless of how the circuit is implemented.

Thevenin’s theorem is a great circuit analysis tool to reduce complicated electrical networks into a single voltage and resistor. When looking back from terminals A–B,  the simplified circuit behaves the same way electrically as the complex circuit it replaces – with identical I-V relationships.

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