3-Lesson_Notes_Lecture22_ee205 - EE 205 Dr A Zidouri...

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EE 205 Dr. A. Zidouri - 1 - Electric Circuits II More about Mutual Inductance Lecture #22
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EE 205 Dr. A. Zidouri - 2 - The material to be covered in this lecture is as follows: o Mutual Inductance in Terms of Self Inductance o Mesh Current Analysis of magnetically coupled Circuits o Procedure for Determining Dot Markings o Energy Calculation After finishing this lecture you should be able to: ¾ Analyze Circuits with Mutual Inductance ¾ Determine the Coefficient of Coupling ¾ Determine the Dot Markings of neighboring Coils ¾ Perform Energy Calculations in Magnetically Coupled Circuits
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EE 205 Dr. A. Zidouri - 3 - Mutual Inductance in Terms of Self Inductance We have seen that 2 11 1 L=Np 2 22 2 Therefore 1 2 1 2 1 2 1 2 11 21 22 12 LL =NNpp =NN ( pp )( ) But for linear system, 21 12 p= p ⎛⎞ ⎜⎟ ⎝⎠ 222 11 22 12 1 21 12 12 LL =NNp 1+ 1+ 2 11 22 12 12 =M 1+ Replacing the positive quantity 11 22 12 12 1+ 1+ by 2 1 k gives a more meaningful expression M=kLL or M=k LL
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EE 205 Dr. A. Zidouri - 4 - k is called the Coefficient of Coupling and must lie between 0 and 1: ≤≤ 0k1 When 12 12 12 Φ = Φ =0 p =0 ⇒∞ 2 1 =, o r k = 0 k If no flux linkage between the coils, obviously M=0 and k=1 , when 11 22 Φ = Φ , which presents the Ideal State.
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EE 205 Dr. A. Zidouri - 5 - Mesh Current Analysis To solve the following example 32-1, Let us reproduce the Mesh Current Equations that describe the following Circuit seen in Lec31: di L dt di M dt + +    1 2 2 di L dt di M dt + +   1 11 2 1 0 g di di M vR i d L dt t −+ + = (Mesh 1) 1 2 2 2 2 0 di L d di M t t Ri d + = (Mesh 2)
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EE 205 Dr. A. Zidouri - 6 - Example 32-1 ¾ Write a Set of Mesh-Current Equations that describe the Circuit in the following Figure: ¾ What is the Coefficient of Coupling of the Magnetically Coupled Coils?
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This note was uploaded on 01/16/2010 for the course EE ee205 taught by Professor Profsyed during the Spring '09 term at King Fahd University of Petroleum & Minerals.

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3-Lesson_Notes_Lecture22_ee205 - EE 205 Dr A Zidouri...

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