7

Closing the loop

7.1

Total transfer function

The compensation network assures stability and good dynamic performance over the application conditions.

The loop of the L3751 is based on the voltage mode control. The embedded wide bandwidth operational amplifier

can be considered ideal in the calculation of the compensator since its frequency response is much larger than

designed system bandwidth.

Figure 23. Voltage mode control loop

VS

PWM

EA

VIN

L

CO

RES

RO

RDC

ZF

ZS

RU

RD

COMP

VREF

Power

section

Compensation

network

switch

HS

switch

LS

The transfer function of the PWM modulator, from the error amplifier output (COMP pin) to the LX pin results in an

almost constant gain, due to the voltage feedforward which generates a sawtooth with amplitude VS directly

proportional to the input voltage.

GPWM0=VINVS= 1KFF=15

(8)

The transfer function of the power section (i.e. the L-C filters and the output load) is:

GLC s = RO∥ RO+1s∙CO

RO∥ RO+1s∙CO +s∙CO+RDC

(9)

given L, RDC, C0, RES and R0 as defined in Figure 10.

For convenience, the GLC can be written as:

GLC s =GLC0∙ 1+ s2π∙fZESR

1+ s2π∙Q∙fLC+ s2π∙fLC2wℎereGLC0= RORO+RDC≈1

(10)

fZESR= 1

2π∙CO∙RES             fLC= 1

2π∙ L∙CO∙ RO+RES

RO+RDC≈ 12π∙L∙CO

(11)

Q= L∙CO∙ RO+RDC RO+RES

L+CO∙ RO∙RDC+RO∙RES+RES∙RDC ≈ L∙CO∙ROL= COL∙RO

(12)

assuming the inductor and output capacitor parasitic resistance, RDC and RES, negligible compared to RO.

The total closed loop gain is:

L3751

Closing the loop

DS13841 - Rev 1

page 23/41