Closing the loop

AN1330

14/31

Equation 7

The zero of this transfer function is given by:

Equation 8

increase the phase margin of the loop.

The poles of the transfer function can be calculated through the following expression:

Equation 9

Equation 10

If the damping coefficient

δ is very close to zero, the roots of the equation become a double

root whose value is

Equation 11

4.3

PWM comparator

The PWM gain is given by the following formula:

Equation 12

minimum value. A voltage feed forward is implemented to ensure a constant GPWM. This is

Equation 13

Where K is equal to 0.076. Therefore the PWM gain is also equal to:

Equation 14

A

()

1

ESR

C

OUT

•

s

•

+

LC

OUT

•

s

2

ESR

C

OUT

•

s1

+

•

+

•

----------------------------------------------------------------------------------------------

=

F

O

1

2

π

•

ESR

•

C

OUT

•

----------------------------------------------------

=

F

PLC1 2

,

ESR

C

OUT

ESR

C

OUT

•

()

2

4L

•

C

OUT

•

–

±

•

–

2L

•

C

OUT

•

------------------------------------------------------------------------------------------------------------------------------------------

=

s

2

2

δ

•ω

n

•

s

ω

2

n

+

•

+

F

PLC

1

2

π

•

LC

OUT

•

•

----------------------------------------------

=

G

()

V

cc

V

OSCMAX

V

OSCMIN

–

()

-------------------------------------------------------------

=

V

OSCMAX

V

OSCMIN

–

KV

CC

•

=

G

()

1

K

----

const

==