L6981 datasheet(21/49 Pages) STMICROELECTRONICS

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Closing the loop

The following image shows the typical compensation network required to stabilize the system.

Figure 23. Block diagram of the loop

7.1

GCO(s) control to output transfer function

The accurate control to output transfer function for a buck peak current mode converter can be written as:

GCOs =RLOAD∙gCS∙

1+RLOAD∙TSW

L ∙ mC∙ 1−D −0.5 ∙

1+ sωZ

1+ sωP ∙FH s

(7)

Where RLOAD represents the load resistance, gCS the equivalent sensing trans-conductance of the current sense

circuitry, ωP the single pole introduced by the power stage and ωZ the zero given by the ESR of the output

capacitor. FH (s) accounts the sampling effect performed by the PWM comparator on the output of the error

amplifier that introduces a double pole at one half of the switching frequency.

ωZ= 1ESR∙COUT

(8)

ωP= 1

RLOAD∙COUT+mC∙ 1−D −0.5

L∙COUT∙fSW

(9)

Where:

mC=1+SeSn

Se=ISLOPE∙fSW

Sn=VIN−VOUT

(10)

Where ISLOPE is equal to 1 A.

Sn represents the ON time slope of the sensed inductor current, Se the ON time slope of the external ramp that

implements the slope compensation to avoid sub-harmonic oscillations at duty cycle over 50 %.

The sampling effect contribution FH (s) is:

L6981

Closing the loop

DS13554 - Rev 1

page 21/49

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