GATE EE 2020 Set 1 — Question 63
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Analog & Digital Electronics → Measurement Principles → Error Analysis
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Question
The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance, , where is the temperature in . The temperature coefficient, , is . Circuit parameters: , , . The error in the output signal (in V, rounded off to 2 decimal places) at is ______.
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Solution
Given: with , , , , a V source feeding the thermistor- divider into the non-inverting input and a V source feeding at the inverting input, with as feedback.1. Thermistor resistance at the stated operating temperature
With the nominal coefficient and :2. Why this blocks the computation
The linear model is only meaningful while , i.e. for with . At the model returns a negative resistance, so the divider voltage at the non-inverting input - and therefore the nominal output signal and its error band obtained from - cannot be evaluated for a physically realizable circuit.3. Consequence
Because the specified operating point is outside the validity range of the given resistance law, the data are mutually inconsistent and no finite error voltage follows from them.Answer: No valid numerical error can be obtained - at the given law makes the thermistor resistance negative, so credit is given irrespective of the response.
With the nominal coefficient and :2. Why this blocks the computation
The linear model is only meaningful while , i.e. for with . At the model returns a negative resistance, so the divider voltage at the non-inverting input - and therefore the nominal output signal and its error band obtained from - cannot be evaluated for a physically realizable circuit.3. Consequence
Because the specified operating point is outside the validity range of the given resistance law, the data are mutually inconsistent and no finite error voltage follows from them.Answer: No valid numerical error can be obtained - at the given law makes the thermistor resistance negative, so credit is given irrespective of the response.
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