Scaling and linearization: Linearization

Linearization is the term applied to the process of correcting the output of an ADC in order to compensate for non-linearities present in the response curve of a measuring system. Non-linearities can arise from a number of different components, but it's often the sensors themselves that are the primary sources.

In order to select an appropriate linearization scheme, it obviously helps to have some idea of the shape of the response curve. The response of the system might be known, as is the case with thermocouples and RTDs. It might even conform to some recognized analytical function. In some applications the deviation from linearity might be smooth and gradual, but in others, the non-linearities might consist of small-scale irregularities in the response curve.

Some measuring systems may also exhibit response curves that are discontinuous or, at least, discontinuous in their first and higher order derivatives.

There are several linearization methods to choose from and what ever method is selected, it must suit the peculiarities of the system's response curve. Polynomials can be used for linearizing smooth and slowly varying functions, but are less suitable for correcting irregular deviations or sharp 'corners' in the response curve. They can be adapted to closely match a known functional form or they can be used in cases where the form of the response function is indeterminate. Interpolation using look-up tables is one of the simplest and most powerful linearization techniques and is suitable for both continuous and discontinuous response curves. Each method has its own advantages and disadvantages in particular applications and these are discussed in the following sections.

The capability to linearize response curves in software can, in some cases, mean that simpler and cheaper transducers or signal conditioning circuitry can be used. One such case is that of LVDT displacement transducers. These devices operate rather like transformers. An AC excitation voltage is applied to a primary coil and this induces a signal in a pair of secondary windings. The degree of magnetic flux linkage and , therefore, the output from each of the secondary coils is governed by the linear displacement of a ferrite core along the axis of the windings. In this way, the output from the transducer varies in relation to the displacement of the core.

Simple LVDT designs employ parallel-sided cylindrical coils.

However, these exhibit severe non-linearities (typically up to about 5 or 10 per cent) as the ferrite core approaches the ends of the coil assembly. The non-linearity can be corrected in a variety of ways, one of which is to layer windings in a series of steps towards the ends of the coil. This can reduce the overall non-linearity to about 0.25 percent. It does, however, introduce additional small-scale non-linearities (of the order of 0.05 to 0.10 per cent) at points in the response curve corresponding to each of the steps.

It is a relatively simple matter to compensate for the large-scale non-linearities inherent in parallel-coil LVDT geometries by using the polynomial linearization technique discussed in the following section. Thus, software linearization techniques allow cheaper LVDT designs to be used and this has the added advantage that no small-scale (stepped winding) irregularities are introduced. This, in turn, makes the whole response curve much more amenable to linearization.

There are many other instances where software linearization techniques will enhance the accuracy of the measuring system and at the same time allow simpler and cheaper components to be used.

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