2. 1 、 grasp mutual inductance and the disappear method of mutual inductance 2 、 grasp the calculation of including mutual inductance 10 Circuit That Contain Mutual Inductance Key: 3 、 grasp the principals of transformer principals 一、 self-inductance and self- inductance voltage Line inductance i u (self-inductance coefficient) review 10. 1 mutual-inductance and mutual-inductance voltage link

3.  11 i 1 ， N 1   11 = N 1  11 L 1 =  11 /i 1  21 = N 2  21 =M 21 i 1 i1i1 Total flux leakage flux Magnet coupling flux （ main flux ）  11 =  21 +   1 11  21 N1N1 N2N2 为线圈 2 对 1 的互感 i 2 ， N 2   22  s2  12 definition ： the mutual inductance coefficient if loop 1 to units H L 2 =  22 / i 2 为线圈 2 的自感 二. Mutual Inductance and Mutual-Inductance Voltage 1. Mutual Inductance ：

4. ① M 12 =M 21 =M 3. coupling coefficient k ： K < 1   1 =   2 =0  11 =  21 ，  22 =  12 K = 1 2. mutual-inductance Properties

5. Generate mutual- inductance voltage Generate self-inductance voltage i1i1  1 1  21 e 2 1 right hand Reference direction i1i1  2 1 right hand u 2 1 consistence i1i1  21 u 2 1 4.Mutual Inductance Voltage

6. a b + – u 21 i1i1  21 a i1i1 – b – u 21 + direction a point direction b point * * * * 三、 mutual-inductance Dotted Terminal )

7.  i 1 1' 2 2' * * 1 1' 2 2'3' 3 * *     example. notice ： dotted terminal must be ensure with two termitals i1i1 ** u 21 +– M i1i1 * –+ M * 四、 through dotted terminal and u, i reference direction to ensure mutual-inductance voltage

8. i1i1 * * L1L1 L2L2 + _ u1u1 + _ u2u2 i2i2 M * * L1L1 L2L2 + _ u1u1 + _ u2u2 i2i2 M i1i1 * * j L1j L1 j L2j L2 + _ j Mj M + _ In sin-current circuit, its phase equations i2i2

9. ** j L1j L1 j L2j L2 + – – + + – + –

10. + _ j  M 12 I 1 + j  M 23 I 3 + _ j  M 13 I 1 + _ j  MI 3 + _ j  MI 2 + _ j  M 13 I 2 * * * L1L1 L2L2 L3L3 i2i2 i1i1 i3i3 M 12 M 23 M 13 _...... V

11. + j  MI –. i * * + M R1R1 R2R2 L1L1 L2L2 + – u + – i R L u + – 10.2 the example of mutual-inductance analysis method and compute 一、 mutual- inductance series 1. Dotted terminal series connection

12. i * * u2u2 + – M R1R1 R2R2 L1L1 L2L2 u1u1 + – u + – i R L u + – 2. Dotted terminal convert connection ：

13. Mutual-inductance measure methods ：

14. i = i 1 +i 2 Solve the relation of u, i ： * * M i2i2 i1i1 L1L1 L2L2 u i + – 二、 mutual-inductance parall 1. Dotted terminal at the same side

15. i = i 1 +i 2 Solve the relation of u, i ： * * M i2i2 i1i1 L1L1 L2L2 u i + – 2. Dotted terminal at the different side

16. º ** M i2i2 i1i1 L1L1 L2L2 º + _ u i Draw equivalent circuit i 2 = i - i 1 º i2i2 i1i1 L1-ML1-M L2-ML2-M + _ u º i M i 1 = i - i 2

17. º * * L1L1 L2L2 º M º L 1 +M L2+ML2+M -M-M º ºº L1-ML1-M L 2 - M º M L1+ML1+M L 2 + M -M-M M ºº * * M L1L1 L2L2

18. j L1j L1 j L2j L2 + – – + + – + – * * j L1j L1 j L2j L2 j Mj M + – + – * Weather to draw the model of voltage controlled current ** what’s the restrict conditions considering k  四、 Equivalent Circuit of Controlled Source

