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MIC2131 Datasheet(PDF) 16 Page - Micrel Semiconductor

Part # MIC2131
Description  High Voltage Synchronous Buck Control IC with Low EMI Option
PDF  20 Pages
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Manufacturer  MICREL [Micrel Semiconductor]
Direct Link  http://www.micrel.com
Logo MICREL - Micrel Semiconductor

MIC2131 Datasheet(HTML) 16 Page - Micrel Semiconductor

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Micrel, Inc.
MIC2130/1
April 2008
16
M9999-042108-C
Control Loop Stability and
Compensation
Figure 10 shows the simplified system schematic. The
internal transconductance error amplifier is used for
compensating the voltage feedback loop by placing a
capacitor (C1) in series with a resistor (R1) and another
capacitor C2 in parallel from the COMP pin-to-ground.
(Note: Ceramic output caps may require type III
compensation).
R1
C1
C2
gm
VREF
VFB
VCOMP
D (s)
VRAMP
RHS
RLS
VIN
VOUT
RESR
RLOAD
C
PWM
Comparator
L
VSW
Figure 10 Simplified System Schematic
In order to have a stable system when the gain of T(s) =
1
⇒ (0db) the phase has to be greater (less negative)
than -180°. The amount the phase is greater than -180°
is called the phase margin, typically 30 to 60 and is a
key parameter predicting the stability of the system and
how much overshoot and undershoot the system
exhibits during transients.
The open loop transfer function is:
T(s) = Gea(s) x GPWMcomp(s) x GPwrs(s) x Gflt(s) x Hfb(s)
And the phase is:
fb
Flt
PwrS
PWMcomp
ea
T
θ
θ
θ
θ
θ
(s)
θ
T(s)
+
+
+
+
=
=
∠
VREF
VFB
VOUT
Gea(s) =
gm ZCOMP
GPWMComp
GPWRS
GFLT
H(s)
VE
VCOMP
D (s)
VSW
T(s)
Figure 11 System Block Diagram
In the system block diagram in figure 11
Gea(s) = gm x Zcomp
Gain of the Error amp
where gm =1.5ms and
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
=
2
1
comp
sC
1
sC
1
R1
Z
0.85
1.1
2.1
0.85
∆V
D
∆V
∆D
(s)
G
ramp
Max
comp
PWMcomp
=
−
=
=
=
Gain of the PWM comparator
D
*
D
V
D
*
∆d(s)
V
∆d(s)
∆V
(s)
G
Max
Out
Out
SW
PwrS
=
=
=
Gain of the
Power Stage
2
0
2
0
out
esr
Flt
ω
s
Qω
s
1
C
sR
1
(s)
G
+
+
+
=
Gain of the Filter
where:
out
Load
Lost
stored
L/C
R
E
E
Q
=
=
(Parallel loaded)
and
out
0
LC
1
ω
=
out
esr
esr
C
R
2π
1
F
=
out
ref
HS
LS
LS
V
V
R
R
R
H(s)
=
+
=
Gain of the feedback
network
For simplicity, combine the PWM comparator gain and
the Power stage gain and call it the modulator gain.
D
*
∆V
V
D
*
D
V
*
∆V
D
(s)
G
*
(s)
G
(s)
G
ramp
out
Max
out
ramp
Max
PWRsw
PWMcomp
Mod
=
=
=
therefore;
T(s) = Gea(s) x GMod(s) x Gflt(s) x Hfb(s) and
fb
flt
Mod
ea
T
θ
θ
θ
θ
(s)
θ
+
+
+
=
The phase of the open loop is the phase of all the blocks
in the loop added together.
The phase of T(s) is
fb
Flt
PwrS
PWMcomp
ea
T
θ
θ
θ
θ
θ
(s)
θ
+
+
+
+
=
fb
Mod
ea
T
θ
θ
θ
(s)
θ
+
+
=
Where
pole1
Zero1
pole0
ea
θ
θ
θ
θ
−
+
−
=
pole0
θ
= phase lag due to the pole at the origin
Zero1
θ
=phase lead due to Zero1
pole1
θ
= phase lag due to pole1
°
= 0
θ
PWMcomp
,
°
= 0
θ
PwrS
°
= 0
θ
fb
therefore;
°
= 0
θ
Mod
The phase of the filter includes the complex poles of LC
and the Zero caused by the ESR of the COUT.
The filter has 2 poles at
0
F and a zero at
esr
F
°
−
= 180
θ
Flt
at
0
F and +90° at
esr
F



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