Datasheet

V
DCR
+
ǒ
V
IN
* V
OUT
Ǔ
DCR
DCR ) w L
V
C
+
ǒ
V
IN
* V
OUT
Ǔ
1
w C
ǒ
R )
1
w C
Ǔ
V
C
+
1
w C
ǒ
R )
1
w C
Ǔ
+
DCR
DCR ) w L
;
L
DCR
+ R C; t
DCRL
+ t
RC
K(T) + 1 ) 0.0039
(
T * 25
)
R
L
DCR
C
R2
R1
R
NTC
R
THE
TPS40090
TPS40091
www.ti.com SLUS578B –OCTOBER 2003– REVISED MAY 2006
THERMAL COMPENSATION OF DCR CURRENT SENSING
Inductor DCR current sensing is a known lossless technique to retrieve a current proportional signal. Equation 14
and Equation 15 show the calculation used to determine the DCR voltage drop for any given frequency. (See
Figure 10)
(14)
(15)
Voltage across the capacitor is equal to voltage drop across the inductor DCR, V
C
= V
DCR
when time constant of
the inductor and the time constant of the R-C network are equal:
(16)
The output signal generated by the network shown in Figure 10 is temperature dependant due to positive thermal
coefficient of copper specific resistance as determined using Equation 17. The temperature variation of the
inductor coil can exceed 100°C in a practical application leading to approximately 40% variation in the output
signal and in turn, respectively move the overcurrent threshold and the load line.
(17)
The relatively simple network shown in Figure 11 (made of passive components including one NTC resistor) can
provide almost complete compensation for copper thermal variations.
Figure 10. Figure 11.
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