Lecture 8 Mesh Current Analysis ECE 205 Prof

Lecture 8 Mesh Current Analysis ECE 205 Prof. Ali Keyhani

Mesh Current Analysis • Restricted to planar circuits • The mesh current are defined for each mesh and a reference direction is assigned to them • Example: meshes in a planar circuit:

Mesh Current Analysis • If Kth two-terminal element is contained in meshes X and Y, then the mesh current is defined as the difference of the two mesh currents: • If the element is contained in only one mesh then:

Example 1 Source: textbook Mesh currents are i. A=5, i. B=5 A, i. C=-3 A, find the element currents i 1 to i 6.

Example 1 Solution:

Formulating Mesh Current Equations • Step 1: Identify a mesh current for each mesh and write element voltages in terms of mesh currents • Step 2: Write the KVL equations in terms of the element voltages around every mesh of the circuit • Step 3: Use the element i-v relationship and KCL to express the element voltages in terms of mesh currents • Step 4: Substitute the element constraints from step 3 into the KVL equations in step 2 and solve the resulting equations to find the unknown mesh currents

• The planar circuit can be analyzed using the mesh current method.

Writing node-voltage equations by inspection • The mesh equations have a symmetrical pattern that is similar to the symmetry observed in node equations • The voltage across resistance in mesh A consists of the following terms: 1. i. A times the sum of resistances in mesh A. 2. -i. B times the sum of resistances common in mesh A and B and similar terms for any mesh adjacent to mesh A • These rules make writing the mesh current equations easy and without need to write the element equations

Example 2 Write the mesh current equations by inspection

Example 3 Find the current in the 2Ω resistor of the given network.

Example 3 Solution:

Mesh Equations with Current Sources • There are three ways to write mesh equations in presence of current sources: 1. Current source is in parallel with a resistor: it can be converted to a voltage source 2. Current source is contained in only one mesh: That mesh current is the source current and is known. One mesh equation is eliminated

Mesh Equations with Current Sources 3. Current source is contained in two meshes: a supermesh is created and the mesh equations written around the supermesh using both mesh currents. The equation of the supermesh is added to complete the set of equations as:

Example 4 Determine the currents I 1 and I 2 in the given resistive circuit by mesh analysis.

Solution: The current source is transformed to voltage source for the mesh analysis as shown in Figure.