Rainbow Electronics MAX1567 - Manual (Page 29)

MAX1566/MAX1567
Six-Channel, High-Efficiency, Digital
Camera Power Supplies
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recalculate R C . Higher substituted C OUT values allow a
higher R
C
, which provides higher transient gain and
consequently less transient droop.
If the output filter capacitor has significant ESR, a zero
occurs at the following:
Z ESR = 1 / (2 π x C
OUT x R ESR )
If Z
ESR
> f
C
, it can be ignored, as is typically the case
with ceramic output capacitors. If Z ESR is less than f C ,
it should be cancelled with a pole set by capacitor C P
connected from CC to GND:
C P = C OUT x R ESR / R C
If C P is calculated to be <10pF, it can be omitted.
Step-Down Component Selection
This section describes component selection for the
step-down converter, and for the main converter if used
in step-down mode (SUSD = GND).
Step-Down Inductor
The external components required for the step-down
are an inductor, input and output filter capacitors, and
compensation RC network.
The MAX1566/MAX1567 step-down converter provides
best efficiency with continuous inductor current. A rea-
sonable inductor value (L
IDEAL ) can be derived from
the following:
L IDEAL = [2(V IN ) x D(1 - D)] / I OUT x f OSC
This sets the peak-to-peak inductor current at 1/2 the
DC inductor current. D is the duty cycle:
D = V OUT / V IN
Given L
IDEAL
, the peak-to-peak inductor current is 0.5
I OUT . The absolute-peak inductor current is 1.25 I OUT .
Inductance values smaller than L IDEAL can be used to
reduce inductor size; however, if much smaller values are
used, inductor current rises, and a larger output capaci-
tance may be required to suppress output ripple. Larger
values than L
IDEAL can be used to obtain higher output
current, but typically with larger inductor size.
Step-Down Compensation
The relevant characteristics for step-down compensa-
tion are as follows:
• Transconductance (from FB to C
C
), gm
EA
(135µS)
• Step-down slope-compensation pole, P SLOPE = V IN /
( πL)
• Current-sense amplifier transresistance, R CS
(0.6V/A)
• Feedback-regulation voltage, V FB (1.25V)
• Step-down output voltage, V SD , in V
• Output-load equivalent resistance, R LOAD , in
Ω =
V
OUT
/ I
LOAD
The key steps for step-down compensation are
as follows:
1) Set the compensation RC to zero to cancel the
R LOAD C OUT pole.
2) Set the loop crossover below the lower of 1/5 the
slope compensation pole or 1/5 the switching
frequency.
If we assume V IN = 2.5V, V OUT = 1.8V, and I OUT =
350mA, then R LOAD = 5.14
Ω.
If we select f OSC = 500kHz and L = 5.6µH.
P
SLOPE
= V
IN
/ ( πL) = 142kHz, so choose f
C
= 24kHz
and calculate C C :
C
C
= (V
FB
/ V
OUT
)(R
LOAD
/ R
CS
)(gm / 2 π x f
C
)
= (1.25 / 1.8)(5.14 / 0.6) x [135µS / (6.28 x 24kHz)]
= 6.4nF
Choose 6.8nF.
Now select R C so transient-droop requirements are
met. As an example, if 4% transient droop is allowed,
the input to the error amplifier moves 0.04 x 1.25V, or
50mV. The error-amp output drives 50mV x 135µS, or
6.75µA across R
C to provide transient gain. Since the
current-sense transresistance is 0.6V/A, the value of R C
that allows the required load-step swing is as follows:
R C = 0.6 I IND(PK) / 6.75µA
In a step-down DC-to-DC converter, if L IDEAL is used,
output current relates to inductor current by the following:
I IND(PK) = 1.25 I OUT
So for a 250mA output load step with V IN = 2.5V and
V OUT = 1.8V:
R C = (1.25 x 0.6 x 0.25) / 6.75µA = 27.8k Ω
Choose 27k Ω.
Note that the inductor does somewhat limit the response
in this case since it ramps at (V
IN
- V
OUT
) / 5.6µH, or
(2.5 - 1.8) / 5.6µH = 125mA/µs.
The output filter capacitor is then chosen so the C OUT
R LOAD pole cancels the R C C C zero:
C OUT x R LOAD = R C x C C
For the example:
C OUT = 27k
Ω x 6.8nF / 5.14Ω = 35.7µF
Since ceramic capacitors are common in either 22µF or
47µF values, 22µF is within a factor of two of the ideal value
and still provides adequate phase margin for stability.