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IR3841MPbF
Where:
Z IN
V OUT
R 8
R 3
C POLE
C 4
Z f
V in = Maximum Input Voltage
V osc = Oscillator Ramp Voltage
F o = Crossover Frequency
F ESR = Zero Frequency of the Output Capacitor
F LC = Resonant Frequency of the Output Filter
R 8 = Feedback Resistor
F z = 0 . 75 *
H(s) dB
Gain(dB)
R 9
Fb
V REF
E/A
Comp
Ve
To cancel one of the LC filter poles, place the
zero before the LC filter resonant frequency pole:
F z = 75 % F LC
1
.......... .......... .......... ....... (22)
2 π L o * C o
Use equations (20), (21) and (22) to calculate
F
F Z
POLE
Frequency
C4.
One more capacitor is sometimes added in
parallel with C4 and R3. This introduces one
more pole which is mainly used to suppress the
V e Z 1 + sR 3 C 4
F P =
.......... .......... .......... ...(23)
2 π * R 3 *
H ( s ) =
R 3
C POLE =
?
.......... .......... ..( 24 )
1 π *R 3 *F s
Fig. 14. Type II compensation network
and its asymptotic gain plot
The transfer function ( V e /V o ) is given by:
= H ( s ) = ? f = ? ..... (18)
V o Z IN sR 8 C 4
The (s) indicates that the transfer function varies
as a function of frequency. This configuration
introduces a gain and zero, expressed by:
......... .......... .......... ......... (19)
R 8
switching noise.
The additional pole is given by:
1
C 4 * C POLE
C 4 + C POLE
The pole sets to one half of the switching
frequency which results in the capacitor C POLE :
1 1
π *R 3 *F s ?
C 4
For a general solution for unconditional stability
F z =
1
2 π * R 3 * C 4
.......... .......... ........ (20)
for any type of output capacitors, and a wide
range of ESR values, we should implement local
feedback with a type III compensation network.
V e Z f
First select the desired zero-crossover frequency
( F o ):
F o > F ESR and F o ≤ ( 1/5 ~ 1/10 ) * F s
Use the following equation to calculate R3:
The typically used compensation network for
voltage-mode controller is shown in figure 15.
Again, the transfer function is given by:
= H ( s ) = ?
V o Z IN
V in * F LC
? C * C 3 ? ?
? C 4 + C 3 ? ? ?
R 3 =
V osc * F o * F ESR * R 8
2
.......... .......... ....... (21)
By replacing Z in and Z f according to figure 15,
the transfer function can be expressed as:
( 1 + sR 3 C 4 ) [ 1 + sC 7 ( R 8 + R 10 ) ]
H ( s ) = ?
?
sR 8 ( C 4 + C 3 ) ? 1 + sR 3 ? 4 ? ? ( 1 + sR 10 C 7 )
? ?
.... (25)
06/18/09
20
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