Cal Poly Pomona ECE 209 - The Mesh-Current Method (4 pages)

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The Mesh-Current Method



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The Mesh-Current Method

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Lecture Notes


Pages:
4
School:
California State Polytechnic University, Pomona
Course:
Ece 209 - Network Analysis II

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The Mesh Current Method We can use the mesh current method in frequency domain circuits as using the same methods in section 4 5 4 7 Example V3 V1 1 j2 1 12 V2 150 0 I1 j3 Ix I2 39Ix j16 For mesh 1 1 12 j 2 16 I1 12 j16 I 2 150 13 j 14 I1 12 j16 I 2 150 1 For mesh 2 1 12 j 3 16 I 2 12 j16 I1 39I x 12 j16 I1 13 j13 I 2 39I x 0 0 and I x I1 I 2 12 j16 I1 13 j13 I 2 39 I1 I 2 0 27 j16 I1 26 j13 I 2 0 2 Using Equation 1 and 2 to find I1 and I2 I1 26 j52 A I 2 24 j58 A I x 2 j 6 A The voltages at nodes V1 1 j 2 I1 78 j104 V V2 12 j16 I x 72 j104V V3 1 j 3 I 2 150 j130 V 39I x 78 j 234V 4 1 9 10 The Transformer Two Topics The Sinusoidal steady state behavior of the linear transformer Ideal Transformer The Analysis of a Linear Transformer Circuit Zs a R1 R2 c jwM I1 j L1 V j L2 b I1 ZL d R1 The resistance of the primary winding R2 The resistance of the secondary winding L1 The self inductance of the primary winding L2 The self inductance of the secondary winding M The mutual inductance Vs The sinusoidal voltage source Zs The internal impedance of the source Vs ZL The internal impedance of the load connected to the secondary winding Ii The primary current I2 The secondary current Lets write two mesh current equation Vs Z s R1 j L1 I1 j MI 2 0 j MI1 R2 Z L j L2 I 2 Let say that Z 11 Z s R1 j L1 Z 22 R2 Z L j L2 Therefore we can find I1 Z 22 Vs Z 11 Z 22 2 M 2 I2 j M j M Vs I1 2 2 Z 22 Z 11 Z 22 M The impedance between node a and b 4 2 Z ab Vs Z 11 Z 22 2 M 2 2M 2 Zs Z s Z 11 Zs I1 Z 22 Z 22 or Z ab R1 j L1 2M 2 R 2 Z L j L 2 The third term in Zab is called reflected impedance Zr 2M 2 R 2 Z L j L 2 We can see that if M becomes zero then Zr becomes zero The Ideal Transformer Determining the Voltage and Current Ratios The primary coil is wound so that it has N1 turns The secondary coil has N2 turns The turn ratio is N N2 N1 The relationship between primary and secondary current in ideal transformer is is V2 N N 2 V1 and I2 N1 I1 N2 V1 I1 N1 N 2 I2 ideal



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