9

 2005 Semtech Corp.

www.semtech.com

SC4809A/B/C

POWER MANAGEMENT

Control-to-Output transfer function for the flyback power

stage operating in CCM is given by:

2

O

2

O

2

z

1

z

P

S

2

I

O

S

Q

S

1

S

1

S

1

N

N

)

D

1

(

V

dD

dV

ω

+

•

ω

+









ω

−

•









ω

+

•

•

−

=

where:

C

L

R

x

)

D

1

(

Q

C

L

D

1

L

D

R

)

D

1

(

C

R

1

1

z

SEC

SEC

O

SEC

2

2

z

C

−

≈

•

−

≈

ω

•

•

−

≈

ω

•

=

ω

Control-to Output transfer function for the flyback power

stage operating in DCM is given by:

P

SEC

S

P

S

I

O

S

1

1

L

2

T

R

N

N

V

dD

dV

ω

+

•

•

•

•

•

=

where:

C

R

2

P

•

=

ω

Peak current mode control requires simpler

compensation, has pulse-by-pulse current limiting, and

has better load current regulation. Primary and secondary

RMS currents can be up to two times higher for

discontinuous mode than for CCM. Discontinuous

conduction mode would require using a transistor with a

higher current rating. Because the output ripple current

is less than it would be continuous mode were used, the

output capacitors are smaller. Continuous conduction

mode (CCM) was therefore chosen.

Application Information (Cont.)

The DC transfer function of a CCM flyback converter is:









−

•

=

−

+

max

max

)

on

(

Rds

(min)

IN

D

O

D

1

D

N

1

V

V

V

V

where V

V

N = turns ratio, equal to N

D = duty cycle.

Transformer Design

The transformer in a flyback converter is actually a coupled

inductor with multiple windings. Transformers provide

coupling and isolation whereas inductors provide energy

storage. The energy stored in the air gap of the inductor

is equal to:

()

2

I

L

E

2

PEAK

=

where E is in Joules, L

Henries, and I

When the switch is on, D1 is reverse biased due to the

dot configuration of the transformer. No current flows in

the secondary windings and the current in the primary

winding ramps up at a rate of:

P

)

on

(

Rds

(min)

IN

L

L

V

V

t

I

−

=

∆

∆

The output capacitor, C

at this time. Because the converter is operating in the

continuous conduction mode,

∆I

inductor current which appears as a positive slope ramp

on a step. The step is present because there is still

current left in the secondary windings when the primary

turns on. When the switch turns off, current flows through

the secondary winding and D1 as a negative ramp on a

step, replenishing C

the load.