MAX16909 Datasheet, PDF (15/18 Pages) Maxim Integrated Products – 36V, 220kHz to 1MHz Step-Down Converter with Low Operating Current

MAX16909
36V, 220kHz to 1MHz Step-Down Converter
with Low Operating Current
The feedback voltage-divider has a gain of GAIN_FB =
V_FB/V_OUT, where V_FB is 1V (typ).
The transconductance error amplifier has a DC gain of
GAIN_EA(DC) = g_m,EA x R_OUT,EA, where g_m,EA is the error-
amplifier transconductance, which is 900FS (typ), and
R_OUT,EA is the output resistance of the error amplifier.
A dominant pole (f_dpEA) is set by the compensa-
tion capacitor (C_C) and the amplifier output resistance
(R_OUT,EA). A zero (f_zEA) is set by the compensation
resistor (R_C) and the compensation capacitor (C_C).
There is an optional pole (f_pEA) set by C_F and R_C to
cancel the output capacitor ESR zero if it occurs near
the crossover frequency (f_C, where the loop gain equals
1 (0dB)). Thus:
f_dpEA
=
2π × C_C
1
× (R_OUT,EA
+ R_C)
f_zEA
=
2π
×
1
C_C
×R_C
f_pEA
=
1
2π × C_F
×R_C
The loop-gain crossover frequency (f_C) should be set
below 1/5th of the switching frequency and much higher
than the power-modulator pole (f_pMOD):
f_pMOD
<<
f_C
≤
f_SW
5
The total loop gain as the product of the modulator gain,
the feedback voltage-divider gain, and the error-amplifier
gain at f_C should be equal to 1. So:
GAIN_MOD(fC)
×
V_FB
V_OUT
× GAIN_EA(fC)
=1
For the case where f_zMOD is greater than f_C:
GAIN_EA(fC) = g_m,EA × R_C
GAIN_MOD(fC)
=
GAIN_MOD(dc)
×
f_pMOD
f_C
Therefore:
GAIN_MOD(fC)
×
V_FB
V_OUT
× g_m,EA
×R_C
=
1
Solving for R_C:
R_C
=
g_m,EA
×
V_OUT
V_FB × GAIN_MOD(fC)
Set the error-amplifier compensation zero formed by R_C
and C_C (f_zEA) at the f_pMOD. Calculate the value of C_C a
follows:
C_C
=
2π
×
1
f_pMOD
×
R_C
If f_zMOD is less than 5 x f_C, add a second capacitor,
C_F, from COMP to GND and set the compensation pole
formed by R_C and C_F (f_pEA) at the f_zMOD. Calculate the
value of C_F as follows:
C_F
=
2π
×
1
f_zMOD
×R_C
As the load current decreases, the modulator pole
also decreases; however, the modulator gain increases
accordingly and the crossover frequency remains the
same.
For the case where f_zMOD is less than f_C:
The power-modulator gain at f_C is:
GAIN_MOD(fC)
=
GAIN_MOD(dc)
×
f_pMOD
f_zMOD
The error-amplifier gain at f_C is:
GAIN_EA(fC)
=
g_m,EA
×
R_C
×
f_zMOD
f_C
Therefore:
GAIN_MOD(fC)
×
V_FB
V_OUT
× g_m,EA
×R_C
×
f_zMOD
f_C
=1
Solving for R_C:
R_C
=
g_m,EA
×
V_FB
V_OUT × f_C
× GAIN_MOD(fC)
×
f_zMOD
Set the error-amplifier compensation zero formed by R_C
and C_C at the f_pMOD (f_zEA = f_pMOD) as follows:
C_C
=
2π
×
1
f_pMOD
×
R_C
If f_zMOD is less than 5 x f_C, add a second capacitor C_F
from COMP to GND. Set f_pEA = f_zMOD and calculate C_F
as follows:
C_F
=
2π
×
1
f_zMOD
×R_C
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