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Matlab Code

clear all; L=1E-3;Vd=100;Ts=50E-6;%IL=zeros(100,1);ILB_max=Vd*Ts/(8*L); N=2*ILB_max/0.01; i=1;while(i<N) IL(i)=0.01*i; i=i+1;endM=size(IL);

for i=1:1:100 Duty=i*0.01; ILB_matrix(1,i)=Duty*Ts/2/L*(Vd-Duty*Vd); ILB_matrix(2,i)=Duty;endplot(ILB_matrix(1,:),ILB_matrix(2,:))hold off;grid on;

figure(1);for j=1:2:9 D=0.1*j; ILB=D*Ts*(Vd-D*Vd)/(2*L); for i=1:1:M(2) if (IL(i)>ILB) ratio(1,i)=D; ratio(2,i)=IL(i); else ratio(1,i)=D^2/(D^2+0.25*IL(i)/ILB_max); ratio(2,i)=IL(i); end end plot(ratio(2,:),ratio(1,:)); hold on;end

初始值

特徵曲線

電感電流極限值

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穩態特徵曲線

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Io

d

o

V

VD=0.9

D=0.7

D=0.5

D=0.3

D=0.1

CCM

DCM

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Buck Converter Circuit

Duty

Iload

4/132

X-Y Curve

Io

d

o

V

V

5/132

Steady State Curve

0.0 0.20 0.40 0.60 0.80Io

0.20

0.40

0.60

0.80

1.00

Vo/Vd

0.0 0.20 0.40 0.60 0.80Io

0.20

0.30

0.40

0.50

0.60

0.70

0.80

Vo/Vd

Io Io

與計算結果有差異 !!!

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作業

• 完成 Duty=0.1, 0.3, 0.5, 0.7, 0.9 之特性曲線• 用Matlab將曲線繪出在同一張圖上• 將 Psim所得之圖與Matlab計算之圖做比較，並分析可能不相等原因 ?

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Step-Down DC-DC Converter: Limits of Cont./Discont. Conduction

CCM

DV

V

d

o

DCM

BCM

(a)

(b)

(c)

combine (a) and (b) ,we can plot (c)

max

2

2

41

LB

od

o

II

D

D

V

V

)1(2

DDL

VTI dsLB )1(4 max, DDII LBLB

CCMDCM

Boundary Curve

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Mathcad Code

Static Characteristics:

I 0 0.05 2

Duty 0 0.01 1

Iob_IlbmaxDuty( ) 4 Duty 1 Duty( )

D1 0.1

Vo1 D1 I( ) VinD1

2

D12 I

4

I 4 D1 1 D1( )if

Vin D1 otherwise

D3 0.3

Vo3 D3 I( ) VinD3

2

D32 I

4

I 4 D3 1 D3( )if

Vin D3 otherwise

D5 0.5

Vo5 D5 I( ) VinD5

2

D52 I

4

I 4 D5 1 D5( )if

Vin D5 otherwise

D7 0.7

Vo7 D7 I( ) VinD7

2

D72 I

4

I 4 D7 1 D7( )if

Vin D7 otherwise

D9 0.9

Vo9 D9 I( ) VinD9

2

D92 I

4

I 4 D9 1 D9( )if

Vin D9 otherwise

D10 1.0

Vo10 D10 I( ) VinD10

2

D102 I

4

I 4 D10 1 D10( )if

Vin D10 otherwise

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Static Curve for Buck converter

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Io/ILB,max

Vo/

Vd

Duty

Vo1 D1 I( )

Vin

Vo3 D3 I( )

Vin

Vo5 D5 I( )

Vin

Vo7 D7 I( )

Vin

Vo9 D9 I( )

Vin

Vo10 D10 I( )

Vin

Iob_Ilbmax Duty( ) I

Vd=ConstantD=1.0

D=0.9

CCM

D=0.7

D=0.5

DCM

D=0.3

D=0.1

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Bode plot

H s( )10

s 10

Min 1

Max 100

n 50

j 0 n

j( )Max

Min

j

n

Mag j( ) H j( ) i( )

j( ) arg H j( ) i( )( )360

2

Phase j( ) j( )

1 10 1000.01

0.1

1

1010

0.01

Mag j( )

1001 j( )

1 10 100100

80

60

40

20

05.711

84.289

Phase j( )

1001 j( )

11/132

參考書目

12/132

REFERENCES

• [1] M.Sanz, A.Lazaro‚ “Improvement of Power Electronics Education with an Interactive Electronic Book based on MathCAD‚” IEEE Power Electronics Education‚ 2005.

• [2] Cristian Domnisoru‚ “Using MATHCAD in Teaching Power Engineering‚” IEEE trans On Education‚ VOL. 48‚NO.1‚ FEBRUARY 2005.

• [3] R. W. Larsen‚ “Introduction to MATHCAD‚” Englewood Cliffs‚ NJ: Prentice-Hall‚ 1999.

• [4] Mathcad User’s Guide‚ MathSoft‚ Cambridge‚MA‚ 2001.

• [5] Alan Felzer, “Introduction to MathCAD,” 2003

• [6] ST AN1089 Application Note

• [7] Lai, J.-S.; Chen, D.‚ “Design consideration for power factor correction boost converter operating at the boundary of continuous conduction mode and discontinuous conduction mode.” in Proc. IEEE Appl. Power Electron. Conf, 7-11, Mar. 1993. pp.267 – 273