Practical skills | Senior engineers summarize 10 complex circuit analysis methods-EEWORLD

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The prerequisite for calculating circuit problems is to correctly identify the circuit and figure out the connection relationship between the various parts. For more complex circuits, the original circuit should be simplified into an equivalent circuit for analysis and calculation.

There are many ways to identify circuits. Here are ten methods introduced with specific examples.

Feature recognition method

The characteristics of series-parallel circuits are: the current does not bifurcate in a series circuit, and the potential at each point decreases gradually; the current bifurcates in a parallel circuit, and the two ends of each branch are at equal potential, and the voltage between the two ends is equal. Identifying circuits based on the characteristics of series-parallel circuits is one of the most basic methods for simplifying circuits.

Example: Try to draw the equivalent circuit shown in Figure 1.

Solution: Assume that the current flows in from terminal A, branches at point a, merges at point b, and flows out from terminal B. The potential of each point in branches a-R1-b and a-R2-R3(R4)-b decreases successively, and the voltage between points a and b of the two branches is equal. Therefore, it is known that R3 and R4 are connected in parallel, then in series with R2, and then in parallel with R1. The equivalent circuit is shown in Figure 2.

Telescopic flip method

When connecting circuits in the laboratory, this operation is often done in this way: the unobstructed wire can be extended or shortened, or it can be turned over and over, or a branch can be turned over to another place, and the two ends of the branch remain stationary when turning over; the wire can also slide along other wires from its node, but it cannot cross the component. This provides a method to simplify the circuit, which we call the telescopic flip method.

Example: Draw the equivalent circuit of Figure 3.

Solution: First shorten the wire connecting nodes a and c, and extend the wire connecting nodes b and d and flip it outside the R3-C-R4 branch, as shown in Figure 4.

Then shrink the wires connecting nodes a and c to a point, shrink the wires connecting nodes b and d to a point, and connect R5 to the extended wire of node d (Figure 5). It can be seen that R2, R3 and R4 are connected in parallel, and then in series with R1 and R5, and connected to the power supply.

Current Direction Method

Current is the core of circuit analysis. Starting from the positive pole of the power supply (for passive circuits, it can be assumed that the current flows in from one end and out from the other end), follow the direction of the current, pass through various resistors and go around the external circuit to the negative pole of the power supply. All resistors that the current flows through in sequence without bifurcation are connected in series, and all resistors that the current flows through separately with bifurcation are connected in parallel.

Example: Try to draw the equivalent circuit shown in Figure 6.

Solution: The current flows out from the positive pole of the power supply through point A and is divided into three paths (the AB wire can be reduced to one point), travels through the external circuit, and flows into the negative pole of the power supply from point D. The first path goes directly to point D through R1, the second path goes to point C through R2, and the third path goes to point C through R3. Obviously, R2 and R3 are connected in parallel between points AC. The second and third paths of current converge at point c and reach point D through R4. It can be seen that R2 and R3 are connected in parallel and then connected in series with R4, and then in parallel with R1, as shown in Figure 7.

Isopotential method

In a more complex circuit, we can often find points with equal potential, and reduce all points with equal potential to one point, or draw them on a line segment. When there is a non-power supply component between two equipotential points, it can be removed and ignored; when a branch has neither power supply nor current, this branch can be cancelled. We call this method of simplifying the circuit the equipotential method.

For example: As shown in Figure 8, given that R1 = R2 = R3 = R4 = 2Ω, calculate the total resistance between points A and B.

Solution: Imagine connecting points A and B to the positive and negative poles of the power supply for analysis. The potentials of points A and D are equal, and the potentials of points B and C are also equal, and they are drawn as two line segments. Resistor R1 is connected to points A and C, that is, connected to points A and B; R2 is connected to points C and D, that is, connected to points B and A; R3 is connected to points D and B, that is, connected to points A and B, and R4 is also connected to points A and B. It can be seen that the four resistors are connected between points A and B and are all connected in parallel (Figure 9). Therefore, PAB=3Ω.

Branch Node Method

A node is the junction of several branches in a circuit. The so-called branch node method is to number each node (by convention: the positive pole of the power supply is the first node, and the nodes passed from the positive pole to the negative pole of the power supply are 1, 2, 3, etc. in order), and draw the branch starting from the first node to the negative pole of the power supply. There may be multiple branches (regulation: different branches cannot pass through the same resistor repeatedly) that can reach the negative pole of the power supply. The principle of drawing is to draw the branch with fewer nodes first, and then the branch with more nodes. Then, according to this principle, draw the branch starting from the second node. And so on, and finally draw the remaining resistors according to the positions of their two ends.

Example: Draw the equivalent circuit shown in Figure 10.

Solution: There are five nodes 1, 2, 3, 4, and 5 in Figure 10. According to the principle of branch node method, there are two branches with fewer nodes coming out from the positive pole of the power supply (node 1): R1, R2, R5 branch and R1, R5, R4 branch. Take one of the R1, R2, R5 branches and draw it as shown in Figure 11.

Starting from the second node, there are two branches that can reach the negative pole, one is R5, R4, the number of nodes is 3, and the other is R5, R3, R5, the number of nodes is 4, and the duplication of R6 is not desirable. Therefore, the R5, R4 branch should be drawn again, and finally the remaining resistor R3 should be drawn, as shown in Figure 12.

Geometric deformation method

The geometric deformation method is to geometrically deform a given circuit based on the characteristics that the wires in the circuit can be arbitrarily extended, shortened, rotated or translated, further determine the connection relationship between the circuit elements, and draw an equivalent circuit diagram.

Example: Draw the equivalent circuit of Figure 13.

Solution: Shorten the wire of the ac branch and geometrically deform the circuit to obtain Figure 14. Then shrink ac to a point and bd to a point. It is obvious that R1, R2 and R5 are connected in parallel and then in series with R4 (Figure 15).

Removal of resistance method

According to the characteristics of series and parallel circuits, in a series circuit, if any one resistor is removed, no current will flow through the other resistors, then these resistors are connected in series; in a parallel circuit, if any one resistor is removed, current will still flow through the other resistors, then these resistors are connected in parallel.

For example: Still taking Figure 13 as an example, assume that the current flows in from terminal A and out from terminal B. Remove R2 first. From Figure 16, we can see that current flows through R1 and R3. Remove resistor R1 again. From Figure 17, we can see that current still flows through R2 and R3. Similarly, when resistor R3 is removed, current also flows through R1 and R2. From the characteristics of the parallel circuit, we can see that R1, R2 and R3 are connected in parallel and then in series with R4.

Independent Branch Method

Let the current flow out from the positive pole of the power supply. On the principle of not passing through the same component repeatedly, see how many paths flow back to the negative pole of the power supply, and how many independent branches there are. The remaining resistance not included in the independent branch is supplemented according to the position of its two ends. When applying this method, the wire must be included in the independent branch.

Example: Draw the equivalent circuit of Figure 18.

Solution 1: Select A—R2—R3—C—B as an independent branch, A—R1—R5—B as another independent branch, and the remaining resistor R4 is connected between D and C, as shown in Figure 19.

Solution 2: Select A—R1—D—R4—C—B as an independent branch, and then arrange the positions of R2, R3 and R5 respectively to form the equivalent circuit diagram 20.

Solution three: Select A—R2—R3—C—R4—D—R5—B as an independent branch, then connect R1 between AD, and connect the wire between C and B, as shown in Figure 21. The result still cannot intuitively determine the series and parallel relationship of the resistors, so when selecting an independent branch, be sure to include the non-resistance wire.

Node spanning method

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