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? ?
? ?
? I OUT ? × ( 1 ? D ) ≈ 18 . 6 kHz
2 π × L
F CROSS =
TYPICAL APPLICATIONS
? V OUT ?
2
5
Plotting the transfer function of G(s) and locating the
crossover frequency, the DC gain needed for the
compensator can be obtained, as shown in Figure 23 .
G 0 = 32.42
F CROSS = 18.6 kHz
}
DC gain needed for the
compensator ≈ 4.0627 dB
Figure 23. Transfer Function of G(s).
This DC gain needed for the compensator is actually the
value of G , whose value can be substituted above. As a
result, R COMP = 126.16 k Ω . A precision 130 k Ω @ 1%
resistor is chosen.
C COMP 2 =
1
2 π × R COMP × F P
? 15 pF
The steps to calculate the compensation capacitors are as
follows:
1. Knowing the frequency of the Right Half Plane Zero ,
3. Set a zero at one fifth of the crossover frequency that
compensates the pole, that comes from the output
capacitor and the “load resistor = V OUT /I OUT ,
? ?
? ?
? I OUT ? × ( 1 ? D ) 2 ≈ 92 . 8 kHz
F RHPZ
=
? V OUT ?
2 π × L
Then,
F Z =
F CROSS
5
≈ 3 . 7 kHz
2. Set a pole F Z at the Right Half Plane Zero, F P = F RHZP ,
then:
C COMP 1 =
1
2 π × R COMP × F Z
? 390 pF
Note: Some jitter (noise) may be present in the switching
frequency of the converter due to certain instability. The
designer should corroborate this effect by using a spectrum
analyzer. Using this instrument, the designer should play with
34848
Analog Integrated Circuit Device Data
Freescale Semiconductor
31
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