I. Overview

The principle of superposition is an important analysis method for linear circuits. A linear circuit is a circuit in which voltage and current are proportional. Its content is: in a linear circuit containing multiple electromotive forces, the current (or voltage) of any branch is the algebraic sum of the current (or voltage) generated in the circuit when each power supply in the circuit acts alone.

The general steps for applying the principle of superposition to analyze complex circuits are as follows:

(1) Set the current direction of each branch to be determined.

(2) Make a separate diagram for each power supply, short-circuit the electromotive force of the rest of the power supplies, and only keep the internal resistance.

(3) According to the analysis method of simple DC circuit, calculate the magnitude and direction of the current of each branch in each sub-diagram.

(4) Find the algebraic sum of the currents generated by each electromotive force in each branch. If the direction of the current (or voltage) is the same as the assumed current (or voltage) in the original circuit, take positive, otherwise take negative.

Second, the processing of the signal source

complex circuit

1. When the voltage source works, the current source does not work. If the current source does not work, it can be considered that the current source is in an open state.

Equivalent circuit when the voltage source works alone

2. When the current source works and the voltage source does not work, the voltage source is short-circuited.

Equivalent diagram of current source working alone

3. Examples

In the circuit shown in the example figure, it is known that E1=18V, E2=12V, R1=R2=R3=4Ω, try the superposition principle to solve the current of each branch.

examples

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(1) Set the current direction of each branch as shown in example (a).

(2) Make a sub-graph when each power source acts independently, as shown in the example diagram (b) and the example diagram (c).

(3) Find the current of each branch when a single electromotive force acts on each sub-graph. In the example figure (b), when E1 acts alone, then:

I1 when E1 works alone

I2, I3 when E1 works alone

In the legend (c), when E2 acts alone, then:

I1 when E2 works alone

I2, I3 when E2 works alone

(4) Find the algebraic sum of the currents generated by each electromotive force in each branch.

The algebra of the current produced by each electromotive force in each branch