Rainbow Electronics MAX15026 - Manual (Page 15)

requirements. Choose the small-signal components for
the error amplifier to achieve the desired closed-loop
bandwidth and phase margin.
To choose the appropriate compensation network type,
the power-supply poles and zeros, the zero crossover
frequency, and the type of the output capacitor must be
determined.
In a buck converter, the LC filter in the output stage intro-
duces a pair of complex poles at the following frequency:
The output capacitor introduces a zero at:
where ESR is the equivalent series resistance of the
output capacitor.
The loop-gain crossover frequency (f O ), where the loop
gain equals 1 (0dB) should be set below 1/10th of the
switching frequency:
Choosing a lower crossover frequency reduces the
effects of noise pick-up into the feedback loop, such as
jittery duty cycle.
To maintain a stable system, two stability criteria must
be met:
1) The phase shift at the crossover frequency f O , must
be less than 180°. In other words, the phase margin
of the loop must be greater than zero.
2) The gain at the frequency where the phase shift is
-180° (gain margin) must be less than 1.
Maintain a phase margin of around 60° to achieve a
robust loop stability and well-behaved transient
response.
When using an electrolytic or large-ESR tantalum output
capacitor the capacitor ESR zero f
ZO typically occurs
between the LC poles and the crossover frequency f O
(f PO < f ZO < f O ). Choose Type II (PI—proportional-inte-
gral) compensation network.
When using a ceramic or low-ESR tantalum output
capacitor, the capacitor ESR zero typically occurs
above the desired crossover frequency f
O , that is f PO <
f
O
< f
ZO
. Choose Type III (PID—proportional, integral,
and derivative) compensation network.
Type II Compensation Network
(Figure 3)
If f ZO is lower than f O and close to f PO , the phase lead
of the capacitor ESR zero almost cancels the phase
loss of one of the complex poles of the LC filter around
the crossover frequency. Use a Type II compensation
network with a midband zero and a high-frequency
pole to stabilize the loop. In Figure 3, R
F and C F intro-
duce a midband zero (f Z1 ). R F and C CF in the Type II
compensation network provide a high-frequency pole
(f
P1 ), which mitigates the effects of the output high-fre-
quency ripple.
Follow the instructions below to calculate the component
values for the Type II compensation network in Figure 3:
1) Calculate the gain of the modulator (GAIN MOD ),
comprised of the regulator’s pulse-width modulator,
LC filter, feedback divider, and associated circuitry
at the crossover frequency:
where V IN is the input voltage of the regulator, V RAMP is
the amplitude of the ramp in the pulse-width modulator,
V
FB is the FB input voltage set-point (0.592V typically,
see the Electrical Characteristics table), and V OUT is
the desired output voltage.
The gain of the error amplifier (Gain EA ) in midband fre-
quencies is:
GAIN EA = g M x R F
where g M is the transconductance of the error amplifier.
The total loop gain, which is the product of the modula-
tor gain and the error amplifier gain at f
O , is 1.
So:
Solving for R F :
2) Set a midband zero (f Z1 ) at 0.75 x f PO (to cancel
one of the LC poles):
f
R C
f
Z
F F
PO 1
1
2
0 75
=
Ч Ч
= Ч
π
.
R
V f L V
V V g ESR
F
OSC O OUT OUT
FB IN M
=
Ч Ч Ч
( )
Ч
Ч Ч Ч
2
π
V
V
ESR
f L
V
V
g R
IN
RAMP O OUT
FB
OUT
M F
Ч
Ч Ч
Ч Ч Ч =
( ) 2
1
π
GAIN GAIN
MOD EA
× = 1
GAIN
V
V
ESR
f L
V
V
MOD
IN
RAMP O OUT
FB
OUT
= Ч
Ч Ч
( )
Ч
2 π
f
f
O
SW ≤
10
f
ESR C
ZO
OUT
=
Ч Ч
1
2 π
f
L C
PO
OUT OUT
=
Ч Ч
1
2
π
MAX15026
Low-Cost, Small, 4.5V to 28V Wide Operating
Range, DC-DC Synchronous Buck Controller
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