Which of the following transducers are not linear ? i. thermistor
ii. thermocouple
iii. IC sensor
i, ii
The IC sensor is the linear one — that is its whole reason for existing — so the non-linear pair is the thermistor and the thermocouple, option 1.
| Sensor | Law | Linear? |
|---|---|---|
| Thermistor | \(R_{T}=R_{0}e^{\beta\left(\frac{1}{T}-\frac{1}{T_{0}}\right)}\) | ✗ Exponential |
| Thermocouple | Polynomial in T, several terms | ✗ Mildly curved |
| IC sensor | \(V=10\ \text{mV}/^{\circ}\text{C}\times T\) | ✓ Linear by design |
The thermistor is the most non-linear of the three by a wide margin. Its resistance falls exponentially with temperature, because the carrier population in a semiconductor rises exponentially as electrons are excited across the band gap. Over a 100 °C span the resistance can change by a factor of fifty, which gives excellent sensitivity but a scale that must be linearised in software or by a shunt resistor.
The thermocouple is only mildly non-linear, but non-linear nonetheless. The Seebeck coefficient itself varies with temperature, so the output is described by a polynomial — standards tables use up to nine or ten terms for accurate work. A type K couple's 41 µV/°C is a convenient average, not a constant.
Why the IC sensor is linear. It does not rely on any bulk material property but on a designed circuit: the difference in base-emitter voltage between two transistors run at different current densities is
\(\Delta V_{BE}=\dfrac{kT}{q}\ln\left(\dfrac{J_{1}}{J_{2}}\right)\)
which is exactly proportional to absolute temperature, since the logarithm is a fixed ratio set by the circuit geometry. On-chip amplification scales this to a convenient 10 mV/°C, and the result needs no linearisation at all.
The trade-off across the three is the useful takeaway: the IC sensor is linear and easy to use but limited to roughly −55 to +150 °C, since it is itself a silicon circuit; the thermistor gives the greatest sensitivity over a narrow band; and the thermocouple, though non-linear and low in output, works from cryogenic temperatures to well over 1500 °C, which neither of the others can approach.
Hence, the non-linear transducers are the thermistor and the thermocouple.
Similar Questions
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Important Questions from Basics of Transducers
_____ converts mechanical displacement into electrical signals.
Which of the following sensors has excellent linearity ?
The mechanical elements that are used to convert the applied force into a displacement are called :
A device used to convert a non-electrical quantity into an electrical signal is called :
Match List - I with List - II.
List - I (Transducers) List - II (Typical Applications) (A) Potentiometric device (I) Relative humidity (B) Resistance hygrometer (II) Velocity (C) Dielectric gauge (III) Displacement (D) Moving coil generator (IV) Thickness Choose the correct answer from the options given below :
