Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Loading in …3
×
1 of 28

電路學 - [第八章] 磁耦合電路

13

Share

Download to read offline

https://www.facebook.com/eeRhapsody
磁耦合電路

Related Books

Free with a 30 day trial from Scribd

See all

電路學 - [第八章] 磁耦合電路

  1. 1. Department of Electronic Engineering National Taipei University of Technology
  2. 2. • • • • • • T π • 2/28 Department of Electronic Engineering, NTUT
  3. 3. • N1 (Flux Linkage) L1 ( ) Department of Electronic Engineering, NTUT3/28 ( ) ( ) ( )1 1 1 1 1t N t L i tλ φ= = + − ( )1i t ( )1v t ( )1 tφ
  4. 4. ( ) • ( ) ( ) ( ) ( )1 1 1 1 1 1 d t d t di t v t N L dt dt dt λ φ = = = ( ) ( ) ( ) ( )1 1 1 1 11 12t N t N t tλ φ φ φ= = +   ( ) ( ) ( )1 11 12t t tφ φ φ= + ( ) ( ) ( ) ( )1 11 12 1 1 1 d t d t d t v t N N dt dt dt λ φ φ = = + ( ) ( ) ( ) ( ) ( ) ( )11 1 12 2 1 1 1 2 d t di t d t di t N N di t dt di t dt φ φ    = +        ( ) ( )1 2 1 12 di t di t L M dt dt = + ( )1 tφ + − + − 1 ( )11 tφ ( )12 tφ ( )1i t ( )1v t ( )2v t ( )2i t 2 1 : Department of Electronic Engineering, NTUT4/28
  5. 5. • 1 • 1 2 • 2 • 2 1 • : ( ) ( ) 11 1 1 1 d t L N di t φ = ( ) ( ) 12 12 1 2 d t M N di t φ = ( ) ( ) ( )1 2 1 1 12 di t di t v t L M dt dt = + ( ) ( ) 21 21 2 1 d t M N di t φ = ( ) ( ) 22 2 2 2 d t L N di t φ = ( ) ( ) ( )1 2 2 21 2 di t di t v t M L dt dt = + ( )1 tφ + − + − 1 ( )11 tφ ( )12 tφ ( )1i t ( )1v t ( )2v t ( )2i t 2 ( )2 tφ + − + − 1 ( )22 tφ ( )21 tφ ( )1i t ( )1v t ( )2v t ( )2i t 2 12 21M M M= = Department of Electronic Engineering, NTUT5/28
  6. 6. • ( ) • ( ) ( )1i t ( )1 tφ 1 2 _ + ( )1 tφ ( )1 tφ′ ( )1i t ( )2i t ( )2v t 1 2 Department of Electronic Engineering, NTUT6/28
  7. 7. 1 ( ) • ( ) + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 0 di t v t M dt = = ( ) ( )2 22 2 0 di t v t L dt = = ( ) ( )1 21 di t v t M dt = + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 0 di t v t M dt = = ( ) ( )2 22 2 0 di t v t L dt = = ( ) ( )1 21 di t v t M dt = − ( ) ( )1 2 di t v t M dt = ( ) ( )1 2 di t v t M dt = − ( ) ( ) ( )1 11 12v t v t v t= + ( ) ( )1 11 1 di t v t L dt = = ( ) ( ) ( )2 22 21v t v t v t= + ( ) ( )1 21 di t v t M dt = = ( ) ( ) ( )1 11 12v t v t v t= + ( ) ( )1 11 1 di t v t L dt = = ( ) ( ) ( )2 22 21v t v t v t= + ( ) ( )1 21 di t v t M dt = = − Department of Electronic Engineering, NTUT7/28
  8. 8. 1 ( ) + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 0 di t v t M dt = = ( ) ( )2 22 2 0 di t v t L dt = = ( ) ( )1 21 di t v t M dt = − ( ) ( ) ( )1 11 12v t v t v t= + ( ) ( ) ( )2 22 21v t v t v t= + + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 0 di t v t M dt = = ( ) ( )2 22 2 0 di t v t L dt = = ( ) ( )1 21 di t v t M dt = ( ) ( ) ( )1 11 12v t v t v t= + ( ) ( ) ( )2 22 21v t v t v t= + ( ) ( )1 2 di t v t M dt = ( ) ( )1 2 di t v t M dt = − ( ) ( )1 11 1 di t v t L dt = = ( ) ( )1 21 di t v t M dt = = − ( ) ( )1 11 1 di t v t L dt = = ( ) ( )1 21 di t v t M dt = = Department of Electronic Engineering, NTUT8/28
  9. 9. 2 ( ) • v1(t) v2(t) i1(t) i2(t) ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 di t v t M dt = − ( ) ( )2 22 2 di t v t L dt = − ( ) ( )1 21 di t v t M dt = ( ) ( ) ( )1 11 12v t v t v t− = + ( ) ( ) ( )2 22 21v t v t v t= + + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( )2i t ( ) ( )1 11 1 di t v t L dt = ( ) ( )2 12 di t v t M dt = − ( ) ( )2 22 2 di t v t L dt = ( ) ( )1 21 di t v t M dt = − ( ) ( ) ( )1 11 12v t v t v t= + ( ) ( ) ( )2 22 21v t v t v t= + + − M + − ( )1i t ( )1v t ( )2v t1L 2L ( )2i t ( ) ( )1 2 1 di t di t L M dt dt = − ( ) ( )1 2 2 di t di t M L dt dt = − ( ) ( )1 2 1 di t di t L M dt dt = − ( ) ( )1 2 2 di t di t M L dt dt = − + Department of Electronic Engineering, NTUT9/28
  10. 10. 3 − ( ) ( ) ( ) ( ) ( )1 2 1 1 1 di t di t di t v t L M L M dt dt dt = − = − ( ) ( ) ( ) ( ) ( )1 2 2 2 2 di t di t di t v t M L M L dt dt dt = − = − ( ) ( ) ( ) ( ) ( ) 1 2 1 2 2 di t v t v t v t L L M dt = − = + − 1 2 2aL L L M= + − + − + − + − M( )1i t ( )2i t( )i t ( )1v t ( )2v t1L 2L ( )v t ( )1i t ( )2i t +−+ − + − M( )1v t ( )2v t 1L 2L ( )v t • v1(t) v2(t) i1(t) i2(t) − + + − + − M( )1i t ( )2i t( )i t ( )1v t ( )2v t1L 2L ( )v t ( )1i t ( )2i t −++ − + − M( )1v t ( )2v t 1L 2L ( )v t ( ) ( ) ( ) ( ) ( )1 2 1 1 1 di t di t di t v t L M L M dt dt dt = − = − ( ) ( ) ( ) ( ) ( )1 2 2 2 2 di t di t di t v t M L L M dt dt dt = − + = − ( ) ( ) ( ) ( ) ( ) 1 2 1 2 2 di t v t v t v t L L M dt = + = + − 1 2 2aL L L M= + − Department of Electronic Engineering, NTUT10/28
  11. 11. 3 − ( ) ( ) ( ) ( ) ( )1 2 1 1 1= di t di t di t v t L M L M dt dt dt + = + ( ) ( ) ( ) ( ) ( )1 2 2 2 2= di t di t di t v t M L L M dt dt dt + = + ( ) ( ) ( ) ( ) ( ) 1 2 1 2 2 di t v t v t v t L L M dt = + = + + 1 2 2aL L L M= + + + − + − + − M( )1i t ( )2i t( )i t ( )1v t ( )2v t1L 2L ( )v t ( )1i t ( )2i t + −+ − + − M( )1v t ( )2v t 1L 2L ( )v t ( ) ( ) ( ) ( ) ( )1 2 1 1 1= di t di t di t v t L M L M dt dt dt + = + ( ) ( ) ( ) ( ) ( )1 2 2 2 2= di t di t di t v t M L L M dt dt dt − + = + ( ) ( ) ( ) ( ) ( ) 1 2 1 2 2 di t v t v t v t L L M dt = − = + + 1 2 2aL L L M= + + − + + − + − M( )1i t ( )2i t( )i t ( )1v t ( )2v t1L 2L ( )v t ( )1i t ( )2i t − ++ − + − M( )1v t ( )2v t 1L 2L ( )v t Department of Electronic Engineering, NTUT11/28
  12. 12. 4 − • ( ) ( ) ( )1 2 1 di t di t v t L M dt dt = + ( ) ( ) ( )1 2 2 di t di t v t M L dt dt = + ( ) ( )1 2 2 1 2 di t L M v t dt L L M − = − ( ) ( )2 1 2 1 2 di t L M v t dt L L M − = − ( ) ( ) ( )1 2i t i t i t= + ( ) ( ) ( ) ( )1 2 1 2 2 1 2 2di t di t di t L L M v t dt dt dt L L M + − = + = − ( ) ( )2 1 2 1 2 2 di tL L M v t L L M dt − = + − 2 1 2 1 2 2 a L L M L L L M − = + − M + − ( )i t ( )1i t ( )2i t 1L 2L( )v t , M + − ( )i t ( )1i t ( )2i t 1L 2L( )v t 2 1 2 1 2 2 a L L M L L L M − = + + 2 1 2 0L L M− ≥ 1 2M L L≤ Department of Electronic Engineering, NTUT12/28
