1.11 Superposition Theorem

Following 1.10 Kirchhoff’s Laws, this section introduces another important approach for solving complex circuit networks.

To find the currents I₁, I₂, and I₃ [A] flowing in the branches of a circuit network with multiple power sources, as shown in Figure 1.11-1(a), the network can be treated as separate circuits, each containing only one power source, as shown in Figure 1.11-1(b) and (c). The actual currents are then found by adding the currents obtained in each circuit.

That is, the branch currents can be obtained from the following equations.

Figure 1.11-1 Superposition Theorem

Note that the current directions follow the reference directions defined in Figure 1.11-1(a). If a current obtained in one of the partial circuits flows in the opposite direction, it is added with a negative sign.

This method is called the superposition theorem and, together with Kirchhoff’s laws, is known as a method for solving complex circuit networks.

For small circuits, solving directly with Kirchhoff’s laws is often more efficient. The superposition theorem, on the other hand, is effective when there are many power sources or when only the contribution of a specific source needs to be evaluated.

[Note]
The superposition theorem holds only for circuits made up of elements in which voltage and current are proportional (linear elements).
For example, it cannot be applied as is to circuits containing nonlinear elements, in which voltage and current are not proportional, such as diodes and transistors.

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References

• Denki Kiso (Jo) [Fundamentals of Electricity, Vol. 1], Corona Publishing, Toshio Utsunomiya, Hiroshi Takahashi, Isao Izumi
• Denki Kairo Tekisuto [Electric Circuit Textbook], Nippon Riko Shuppankai, Koichiro Seya

*This article was compiled based on the author’s understanding, with reference to the above literature.