DC to DC Synchronous Converter Design

Abdus Sattar, IXYS Corporation

IXAN0068

4

period when

)

(

I

L

Δ ) 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,

Vo

Vin

dt

di

L

V

L

−

=

= 1

, or,

1

)

(

)

(

1

L

Vo

Vin

t

t

I

i

L

−

Δ

=

Δ

=

Δ

, here,

DTs

Ton

t

=

=

Δ

The inductor ripple current is,

)

(

I

L

Δ

=

1

)

(

1

L

f

Vo

Vin

D

L

Vo

Vin

DTs

−

=

−

(1)

The charge, Q

Δ , indicated in Figure 5, can be determined by calculating the area of the

triangle with height

2

)

(

I

L

Δ

and width

2

Ts

shown in Figure 5.

S

L

S

L

S

L

f

t

I

T

t

I

T

t

I

Q

8

)

(

8

)

(

2

2

)

(

2

1

1

1

1

Δ

=

•

Δ

=

•

Δ

•

=

Δ

The ripple voltage is,

)

(

)

(

2

)

1

(

1

1

8

)

1

(

1

8

)

(

1

)

(

2

2

2

1

t

V

f

f

Vo

D

C

L

VinTs

D

D

C

Ts

t

I

C

Q

t

V

O

S

C

L

L

Δ

=

−

=

−

=

Δ

=

Δ

=

Δ

π

(2)

Where,

1

1

2

1

C

L

f

C

π

=

, Output low pass filter (LPF) resonant frequency,

=

S

f

The

switching frequency. The inductor value of L1 and the effective series resistance (ESR)

of the output capacitor, C1, affect the output ripple voltage,

L

V

lowest possible ESR is recommended for the application. For example, 4.7–10 uF

Summary of design equations:

Ripples voltage/current, Inductor and Capacitor:

Output ripple voltage,

S

L

L

L

f

C

t

I

C

Ts

t

I

t

V

1

8

)

(

1

8

)

(

)

(

1

1

Δ

=

Δ

=

Δ

(3)

Inductor ripple current,

)

(

1

8

)

(

1

t

V

f

C

t

I

L

S

L

Δ

•

=

Δ

(4)

Output inductor,

)

(

)

(

)

(

1

1

1

t

I

f

Vo

Vin

D

t

I

Vo

Vin

DTs

L

L

S

L

Δ

•

−

=

Δ

−

≥

(5)

Output capacitor,

Vo

f

I

C

s

L

Δ

Δ

≥

8

1

1

since

Vo

C

Ts

t

I

Q

L

Δ

•

=

•

Δ

•

=

Δ

1

2

2

)

(

2

1

1

(6)

Output filter cut-off frequency,

1

1

2

1

C

L

f

C

π

=

(7)