Datasheet
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R
REL(L)
+ 1 ) TC
L
ǒ
T
L
* T
BASE
Ǔ
(dimensionless)
(7)
gm
(REL)
+ 1 ) TC
GM
ǒ
T
IC
* T
BASE
Ǔ
(dimensionless)
(8)
T
IC
* T
BASE
+
ǒ
T
L
* T
BASE
Ǔ
k
THM
(9)
R
REL(eff)
+ R
REL(L)
gm
REL
+
ƪ
1 ) TC
L
ǒ
T
L
* T
BASE
Ǔƫ
ƪ
1 ) k
THM
TC
GM
ǒ
T
L
* T
BASE
Ǔƫ
(dimensionless)
TPS40100
SLUS601–MAY 2005
APPLICATION INFORMATION (continued)
The relative resistance change in the inductor is given by:
where
• R
REL(L)
is the relative resistance of the inductor at T
L
compared to the resistance at T
BASE
• TC
L
is the temperature coefficient of copper, 4000 ppm/°C or 0.004
• T
L
is the inductor copper temperature (°C)
• T
BASE
is the reference temperature, typically lowest ambient (°C)
The relative gain of the current sense amplifier is given by a similar equation:
where
• gm
REL
is the relative gain of the amplifier at T
IC
compared to the gain at T
BASE
• TC
GM
is the temperature coefficient of the amplifier gain, -2000 ppm/°C or -0.002
• T
IC
is the device junction temperature (°C)
• T
BASE
is the reference temperature, typically lowest ambient (°C)
The temperature rise of the device can usually be related to the temperature rise of the inductor. The relationship
between the two temperature rises can be approximated as a linear relationship in most cases:
where
• T
IC
is the device junction temperature (°C)
• T
BASE
is the reference temperature, typically lowest ambient (°C)
• T
L
is the inductor copper temperature (°C)
• k
THM
is the constant that relates device temperature rise to the inductor temperature rise and must be
determined experimentally for any given design
With these assumptions, the effective inductor resistance over temperature is:
(10)
R
REL(eff)
is the relative effective resistance that must be compensated for when doing the compensation. The
circuit of Figure 4 shows a method of compensating for thermal shifts in current limit. The NTC thermistor (R
NTC
)
must be well coupled to the inductor. C
FLT
should be located as close to the device as possible.
12