Dynamics of a Zeta Converter (3/3)

Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

Previous Chapter

Dynamics of a Zeta Converter (2/3)

Verification of Obtained Results

22 1. EXTRACTION OF SMALL-SIGNAL TRANSFER FUNCTIONS

diL1_dt_MOSFET_open );

averaged_diL2_dt =simplify(d*diL2_dt_MOSFET_close +(1-d)*

diL2_dt_MOSFET_open );

averaged_dvC1_dt =simplify(d*dvC1_dt_MOSFET_close +(1-d)*

dvC1_dt_MOSFET_open );

averaged_dvC2_dt =simplify(d*dvC2_dt_MOSFET_close +(1-d)*

dvC2_dt_MOSFET_open );

averaged_vo =simplify(d*vo_MOSFET_close +(1-d)* vo_MOSFET_open);

%Substituting the steady values of input

%DC voltage source , Diode voltage drop ,

%Duty cycle and output current source

%and calculating the DC operating point

right_side_of_averaged_diL1_dt =subs(averaged_diL1_dt ,

[vg vD d io],[VG VD D IO ]);

right_side_of_averaged_diL2_dt =subs(averaged_diL2_dt ,

[vg vD d io],[VG VD D IO ]);

right_side_of_averaged_dvC1_dt =subs(averaged_dvC1_dt ,

[vg vD d io],[VG VD D IO ]);

right_side_of_averaged_dvC2_dt =subs(averaged_dvC2_dt ,

[vg vD d io],[VG VD D IO ]);

DC_OPERATING_POINT =

solve(right_side_of_averaged_diL1_dt ==0,

right_side_of_averaged_diL2_dt ==0,

right_side_of_averaged_dvC1_dt ==0,

right_side_of_averaged_dvC2_dt ==0,'iL1','iL2 ','vC1 ','vC2 ');

IL1=eval(DC_OPERATING_POINT .iL1);

IL2=eval(DC_OPERATING_POINT .iL2);

VC1=eval(DC_OPERATING_POINT .vC1);

VC2=eval(DC_OPERATING_POINT .vC2);

VO=eval(subs( averaged_vo ,[iL1 iL2 vC1 vC2 io],

[IL1 IL2 VC1 VC2 IO]));

disp('Operating point of converter ')

disp('----------------------------')

disp('IL1(A)=')

disp(IL1)

1.4. DYNAMICS OF CCM CONVERTERS 23

disp('IL2(A)=')

disp(IL2)

disp('VC1(V)=')

disp(VC1)

disp('VC2(V)=')

disp(VC2)

disp('VO(V)=')

disp(VO)

disp('----------------------------')

%Linearizing the averaged equations around

%the DC operating point . We want to obtain

%the matrix A, B, C, and D.

% x=Ax+Bu

% y=Cx+Du

%

%where ,

% x=[ iL1 iL2 vC1 vC2 ]'

% u=[ io vg d]'

%Since we used the variables D for steady

%state duty ratio and C to show the capacitors

%values we use AA , BB, CC, and DD instead of A,

%B, C and D.

%Calculating the matrix A

A11=subs(simplify(diff(averaged_diL1_dt ,iL1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A12=subs(simplify(diff(averaged_diL1_dt ,iL2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A13=subs(simplify(diff(averaged_diL1_dt ,vC1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A14=subs(simplify(diff(averaged_diL1_dt ,vC2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A21=subs(simplify(diff(averaged_diL2_dt ,iL1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A22=subs(simplify(diff(averaged_diL2_dt ,iL2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A23=subs(simplify(diff(averaged_diL2_dt ,vC1)),

24 1. EXTRACTION OF SMALL-SIGNAL TRANSFER FUNCTIONS

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A24=subs(simplify(diff(averaged_diL2_dt ,vC2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A31=subs(simplify(diff(averaged_dvC1_dt ,iL1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A32=subs(simplify(diff(averaged_dvC1_dt ,iL2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A33=subs(simplify(diff(averaged_dvC1_dt ,vC1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A34=subs(simplify(diff(averaged_dvC1_dt ,vC2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A41=subs(simplify(diff(averaged_dvC2_dt ,iL1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A42=subs(simplify(diff(averaged_dvC2_dt ,iL2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A43=subs(simplify(diff(averaged_dvC2_dt ,vC1)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

A44=subs(simplify(diff(averaged_dvC2_dt ,vC2)),

[iL1 iL2 vC1 vC2 d io],[IL1 IL2 VC1 VC2 D IO]);

AA=eval ([ A11 A12 A13 A14;

A21 A22 A23 A24;

A31 A32 A33 A34;

A41 A42 A43 A44]);

%Calculating the matrix B

B11=subs(simplify(diff(averaged_diL1_dt ,io)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B12=subs(simplify(diff(averaged_diL1_dt ,vg)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B13=subs(simplify(diff(averaged_diL1_dt ,d)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B21=subs(simplify(diff(averaged_diL2_dt ,io)),

1.4. DYNAMICS OF CCM CONVERTERS 25

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B22=subs(simplify(diff(averaged_diL2_dt ,vg)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B23=subs(simplify(diff(averaged_diL2_dt ,d)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B31=subs(simplify(diff(averaged_dvC1_dt ,io)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B32=subs(simplify(diff(averaged_dvC1_dt ,vg)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B33=subs(simplify(diff(averaged_dvC1_dt ,d)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B41=subs(simplify(diff(averaged_dvC2_dt ,io)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B42=subs(simplify(diff(averaged_dvC2_dt ,vg)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

B43=subs(simplify(diff(averaged_dvC2_dt ,d)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

BB=eval ([ B11 B12 B13;

B21 B22 B23;

B31 B32 B33;

B41 B42 B43]);

%Calculating the matrix C

C11=subs(simplify(diff(averaged_vo ,iL1)),

[iL1 iL2 vC1 vC2 d io],

[IL1 IL2 VC1 VC2 D IO]);

C12=subs(simplify(diff(averaged_vo ,iL2)),

26 1. EXTRACTION OF SMALL-SIGNAL TRANSFER FUNCTIONS

[iL1 iL2 vC1 vC2 d io],

[IL1 IL2 VC1 VC2 D IO]);

C13=subs(simplify(diff(averaged_vo ,vC1)),

[iL1 iL2 vC1 vC2 d io],

[IL1 IL2 VC1 VC2 D IO]);

C14=subs(simplify(diff(averaged_vo ,vC2)),

[iL1 iL2 vC1 vC2 d io],

[IL1 IL2 VC1 VC2 D IO]);

CC=eval ([ C11 C12 C13 C14 ]);

D11=subs(simplify(diff(averaged_vo ,io)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

D12=subs(simplify(diff(averaged_vo ,vg)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

D13=subs(simplify(diff(averaged_vo ,d)),

[iL1 iL2 vC1 vC2 d vD io vg],

[IL1 IL2 VC1 VC2 D VD IO VG]);

%Calculating the matrix D

DD=eval ([ D11 D12 D13 ]);

%Producing the State Space Model and obtaining

%the small signal transfer functions

sys=ss(AA ,BB ,CC ,DD);

sys.inputname={'io';'vg';'d'};

sys.outputname ={ 'vo '};

vo_io=tf(sys (1,1)); %Output impedance transfer

%function vo(s)/io(s)

vo_vg=tf(sys (1,2)); %vo(s)/vg(s)

vo_d=tf(sys (1,3)); %Control -to - output(vo(s)/d(s))

%drawing the Bode diagrams

figure (1)

bode(vo_io),grid minor ,title('vo(s)/io(s)')

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

3.149.213.209