【正文】
?? ?211221222111 InLjUIMjLjUMnjMjILjUI ??????? ????????????Circuit model of an unity coupling transformer: 1Lj?21 In ??* * 1 ?I2 ?I+ – 2 ?U+ – 1 ?Un : 1 ideal transformer 2Lj?* * 1 ?I2 ?I+ – 2 ?U+ – 1 ?Un : 1 ideal transformer Ex1. The selfresistance of the power RS=1k?,RL=10?。 Determine the turns ratio n of the ideal transformer to ensure that RL absorb the maximum power. * * n : 1 RL + – uS RS Ex2. 1 ?I2 ?I* * + – 2 ?U+ – 1 ?U1 : 10 50? + – V010 o?1? . find 2 ?U9. 5 Circuit Models of Transformers 1. ideal transformer( perfectly coupling, lossless, m=? , linear transformer ) 21 UnU ?? ?211 InI ?? ?? 21 nuu ?211 ini ??* * + – + – n : 1 i1 i2 u1 u2 2. unitycoupling transformer(k=1, lossless , m??, linear) 21212121 //NNLLLMMLnUU???????* * j? L1 1 ?I2 ?Ij? L2 j? M + – 2 ?U+ – 1 ?U 21 UnU ?? ?2111 1 j 1 InUωLI ??? ??* * j? L1 1 ?I2 ?I+ – 2 ?U+ – 1 ?Un : 1 ideal transformer L1: magizing inductance 0I?( exciting current with no loads) 3. lossless transformer(k?1, m??, linear) ?21 i1 i2 + + – – u1 u2 ?12 ?1s ?2s N1 N2 )2 c o i l off l u x l e a k a g e( ) 1 c o i l off l u x l e a k a g e(2S12222121111??????????????SSS211222122111??????????????SS perfect coupling flux Circuit model of lossless transformer: * * L10 + – + – n : 1 Unitycoupling transformer L1S L2S i1 u1 u2 i2 + – u139。 + – u239。 L1S, L2S: leakage inductance 4. transformer with losses in the coils and ironcore(k?1,m??, linear) * * L10 + – + – n : 1 L1S L2S i1 u1 u2 i2 Rm R1 R2 Summary : Transformers are essentially the coils having mutual inductances. There are some conventional methods to deal with them: Aircore transformer: L L M, store energy Ideal transformer: the turns ratio is n, neither store nor dissipate energy。 transform voltage 、current and impedance。 its equivalent circuit is: Z11 Zr n2Z2 Note: ideal transformer is different from unitycoupling transformer. ironcore transformer: L1, L2, n, M , R1, R2 .