Apogee SL-510, Owner'S Manual

Page: 13 / 18

13
An excitation voltage of 2.5 V DC is recommended to minimize self-heating and current drain, while still
maintaining adequate measurement sensitivity (mV output from thermistor per C). However, other excitation
voltages can be used. Decreasing the excitation voltage will decrease self-heating and current drain, but will also
decrease thermistor measurement sensitivity. Increasing the excitation voltage will increase thermistor
measurement sensitivity, but will also increase self-heating and current drain.
The internal thermistor provides a temperature reference for calculation of target temperature. Resistance of the
thermistor changes with temperature. The thermistor resistance (R
T
, in Ω) is measured with a half-bridge
measurement, requiring an excitation voltage input (V
EX
) and a measurement of output voltage (V
OUT
):
 








OUT EX
OUT
T
V V
V
24900 R








R
R
T
V 1
V
24900 R
where 24900 is the resistance of the bridge resistor in Ω. In the generic equation 1b, V
R
is the direct output from
the half bridge measurement, where V
R
is equal to the ratio of V
OUT
to V
EX
(i.e. V
OUT
= V
R
* V
EX
).
From thermistor resistance (R
T
), temperature (T
K
, in Kelvin) is calculated with the Steinhart-Hart equation and
thermistor specific coefficients (30 kOhm @ 25 C):
3
T T
K
)) R (ln( C ) R ln( B A
1
T
 

For temperatures less than zero Celsius: A = 9.32960 x 10
-4
, B = 2.21424 x 10
-4
, and C = 1.26329 x 10
-7
For temperatures greater than zero Celsius: A = 9.32794 x 10
-4
, B = 2.21451 x 10
-4
, and C = 1.26233 x 10
-7
Longwave Radiation Measurement
The detector output from SL-510 and SL-610 pyrgeometers follows the fundamental physics of the Stefan-
Boltzmann Law, where radiation transfer is proportional to the fourth power of absolute temperature. The mV
signal from the detector is linearly proportional to the longwave radiation balance between the target and
detector, analogous to longwave radiation emission being linearly proportional to the fourth power of
temperature in the Stefan-Boltzmann Law. A modified form of the Stefan-Boltzmann equation is used to calibrate
sensors, and subsequently, calculate longwave irradiance from target:
4
D 2 D 1 i
T k S k LW
  
where LW
i
is longwave radiation emitted from target [W m
-2
], S
D
is the millivolt signal from the detector, T
D
is the
temperature measured with a thermistor thermally bonded to the detector [K], σ is Stefan-Boltzmann constant =
5.6704 x 10
-8
W m
-2
K
-4
, and k
1
and k
2
are custom calibration coefficients. During the calibration process, k
1
and k
2
are determined by minimizing the difference between measurements of LW
i
from each sensor and reference LW
i
measured with transfer standard pyrgeometers. The derived k
1
and k
2
coefficients are the custom calibration
coefficients listed on the calibration certificate (shown above) that comes with each SL-510 and SL-610
pyrgeometer.
LW
i
Incoming Longwave, in W m
-2
k
1
Calibration coefficient 1 (see cal. sheet)
k
1
Calibration coefficient 2 (see cal. sheet)
S
D
Signal from detector, mV (Apprx. -23.5 to 23.5 mV)
σ Stefan-Boltzmann constant, 5.6704 x 10
-8
W m
-2
K
-4
T
D
Detector temperature, in K