The mesh analysis method is one of the basic analysis methods of the circuit. Taking the mesh current as the variable to be determined, the method of solving the circuit by KVL is established.
According to Kirchhoff's law: the number of loops that can provide independent KVL equations is b-n+1, ​​and the mesh is just one of them.
Mesh current: A closed, imaginary current that flows by itself along the boundaries of each cell. Generally for M meshes, self-resistance × local cell current + ∑ (±) mutual resistance × adjacent.
Mesh current + voltage rise in the cell.
Analysis method of mesh analysis method1. Select the mesh current as a variable and mark the direction of the variable (standing clockwise)
2. According to the law, use the observation method to analyze the mesh
a. The current source in the cell is considered an open circuit and the voltage source is considered to be a short circuit.
b. Based on KVL, list the voltage equations of self-guide and mutual conductance in the cell
3, solve the mesh current
4. Calculate other quantities to be determined from the mesh current
Note: Processing of current source and controlled source
(1) Select a group of cells to indicate the cell current and its reference direction;
(2) The direction of the cell current is the direction of the cell, and the KVL equation of each cell is written;
(3) Solve the above equation to obtain the mesh current;
(4) The current of the original circuit éŸ common branch is equal to the cell current.
The current of the common branch of the original circuit is equal to the algebraic sum of the cell currents.
Mesh analysis equation[Mesh current] According to the continuity of the current, it can be assumed that a current flows in the specified mesh. This current is called the mesh current. For each node in the circuit, the mesh current flows once and once again, so When the mesh current is used as the circuit to be determined, the KCL equation of the circuit is automatically satisfied, and only the KVL equation of b-n+1 cells is listed.
[Mesh Analysis Method] Using the mesh current as the variable to be determined, the method of solving the equation by KVL is called the mesh analysis method. Its mesh current equation is also called the mesh equation.
[Example 3-2-1] The circuit shown in Figure 3-2-1 lists the mesh equation.
Solution: Assume mesh current 
Flow in the cells 1, 2, and 3 respectively. The reference direction of the cell current is shown in Figure 3-2-1.
Taking the branch current as a variable, the KVL equation for each mesh is listed as
In order to obtain a circuit equation with the mesh current as an unknown variable, the current of each branch is represented by the mesh current, that is,
By substituting the above formulas into the KVL equation, the mesh current equation can be obtained.
That is, the mesh equation of the circuit, obviously, the three equations can solve the mesh current.
General procedure for mesh current method1 Select the mesh as an independent loop and determine its direction of detour;
2 Write the (b-(n-1))KVL equation (listed directly to the standard form) with the mesh current as an unknown quantity;
3 Solve the above equation to get 1 mesh current;
4 Find the current of each branch, and then solve other circuit parameters according to the requirements of the topic;
Features of the mesh current method: only for planar circuits.
1. Cell analysis method for solving current I
2, mesh analysis method to solve the current of each branch
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