Mesh analysis

As mesh current method, we describe a method used in electrical network analysis. With this method, we can determine the branch currents. Because each electrical network can be ( at in - stationary processes with capacitors and inductors ) described and calculated in this manner by a linear system of equations ( in the steady state with linear elements ) or by a system of differential equations. Advantageous for a calculation using the mesh current method is a network that can be represented by a planar graph, ie has no line crossings. The calculation of the non- planar networks is also possible, but less suitable for hand calculation. Alternatively, the node potential method may be used.

Procedure

• Simplify the network, ie combining parallel circuits.
• Select Ideal current sources as tendon, the system of equations is simplified thereby.
• Convert non- ideal current sources into equivalent voltage sources.
• Mark tree.

• Each mesh (M) runs over only a string, otherwise it closes over the branches of the tree
• With every stitch of the sense of rotation must be specified. From the machining direction of the choice of sign depends.

In the main diagonal of the resistance matrix is carrying the sum of all resistances over which closes the respective mesh, a. The dimension of the matrix is the number of meshes of the net ideal current sources in the network.

In the other fields, you will enter the sum of the resistances, which overlap the mesh. When opposites of circulation, the sum gets a negative sign.

In the source voltage matrix, carrying a sum of all the voltage sources that lie in each stitch. The sign is positive if the sense of rotation is equal to the voltage arrow.

Ideal current sources ( Iq) must be treated differently. The corresponding mesh ( MIQ ) is not included in the matrix, accounting for both row and column. The solution of the mesh current is present, IMi = Iq. The overlap with the other mesh is taken into account by the voltage drop on the common resistors by the ideal current source in the source voltage matrix evaluated with.

The established equations forming a system of linear equations, for which there are a large number of solution methods.

According to the principle of superposition, the current calculated in a branch ( with the correct sign ) from the sum of the mesh currents that run through them.

Example: