Superposition principle: concept and solution process

I. Overview

The superposition principle 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 currents (or voltages) generated in the circuit when each power source in the circuit acts alone.

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

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

(2) Draw a separate diagram of each power supply's separate function, short-circuit the electromotive force of the remaining power supplies, and retain only the internal resistance.

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

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

2. Processing of signal sources

complex circuit

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

Equivalent circuit when the voltage source works alone

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

Equivalent diagram of current source working alone

3. Example questions

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

examples

untie:

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

(2) Make a partial diagram of each power supply acting alone, as shown in the example diagrams (b) and (c).

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

When E1 works alone I1

When E1 works alone, I2, I3

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

I1 when E2 works alone

I2 and 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 generated by each electromotive force in each branch