A5975AD datasheet(21/50 Pages) STMICROELECTRONICS

21 / 50 page

A5975AD

Closing the loop

Doc ID 018761 Rev 1

21/50

Equation 4

whereas the zero is defined as:

Equation 5

FP1 is the low frequency which sets the bandwidth, while the zero FZ1 is usually put near to

the frequency of the double pole of the LC filter (see below). FP2 is usually at a very high

frequency.

7.2

LC filter

The transfer function of the LC filter is given by:

Equation 6

where RLOAD is defined as the ratio between VOUT and IOUT.

If RLOAD>>ESR, the previous expression of ALC can be simplified and becomes:

Equation 7

The zero of this transfer function is given by:

Equation 8

F0 is the zero introduced by the ESR of the output capacitor and it is very important to

increase the phase margin of the loop.

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

Equation 9

In the denominator of ALC the typical second order system equation can be recognized:

Equation 10

If the damping coefficient

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

root whose value is

π R

()

⋅⋅

⋅

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

π R

⋅⋅

⋅

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

LC s

()

LOAD

1ESR C

OUT

⋅⋅

()

⋅

OUT

ESR

LOAD

() sESR C

OUT

LOAD

⋅⋅

() R

LOAD

⋅

⋅⋅

⋅

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

LC s

()

1ESR C

OUT

⋅⋅

OUT

ESR C

OUT

⋅⋅

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

π ESR C

OUT

⋅⋅

⋅

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

PLC1 2

ESR C

OUT

ESR C

OUT

⋅

()

4L C

OUT

⋅⋅

–

⋅

–

2LC

OUT

⋅⋅

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

δω

⋅⋅

⋅

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