Datasheet
The ESR-induced ripple usually dominates this last
equation, so typically output capacitor selection is based
mostly upon the capacitor's ESR, voltage rating, and rip-
ple current rating. Use the following formula to determine
the maximum ESR for a desired output ripple voltage
(V
RIPPLE-D
):
R
ESR
= V
RIPPLE-D
/ I
LPP
Select a capacitor with ESR rating less than R
ESR
. The
value of this capacitor is highly dependent on dielectric
type, package size, and voltage rating. In general, when
choosing a capacitor, it is recommended to use low-ESR
capacitor types such as ceramic, organic, or tantalum
capacitors. Ensure that the selected capacitor has suffi-
cient margin to safely handle the maximum RMS ripple
current.
For continuous inductor current the maximum RMS ripple
current in the output filter capacitor is:
2
LOAD
RMS MAX MAX
MAX
I
I xD D
ID
−=
−
Choosing Compensation Components
The MAX1846/MAX1847 are externally loop-compensat-
ed devices. This feature provides flexibility in designs to
accommodate a variety of applications. Proper compen-
sation of the control loop is important to prevent excessive
output ripple and poor efficiency caused by instability. The
goal of compensation is to cancel unwanted poles and
zeros in the DC-DC converter’s transfer function created
by the power-switching and filter elements. More precise-
ly, the objective of compensation is to ensure stability by
ensuring that the DC-DC converter’s phase shift is less
than 180° by a safe margin, at the frequency where the
loop gain falls below unity. One method for ensuring ade-
quate phase margin is to introduce corresponding zeros
and poles in the feedback network to approximate a sin-
gle-pole response with a -20dB/decade slope all the way
to unity-gain crossover.
Calculating Poles and Zeros
The MAX1846/MAX1847 current-mode architecture takes
the double pole caused by the inductor and output
capacitor and shifts one of these poles to a much higher
frequency to make loop compensation easier. To compen-
sate these devices, we must know the center frequencies
of the right-half plane zero (z
RHP
) and the higher frequen-
cy pole (p
OUT2
). Calculate the z
RHP
frequency with the
following formula:
( )
( )
( )
2
MAX IN(MIN) OUT LOAD
RHP
OUT
1 D x V V xR
Z
2 xV L
−− −
=
π×
The calculations for p
OUT2
are very complex. For most
applications where V
OUT
does not exceed -48V (in a neg-
ative sense), the p
OUT2
will not be lower than 1/8th of the
oscillator frequency and is generally at a higher frequency
than z
RHP
. Therefore:
p
OUT2
≥ 0.125 × f
OSC
A pole is created by the output capacitor and the load
resistance. This pole must also be compensated and its
center frequency is given by the formula:
p
OUT1
= 1 / (2π × R
LOAD
× C
OUT
)
Finally, there is a zero introduced by the ESR of the out-
put capacitor. This zero is determined from the following
equation:
zESR = 1 / (2π × C
OUT
× R
ESR
)
Calculating the Required Pole Frequency
To ensure stability of the MAX1846/MAX1847, the gain
of the error amplifier must roll-off the total loop gain to
1 before Z
RHP
or P
OUT2
occurs. First, calculate the DC
open-loop gain A
DC
:
xx
M O MAX LOAD
DC
CS CS
B x G R (1 D ) R
A
A xR
−
=
where:
A
CS
is the current sense amplifier gain = 3.3
B is the feedback-divider attenuation factor =
R2
R1 R2+
G
M
is the error-amplifier transconductance =
400 µA/V
R
O
is the error-amplifier output resistance
=
3 MW
R
CS
is the selected current-sense resistor
Determining the Compensation Component Values
Select a unity-gain crossover frequency (f
CROS
), which is
lower than z
RHP
and p
OUT2
and higher than p
OUT1
. Using
f
CROS
, calculate the compensation resistor (R
COMP
).
CROS O
COMP
DC OUT1 CROS
f xR
R
A xP f
=
−
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MAX1846–MAX1847 High-Efciency, Current-Mode,
Inverting PWM Controller