Datasheet

Feedback loop calculation guidelines AN4165
24/37 Doc ID 023661 Rev 1
11 Feedback loop calculation guidelines
11.1 Transfer function
The set PWM modulator + power stage is indicated with G
1
(f), while C(f) is the “controller”,
i.e. the network which is in charge of ensuring the stability of the system.
Figure 34. Control loop block diagram
The mathematical expression of the power plant G
1
(f) is the following:
Equation 2
where V
OUT
is the output voltage, Ipkp is the primary peak current, fp is the frequency of the
pole due to the output load:
Equation 3
and fz the frequency of the zero due to the ESR of the output capacitor:
Equation 4
AM11582v1
)
fp
j
(1),(
)
fz
(1V
)
p
2j
(1),(
)
z
2
(1V
=
I
V
(f)G
OUTOU T
pk
OUT
1
f
VdcfswIpkp
fj
f
VdcfswIpkp
fj
⋅
+⋅
⋅
+⋅
=
⋅⋅⋅
+⋅
⋅⋅⋅
+⋅
Δ
Δ
=
π
π
2ESR)+·(RC
1
fp
OUTOUT
⋅
=
π
·ESRC2
1
fz
OU T
⋅⋅
=
π