3-Lesson_Notes_Lecture24_ee205 - EE 205 Dr. A. Zidouri...

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EE 205 Dr. A. Zidouri - 1 - Electric Circuits II The Ideal Transformer Lecture #24
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EE 205 Dr. A. Zidouri - 2 - The material to be covered in this lecture is as follows: o The Ideal Transformer o Determining the Voltage and Current Ratios o Rules For Assigning Proper Algebraic Sign For Relating The Voltage And Current o Impedance Matching After finishing this lecture you should be able to: ¾ Understand the Behavior of Ideal Transformers ¾ Determine the polarity of the Voltage and Current Ratios ¾ Analyze Circuits Containing Ideal Transformers ¾ Use The Ideal Transformer For Impedance Matching
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EE 205 Dr. A. Zidouri - 3 - The Ideal Transformer An ideal transformer consists of two magnetically coupled coils having N 1 and N 2 turns respectively, and exhibiting these three properties: o The coefficient of coupling is unity k=1, o The self-inductance of each coil is infinite 12 L=L= o The coil losses, due to parasitic resistance, are negligible. Understanding the behavior of ideal transformers begins with equation (33-11) which describes the impedance Z ab we repeat this below +− + 22 ab 11 S 1 1 22 2 2 L ω M ω M == R + j ω L+ R+ j ω L ZZ Z ( 3 4 - 1 ) Let us consider the same circuit as in Fig.33-1 of previous lecture Fig.34-1 Frequency-domain model of a Linear Transformer
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EE 205 Dr. A. Zidouri - 4 - Exploring Limiting Values To show how Z ab changes when 12 k = 1, L and L approach infinity we use the notation: ( ) j ++ 22 2 L 2 L 22 22 =R +R +j ω L= R ZX X (34-2) Then rearrange ⎛⎞ + ⎜⎟ ⎝⎠ 644474448 6447 4 48 ab ab X R 22 22 22 ab 1 1 22 22 22 22 ω MR ω MX =R +j ω L- R+ X X Z (34-3) Before we let L 1 and L 2
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3-Lesson_Notes_Lecture24_ee205 - EE 205 Dr. A. Zidouri...

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