M
Quick-PWM Slave Controller with
Driver Disable for Multiphase DC-DC Converter
______________________________________________________________________________________
19
Inductor Selection
The switching frequency and operating point (% ripple
or LIR) determine the inductor value as follows:
where
η
is the number of phases. Example:
η
= 2,
I
LOAD
= 40A, V
IN
= 12V, V
OUT
= 1.3V, f
SW
= 300kHz,
30% ripple current or LIR = 0.3:
Find a low-loss inductor having the lowest possible DC
resistance that fits in the allotted dimensions. Ferrite
cores are often the best choice, although powdered
iron is inexpensive and can work well at 200kHz. The
core must be large enough not to saturate at the peak
inductor current (I
PEAK
):
where
η
is the number of phases.
Transient Response
The inductor ripple current affects transient-response
performance, especially at low V
IN
- V
OUT
differentials.
Low inductor values allow the inductor current to slew
faster, replenishing charge removed from the output fil-
ter capacitors by a sudden load step. The amount of
output sag also is a function of the maximum duty fac-
tor, which can be calculated from the on time and mini-
mum off time:
where t
OFF(MIN)
is the minimum off time (see the
Electrical Characteristics
),
η
is the number of phases,
and K is from Table 3.
The amount of overshoot due to stored inductor energy
can be calculated as:
≈
(
2
η
Setting the Current Limits
The master and slave current-limit thresholds must be
great enough to support the maximum load current,
even under worst-case operating conditions. Since the
master
’
s current limit determines the maximum load
(see the
Current-Limit Circuitry
section), the procedure
for setting the current limit is sequential. First, the mas-
ter
’
s current limit is set based on the operating condi-
tions and the characteristics of the low-side MOSFETs.
Then the slave controller is configured to adjust the
master
’
s current-limit threshold based on the precise
current-sense resistor value and variation in the MOS-
FET characteristics. Finally, the resulting valley current
limit for the slave
’
s inductor occurs above the master
’
s
current-limit threshold. This is acceptable since the
slave
’
s inductor current limit only serves as a fail-safe in
case the master and slave inductor currents become
significantly unbalanced during a transient.
The basic operating conditions are determined using
the same calculations provided in any Quick-PWM reg-
ulator data sheet. The valley of the inductor current
(I
LIMIT(VALLEY)
) occurs at I
LOAD(MAX)
divided by the
number of phases minus half of the peak-to-peak
inductor current:
where the peak-to-peak inductor current may be deter-
mined by the following equation:
The master
’
s high current-limit threshold must be set
high enough to support the maximum load current,
even when the master
’
s current-limit threshold is at its
minimum tolerance value, as described in the master
controller
’
s data sheet. Most Quick-PWM controllers
that may be chosen as the master controller use the
low-side MOSFET
’
s on-resistance to sense the inductor
current. In these applications, the worst-case maximum
value for R
DS(ON)
plus some margin for the rise in
R
DS(ON)
over temperature must be used to determine
the master
’
s current-limit threshold. A good general rule
is to allow 0.5% additional resistance for each
°
C of
temperature rise. Set the master current-limit threshold
to support the maximum load current for the maximum
R
DS(ON)
and minimum current-limit tolerance value:
V
ITHM(HIGH)
≥
(I
LIMIT(VALLEY)
)R
DS(ON)(MAX)
I
V
V
V
L
V f
INDUCTOR
OUT
IN
OUT
=
(
)
I
I
I
LIMIT VALLEY
(
LOAD MAX
η
INDUCTOR
2
)
(
)
≥
V
I
L
C
SOAR
LOAD MAX
OUT OUT
)
(
)
2
V
L
I
V
K
V
t
C
V
V
V
K
)
t
SAG
LOAD MAX
OUT
IN
OFF MIN
(
OUT OUT
IN
OUT
IN
OFF MIN
(
=
(
)
(
+
(
)
)
)
2
2
η
-
I
I
LIR
2
η
PEAK
LOAD MAX
=
+
(
)
2
L
V x
300
V
V x
A x
40
V x
kHz x
H
=
(
=
1 3
.
12
1 3
.
2
0 3
.
12
0 64
.
-
μ
L
V
x V
xI
V
x
xLIR
V
x f
OUT
IN
OUT
IN
SW
LOAD MAX
=
)
-
η
(
)