rt9212 Richtek Technology Corporation, rt9212 Datasheet - Page 12

• Manufacturer Part Number: rt9212
• Description: Dual Synchronous Buck Dc-dc Linear Power Controller
• Manufacturer: Richtek Technology Corporation

Modulator Frequency Equations
The modulator transfer function is the small-signal transfer
function of V
by a DC gain and the output filter (L
pole frequency at F
the modulator is the input voltage (V
to-peak oscillator voltage V
The first step is to calculate the complex conjugate poles
contributed by the LC output filter.
The output LC filter introduces a double pole,
gain slope above its corner resonant frequency, and a total
phase lag of 180 degrees. The Resonant frequency of the
LC filter expressed as follows :
The next step of compensation design is to calculate the
ESR zero. The ESR zero is contributed by the ESR
associated with the output capacitance. Note that this
requires that the output capacitor should have enough ESR
to satisfy stability requirements. The ESR zero of the
output capacitor expressed as follows :
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12
RT9212
Comparator
PWM
OUT
VRAMP
F
/V
F
Z(ESR)
P(LC)
E/A
PWM
LC
+
-
. This transfer function is dominated
and a zero at F
=
=
Figure 1
2
2
π
π
RAMP
×
×
Vin
C
.
Zf
L
1
O
1
Compensator
O
×
O
+
-
×
IN
ESR
and C
C
) divided by the peak-
Lo
ESR
O
VREF
Zc
. The DC gain of
O
), with a double
−
40dB/decade
ESR
Co
Vout
Preliminary
Compensation Frequency Equations
The compensation network consists of the error amplifier
and the impedance networks Z
Figure 3 shows the DC-DC converter's gain vs. frequency.
The compensation gain uses external impedance networks
Z
High crossover frequency is desirable for fast transient
response, but often jeopardize the system stability. In order
to cancel one of the LC filter poles, place the zero before
the LC filter resonant frequency. In the experience, place
the zero at 75% LC filter resonant frequency.Crossover
frequency should be higher than the ESR zero but less
than 1/5 of the switching frequency.
The second pole be place at half the switching frequency.
F
F
F
C
P1
Z1
P1
and Z
=
=
=
0
2
2
-20
-40
-60
80
60
40
20
0
π
π
- 4 0
- 6 0
F
8 0
4 0
10
0
1 0 H z
×
×
Modulator
to provide a stable, high bandwidth loop.
v d b ( v o ) v d b ( c o m p 2 ) v d b ( l o )
R
R
1
Gain
2
2
COMP1
×
1
(C
RT9212
C
1
100
1 0 0 H z
2
//
Loop Gain
R2
EA
C
+
Zf
-
2
C1
)
VREF
C2
Figure 3
Figure 2
1 . 0 K H z
1k
Frequency (Hz)
FB1
F r e q u e n c y
C
and Z
DS9212-05 March 2007
Rf
1 0 K H z
10k
Zc
R1
F
as Figure 2 shows.
Compensation
100k
1 0 0 K H z
Gain
V
OUT
1 . 0 M H z
1M