Figure 10. Switching regulator control loop simplified model

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 feed-forward which generates a sawtooth with amplitude VS directly

proportional to the input voltage.

GPWO=VINVS= 1kFF=30

(14)

The synchronization of the device with an external clock provided through the SYNCH pin can modify the PWM

modulator gain (see Section 5.1 Oscillator and synchronization to understand how this gain changes and how to

keep it constant in spite of the external synchronization).

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

GLC(s)= R0//RES+ 1sC0

R0//RES+ 1sC0 +sL+RDC

=

R0⋅ 1+sC0RES

s2LC0⋅ R0+RES +s(L+C0R0RDC+C0RESRDC+C0RESR0)+RDC+R0

(15)

given L, RDC, C0, RES and R0

the parameters shown in Figure 10. Switching regulator control loop simplified model. The power section transfer

function can be rewritten as follows:

GLC(s)=GLC0⋅ 1+ s2π⋅fzESR

1+ s2π⋅Q⋅fLC+ s2π⋅fLC2;GLC0= R0R0+RDC≅1

(16)

fzESR= 12π⋅C0RES;fLC= 1

2π LC0 R0+RES

R0+RDC≅

1

2π LC0 R0+RESR0

(17)

Q= LC0⋅ R0+RDC⋅ R0+RES

L+C0⋅ R0RDC+R0RES+RESRDC ≅ LC0⋅ R0⋅(R0+RES)

L+C0R0RES

(18)

with the assumption that the inductor parasitic resistance, RDC, is negligible compared to RO. The closed loop

gain is then given by:

GLOOP(s)=GLC(s)⋅GPWO(s)⋅GCOMP(s)

(19)

A7987

Compensation network

DS12928 - Rev 3

page 17/36