  13. 13. 5 • is(t) = cost v2(t) ( ) + − ( )si t ( )2v t 2 F 1 Ω 3 H 1 H 2 Ω ( )2i t ( )1i t ( )1v t 1 HM = 1 1 23V j I j Iω ω= − 2 1 2V j I j Iω ω= − − 2 1 2 1 3 2 2 I V V j jω ω = + 1 1 2 1 1 2 2 I V V j jω ω = + ( ) 1 2 11 2 2 sj V j V I Iω ω+ − = − 1 2 2 1 2 2 2 j V j V Iω ω   − + + = −    1 2 1 1 1 2 2 2 2 sj V j V I j j ω ω ω ω     + + + − =        1 2 1 1 3 2 2 0 2 2 2 j V j V j j ω ω ω ω     − + + + =        KCL: I1 I2 1 2 3 5 1 1 2 2 j V j V   + − =    1 2 5 1 1 + 0 2 2 2 j V j V   − + =    2 10 0.408 78.2 24 5 j V j = = ∠ + ( ) ( )( )2 0.408cos 78.2 Vv t t= + 1 0sI = ∠ 1ω =( ) cossi t t= , , Department of Electronic Engineering, NTUT13/28
  14. 14. (Ι) • 1 (Unity Coupled Coil) • + − + − ( )1i t 1N ( )1v t ( )2v t 2N ( )2i t ( )1 tφ Department of Electronic Engineering, NTUT14/28
  15. 15. (II) • • (Turns Ratio) a 1 ; a 1 2 1 N a N = ( ) ( ) ( ) ( )2 2 1 2 1 1 N v t v t v t av t N = ⇒ = ( ) ( )2 2 1 1 N v t v t N = ( ) ( )1 2i t ai t= − + − + − ( )1v t ( )2v t ( )1i t ( )2i t 1 2:N N − + + − + − ( )1i t ( )2i t ( )1v t ( )2v t( ) 2 2 1 N i t N ( ) 2 1 1 N v t N Department of Electronic Engineering, NTUT15/28
  16. 16. (III) • ( ) ( )2 2 1 1 N v t v t N = − ( ) ( )2 1 2 1 N i t i t N = + − + − ( )1v t ( )2v t ( )1i t ( )2i t 1 2:N N − + + − + − ( )1i t ( )2i t ( )1v t ( )2v t( ) 2 2 1 N i t N ( ) 2 1 1 N v t N − Department of Electronic Engineering, NTUT16/28
  17. 17. (I) Department of Electronic Engineering, NTUT (a) + − + − + − ( )1i t ( )2i t 1 2:N NsR ( )1v t ( )2v t LR( )sv t + − sR 1 2:N N ( )sv t 2 1 2 L N R N       LR (b) + − sR ( )sv t 2 1 2 L N R N       (c) • RL 2 1 2 N N       17/28
  18. 18. (II) • L • C RLC + − + − ( )1v t sR ( )sv t ( )1i t + − ( )2v t LZ ( )2i t 1 2:N N Department of Electronic Engineering, NTUT 2 1 2 N L N       2 2 1 N C N       18/28
  19. 19. (III) • (a) (b) • 2 2 1 N N       + − a b (b) + − a b (a) 1 2:N NsR ( )sv t 2 2 1 s N R N       ( ) 2 1 s N v t N Department of Electronic Engineering, NTUT19/28
  20. 20. 6 • Vs I1 RL V0 I1 I2 I1 − + − + + − sV 1R 1I :1a 2I LR 0V 1V 2V 2R ( )1 2 1 2 2 1sR R I R I V V+ − = − ( )2 2 2 2LR I R R V− + + = 2 1 1 V V a = 2 1I aI=, ( ) 2 1 1 1 1 0La R aR I V a − + − =   ( )1 2 1 11 sR a R I V V+ − + =   ( ) ( )1 2 2 1 2 A 1 s L V I R a R a R = + − + ( ) ( )0 2 1 1 2 V 1 2 2 L L L s L aR V I R aI R V R a R a R = = = + − + Department of Electronic Engineering, NTUT20/28
  21. 21. 7 • a-b 1. (a) b + − aa b (a) b + − a b 2. (b) 3. a-b (c) a ( ) 3sinsv t t= 25 Ω 4 Ω 1: 5 12sint 4 Ω 1: 5 25 Ω 100 Ω 25 Ω 60sint 125 Ω 60sint (b) (c) Department of Electronic Engineering, NTUT21/28
