### Isolated DC-DC converter - SMPS

```SMPS - Switch Mode Power Supply
DC Power Supply
INTRODUCTION
• Previous DC-DC converters (Buck, Boost, Buck-Boost) do not provide electrical
isolation between input and output - these are non-isolated DC-DC converters
• In most applications, isolation is required and this can be provided by
transformers
One possible solution:
AC, 50hz supply
Controls
DC-DC
Converters
(non-isolated)
PROBLEMS:
Transformer operated at 50Hz frequency require large
magnetic core – bulky, heavy and expensive !
SOLUTIONS:
Use transformer at switching frequency – smaller core size
Turns-ratio provides flexibility to the design
Can provide multiple outputs
Typical SMPS block diagram:
Typical SMPS block diagram:
TRANSFORMER MODEL
For SEE 4433 simplified model of transformer will be used to describe the
circuit operation of SMPS
I1
I2
+
V1
+
V2


V1 I 2 N1
= =
V2 I1 N 2
Simplified model: no leakage and
winding resistances
Lm
R1
Ideal model,
Ll1
Ll2
Rc
Lm
✔
✔
R2
Detailed model: leakage
inductances, winding
resistances, magnetizing
inductance, losses
FLY-BACK
•
•
Derived from Buck-Boost
converter
Isolation provided by high
frequency transformer
FLY-BACK
Derivation of output voltage , Vo
(ΔiL)closed + (ΔiL)open=0
OR
Inductor volt-second balanced
(Average inductor voltage = 0)
FLY-BACK
Derivation of output voltage , Vo
Switch CLOSED (ON)
( DiLm )closed =
Vs DT
Lm
vLm = Vs
Switch OPEN (OFF)
-Vo (1- D)T æ N1 ö
ç ÷
( DiLm )open =
Lm
è N2 ø
æN ö
vLm = -Vo ç 1 ÷
è N2 ø
FLY-BACK
Derivation of output voltage , Vo
Switch CLOSED (ON)
( DiLm )closed
V DT
= s
Lm
vLm = Vs
(ΔiL)closed + (ΔiL)open=0
Vs DT -Vo (1- D)T æ N1 ö
+
ç ÷=0
Lm
Lm
è N2 ø
æ D öæ N 2 ö
Vo = Vs ç
÷ç ÷
è 1- D øè N1 ø
Switch OPEN (OFF)
-Vo (1- D)T æ N1 ö
ç ÷
( DiLm )open =
Lm
è N2 ø
æN ö
vLm = -Vo ç 1 ÷
è N2 ø
Inductor volt-second balanced
(Average inductor voltage = 0)
æN ö
(DT )Vs -Vo ç 1 ÷ (1- D)T = 0
è N2 ø
æ D öæ N 2 ö
Vo = Vs ç
÷ç ÷
è 1- D øè N1 ø
FLY-BACK
Waveforms for Fly-back Converter
Closed
Open
FLY-BACK
Minimum Lm for continuous current
Boundary condition when ILm,min = 0
It can be shown that:
FLY-BACK
Output voltage ripple
Derivation of output voltage ripple is similar to Buck-Boost converter
It can be shown that the ration of the ripple to the output voltage is
given by:
FULL-BRIDGE DC-DC CONVERTER
The switches are switched in a pair:
(SW1, SW2) and (SW3,SW4)
(SW1, SW2) closed:
(i) vp = Vs
(ii) D1 ON, D2 OFF
æN ö
(iii) vx = Vs ç s ÷
çN ÷
è pø
(SW3, SW4) closed:
(i) vp = -Vs
(ii) D1 OFF, D2 ON
æN ö
(iii) vx = Vs ç s ÷
çN ÷
è pø
FULL-BRIDGE DC-DC CONVERTER
Derivation of output voltage , Vo
Inductor volt-second balanced
(Average inductor voltage = 0)
æ æN ö
ö
çVs çç s ÷÷ -Vo ÷ DT -Vo ( 0.5 - D) T = 0
ç N
÷
è è pø
ø
æN ö
Vo = 2Vs çç s ÷÷ D
è Np ø
æN ö
Vs çç s ÷÷ -Vo
è Np ø
-Vo
vLx
iLx
FULL-BRIDGE DC-DC CONVERTER
Minimum Lx for continuous current
I Lx,max = I Lx +
I Lx,min = I Lx -
DiLx
2
DiLx
I Lx
2
æ Vo ö æ Vo ( 0.5 - D) T ö
I Lx,max = ç ÷ + ç
÷
èRø è
2Lx
ø
æ V ö æ V ( 0.5 - D) T ö
I Lx,max = ç o ÷ + ç o
÷
èRø è
2Lx
ø
Minimum Lx when ILx,min = 0
\Lx,min =
( 0.5 - D) R
2f
FULL-BRIDGE DC-DC CONVERTER
Output voltage ripple
iC
DQ = CDVo
DiLx
2
From the figure
æ T öæ 1 ö Vo ( 0.5 - D) T Vo ( 0.5 - D)
=
è 4 øè 2 ø
2Lx
16Lx f 2
DQ = ç ÷ç ÷
\
DVo
Vo
=
(0.5 - D)
16LxCf 2
=
Vo ( 0.5 - D) T
2Lx
HALF-BRIDGE DC-DC CONVERTER
Capacitors (C1 and C2) equally divide input
voltage, therafore Vs/2 appear across primary
when Sw1 closed and –Vs/2 when Sw2 closed.
Hence
æN ö
Vo = Vs çç s ÷÷ D
è Np ø
```