Do the FPC, the several efficient methods of circuit analysis to be remembered

            Do the FPC, the several efficient methods of circuit analysis to be remembered

     A lot of methods to analyze circuit, such as the superposition theorem, branch analysis and mesh analysis, node analysis method, thevenin and NORTON's theorem. According to the specific circuit and related conditions apply these methods, the analysis of the basic circuit has an important significance. Regarding the specific circuit adopts different methods are compared and the following.

Branch current method01Branch current method based on branch current and volume, using the kirchhoff's law of two list circuit equations, so as to work out a method of branch current.

A branch circuit analysis steps1) assume that each branch current reference direction, mark loop in the direction of the selected loop. If there are n nodes, according to the kirchhoff's current law column (n - 1) current independent node equation.

3) solution of equations, and the branch current.

As shown in the above example 1 circuit is car generator (US1), battery (US2 billion) and the schematic diagram of load (R3) in parallel. Known US1-12 v, US2 billion - 6 v, R1 R2 = 1 q, R3-50, and each branch current.

Analysis: the imlet and m = 3; Number of nodes n = 2; Mesh number = 2, each branch current reference direction as shown in figure, loop in clockwise direction. Three branch circuit, need to solve the three current unknowns, so we need three equations.

Solution: according to KCL, current column node equation (column (n - 1) independent equation) a node: 11 + 12-13

According to the KVL, loop voltage equation:1:11 r1-12r2-us1-us2Mesh 2:12 R2, r3 13 - Us2 billionSolution: 11-3.8 - A 12-13-1.6 A 2.2 A

Superposition theorem02In a linear circuit, all the response of the independent power supply to produce (voltage or current), equal to the power supply effect produced by the response of vertical and alone.

In the application of superposition theorem, attention should be paid to the following:1) when considering a power alone, want to assume that other independent power supply to zero value. Voltage source replace, with short circuit electromotive force is zero. Current source open circuit, the current is zero. But the power of internal resistance should be retained in the same place. The connection of other components.

2)when considering power supply a separate function, the reference direction should be chosen with the original circuit corresponding to the response of the reference in the same direction, when superposition with numerical generation into the response. Or in that of voltage and current in the circuit reference direction, points the voltage and current reference direction and be consistent when the plus sign, inconsistent when take a minus sign.

3)snow add theorem can only be used to calculate linear circuit of voltage and current, but not such as computing power and voltage or current is not a linear relationship between the parameters.

4)do not belong to the independent power supply, controlled source must be retained for all in their branch.

5)[example 2] in the following circuit, using superposition theorem for the current in the circuit 13Solution: according to the superposition theorem can see circuit diagram in figure a, as in figure b and c circuit of the stack

(1)Mesh analysis03Mesh currents to be variable, by KVL established equation method of the circuit is called mesh analysis. The mesh current equation is also called mesh equation.In the application of mesh analysis method should be paid attention to the following:. 1) based on the mesh from the resistance, resistance to each other, the meaning and calculation method of equivalent voltage source, you can directly write column mesh analysis equation of the final form, referred to as the inspection method2) the circuit containing controlled voltage source, controlled source as independent power supply first, in accordance with the inspection method of regular column write mesh equation, then the amount of control will be controlled source with mesh currents.

Nodal analysis method04In a circuit with nodes, choose a nodes as a reference, the rest of the nodes to the reference voltage is referred to as the nodes of the potential. To the node potential to be variable, each branch current in node voltage, column written in addition to the reference node KCL equation of all other nodes, node voltage is obtained after determine the circuit analysis method of other variables, called the node analysis method.

A variety of methods to compareThe above circuit analysis method is illustrated by several examples of rational choice. Some problems, several methods to comprehensive application, here no longer, for example. All in all, the problem solving method choice is proper, can make the problem solving process is simple, improve the efficiency of problem solving. Each of the circuit analysis method, the general has its scope of application.Application for solving hoff laws applied in the branch of the current, the circuit can't be too complicated; Power supply method of equivalent transformation method is suitable for the power supply more circuit; Node potential method is suitable for the branch number, less node circuit; Mesh analysis method is suitable for the branch number, node number, but the mesh less circuit; Thevenin theorem and send add theorem applies to a branch of the current or circuit voltage on both ends a long period. The above examples, the circuit is simpler, can choose any a kind of method, for some of the more complex circuit but has certain characteristics, must choose the appropriate method, to make the problem solving process is simple, easy to correct solution.

1)superposition theorem applies only to linear circuits, application of superposition theorem analysis containing controlled source circuit, usually don't separate ACTS on the controlled source circuits, the controlled source as resistance element. When an independent power supply on the circuit, keep controlled source in the circuit. Og overtime should be paid attention to each response component reference direction are consistent with the original response variable direction, in the same direction, the response components should be taken before the "+", inconsistent response components should be taken before the ". ". Base plus theorem cannot abuse, is often used to power function circuit is easy to solve alone, is often used in circuit structure and parameter is unknown.

2) for the branch current method, the equation number is equal to the team, using computer is easy to solve, but if an unknown quantity is less, such as three, regardless of the generation of elimination or determinant method, the amount of calculation is too big. If reduce the unknown variables, the equation of the reduced. Including mesh current method, loop current method, the node voltage method, much less an unknown quantity, reduce proposed equation.

3) the essence of the node analysis method, the essence of the node analysis method based on node voltage and variables, column n - 1 KCL equation of independence, circuit is particularly applicable to the junction points less. Once the reference node is selected, the remaining nodes relative to the reference node is the node voltage potential, an unknown quantity is very easy to confirm, so in a circuit with nodal analysis method in the computer aided analysis.

4) the thevenin's and NORTON's theorem are commonly used to simplify a complex network, especially suitable for the calculation of voltage or current of a line, or analyze a component parameter changes impact on the branch, and so on and so forth. The application steps: six branch circuit as a port of active network, the network of open circuit voltage, short circuit current calculation, the input resistance of any two of the three parameters.

5) in a linear circuit, all independent power combination of response (voltage or current), equal to the power generated by separate action response superposition.