Question

An IR sensor is required to develop an output of 5 V for an IR radiation of 20 mW/cm². For increased sensitivity, aluminum/silicon thermocouples are used because they have an output of 446mV/°C. An aluminum absorber of area 4cm² and thickness 20µm is used with an absorption efficiency of 80%. Aluminum has a density of 2.712 g/cm³ and a heat capacity of 0.897J/g/°C. The required output must be obtained within 100ms.

a. What is the increase in the temperature of the absorber?

b. Calculate the number of thermocouples needed to obtain the required output.

c. If the output of the device is measured using a digital voltmeter with a resolution of 0.1V, what is the effective resolution of the sensor?

Answer 1

According to Stefan-Boltzman law relates the total amount of radiation emitted by an object to its temperature

E= * T^4 where E=total amount of radiation emitted by an object per square meter

=Stefan-Boltzman constant= 5.67 *10 ^-8 Watts m^-2 K^-4

T is the temperature of the object (Kelvin)

E=20 mW/m^2 (given)

a)

T=2.43 kelvin

b) Number of thermocouples

output voltage of a simple thermocouple(V) at reference temperature at zero degrees=

V=A*T +0.5 *B * T^2 +0.33* C*T^3 ;where T is the temperature of measuring junction in degree celusis

A ,B,C are constants that depend on thermocouple material

Sensitivity= =A +B * T + C*T^2

446 *10^-3 =A +B * T + C*T^2

RESOLUTION= V_reference/ 2 ^N

0.1= 5/ 2 ^N ; N=6