DC to DC Synchronous Converter Design
Abdus Sattar, IXYS Corporation
IXAN0068
period when IL1 (t) is greater than Io. The charge (ΔQ ) that flows into C1 at this time
divided by the value of C1 is the output voltage ripple component.
Output Inductor Ripple Current and Voltage:
The inductor voltage can be defined as,
di
Δt(Vin −Vo)
L1
VL = L1 = Vin −Vo , or, Δi = ΔIL1 (t) =
, here, Δt = Ton = DTs
dt
The inductor ripple current is,
Vin −Vo D(Vin −Vo)
ΔIL1 (t) = DTs
=
(1)
L1
fS • L1
The charge, ΔQ , indicated in Figure 5, can be determined by calculating the area of the
ΔIL1 (t)
Ts
triangle with height
and width
shown in Figure 5.
2
2
ΔIL1 (t) TS ΔIL1 (t) •T S ΔIL1 (t)
1
2
ΔQ =
•
•
=
=
2
2
8
8 fS
The ripple voltage is,
ΔQ
C1
D(1− D)VinTs2 π 2 (1− D)Vo
ΔIL1 (t)Ts
f
ΔVL (t) =
=
=
=
(
C )2 = ΔVO (t)
(2)
8C1
8L1C1
2
fS
1
Where, fC =
, Output low pass filter (LPF) resonant frequency, fS = The
2π L1C1
switching frequency. The inductor value of L1 and the effective series resistance (ESR)
of the output capacitor, C1, affect the output ripple voltage, ΔVL . A capacitor with the
lowest possible ESR is recommended for the application. For example, 4.7–10 uF
capacitors in X5R/X7R technology have ESR approximately 10 mΩ..
Summary of design equations:
Ripples voltage/current, Inductor and Capacitor:
ΔIL1 (t)Ts ΔIL1 (t)
Output ripple voltage, ΔVL (t) =
=
(3)
8C1
8C1fS
Inductor ripple current, ΔIL1 (t) = 8C1fS • ΔVL (t)
Vin −Vo D(Vin −Vo)
(4)
(5)
Output inductor, L1 ≥ DTs
=
ΔIL1 (t)
fS • ΔIL1 (t)
ΔIL1
8 fs ΔVo
ΔIL1 (t)
1
Ts
Output capacitor, C1 ≥
since ΔQ = •
•
= C1• ΔVo (6)
2
2
2
1
Output filter cut-off frequency, fC =
(7)
2π L1C1
4