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AN4106 Datasheet(PDF) 25 Page - STMicroelectronics

Part # AN4106
Description  This document describes a 12 V-1 A power supply
PDF  39 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN4106 Datasheet(HTML) 25 Page - STMicroelectronics

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AN4106
Feedback loop calculation guidelines
Doc ID 023156 Rev 1
25/39
11
Feedback loop calculation guidelines
11.1
Transfer function
The set PWM modulator + power stage is indicated with G1(f), while C(f) is the “controller”,
i.e. the network which is in charge to ensure the stability of the system.
Figure 34.
Control loop block diagram
The mathematical expression of the power plant G1(f) is the following:
Equation 2
where VOUT 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
The mathematical expression of the compensator C(f) is:
AM11582v1
)
fp
j
(1
)
,
(
)
fz
(1
V
)
p
2
j
(1
)
,
(
)
z
2
(1
V
=
I
V
(f)
G
OUT
OUT
pk
OUT
1
f
Vdc
fsw
Ipkp
f
j
f
Vdc
fsw
Ipkp
f
j
⋅
+
⋅
⋅
+
⋅
=
⋅
⋅
⋅
+
⋅
⋅
⋅
⋅
+
⋅
Δ
Δ
=
π
π
2ESR)
+
·(R
C
1
fp
OUT
OUT
⋅
=
π
·ESR
C
2
1
fz
OUT
⋅
⋅
=
π



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