LTC3536_15 Datasheet, PDF (20/28 Pages) Linear Technology – 1A Low Noise, Buck-Boost DC/DC Converter

LTC3536
Applications Information
occur at the same frequency, f_Z, and both higher order poles
(f_POLE2 and f_POLE3) occur at the common frequency, f_P .
This is a good starting point for determining the compen-
sation network. However the Bode plot for the complete
loop should be checked overall operating conditions and
for variations in components values to ensure that suf-
ficient phase margin and gain margin exists in all cases.
A reasonable choice is to pick the frequency of the poles,
f_P, to be about 50 times higher than the frequency of the
zeros, f_Z, which provides a peak phase boost of approxi-
mately Φ_MAX = 60° as was assumed previously. Next, the
phase boost must be centered so that the peak phase
occurs at the target crossover frequency. The frequency
of the maximum phase boost, f_C, is the geometric mean
of the pole and zero:
f_C = f_P • f_Z = 50 • f_Z2 = 7 • f_Z
Therefore, in order to center the phase boost given a factor
of 50 separation between the pole and zero frequencies,
the zeros should be located at one-seventh of the cross-
over frequency and the poles should be located at seven
times the crossover frequency as given by the following
equations:
f_Z
=
1
7
•
f_C
=
1
7
•
(37.8kHz
)
=
5.4kHz
f_P = 7 • f_C = 7 • (37.8kHz) = 264.6kHz
This placement of the poles and zeros will yield a peak phase
boost of 60° that is centered at the crossover frequency,
f_C. Next, in order to produce the desired target crossover
frequency, the gain of the compensation network at the
point of maximum phase boost, G_CENTER, must be set to
+2dB. The gain of the compensated error amplifier at the
point of maximum phase gain is given by:
( ) ( ) ^
G_CENTER
=
10log ^

2πf_Z
2πf_P
3 _RTOPCFB


2 _
Assuming a multiple of 50 separation between the pole
frequencies and zero frequencies this can be simplified
to the following expression:
( )( ) ^
G_CENTER
=
20log


2πf_C
50
R_TOPC_FB



The first step in defining the compensation component
values is to pick a value for R_TOP that provides an accept-
ably low quiescent current through the resistor divider.
A value of R_TOP = 845k is a reasonable choice. Next, the
value of C_FB can be found:
G_CENTER = 2dB
C_FB
50
2dB ^{= 198pF ≈ 180pF}
2π • (37.8kHz) • 845kΩ • 10 ²⁰
The compensation poles can be set at 264.6kHz and the
zeros at 5.4kHz by using the expressions for the pole and
zero frequencies given in the previous section. Setting the
frequency of the first zero, f_ZERO1, to 5.4kHz results in the
following value for R_FB:
R_FB
=
2π
•
1
(180pF
)
•
5.4kHz
=
163kΩ
≈
162kΩ
This leaves the free parameter, C_POLE, to set the frequency
f_POLE1 to the common pole frequency of 264.6kHz as given:
C_POLE
=
2π
•
1
(162kΩ)
•
264.6kHz
=
3.71pF
≈
3.9pF
Next, C_FF can be chosen to set the second zero, f_ZERO2, to
the common zero frequency of 5.4kHz.
C_FF
=
2π
•
1
(845kΩ)
•
5.4kHz
=
34.9pF
≈
33pF
Finally, the resistor value R_FF can be chosen to place the
second pole at 264.6kHz:
R_FF
=
2π
•
1
(33pF) •
264.6kHz
=
18.2kΩ
3536fa
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