Datasheet

LTC3883/LTC3883-1
60
3883fa
For more information www.linear.com/LTC3883
APPLICATIONS INFORMATION
ACCURATE DCR TEMPERATURE COMPENSATION
Using the DC resistance of the inductor as a current shunt
element has several advantages—no additional power
loss, lower circuit complexity and cost. However, the
strong temperature dependence of the inductor resistance
and the difficulty in measuring the exact inductor core
temperature introduce errors in the current measurement.
For copper, a change of inductor temperature of only 1°C
corresponds to approximately 0.39% current gain change.
Figure 30 shows a DC/DC converter sample layout (right)
and its corresponding thermal image (left). The converter
is providing 1.8V, 1.5A to the output load.
Heat dissipation in the inductor under high load condi
-
tions creates transient and steady state thermal gradients
between
the inductor and the temperature sensor, and the
sensed temperature does not accurately represent the
inductor core temperature. This temperature gradient is
clearly visible in the thermal image of Figure 30. In addition,
transient heating/cooling effects have to be accounted for
in order to reduce the transient errors introduced when
load current changes are faster than heat transfer time
constants of the inductor. Both of these problems are
addressed by introducing two additional parameters: the
thermal resistance θ
IS
from the inductor core to the on-
board temperature sensor, and the inductor thermal time
constant τ
. The thermal resistance θ
IS
[°C/W], is used to
calculate the steady-state difference between the sensed
temperature T
S
and the internal inductor temperature T
I
for a given power dissipated in the inductor P
I
:
T
I
– T
S
= θ
IS
P
I
= θ
IS
V
DCR
I
OUT
The additional temperature rise is used for a more accurate
estimate of the inductor DC resistance R
I
:
R
I
= R0 (1 + a [T
S
– T
REF
+ θ
IS
V
DCR
I
OUT
])
In the equations above, V
DCR
is the inductor DC voltage
drop, I
OUT
is the RMS value of the output current, R0 is
the inductor DC resistance at the reference temperature
T
REF
and a is the temperature coefficient of the resistance.
Since most inductors are made of copper, we can expect
a temperature coefficient close to a
CU
= 3900ppm/°C.
For a given a, the remaining parameters θ
IS
and R0 can
be calibrated at a single temperature using only two load
currents:
R
O =
R2 – R1
( )
P2+P1
( )
– R2+R1
( )
P2 – P1
( )
a T2 – T1
( )
P2+P1
( )
– P2 – P1
( )
2+ a T1+ T2 – 2T
REF
[ ]
( )
θ
IS
=
1
aRO
•
a R1+R2
( )
T2 – T1
( )
– R2 –R1
( )
2+ a T1+ T2 – 2T
REF
[
]
(
)
a T2 – T1
( )
P2+P1
( )
– P2 – P1
( )
2+ a T1+ T2 – 2T
REF
[ ]
( )
The inductor resistance, R
K
= V
DCR(K)
/I
OUT(K)
, power dis-
sipation P
K
= V
DCR(K)
I
OUT(K)
and the sensed temperature
T
K
, (K = 1, 2) are recorded for each load current. To increase
Figure 30. Thermal Image and Layout Photo
DC/DC
CONVERTER
3883 F30
INDUCTOR
TEMPERATURE
SENSOR