A5974AD

Closing the loop

Doc ID 018762 Rev 1

21/49

whereas the zero is defined as:

Equation 5

frequency.

7.2

LC filter

The transfer function of the LC filter is given by:

Equation 6

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

ω

Equation 11

F

Z1

1

2

π R

c

C

c

⋅⋅

⋅

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

=

A

()

R

LOAD

1ESR C

OUT

s

⋅⋅

+

()

⋅

s

2

LC

OUT

ESR

R

LOAD

+

() sESR C

OUT

R

LOAD

L

+

⋅⋅

() R

LOAD

+

⋅

+

⋅⋅

⋅

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

=

A

()

1ESR 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

⋅⋅

()

–

±

⋅

–

2LC

OUT

⋅⋅

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

=

s

2

2

δω

n

s

ω

2

n

+

⋅⋅

⋅

+

F

PLC

1

2

π

⋅

LC

OUT

⋅

•

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

=