19. M + _ + _  L1L1 L2L2 L3L3 R1R1 R2R2 R3R3 Branch methods ： 2. State the equations of following circuit 。

20. M + _ + _  L1L1 L2L2 L3L3 R1R1 R2R2 R3R3 Loop current method: (1) Not consider mutual-inductance (2 ) Consider mutual-inductance notice: the expression of voltage of mutual –inductance and its char’+’,’-’

21. First draw the equivalent circuit,then state the equations M 12 * *    M 23 M 13 L1L1 L2L2 L3L3 L 1 –M 12 +M 23 –M 13 L 2 –M 12 –M 23 +M 13 L 3 +M 12 –M 23 –M 13 * *   M 23 M 13 L1L1 L2L2 L3L3 –M 12 +M 12 –M 12   M 13 L1L1 L2L2 L3L3 –M 12 +M 23 +M 12 –M 23 –M 12 –M 23

22. + _ jMjM M + _ + _  L1L1 L2L2 R1R1 R2R2 Solve Thevenin’s theorem + _ Z1Z1 –+ + – Supplement ：

23. + _ jMjM + _ jMjM M  L1L1 L2L2 R1R1 R2R2 + _ Solve inter resistance ： Z i （ 1 ） Add voltage source to solve current ： state loop current equation

24. Secondary loop total resistance Z 22 =(R 2 +R)+j(  L 2 +X) + – Z 11 Primary equation circuit Z=R+jX M + j  M I 1. - + j  M I 2. - * * L1L1 L2 L2 + – R1R1 R2R2 10.3 Hollow Transformer Primary loop total resistance Z 11 =R 1 +j  L 1

25. Z l = R l +j X l ： Secondary reflect on primary loop’s inductance * * j L1j L1 j L2j L2 j Mj M + – R1R1 R2R2 Z=R+jX + – Z 11 Primary equation circuit

26. + j  M I 1. - + j  M I 2. - * * j L1j L1 j L2j L2 j Mj M + – + – Complete Coupling Transformer 10. 4 Ideal Transformer

27. 1 1' 2 2' N1N1 N2N2 u1u1 u2u2 i1i1 i2i2

28.   ， L 1,M, L 2   ， L 1 /L 2 ration no 二. ideal transformer ： * * + – + – n : 1 ideal transformer element characteristic ideal transformer’s circuit model Perfect Coupling transformer’s the relation of voltage and current ：

29. Load Operation and Current Conversion 1.The balance of magnet I 0 of Empty load is very little 一、 apparent power is equal

30. (a) Impedance Conversion * * + – + – n : 1 Z + – n2Zn2Z Characteristic of Ideal Transformer

31. 【 supplememt ：】 one degrade voltage transformer whose voltage ratio is 220/110 V ， if the second grade connect with a resistance with 55  ， solve the input impedance of transformer’s primary grade solution 1 ： second grade current Initial currentInput inductance solution 2 ：

32. (b) power Characteristic equations of Ideal Transformer ， so non memory function 。 * * + – n : 1 u1u1 i1i1 i2i2 + – u2u2 So Ideal Transformer not only can not store energy but also not consume energy. It only transmitt signal and energy

33. Given resistance R S =1k  ， load resistance R L =10  。 In order to attain the max-power of R L ， solve the ideal transformer ratio n 。 * * n : 1 RLRL + – uSuS RSRS n2RLn2RL + – uSuS RSRS When n 2 R L =R S 10n 2 =1000  n 2 =100 ， n=10. supplement example.

34. * * + – + – 1 : 10 50  + – 11 solution1 ： state equation example 2.

35. None core transformer ： circuit reference L 1 、 L 2 、 M, store energy 。 Ideal transformer ： circuit reference n, non- consume energy 、 non-store energy change voltage,current, and inductance Z 11 Z 引入 n2Z2n2Z2 icon core transformer ： circuit reference L 1, L 2, n, M, R 1, R 2. conclusion ： Assignment ： 10—1. 7. 8. 11. 12. 17. 18. 19

36. Some questions in assignment ： units V speaking ： 10-7