
REV. 0
–12–
ADP3166
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 the static output droop
resistance (R
O
).
The output current is measured by summing together the voltage
across each inductor and then 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
PH(X)
R =
R
CS
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
, and then solve for
R
PH(X)
by
rearranging Equation 6.
=R
PH(X)
R
R
R
L
O
CS
×
R
=
1. m
k =
PH(X)
1. m
100
145. k
×
Next, use Equation 6 to solve for
C
CS
:
C
=
nH
100
×
1. m
k
=3 75
nF
CS
600
It is best to have a dual location for
C
CS
in the layout so stan-
dard 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 10% capacitor. The closest standard 1% value for R
PH(X)
is
147 k
.
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
(T
C
) 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 tem-
perature variation of the inductor’s DCR. Due to the nonlinear
nature of NTC thermistors, resistors R
CS1
and R
CS2
(see Figure 2)
are needed to linearize the NTC and produce the desired tem-
perature tracking.
CSSUM
18
CSCOMP
PLACE AS CLOSE AS POSSIBLE
TO NEAREST INDUCTOR
OR LOW SIDE MOSFET
17
CSREF16
ADP3166
C
CS
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 2. 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 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 to use that work well are
50
°
C and 90
°
C. We will call these resistance values A (A is
R
TH(50
°
C)
/R
TH(25
°
C))
and B (B is R
TH(90
°
C)
/R
TH(25
°
C))
. Note that
the NTC’s relative value is always 1 at 25
°
C.
3.Next, find the relative value of R
CS
required for each of these
temperatures. This is based on the percentage change needed,
which we will initially make 0.39%/
°
C. We will call these r
1
(
r
1
is 1/(1 + TC (
T
1
– 25))) and r
2
(r
2
is 1/(1 + TC (
T
2
– 25)))
,
where T
C
= 0.0039,
T
1
= 50
°
C and
T
2
= 90
°
C.