M
High-Effic ienc y, Quad Output, Main Power-
S upply Controllers for Notebook Computers
______________________________________________________________________________________
25
Induc tor S elec tion
The switching frequency (on-time) and operating point
(% ripple or LIR) determine the inductor value as follows:
(
+ × ×
Example: I
LOAD(MAX)
= 5A, V+ = 12V, V
OUT5
= 5V, f =
200kHz, 35% ripple current or LIR = 0.35:
(
×
×
12
200
Find a low-loss inductor having the lowest possible DC
resistance that fits in the allotted dimensions. Ferrite cores
are often the best choice. The core must be large enough
not to saturate at the peak inductor current (I
PEAK
):
I
PEAK
= I
LOAD(MAX)
+ [(LIR/2) x I
LOAD(MAX)
]
The inductor ripple current also impacts transient-
response performance, especially at low V+ - V
OUT_
difference. Low inductor values allow the inductor cur-
rent to slew faster, replenishing charge removed from
the output filter capacitors by a sudden load step. The
peak amplitude of the output transient (V
SAG
) is also a
function of the maximum duty factor, which can be cal-
culated from the on-time and minimum off-time:
where minimum off-time = 0.350μs (max) and K is from
Table 2.
Determining the Current Limit
The minimum current-limit threshold must be great
enough to support the maximum load current when the
current limit is at the minimum tolerance value. The val-
ley of the inductor current occurs at I
LOAD(MAX)
minus
half of the ripple current; therefore,
I
LIMIT(LOW)
> I
LOAD(MAX)
- [(LIR / 2) x I
LOAD(MAX)
]
where I
LIMIT(LOW)
= minimum current-limit threshold
voltage divided by the R
DS(ON)
of N2/N4 (MAX1999).
For the MAX1777/MAX1977/MAX1999, the minimum
current-limit threshold voltage is 93mV (ILIM_ = V
CC
).
Use the worst-case maximum value for R
DS(ON)
from
the MOSFET N2/N4 data sheet and add some margin
for the rise in R
DS(ON)
with temperature. A good gener-
al rule is to allow 0.5% additional resistance for each °C
of temperature rise.
Examining the 5A circuit example with a maximum
R
DS(ON)
= 12m
at high temperature reveals the following:
I
LIMIT(LOW)
= 93mV / 12m
> 5A - (0.35 / 2) 5A
7.75A > 4.125A
7.75A is greater than the valley current of 4.125A, so
the circuit can easily deliver the full-rated 5A using the
fixed 100mV nominal current-limit threshold voltage.
Connect the source of the synchronous rectifier to a
current-sense resistor to GND (MAX1777/MAX1977),
and connect CS_ to that junction to set the current limit
for the device. The MAX1777/MAX1977/MAX1999 limit
the current with the sense resistor instead of the
R
DS(ON)
of N2/N4. The maximum value of the sense
resistor can be calculated with the equation
I
LIM_
= 93mV / R
SENSE
Output Capac itor S elec tion
The output filter capacitor must have low enough equiv-
alent series resistance (ESR) to meet output ripple and
load-transient requirements, yet have high enough ESR
to satisfy stability requirements. The output capaci-
tance must also be high enough to absorb the inductor
energy while transitioning from full-load to no-load con-
ditions without tripping the overvoltage fault latch. In
applications where the output is subject to large load
transients, the output capacitor’s size depends on how
much ESR is needed to prevent the output from dip-
ping too low under a load transient. Ignoring the sag
due to finite capacitance:
where V
DIP
is the maximum tolerable transient voltage
drop. In non-CPU applications, the output capacitor’s
size depends on how much ESR is needed to maintain
an acceptable level of output voltage ripple:
where V
P-P
is the peak-to-peak output voltage ripple.
The actual capacitance value required relates to the
physical size needed to achieve low ESR, as well as to
the chemistry of the capacitor technology. Thus, the
capacitor is usually selected by ESR and voltage rating
rather than by capacitance value (this is true of tanta-
lum, OS-CON, and other electrolytic-type capacitors).
R
V
I
LIR
ESR
P P
LOAD MAX
≤
×
(
)
R
V
I
ESR
DIP
(
LOAD MAX
≤
)
V
I
L KV
V
t
C
V
K
V
V
+
V
t
SAG
LOAD MAX
OUT
OFF MIN
(
OUT
OUT
OUT
OFF MIN
(
=
(
)
×
+
+
×
×
+
(
)
_
)
_
_
)
2
2
L
V
V
V
V
kHz
A
H
=
)
×
=
5 12
5
0 35
.
5
8 3
.
μ
L
V
V
V
V
f
LIR
I
OUT
OUT
LOAD MAX
=
+
)
×
_
_
(
)