1/9/20111E E 2315Lecture 02 -Mesh Current AnalysisIntroduction to Mesh Current Method• More direct than branch equations• Fewer equations to solve• Express all variables in terms of mesh currents• Solution is set of mesh currents• Solution completely defines the circuit• Most Convenient Method to Model Magnetic Coupling (E E 2446 Topic)1/9/20112Mesh Current Example 1 (1/2)KVL at Mesh 1:KVL at Mesh 2:Using Ohm’s Law:10sacVvv20cbsvvV 2122scbVRIIRI  Mesh Current Example 1 (2/2)Above linear equations can be solved for mesh currents I1and I2.1122saccscbcVRRRIVRRRI   1/9/20113Mesh Current Example 1a (1/2)120 V 64 V8 24 I1I26 KVL at Mesh 1:KVL at Mesh 2:1120 120 6 24III 12120 30 2464 24 32II   Solve:1262.5IAIAMesh Current Example 2 (1/2)KVL @ Mesh 1:KVL @ Mesh 2:But:11210scbVRII RI2210xa ciRIRII  1/9/20114Mesh Current Example 2 (2/2)Solve for I1and I2:112sbc cVRRIRI  120cacRI R R I  Mesh Current Example 2a (1/2)KVL @ Mesh 1:KVL @ Mesh 2:But:12 10 120 24 8III2210410 24xiI II  1/9/20115Mesh Current Example 2a (2/2)12120 32 2402030II   Solve for I1and I2:127.5 5IAI AForced Mesh (1/2)• No KVL equation possible for mesh 2•But I2is known: I2= Is1/9/20116Forced Mesh (2/2)KVL for mesh 1:Substitute and Solve:1120sa cVRIRII  Forced Mesh Example 3a 108 V 5 A6  8 20 I1I2KVL for mesh 1:Substitute and Solve:110 108 6 20 5II 1108 100620I1/9/20117Supermesh Example (1/5)• No KVL possible for meshes 1 or 2• Use Supermesh (dotted loop) for KVLVs1Vs2IsRaRbRcRdReI1I2I3Supermesh Example (2/5)Supermesh KVL:Mesh 3 KVL:Vs1Vs2IsRaRbRcRdReI1I2I3112223 130()()sa b sdcVRIRIVRI I RI I   31 32 30( )( )cd eRI I RI I RI 1/9/20118Supermesh Example (3/5)Also:Vs1Vs2IsRaRbRcRdReI1I2I321 2 1ssIII III  12 1 113 13()()()ss a bsds cVV RIRIIRI I I RI I    Subst for I2:Supermesh Example (4/5)And:Rearranging the equations:Vs1Vs2IsRaRbRcRdReI1I2I331 3 1 30( )( )cdseRII RIII RI1/9/20119Supermesh Example (5/5)Vs1Vs2IsRaRbRcRdReI1I2I312 13s s bds abcdcdVV RRI RRRRIRRI   13ds c d c d eRIRRIRRRI    Supermesh with Numbers (1/3)1/9/201110Supermesh with Numbers (2/3)1340 30 20160 20 40IVIV    1367IAIASupermesh with Numbers