Datasheet

48
1
8 33
POS
A
R
. k
=
æ ö
+
ç ÷
W
è ø
0 500 1500 2000
R
POS
- W
49
1000
Amp Gain - V/V
Current Sense AMP Gain
vs
RPOS
Normal Gain
Minimum Gain Corner
(minimum sheet and hot
temperature)
Maximum Gain Corner
(minimum sheet and Cold
temperature)
48
47
46
45
44
43
42
41
40
39
38
37
36
35
UCD7230
www.ti.com SLUS741D –NOVEMBER 2006–REVISED JANUARY 2010
With the addition of R
POS
and R
NEG
, the natural gain, A, of the current sense is predictably decreased as:
(3)
For R
POS
<< 8.33 kΩ, the gain is 48. While the 400 kΩ and 8.33 kΩ are well matched, it is important to keep
R
POS
as small as possible since they have absolute variation from chip-to-chip and over temperature. The graph
in Figure 6 shows the band of expected gain for A as a function of R
POS
. The gain variation at R
POS
= 1 kΩ
results in around ±4% error. However, the tolerance of the value of R in the inductor has a more significant effect
on measurement accuracy as does the temperature coefficient of R. Copper has a temperature coefficient of
approximately 3800 ppm/°C. For a 100°C rise in winding temperature, the dc resistance of the inductor increases
by 38%. The worst case scenario would be a cracked core or under-designed inductor in which cases the core
could tend towards saturation. In that scenario, inductor current could change slope drastically and is not
correctly modeled by the capacitor voltage.
Note that inferring inductor current by use of a parallel RC has an additional caveat. As long as T
RC
= R
POS
C is
the same as T
LR
= L/R, then the voltage across C is the same as the IR drop across the equivalent R of the
inductor. If the time constants don't match, the average voltage across C is still the same as the average voltage
across R, but the indication of ripple current amplitude will be off. Furthermore, load transients results in reported
current that appears to have overshoot or undershoot if T
RC
is respectively faster or slower than T
LR
.
While the amp faithfully passes the sensed dc current signal, it should be noted that the amplifier is bandwidth
limited for normal switching frequencies. Therefore, AO represents a moving average of the sensed current.
Figure 6. Current Sense Amp Gain as a Function of R
POS
Copyright © 2006–2010, Texas Instruments Incorporated 13
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