EEGR2111 L9

Mesh analysis
  • Mesh - a loop not containing any other loops
  • Planar circuits!
  • Mesh current - current that flows around the mesh
  • Physical current through an element is the ALGEBRAIC sum of the mesh currents through it
  • How many meshes in the circuit below?

  • Given circuit with N meshes, N KVL equations are required
    Solve for N mesh currents

    PROCEDURE:

  • Label CLOCKWISE mesh currents a, b, c, ... or 1, 2, 3 ...
  • Apply KVL to all N meshes
  • Solve the resulting set of N simultaneous equations

    • Example L8-1:
  • For the above circuit find the mesh equations and solve for the mesh currents
  • Mesh 1:
    i1 R1 + (i1 -i2) R2 - VS1 =0
    (R1 + R2) i1 + (- R2) i2 = VS1
    (5) i1 + (- 4) i2 = 3
  • Mesh 2:
    i2 R3 + i2 R4 + (i2 -i1) R2 =0
    (- R2) i1 +( R2 + R3 + R4) i2 =0
    (- 4) i1 + ( 20 ) i2 =0
    
      |  5    -4   |   |i1|      |  3 |
      | -4    20   |   |i2|  =   |  0 |
 

    
            |  3    -4   |   
     det    |  0    20   |       60
i1 =  --------------------   =   --  A
     det    |  5    -4   |       84   
            | -4    20   |   


i2 = 12 / 84 A
  • If we did nodal analysis how many nodal equations would be needed?

    • Example L9-1
  • What would the mesh analysis be for the following circuit?

  • Mesh 1:
    i1 = is
  • Mesh 2:
    i2 R3 + i2 R4 + (i2 -i1) R2 =0
    (- R2) i1 +( R2 + R3 + R4) i2 =0
    (- 4) i1 + ( 20 ) i2 =0
  • So: this is similar to "case 1" nodal analysis with an independent source connected to ground

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