L6986H datasheet(35/68 Pages) STMICROELECTRONICS

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Closing the loop

Figure 35. Block diagram of the loop

5.1

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:

GCO(s)=RLOAD⋅gCS⋅

1+RLOAD⋅TSW

L ⋅[mC⋅(1−D)−0.5]⋅

1+ SωZ1+Sωp⋅FH(s)

(18)

where RLOAD represents the load resistance, gCS the equivalent sensing transconductance of the current sense

circuitry, wp the single pole introduced by the power stage and wz 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

(19)

ωp= 1

RLOAD⋅COUT+mc⋅(1−D)−0.5

L⋅COUT⋅fSW

(20)

where:

mC=1+SeSn

Se=VPP⋅gCS⋅fSW

Sn=VIN−VOUT

(21)

Sn represents the on time slope of the sensed inductor current, Se the on time slope of the external ramp (VPP

peak-to-peak amplitude) that implements the slope compensation to avoid sub-harmonic oscillations at duty cycle

over 50%.

Se can be calculated from the parameter VPP × gCS given in Table 1 .

L6986H

Closing the loop

DS12905 - Rev 2

page 35/68

L6986H 데이터시트(PDF) 35 Page - STMicroelectronics