handbook of modern sensors

Table 16.3. NTC Thermistor. Practical Use of Three Models a
Simple Model Fraden Model Steinhart–Hart Model
Maximum Error ±0.7 ◦ C ±0.03 ◦ C ±0.003 ◦ C
from 0 ◦ Cto70 ◦ C
Number of 2 3 0
characterizing
temperatures
Number of 2 2 3
calibrating
temperatures
Resistance– S = S 0 e βm(1/T−1/T 0 ) S = S 0 e β 0 [1+γ(T−T 0 )](1/T−1/T 0 ) S = e (A 0 +A 1 /T+A 2 /T2 +A 3 /T 3 )
temperature
dependence
Characterizing points
No characterization
required for a
two-point calibration
Characterizing factor γ =
Characterizing a Production Lot or Type of Thermistors
S a at T a , S b at T b , and S c at T c
for a temperature range from T a to T c
where T b is in the middle of the range
( βx
β y
− 1
)
1
T c − T a
, where
β x = ln(S c/S b )
(1/T c − 1/T b ) ,β y = ln(S a/S b )
(1/T a − 1/T b )
Calibrating an Individual Thermistor
No characterization required
472 16 Temperature Sensors
Calibrating points S 0 at T 0 and S 1 at T 1 S 0 at T 0 and S 1 at T 1 S 1 at T 1 , S 2 at T 2 , and S 3 at T 3
Insert resistance S,
the characterizing
factors and the
calibrating
factors into the
equation
( 1
T = + ln(S )
1/S 0 ) −1
T 0 β m
where β m = ln(S 1/S 0 )
(1/T 1 − 1/T 0 )
Analytic Computation of Temperature T (in Kelvin) from Resistance S
( ) 1 ln(S/S
T = +
0 ) −1
T 0 β m [1 − γ(T 1 − T r )]
( 1
+ ln(S/S ) −1
0)
T 0 β m
where T r =
and β m = ln(S 1/S 0 )
(1/T 1 − 1/T 0 )
T =[A + B ln S + C(ln S) 3 ] −1 where
(
C = G − ZH )[ (
ln S 3 )
F 1 − ln S3 2 − Z F
B = Z −1 [ (
G − C ln S
1 3 )]
− ln S3 2
A = T −1 − C ln S
1 3 − B ln S 1
Z = ln S 1 − ln S 2 ,F = ln S 1 − ln S 3
H = T −1 − T −1 ,G= T −1 − T −1
1
1
3
1
2
(
ln S1 3 ) ] −1
− ln S3 3
a A thermistor type or lot should be characterized first to find the characterizing factors. An individual thermistor is calibrated to determine the calibrating factors. To compute
any temperature T , measure the thermistor resistance S and calculate the temperature with use of the characterizing and calibrating factors. All temperatures are in Kelvin.