linearising a sensor

I linearize stuff with a PIC with a compensation table in memory.

D from BC

1. Put it in a loop. If the sensor has some manner of feedback (such as adding another transducer to feed back to the sensor, etc.), sufficient negative feedback will linearize it. Baxandall(?) covered this almost a century ago (and likely, mechanical engineers even earlier).

1. Construct an inverse function, perhaps out of piecewise functional blocks (op-amps with lots of diodes and resistors), or components with specific properties (e.g., FET for squared terms, silicon junction for exponential terms) to effectively neutralize the sensor's own nonlinearity.

2. Combine 1. and 2., by using a (known to be linear) transducer to excite an identical isolated sensor, enclosing this in a feedback loop. The error signal from this sensor feedback loop is the exact inverse function of the sensor's nonlinearity (within reason). Add the sensor's signal to this function block and you will get a linear output.

#1 and 3 have relatively slow response time, but can be arbitrarily accurate (the limiting factor is how much feedback you apply and the delay time you can allow for it to settle to that accuracy). #1 may not be practical, especially if your pressure sensor must connect to other things; connecting pressures "in series" may not be very practical. #2 is the fastest (effectively instantaneous), but must be tediously adjusted to accuracy.

If you're digitizing the signal anyway, you might as well calibrate your own correction table for the sensor, forgoing the analog solution. Sensor voltage maps to address in memory, which then maps to the corrected value. What's more, if you have a linear sensor, you could generate the conversion easily enough automatically. (This of course begs the question, why don't you have a linear sensor to begin with? I'd assume you have some sort of standard somewhere.)

Tim

-- Deep Fryer: A very philosophical monk. Website @

If you mean that the output is a function, just not a linear function, you can calibrate with a few points (depending on what the function is). This is how you work with an NTC thermistor, for example. If you mean the output isn't even monotonic, then you've got a much more complex problem. If it's monotonic but "unpredictable" you could build a jig to calibrate it over all possible conditions.

As posed your question is unanswerable. You don't say what the sensor transfer function is or over what dynamic range you are hoping to compensate the thing over. Knowing the sensor type and application would help. Vacuum gauges have very different calibration problems to diamond anvil controllers (picking the 2 extremes).

Do you mean it is linear with small non-linear deviations, or gives a reciprocal, square law or logarithmic response ?

Basically if it has to work with a range of sensors then you need to be able to calibrate the system against a suitable number of fixed points when the new sensor is installed. If you already know the functional form of the transfer function then you need slightly fewer calibration points to get a decent result. And watch out for numerical instabilities when inverting anything beyond a cubic polynomial.

Regards, Martin Brown

This is why some instruments are so expensive - they are individually calibrated and sometimes even individually temperature compensated by running them at different temperatures in an environmental chamber. By a person. This process can be semi-automated if the production run is large enough. Like many things in life, it sounds simple when your boss tells you to do it, but when you begin looking into exactly how to do it...

I would think, though, that if you have the sensor datasheet, the manufacturer will show a graph or something to show you the shape of the response, and hopefully some suggestions about how to use the sensor.

As a rule of thumb, cheap sensors have lots of individual variation, and can often only be used as a threshold detector. To get a sensor good enough to measure quantitatively with, you need to spend more.

With pressure sensors, watch out for temperature compensation. If you don't have a temperature compensated sensor, then you may have to add your own compensation circuitry. That is not easy to do, and there are often multiple adjustment factors that can be interactive i.e, adjust one and it upsets the other.

With regards to linearity, use the linear sensor and then scale the output voltage. That is much simpler than trying to linearise a non- linear sensor.

Dave.