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IXTP220N04T2

DC to DC Synchronous Converter Design

IXYS CORPORATION 

DC to DC Synchronous Converter Design

Abdus Sattar, IXYS Corporation

IXAN0068

period when I L1(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,

VL

=

L1 di

dt

= Vin − Vo ,

or,

Δi

=

ΔI L1 (t)

=

Δt(Vin − Vo)

L1

,

here,

Δt

= Ton

=

DTs

The inductor ripple current is,

ΔI

L1

(t

)

=

DTs

Vin − Vo

L1

=

D(Vin − Vo)

f S • L1

(1)

The charge, ΔQ , indicated in Figure 5, can be determined by calculating the area of the

triangle with height ΔI L1 (t) and width Ts shown in Figure 5.

2

2

ΔQ = 1 • ΔI L1 (t) • TS = ΔI L1 (t) •T S = ΔI L1 (t)

22 2

8

8 fS

The ripple voltage is,

ΔVL (t) =

ΔQ

C1

=

ΔI L1 (t)Ts

8C1

=

D(1 − D)VinTs 2

8L1C1

=

π 2 (1 − D)Vo (

2

fC )2

fS

= ΔVO (t)

(2)

Where, fC = 2π

1 , Output low pass filter (LPF) resonant frequency,

L1C1

f S = The

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 m Ω. .

Summary of design equations:

Ripples voltage/current, Inductor and Capacitor:

Output

ripple

voltage,

ΔVL (t)

=

ΔI L1 (t)Ts

8C1

=

ΔI L1 (t)

8C1 f S

(3)

Inductor ripple current, ΔI L1 (t) = 8C1 f S • ΔVL (t)

(4)

Output inductor, L1 ≥ DTs Vin − Vo = D(Vin − Vo)

(5)

ΔI L1 (t) f S • ΔI L1 (t)

Output capacitor, C1 ≥ ΔI L1 since ΔQ = 1 • ΔI L1 (t) • Ts = C1• ΔVo (6)

8 f s ΔVo

22 2

Output filter cut-off frequency,

fC = 2π

1

L1C1

(7)

4

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