# 功率电感耦合及在开关电源上的应用_图文

1

M L1

Lk1

1: n

Lk2

*

*

L2

Lm

* *

L1 = Lk1 + Lm
L2 = Lk 2 + Lm n 2

M = Lm n

Lk Lm

1:n

Lk1 Lm

1:n

Lk2

Lk1 1:n=N2/N1 Lk2 Lm

2

DCM Vi+Vo*n Vi Lk Lm Cp CCM Vi+Vo*n
Lk Cp Lm

Lk Lm Cp

Vds Cds

Vds Cds

n:1

Cds

E形结构

3

Rm0 N Rm N Rm
Lk Lm n=1 Lk

Lk n=1 Lk

Rm0

Rm

Rm

Lm

Lm Lk N2 + Lk = Lm + Lk Rmo + Rm

Rm0

Lk

n=1

Lk

Rm
Lm

Rm

Lm + Lk = N 2 /(

Rmo Rm + Rm ) Rmo + Rm

Lm =

1 N 2 Rmo ) ( 2 Rmo + Rm Rm

Lk =

N2 2 Rmo + Rm

k=

Lm Rmo = Lm + Lk Rmo + Rm

L1 L1_2o=Lk+Lm

L2

L2_1o=Lm*n2

L1+L2+2*M

L1_2s=Lk

M L1 L2

Lk Lm

1:n

4

M L1 L2 Lk Lm 1:n

k=

M L1 L2

k=

Lm Lm + Lk

1:n

Lk 耦合系数 K

0

Lm

1
Lk 1:n

Lm

L

L M

L M L

L

L

5

10 10 9 8 6 5 4 3 2 0
10 10 9 8 7 i1( t ) i2( t ) 6 5 4 3 2 1

Vo1

1,输出回路电阻(包括电感绕组电阻); 2,二极管的压降; 3,变压器副边各绕组的耦合;

Vo2

4,各路的电流工作模式,CCM或DCB.

D

1-D=D1

Io1 7
i1( t ) i2( t )

D

D1

Io21
0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 t 0.8 0.9

1
1 1

0

0

1
0 0 0.1 0.2 0.3 0.4 0.5 0.6 t 0.7 0.8 0.9 1 1

Vlm
10 10 9 8 7 i1( t ) 6 5 4 3 2

Lk1
Vlk1

Lm

Io1 Vo1
i2( t )

i1

* n1

Vi1 Vin n2

Vi1=24, Vi2=12, fs=100KHz Io1=5, Io2=2 Vo1=6 n=n2/n1=0.5 Lk1=1uH, Lk2=1uH, Lm=10uH

Lk2
Vlk2

*
i2

Io2
0

1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 t 0.8 0.9

1
1 1

D=0.25, Vo2=3

D

Vi2

Vo2
10 10 9 8 7 i1( t ) i2( t ) 6 5 4 3 2 1 0 0

During D

Vlk1 + Vlm = Vi1 Vo1 Vlk 2 + Vlm n = Vi 2 Vo 2 Vlm Vlk1 Vlk 2 = + n Lm Lk1 Lk 2
Vlk1 + Vlm = 0 Vo1 Vlk 2 + Vlm n = 0 Vo 2 Vlm Vlk1 Vlk 2 = + n Lm Lk1 Lk 2 Vlk1 + Vlm = 0 Vo1 Vlm Vlk1 = Lm Lk1

D

D1

1-D-D1

Vi1=24, Vi2=12, fs=100KHz Io1=5, Io2=0.5 Vo1=6 n=n2/n1=0.5 Lk1=1uH, Lk2=1uH, Lm=10uH

1 D=0.25, D1=0.45, Vo2=3.117
0 0 0.1 0.2 0.3 0.4 0.5 t 0.6 0.7 0.8 0.9 1 1

During D1

During 1-D-D1

6

Tr Np Ns L1

L1
Vo

D1 D2

Tr Np Ns

D1 D2 L2

Vo

L2

Vs t
Δ i1
~ ~

Vs t
Δ i1
~ ~

t

t

Δ i2
~ ~

Δ i2
~ ~

t

Δ io
~ ~

t

Δ io
t

~ ~

t

30.623 31 30.5 i1( t ) i2( t ) 30 29.5 29.375 29

30.931

31 30.5

i1( t ) i2( t ) 30 29.5 29.066 29

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 t 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 t 1

