R5973D datasheet(18/39 Pages) STMICROELECTRONICS

18 / 39 page

Closing the loop

R5973D

18/39

DocID026876 Rev 1

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 L-C filter (see below). FP2 is usually at a very high

frequency.

7.2

LC filter

The transfer function of the L-C 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

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

root whose value is

n.

FZ1





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

ALC s



RLOAD 1 ESR COUT s







LCOUT ESR RLOAD

 s

ESR COUT



RLOAD L



 R

LOAD



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

ALC s



1 ESR COUT



LCOUT



ESR COUT



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





ESR



COUT



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

FPLC1 2



ESR COUT







COUT



–





–



COUT



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











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