Buck Boost

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6. Buck-boost Converter Circuit and its parameters:
Q1 Diode out Dideal L
VI

MOSFET V1 12Vdc pulse

100uH IC = 0 V2

R1

PARAMETERS:
Fs = 100k D = 0.6

C 200u IC = 0

3

TD = 0 TF = 10n PW = {D/Fs} PER = {1/Fs} V1 = 0 TR = 10n V2 = 15

0

V+

Basic Formula: Vo D = Vg 1 − D Pspice Simulation: Io = ID = Vo R I D = (1 − D) I L I g = I s = DI L

vout iL

Calculation:
Circuit Parameters: Vg := 12 Vo := 18 L := 100 ⋅ 10
−6

C := 200 ⋅ 10

−6

f := 100 ⋅ 10 D := 0.5

3

R := 3

Initial guess Given Vo Vg D 1−D D := Find( D) D = 0.6

VL( t) :=

(Vg) if 0 < t < D ⋅ T (−Vo) otherwise
1 ∆iL := ⋅ Vg ⋅ D ⋅ T L ∆iL = 0.72

T :=

1 f

Vo Io := R

Io = 6

Io IL := 1−D iLmin = 14.64 iLmax = 15.36

IL = 15

∆iL iLmin := IL − 2 ∆iL iLmax:= IL + 2

The waveforms are a piecewise linear. Collect numbers for plotting.

 0    D⋅ T t := D⋅ T  T   

 Vg     Vg  VL :=    −Vo   −V   o

 iLmin     iLmax iL :=    iLmax i   Lmin 

 iLmin     iLmax is :=  0     0 

 0   0  iD := i  Lmax i  Lmin 

 −Io     −Io  ic :=    iLmax − Io  i   Lmin − Io 

icmax := iLmax − Io

icmax = 9.36

20 13.33 VL 6.67 0

Inductor Voltage
15.5 iL 5 .10
6

Inductor Current

15.25 15 14.75 14.5 0 2.5 .10
6

6.67 13.33 20

1 .10

5

5 .10

6

t

7.5 .10

6

1 .10

5

t

20 15 is 10 5 0

Switch current

20 15 iD 10 5

Diode current

5 .10

6

t

1 .10

5

0

5 .10

6

t

1 .10

5

Is := D ⋅ IL

Is = 9

ID := ( 1 − D) ⋅ IL

ID = 6

10 6.67 ic 3.33 3.33 0 6.67 10

Capacitor current

∆v o :=
5 .10
6

1 C

⋅ Io ⋅ D ⋅ T

∆v o = 0.18

1 .10

5

t

Ig := Is

Ig = 9

Vg = 12 Pg = 108

Io = 6 Po := Vo ⋅ Io

Vo = 18 Po = 108

Pg := Vg ⋅ Ig

Due to ideal components (switch, diode, L and C) that we assume, the circuit is lossless, the efficiency is 100% and as such Pg = Po.

DCM/CCM Boundary Case I: L, f, and other parameters are kept constant, R is varied iLmin := 0 iLmax:= ∆iL

 iLmin    ∆iL  iLmax IL := 2 iL1 :=   iLmax Vo   i  R := Io  Lmin 

IL = 0.36 R = 125

Io := ( 1 − D) ⋅ IL

Io = 0.144

Case II: R, f, and other circuit parameters are kept constant, L is varied R := 3 Vo Io := R Io IL := 1−D iLmax = 30

Io = 6

IL = 15 ∆iL := iLmax iLmax = 30

iLmin := 0

iLmax:= 2 ⋅ IL

 iLmin     iLmax iL2 :=    iLmax i   Lmin 

∆iL = 30 ∆iL 1 L ⋅ Vg ⋅ D ⋅ T Lmin := 1 ∆iL ⋅ Vg ⋅ D ⋅ T Lmin = 2.4 × 10 −6

Case III: R, L, and other circuit parameters are kept constant, f is varied Vo Io := R Io IL := 1−D

R := 3

Io = 6

IL = 15

iLmin := 0

iLmax:= 2 ⋅ IL

iLmax = 30

∆iL := iLmax

iLmax = 30

∆iL = 30 ∆iL 1 L ⋅ Vg ⋅ D ⋅ 1 f fmin := 1 ∆iL ⋅ Vg ⋅ D ⋅ 1 L fmin = 2.4 × 10 3

Collect numbers for plotting

     t1 :=     

  D  fmin  D   fmin  1   fmin  0

 iLmin     iLmax iL3 :=    iLmax i   Lmin  1 fmin

 15     15  IL3 :=  15   15   

IL2 := IL3

 0.36     0.36  IL1 :=  0.36   0.36   

Tmax :=

Tmax = 4.167 × 10

−4

Waveforms for iL and IL: Case I
iL2 IL2

1 iL1 0.75 IL1 0.5 0.25 0 0

40 30 20 10

Case II

5 .10

6

t

1 .10

5

0 0

5 .10

6

t

1 .10

5

40 iL3 IL3 20

Case III

0 0

2 .10

4

4 .10 t1

4

6 .10

4

-tammat-

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