K=0.827
31.549 32 31 i1( t ) i2( t ) 30 29 28.448 28

K=0.557

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 t 1

K=0.202

7

Cuk电路中的耦合电感
L1 M, k L2 v2

i1

i2

vi

v1

-

vo
+

v1

v1=v2 vi vo

+

v2 vi vo

di1 di +M 2 dt dt di2 di v2 = L2 +M 1 dt dt v1 = L1

di1 vL = dt L1eq
di2 v = L dt L2 eq

L1eq = L1 (1 + k ) L2eq = L2 (1 + k )

1 k 1 k L1 L2 1 k 1 k L2 L1

v2 = v1 = vL

Cuk电路耦合电感的电流纹波
L1eq = L1 (1 + k ) 1 k 1 k L1 L2 L2eq = L2 (1 + k ) 1 k 1 k L2 L1
Δi% vs. k
1 1

1

Δi% vs. k for i1 and i2

for i2 for i1

Δi% =

1 1+ k

Δi1 ( k )

0.5

Δi2 ( k )

0.5

0

0

0

0 0

0.2

0.4 k

0.6

0.8 1

0 0

0.2

0.4 k

0.6

0.8 1

L=L1=L2

L1>L2

k=

L2 L1

L1eq = L2eq = L (1 + k )

L1eq → ∞

1 k L1 L2 = 0

L2eq → ∞

1 k L2 L1 = 0

8

84 效 率 (%) 82 80 78 76 74 72 75 150 225 300 375 450 525 600 电感量(nH)

f=400kHz条件下 电感大 电感小

VRM电路的耦合电感

51.94 60 54 48 42 36 30 24 18 12 6 0 0 0 0 0.1

1

i1

L i0

V in
2 i2 L

Vo

io i1 i2
0.2 0.3 0.4 0.5 t 0.6 0.7 0.8 0.9 1 1

i1( t , Io1t0 ) i2( t , Io2t0 ) io( t )

L=200nH

0

Lm 1 L
51.94 60 54 48 42

V in
2 L

Vo
0

i1( t , Io1t0 )

io i1 i2
0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 t 0.9 1 1

36 i2( t , Io2t0 ) 30 io( t ) 24 18 12 6 0 0

L=200nH Lm=500nH

9

VRM耦合电感的等效稳态与动态电感
0o Vin
1

i1 L1

M
180o
2

0

Vo io

L2

i2

di1 di +M 2 dt dt di2 di1 + L2 V34 = M dt dt V12 = L1

Leq1 =

L2 M 2 D M L+ 1 D

Leq 2 = L + M
Leq 3 =
2

Leq 4 = Leq 2 = L + M
L M2 1-D L+ M D

Leq1 与电纹波有关,定义为等效稳态电感 Leq2 与动态响应有关,定义为等效动态电感 只有当M<0(反耦合时),Leq1增加,而Leq2低

VRM耦合电感的等效稳态与动态电感
Lm 1 Lk 0 Lk 2

V in

Vo

di1 d (i i ) + Lm 1 2 = v12 L k1 dt dt di2 d (i1 i2 ) L Lm = v34 k 2 dt dt

Leq1 =

Lk ( Lk + 2 Lm ) D Lk + L m Lm 1 D

Leq 2 = Lk
Leq3 =

Leq 4 = Leq 2 = Lk
Lk ( Lk + 2 Lm ) 1 D Lk + L m Lm D

10

1.0

2

L M
2

D LM 1 D

Lk ( Lk + 2 Lm ) D Lm Lk + Lm 1 D

Ltransient = L M
L1=L2=L, Lk1=Lk2=Lk

Ltransient = Lk

KL
0.9 0.8 0.7 0.6 0.5 0.4

KL =

For two-phase

β=Lm/Lk

2 4 6

10

β =

Lm Lk

0

3

8

VRM耦合电感的设计指导
Y (mm )
0 .74
0.63

#3

X

Y

1,沿虚线稳态性能相同,但 动态性能沿箭头方向变差; 2,稳态性能离稳态方程曲线 越远,稳态性能越好. 1,沿虚线动态性能相同,但 稳态性能沿箭头方向变差; 2,动态性能离动态方程曲线 越远,动态性能越好.

0 .33
0 .28

#1

i

1

i

2

Rm

1

1

Rm R mc

2

2

v 12

v 34
N × i
1 1

c

#2(无耦合)
2 2

+ -

N × i

+ -

0
0.05

● 0.33 X减小,对稳态和动态性能改善都有益

X (mm )

11

12