  22. 22. (Primary Winding) (Secondary Winding) + − + − M1R 2R sV 1I 2I1L 2L LVLZ ( )1 1 1 2 sR sL I sMI V+ − = ( ) 2 2 1 L s R sI Z I V s + + = ∆ ( )2 s sM I V s = ∆ ( ) ( ) 2 2 1 1 1 2 2 s i L V s M Z s R sL I R sL Z = = + − + + ( ) 2 1 2 2 i L I sM H s I R sL Z = = + + ( ) ( ) L L v s V sMZ H s V s = = ∆ ( ) ( ) ( ) ( )2 2 1 2 1 2 2 1 1 2L Ls L L M s R L R Z L s R R Z∆ = − + + + + +   ( )2 2 2 1 0LR sL I sMI V+ − + = , Department of Electronic Engineering, NTUT22/28
  23. 23. • (–M) M ( ) ( ) 2 2 1 1 1 2 2 s i L V s M Z s R sL I R sL Z = = + − + + ( ) ( ) ( )1i fZ s Z s Z s= + ( ) 2 2 2 2 f L s M Z s R sL Z = − + + ( )1 1 1Z s R sL= + s jω= L L LZ R jX= + ( ) ( ) ( ) 2 2 2 2 f f f L L M Z j R jX R R j L X ω ω ω = = + + + + ( ) ( ) ( ) 2 2 2 2 2 2 2 L f L L M R R R R R L X ω ω + = + + + ( ) ( ) ( ) 2 2 2 2 2 2 2 L f L L M L X X R R L X ω ω ω − + = + + +, Department of Electronic Engineering, NTUT23/28
  24. 24. 8 • (a) (a) I1 (b) (b) (a) (b) + − (a) 100 0° ∠ 1I j j2j 1 + − 2j 1I 100 0° ∠ 1 2 1 2 j− fZ ( ) 2 2 2 2 f L s M Z s R sL Z = − + + ( ) 2 2 2 1 1 1 1 2 2 f M Z j j L R j ω ω = = = − + + ( ) ( )2 1 1 1 1 100 0 20 60 A 63.2 71.6 A 2 2 I j j j I   = ∠ + − = − = = ∠ −    ( ) 2 2 1 f M Z j j L j ω ω = = = − ( 1j )( )2iZ j j j= − = Ω (b) Department of Electronic Engineering, NTUT24/28
  25. 25. T • T π (c) T T + − + − (a) ( )1i t ( )2i t ( )1v t ( )2v t M 1L 2L + − + − + − + − ( )1i t M ( )2i t ( )1v t ( )2v t( )2di t M dt ( )1di t M dt + − + − ( )2i t( )1i t( )1v t ( )2v tM 1L M− 2L M− ( ) ( ) ( )1 2 1 1 di t di t v t L M dt dt = + ( ) ( ) ( )1 2 2 2 di t di t v t M L dt dt = + ( ) ( ) ( ) ( ) ( )1 1 1 1 2 di t d v t L M M i t i t dt dt = − + +   ( ) ( ) ( ) ( ) ( )1 2 2 1 2 di td v t M i t i t L M dt dt = + + −   (b) (c) Department of Electronic Engineering, NTUT25/28
  26. 26. 9 • (a) ω = 500 / 0.6 T I1 V2 + − + − M (a) ( )100 0 VsV ° = ∠ 1 40 mHL = 2 70 mHL = 1 15R = Ω 2 10R = Ω 1I 2V30LR = Ω 2 70mHL =1 40mHL = 0.6k = ( )( )0.6 40 70 31.7mHM = = ( ) ( )1 1 2 2 2 2 sR j L M j M R I j M R I Vω ω ω+ − + + − + =   ( ) ( )2 2 2 2 2 0j M R R j M j L M R Iω ω ω− + + + + − + =   ( ) ( )1 225 20 10 15.9 100j I j I+ − + = ( ) ( )1 210 15.9 40 35 0j I j I− + + + = ( )2 2 39.3 13.70 VLV I R= = ∠− , , + − (b) 30LR = Ω 31.7 mHM = 2 10R = Ω 1I 2I 1 15R = Ω ( )100 0 VsV ° = ∠ ( )1 8.3 mH L M− = ( )2 38.3 mH L M− = + − 2V ( )1 3.72 30.3 AI = ∠ − ( )2 1.31 13.70 AI = ∠ −, Department of Electronic Engineering, NTUT26/28
  27. 27. π • π Y ∆ T π sL R Y ∆ T + − + − ( )2i t( )1i t( )1v t ( )2v t3L 1L 2L + − + − ( )1i t ( )2i tBL ( )1v t ( )2v tAL CL 1 2 2 3 3 1 2 A R R R R R R R R + + = 1 2 2 3 3 1 3 B R R R R R R R R + + = 1 2 2 3 3 1 1 C R R R R R R R R + + = 1 1L L M= − 2 2L L M= − 3L M= 2 1 2 2 A L L M L L M − = − 2 1 2 B L L M L M − = 2 1 2 1 C L L M L L M − = − , , , , , , Y ∆ T π Department of Electronic Engineering, NTUT27/28
  28. 28. • • • • AC Department of Electronic Engineering, NTUT28/28

×