Texas Instruments LM3431 Evaluation Board LM3431EVAL/NOPB LM3431EVAL/NOPB Datenbogen
Produktcode
LM3431EVAL/NOPB
f
ZC
=
1
2
S
x R
C
x C
C
f
PC
=
1
2
S
x R
O
x C
C
fp1
fz1
fpn
RHPz
G
A
IN
(d
B
)
FREQUENCY
KD = 1+
'¶
2
x 75 mV
I
OUT
x R3
'¶
3
x R
L
L x f
SW
x 2
+
R
L
=
V
OUT
I
OUT
SNVS547G – NOVEMBER 2007 – REVISED MAY 2013
(23)
Since the control-to-output response will shift with input voltage, the compensation should be calculated at both
the minimum and maximum input voltage.
the minimum and maximum input voltage.
The zero created by the ESR of the output capacitor, f
z1
, is generally at a very high frequency if the ESR is small.
If low ESR capacitors are used f
z1
can be neglected and if high ESR capacitors are used, C
C2
can be added (see
below).
A current mode control boost regulator has an inherent right half plane zero, RHPz. This has the effect of a zero
in the gain plot, causing a +20dB/decade increase, but has the effect of a pole in the phase, subtracting 90° in
the phase plot. This can cause instability if the control loop is influenced by this zero. To ensure the RHP zero
does not cause instability, the control loop must be designed to have a bandwidth of less than one third the
frequency of the RHP zero. The regulator also has a double pole, fpn, at one half the switching frequency. The
control loop bandwidth must be lower than 1/5 of fpn. A typical control-to-output gain response is shown in
in the gain plot, causing a +20dB/decade increase, but has the effect of a pole in the phase, subtracting 90° in
the phase plot. This can cause instability if the control loop is influenced by this zero. To ensure the RHP zero
does not cause instability, the control loop must be designed to have a bandwidth of less than one third the
frequency of the RHP zero. The regulator also has a double pole, fpn, at one half the switching frequency. The
control loop bandwidth must be lower than 1/5 of fpn. A typical control-to-output gain response is shown in
below.
Figure 19. Typical Control-to-Output Bode Plot
Once the control-to-output response has been determined, the compensation components are selected. A series
combination of Rc and Cc is recommended for the compensation network, shown as R9 and C4 in the typical
application circuit. The series combination of Rc and Cc introduces a pole-zero pair according to the following
equations:
combination of Rc and Cc is recommended for the compensation network, shown as R9 and C4 in the typical
application circuit. The series combination of Rc and Cc introduces a pole-zero pair according to the following
equations:
where
•
R
O
is the output impedance of the error amplifier, approximately 500 k
Ω
.
(24)
The initial value of R
C
is determined based on the required crossover frequency from the following equations
using the maximum input voltage:
Copyright © 2007–2013, Texas Instruments Incorporated
17
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