Thevenin's theorem: introduction to the concept and its solution process

1. Concept

Any network, no matter its internal structure is simple or complex, as long as there are two terminals connected to the external circuit, it is called a two-terminal network. The two-terminal network can be divided into an active two-terminal network and a passive two-terminal network according to whether it contains a power supply. Any passive two-terminal network can be replaced by an equivalent resistance. This resistance is called the input resistance of the two-terminal network, that is, the total resistance seen from the two terminals, as shown below:

passive network

Any linear active two-terminal network can be simplified to a voltage source according to Thevenin's theorem, as shown in the figure below, the content of Thevenin's theorem: An active two-terminal network can be replaced by an equivalent power supply.

active network

Simply put, an active network is a network with power, and a passive network is a network without power. Just like active filters and passive filters are the same, passive filters are built with resistors, capacitors, and inductors and do not require an external power supply, while active filters are made of op amps plus resistors and capacitors, and The op amp requires power, so it is called an active filter.

2. Solving steps

Apply Thevenin's theorem to simplify complex circuits, and the general steps to solve a certain branch current are as follows:

(1) Divide the circuit into an active two-terminal network and a branch to be sought.

(2) Remove the branch to be found and find the open circuit voltage U0 of the active two-terminal network. Then the electromotive force of the equivalent power supply E0 = U0, and the polarity of the equivalent power supply should be consistent with the open circuit voltage.

(3) Short-circuit all the electromotive forces in the active two-terminal network to turn it into a passive two-terminal network. Find the resistance r0, which is the internal resistance of the equivalent power supply.

(4) Draw the equivalent circuit of the active two-terminal network, connect the branch to be found, and find the current.

3. Examples

As shown in the example diagram of the circuit, it is known that E1=45V, E2=20V, R1=10Ω, R2=15Ω, R3=64Ω. Use Thevenin’s theorem to solve the current flowing through R3.

examples

untie:

(1) Divide the circuit into an active two-terminal network and a branch to be found, as shown in Figure (a).

(2) Remove the branch to be found, and the open-circuit voltage U0 is the electromotive force E0 of the equivalent power supply, as shown in the example (b).

Open circuit voltage U0

(3) Short-circuit all the electromotive forces in the active two-terminal network to turn it into a passive two-terminal network. Find the input resistance r0, which is the internal resistance of the equivalent power supply, as shown in the legend (c).

internal resistance

(4) Draw the equivalent circuit of the active two-terminal network and connect the branch R3 to be found, as shown in the example (d).

Find the current I3

Notice:

(1) Thevenin's theorem is only equivalent to external circuits, but not to internal circuits. That is to say, you cannot apply this theorem to find the equivalent power source electromotive force and internal resistance, and then go back to find the current and power of the original circuit (ie, the internal circuit of the active two-terminal network).

(2) When applying Thevenin's theorem for analysis and calculation, if the active two-terminal network after the branch is still a complex circuit, the Thevenin's theorem can be used again until it becomes a simple circuit.

(3) Thevenin's theorem only applies to linear active two-terminal networks. If the active two-terminal network contains nonlinear components, Thevenin's theorem cannot be applied.

(4) Appropriate selection of Thevenin's theorem and Norton's theorem will greatly simplify the circuit.