Datasheet

DocID024275 Rev 2 17/29
AN4260 Feedback loop calculation guidelines
7 Feedback loop calculation guidelines
7.1 Transfer function
The set PWM modulator + power stage is indicated with G1(f), while C(f) is the "controller",
the network in charge to ensure the stability of the system.
Figure 31. Control loop block diagram
The mathematical expression of the power plant G1(f) in DCM is the following:
Equation 2
where fz is the zero due to the ESR of the output capacitor:
Equation 3
and fp is the pole due to the output load
Equation 4
with:
C(f)
G1(f)
COMP
∆δ
1/H
V
∆
OUT
V
∆
COMP
V
∆
∆δ
COMP
∆δ
OUT
V
∆
∆
OUT
V
AM16666v1
G1 f()
V
OUT
Δ
∂Δ
--------------- G10
1
jf⋅
fz
-------+
1
jf⋅
fp
-------+
-----------------⋅==
fz
1
2 π C
OUT
ESR⋅⋅ ⋅
---------------------------------------------=
fp
1 β R
OUT
⋅+
2 π C
OUT
ESR R
OUT
ESR β R
OUT
⋅⋅++()⋅⋅ ⋅
----------------------------------------------------------------------------------------------------------------=