GATE 2020 EE – Question 63
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, $R_{thermistor}=2(1+\alpha T)\ \text{k}\Omega$, where $T$ is the temperature in $^\circ$C. The temperature coefficient, $\alpha$, is $-(4\pm0.25)$ %/$^\circ$C. Circuit parameters: $R_1=1\ \text{k}\Omega$, $R_2=1.3\ \text{k}\Omega$, $R_3=2.6\ \text{k}\Omega$. The error in the output signal (in V, rounded off to 2 decimal places) at 150$^\circ$C is ________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.26 to 0.28
Explanation
The circuit is a non-inverting amplifier with gain $1+\frac{R_3}{R_2}=3$ fed by the divider $V_+=\frac{3R_1}{R_{th}+R_1}$, with the $0.1$ V source shifting the output by $-\frac{R_3}{R_2}(0.1)=-0.2$ V. Using the extreme values $\alpha=-4.25\%$ and $-3.75\%$ at 150 C gives $V_+$ values that differ from the nominal by $0.026$ V and $0.030$ V, i.e. output errors of about $0.23$ V to $0.27$ V. The value shown is the larger deviation.