AN1723 datasheet(13/24 Pages) STMICROELECTRONICS

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AN1723

Closing the loop

Doc ID 9553 Rev 4

13/24

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 11

The zero of this transfer function is given by:

Equation 12

F0 is the zero introduced by the ESR of the output capacitor and 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 13

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

Equation 14

If the damping coefficient

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

root whose value is

ωn.

Similarly for ALC, the poles can usually be defined as a double pole whose value is:

Equation 15

5.3

PWM comparator

The PWM gain is given by the following formula:

Equation 16

where VOSCMAX is the maximum value of a sawtooth waveform, and VOSCMIN is the

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

obtained generating a sawtooth waveform directly proportional to the input voltage VCC.

()

ESR

OUT

⋅⋅

OUT

ESR

OUT

⋅⋅

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

ESR

OUT

⋅⋅

⋅

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

PLC1 2

ESR

OUT

ESR

OUT

⋅

()

OUT

⋅⋅

()

–

⋅

()

–

2LC

OUT

⋅⋅

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

δω

⋅⋅

⋅

PLC

OUT

⋅

⋅⋅

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

PWM

()

OSCMAX

OSCMIN

–

()

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

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