Rainbow Electronics MAX15023 - Manual (Page 20)

MAX15023
Wide 4.5V to 28V Input, Dual-Output
Synchronous Buck Controller
20 ______________________________________________________________________________________
It is recommended to have a phase margin around
+50° to +60° to maintain a robust loop stability and
well-behaved transient response.
If an electrolytic or large-ESR tantalum output capacitor
is used, the capacitor ESR zero f
ZO typically occurs
between the LC poles and the crossover frequency f O
(f PO < f ZO < f O ). In this case, use a Type II (PI or pro-
portional-integral) compensation network.
If a ceramic or low-ESR tantalum output capacitor is
used, the capacitor ESR zero typically occurs above
the desired crossover frequency f
O , that is f PO < f O <
f ZO . In this situation, choose a Type III (PID or propor-
tional-integral-derivative) compensation network.
Type II Compensation Network
(See Figure 4)
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. Therefore, a Type II compen-
sation network with a midband zero and a high-fre-
quency pole can be used to stabilize the loop. In Figure
4, R
F and C F introduce a midband zero (f Z1 ). R F and
C CF in the Type II compensation network also provide a
high-frequency pole (f P1 ), which mitigates the effects of
the output high-frequency ripple.
To calculate the component values for Type II compen-
sation network in Figure 4, follow the instruction below:
1) Calculate the gain of the modulator (Gain MOD )—
composed of the regulator’s pulse-width modulator,
LC filter, feedback divider, and associated circuitry
at crossover frequency:
where V
IN
is the regulator’s input voltage, V
OSC
is the
amplitude of the ramp in the pulse-width modulator,
V
FB is the FB_ input voltage set-point (0.6V typically,
see Electrical Characteristics table), and V OUT is the
desired output voltage.
The gain of the error amplifier (Gain EA ) in midband fre-
quencies is:
where g
m
is the transconductance of the error amplifier.
The total loop gain as the product of the modulator gain
and the error amplifier gain at f
O should equal 1. So:
Therefore:
Solving for R F :
2) Set a midband zero (f Z1 ) at 0.75 x f PO (to cancel
one of the LC poles):
Solving for C F :
3) Place a high-frequency pole at f P1 = 0.5 x f SW (to
attenuate the ripple at the switching frequency, f
SW
)
and calculate C CF using the following equation:
C
R f
C
CF
F SW
F
=
Ч Ч
−
1
1
π
C
R f
F
F PO
=
Ч Ч Ч
1
2 0 75
π
.
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
OSC O OUT
FB
OUT
m F
Ч
Ч Ч
Ч Ч Ч =
( ) 2
1
π
Gain Gain
MOD EA
× = 1
Gain g R
EA m F
= ×
Gain
V
V
ESR
f L
V
V
MOD
IN
OSC O OUT
FB
OUT
= Ч
Ч Ч
( )
Ч
2 π
V REF
R 1
V OUT
R 2
g m
R F
COMP
C F C CF
Figure 4. Type II Compensation Network