MAX1955 Datasheet, PDF (19/22 Pages) Maxim Integrated Products – 1.6V to 5.5V Input, 0.5% Accurate, Dual 180° Out-of-Phase Step-Down Controllers

1.6V to 5.5V Input, 0.5% Accurate, Dual
180° Out-of-Phase Step-Down Controllers
must compensate for this gain drop and phase shift in
order to achieve a stable high-bandwidth closed-loop
system.
The basic regulator loop consists of a power modulator,
an output feedback divider, and an error amplifier. The
power modulator has DC gain set by V_IN/V_RAMP, with a
double pole set by the inductor and output capacitor
and a single zero set by the output capacitor (C_OUT)
and its ESR. Equations that define the power modulator
follow:
The DC gain of the power modulator:
G_MOD(DC)
=
V_IN
V_RAMP
where V_RAMP = 1V. The double-pole frequency
because of the inductor and output capacitor is:
f_PMOD =
1
2π LC_OUT
The zero frequency because of the output capacitor’s
ESR is:
f_ZESR
=
2π
×
1
ESR ×
C_OUT
The output capacitor is usually composed of several
same-value capacitors connected in parallel. With n
capacitors in parallel, the output capacitance is:
C_OUT = n × C_EACH
The total ESR is:
ESR = ^ESREACH
n
The ESR zero (f_ZESR) for a parallel combination of
capacitors is the same as that of an individual capacitor.
The feedback divider has a gain of G_FB = V_FB/V_OUT,
where V_FB is 0.8V.
The transconductance error amplifier has DC gain
G_EA(dc) of 80dB. A dominant pole is set by the com-
pensation capacitor (C_C), the amplifier-output resis-
tance (R_O ≅ 5MΩ), and the compensation resistor (R_C):
f_PEA
=
2π
×
C_C
1
× (R_O
+ R_C)
A zero is set by the compensation resistor and the
compensation capacitor:
f_ZEA
=
2π
×
1
C_C
× R_C
The total closed-loop gain must equal unity at the
crossover frequency, where the crossover frequency
should be higher than f_ZESR, so that the -1 slope is used
to cross over at unity gain. Also, the crossover frequency
should be less than or equal to 1/5 the switching
frequency:
f_ZESR
<
f_C
<
f_SW
5
The loop-gain equation at the crossover frequency is:
V_FB
V_OUT
×
G_EA(fc) × G_MOD(fc) = 1
where:
G_EA(fc) = g_mEA ✕ R_C, and
G_MOD(fc) = G_MOD(DC) ✕ (f_PMOD)² / (f_ESR ✕ f_C)
The compensation resistor (R_C) is calculated from:
R_C =
g_mEA
×
V_OUT
V_FB × G_MOD(fc)
where g_mEA = 2mS.
Because of the underdamped (Q > 1) nature of the out-
put LC double pole, the error amplifier compensation
zero should be approximately 0.2 f_PMOD to provide
good phase boost. C_C is calculated from:
C_C
=
2π
×
5
R_C ×
f_PMOD
A small capacitor (C_F) also can be added from COMP
to GND to provide high-frequency decoupling. C_F adds
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