Why is the linearity of a sensor a desirable feature?

Question

I mean, a sensor can have a characteristics like Y=X^2 (X = the input, Y=the output).
That is, I can easily find X if I know Y.
Why is the linearity so important?

Answer 1

First of all multiply and divide are more basic operations compared to square root and this might imply that you need much more complex(and expansive) electronics to convert the signal into the actual measure.

Then the inverse conversion is not unique, i mean that -X produces the exact same Y of +X... otherwise if a negative input produces a negative output could also give problems(remember that square root of a negative number don't exist in real numbers).

Another problem is that small measures give infinitesimal signals while large measures give enormous signals.

Imagine for exampre your sensor output is in volts, if the measure is 0.1 the transducer output signal would be 0.01V, while if the measure is 10 the output signal would be 100V....if the measure is 100 the output would be 10000V. this is quite inpractical....

Actually a sensor that sometimes is better than linear could be logaritmic cause "amplifies" small measures and attenuates higher measures(0.1 would be -1, 1000 would be 3, 1000000 would be 6) and allows you to manage both very small measures and very large measures at the same time.... the quadratic sensor does exactly the opposite. The drowback of logaritmic sensors is that they also need more complex devices to work with compared to linear that are the easiest to manage. this drowback is sometimes small compared to the advantages of a logaritmic sensor but it would be a nonsense with the disvantages of a quadratic sensor.

Answer 2

there are very few sensors which are ideally linear. perhaps speed sensor based on number of pulses per sec is one. The RTD is a resistance sensor and has its deviation form linearity if if we assume the resistance to follow the law R0*(1+ alpha T) as the actually it follows R0*(1+alpha T + beta. T^2). the beta is small and you get a deviation of less than 0.5% when you measure 0 to 200 degC even if you assume the resistance variation to be R0*(1+ alpha T). Well that is in the case of idela sensor which is supposed to have a resistance of 100.000 ohms at zero degC. Practically many sensors do not have (and need not have) this precise value at 0 degC. It could be 100.00 +/- 0.1 ohm or even worse, and one can get away with it during calibration.

If you have an angle sensor whose output is proportional to sin(angle), then again within reasonable (what is reasonable) values, one can pretend that the linear law holds good say for 0 to 30 deg. But if you are measuring 30 to 85 degrees, linearly law just does not hold good. nevertheless it is possible to fit an exact relationship and go ahead with no error provided, the behavior of the sensor is exactly Sine of angle. this is where practical sensors fail, as they do not necessarily have such a rigid relationship. and when a sensor is changed, the one iwhich is placed instead may have a slightly different performance. One may do "recalibration' and make the performance within limits. But if the sensor output is way different from sqroot or square then the errors will be much higher than otherwise. One keeps looking for sensors which have the power as between 1/2 and 2 so that errors are limited. In rear cases, one has to use powers exceeding 2 or less than 0.5. Intensity measurement of light and sound are when logarithmic sensors are required and they cover wide ranges such as with ratios of 10^6 or even more. The ability to measure even a mV while measuring 1000V is seldom necessary. But if you can measure a change of 1mV while measuring 1V or a change of 1V while measuring 1000 V is what is required and what is achieved in practice when you use logarithmic sensor.

Anyway who cares for haggling for a $1 when purchase cost is $1000 ?? so a 0.1% measurement is all that is often necessary, though in many cases, a 1% measurement will be cheaper and if acceptable should be used.



Sensor expert.

Answer 3

The term linearity usually refers to the deviation of the output of a sensor from the ideal value, rather than the law of output / input. In other words it's about its accuracy rather than how it responds to an input.

You could have a sensor with a square law, a square root law or any mathematical function, and they would be perfectly useful, but you'd still want to know what the maximum error in the sensor's output was. In that case it wouldn't be correct to talk about the sensor's linearity, you'd use "error" or "deviation".



Having said all that, in most cases a linear sensor is still preferable purely because it's easier to read; it requires less hardware and/or software.

Answer 4

Offset and accuracy. Y=x^2 is actually Y=(X+/-a)^2. So if a=1 then if x=5 then y= 16 to 36

If it's linear then 4 to 6 is not so bad.

Offset: consider a system where the sensor "zero" is an estimate.

Answer 5

I can answer as an analytical chemist, not an engineer.



One problem with a power-function response is that when the response curve is used to solve for an unknown X based on a response Y, a non-linear equation is required which makes the solution much more difficult compared to a linear response function (this is especially true when the response curve's Y-intercept is not statistically equivalent to zero.)



I am not sure of the 'engineering aspect' of this other part: typically, when one analyzes the data, one includes both the linear (X) and higher-order (e.g., X^2) terms in the regression and performs a statistical test to determine whether the higher-order terms are statistically significant and need to be included in the regression. For powers greater than 2, this gets messy really fast, and it is easier to use chemometric analysis (e.g., MLR or PCA) to analyze the data and develop a model.

Answer 6

Linear sensor just make life easier.