
ADP3180
–13–
Selecting a Standard Inductor
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Output Droop Resistance
The design requires that the regulator output voltage measured
at the CPU pins drops when the output current increases. The
specified voltage drop corresponds to a dc output resistance (R
O
).
The output current is measured by summing together the voltage
across each inductor and passing the signal through a low-pass
filter. This summer filter is the CS amplifier configured with
resistors
R
PH(X)
(summers), and
R
CS
and
C
CS
(filter). The output
resistance of the regulator is set by the following equations, where
R
L
is the DCR of the output inductors:
R
R
R
R
O
CS
PH X
L
=
×
(6)
C
L
×
R
R
CS
L
CS
=
(7)
One has the flexibility of choosing either
R
CS
or
R
PH(X)
. It is best
to select
R
CS
equal to 100 k
W
, and then solve for
R
PH(X)
by rear-
ranging Equation 6.
R
R
R
1 6
1 3
.
R
R
m
m
k
k
PH X
L
O
.
CS
PH X
=
×
=
×
=
100
123
Next, use Equation 6 to solve for
C
CS
:
C
nH
×
100
m
k
nF
CS
=
=
600
1 6
.
3 75
.
It is best to have a dual location for
C
CS
in the layout so standard
values can be used in parallel to get as close to the value desired.
For this example, choosing
C
CS
to be a 1.5 nF and 2.2 nF in
parallel is a good choice. For best accuracy,
C
CS
should be a 5%
or 10% NPO capacitor. The closest standard 1% value for
R
PH(X)
is 124 k
W
.
Inductor DCR Temperature Correction
With the inductor’s DCR being used as the sense element and
copper wire being the source of the DCR, one needs to com-
pensate for temperature changes of the inductor’s winding.
Fortunately, copper has a well known temperature coefficient
(TC) of 0.39%/°C.
If R
CS
is designed to have an opposite and equal percentage
change in resistance to that of the wire, it will cancel the tempera-
ture variation of the inductor’s DCR. Due to the nonlinear nature
of NTC thermistors, resistors R
CS1
and R
CS2
are needed (see
Figure 5) to linearize the NTC and produce the desired tempera-
ture tracking.
CSSUM
18
CSCOMP
PLACE AS CLOSE AS POSSIBLE
TO NEAREST INDUCTOR
OR LOW SIDE MOSFET
17
CSREF16
ADP3180
C
1.8nF
R
CS1
R
TH
R
CS2
KEEP THIS PATH
AS SHORT AS POSSIBLE
AND WELL AWAY FROM
SWITCH NODE LINES
TO
SWITCH
NODES
TO
V
SENSE
R
PH1
R
PH3
R
PH2
Figure 5. Temperature Compensation Circuit Values
The following procedure and expressions will yield values to use
for R
CS1
, R
CS2
, and R
TH
(the thermistor value at 25°C) for a given
R
CS
value.
1. Select an NTC to be used based on type and value. Since
we do not have a value yet, start with a thermistor with a
value close to R
CS
. The NTC should also have an initial
tolerance of better than 5%.
2. Based on the type of NTC, find its relative resistance value
at two temperatures. The temperatures that work well
are 50°C and 90°C. We will call these resistance values
A (R
TH(50°C)
/R
TH(25°C)
) and B (R
TH(90°C)
/R
TH(25°C)
). Note that
the NTC’s relative value is always 1 at 25°C.
3. Find the relative value of R
CS
required for each of these
temperatures. This is based on the percentage change need-
ed, which we will initially make 0.39%/°C. We will call these
r
1
(1/(1+ TC (T
1
– 25))) and
r
2
(1/(1 + TC (T
2
– 25))),
where TC = 0.0039, T
1
= 50°C and T
2
= 90°C.
4. Compute the relative values for
R
CS1
,
R
CS2
, and
R
TH
using:
(
×
(
(
R
A
B
r
r
)
×
A
B
1
(
r
)
×
B
A
B
r
A
B
)
r
B
A
r
A
R
A
R
A
R
r
R
R
R
CS
CS
CS
CS
TH
CS
CS
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
(
1
(
1
1
1
1
1
1
1
=
)
×
×
×
)
×
+
×
(
)
×
)
×
=
=
(8)
REV. 0