Question

Suppose you use phase sensitive detection to measure the voltage acrose a temperature sensor, immersed in a bath of water. Suppose you wish to measure every 10 degrees Celsius as you heat the water from 0C to 100C. If the water is heated at one degree per minute, you want the time constant to be small enough to track temperature changes every 10C.

A) Determine an appropriate RC time constant which will allow you to track the changes in temperature.

B) Determine an appropriate modulation frequency for the temperature experiment. Try to average just over 100 modulation cycles within one time constant.

Answer 1

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A. For racking 10 degree C , the time required is every 10 mins because temp changes by 1 degree C every minute. Thus, the measurement frequency is every 10 mins, which means the temperature should have settled by 10 mins. Thus, we can safely equate 10 times the time constant to 10 mins, yielding a time constant of 1 minute. Therefore, RC = 1 minute = 60 secs

?B. For obtaining 100 cycles of modulation in one time constant, we need 100 cycles in 60 secs i.e. a modulation frequency of 100/60 Hz i.e. around 17Hz. A safe value would be 20Hz.