A thermoelectric-based power meter has a response time of 20 s and sensitivity (output voltage per unit incident power) of 90 mV/W. If the time response is reduced to 8 s by increasing the thermal conductance between the sensor element and heat sink, what will be the new sensitivity?
To calculate the new sensitivity of the thermoelectric-based power meter, we need to use the principle of time constant or thermal time constant.
The time constant (τ) of a system is the time it takes for the system to reach approximately 63.2% of its final response when subjected to a step input. It is given by the equation:
τ = Response time / ln(2)
In this case, the initial time constant is 20 seconds. So, we have:
τ = 20 s / ln(2) ≈ 28.85 s
Now, if the time response is reduced to 8 seconds, we need to find the new time constant:
τ' = 8 s / ln(2) ≈ 11.54 s
The relationship between the sensitivity and the time constant in thermoelectric-based power meters is given by the equation:
Sensitivity ∝ 1 / (time constant)
Therefore, we can calculate the new sensitivity using the following formula:
New Sensitivity = Initial Sensitivity × (Initial Time Constant / New Time Constant)
New Sensitivity = 90 mV/W × (28.85 s / 11.54 s)
New Sensitivity ≈ 225 mV/W
So, the new sensitivity of the thermoelectric-based power meter will be approximately 225 mV/W.