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lecture02

# lecture02 - INTRODUCTION TO NUMERICAL SIMULATION L DANIEL...

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I NTRODUCTION TO N UMERICAL S IMULATION - L. D ANIEL M.I.T. L ECTURE 2. Equation Formulation & Node-Branch Stamping 1 T ODAY S O UTLINE : Formulating Equations Circuit Example Struts and Joints Example Matrix Construction From Schematics Node-Branch “Stamping Procedure” Circuits Struts and Joints F ORMULATING E QUATIONS FROM S CHEMATICS Circuit Example Step 1: Identifying Unknowns i s A i s B i s C 0 1 2 3 4 Assign each element a current. i A i B i E i D i C i s A i s B i s C 0 1 2 3 4 Assign each node a voltage, with one node as 0. i s A i s B i s C

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I NTRODUCTION TO N UMERICAL S IMULATION - L. D ANIEL M.I.T. L ECTURE 2. Equation Formulation & Node-Branch Stamping 2 Step 2: Conservation Laws Sum of currents = 0 (Kirchhoff’s Current Law) Step 3: Constitutive Equations Use Constitutive Equations to relate branch currents to node voltages (Currents flow from plus node to minus node) R C i C = V 3 – V 4 R D i D = V 4 – 0 R E i E = 0 – V 2 i s A i s B i s C 0 1 2 3 4 i A i B i E i D i C R E R A R C R D R A i A = 0 – V 1 R B i B = V 1 – V 2 R B i s A i s B i s C 0 1 2 3 4 i A i B i E i D i C i A + i E i D = 0 i s B + i s C i B i E = 0 i s A i A + i B = 0 I D i s A i s B i C = 0 i C i s C = 0