THE ADVANTAGES OF DIGITAL DISPLACEMENT
TRANSDUCER OVER LVDT

(Technical Note #105)

The use of the Linear Variable Differential Transformer (LVDT) in dilatometry is a widespread practice that has its roots in the historical development of this technique. LVDTs were , for a long time, the only displacement transducers readily adoptable for this application, easy to integrate with analog data recorders, and affordable in cost. Digital transducers, although in principle have been known for many years, became practical to use and affordable in price only in the past decade. They are much more complex than LVDTs and are considerably more difficult to integrate into systems. Perhaps due to these initial difficulties and development costs, other dilatometer manufacturers have been reluctant to capitalize on this new technology.

Comparison:

A digital device is distinguished from an analog device in that its response to a displacement is a series of discrete pulses or voltage levels (each representing a well-defined amount of travel) rather than a continuously variable proportional signal. When properly registered, these finite steps resemble a staircase with a displacement being defined by the number of steps it takes to reach. Digital transducers employ mechanical means to generate such step signals and therefore they will remain just as stable as the mechanical parts themselves used to generate those signals. For example, such a device can be constructed by painting stripes at uniform intervals on a piece of glass and pass it in front of a light sensor. The distance the glass travels can be expressed with the number of "dark" and "light" transitions it causes. When the distance between the stripes is accurately known, then the exact magnitude of the displacement can be derived. It is easy to see that the measurement will be highly repeatable as long as the glass or the markings do not change, and that it will not be sensitive to variations in light level or sensor gain at all. It is further recognizable that once such a system is made, it requires no periodic calibration as there is nothing one can calibrate, thus its accuracy remains constant with time.

Analog displacement systems, on the other hand, rely on a transduction process that is continuous, and a finite displacement causes a corresponding proportional electrical signal. For example, in the case of the LVDT, the electromagnetic coupling of the primary to the secondary coils is varied by shifting the iron core within. The signal generated by a given displacement of this core will be governed by the displacement and also the input (primary) voltage, the load on the output (secondary) coil, and the gain of the amplifier sensing it, just to mention a few. None of these are inherently related to distance, therefore it is necessary to adjust gains and offsets in the signal processing network until the output signal becomes proportional to the core displacement. Once this condition of "calibration" is achieved, it must be maintained over long periods of time, a task not easy to accomplish even with modern integrated circuits. To further complicate matters linear relationship can be observed only over a narrow portion of the coil. Since there is an ever present mechanism for loss of calibration (amplifier drift, excitation voltage variation, temperature sensitivity of resistors and potentiometers, etc.) even in the short term, it is necessary to frequently verify the signal to displacement proportionality and recalibrate if necessary.

Performance:

Calibration for the Anter digital transducer is intrinsic and it is done in the factory when the dark lines are accurately photo engraved on the nearly zero expansion glass substrate. There is nothing further (such as periodic calibration) one can or should do. In contrast, for any analog device, one must provide some well-defined means, such as a micrometer to move the sensor tip (the core in case of the LVDT) a known amount and then measure the corresponding electrical signal and adjust it to a defined relationship. In the digital circuits, no such adjustments are needed, as it makes no difference at what light level the optical sensor operates to pick up the light-to-dark transitions.

In light of this, it is worthwhile to examine the analog calibration process itself, as it has a profound effect on the ultimate performance of a dilatometer. Using a micrometer to generate the known displacement limits the accuracy to that of the micrometer itself, reduced somewhat by the errors in visually lining up the markings. Therefore it is meaningless to expect accuracy from such a system that is better than the resolution of the micrometer. Using a normal, small thimble micrometer with 0.01mm markings, to calibrate a short stroke LVDT with the total displacement only ±2mm, thus the best accuracy one can achieve is about ±0.15% of range, or ±0.01mm.

The digital displacement transducers Anter employs are made to measure in 0.001mm discrete steps over a 25mm travel, yielding a ±0.005% of range resolution, but more importantly it is 15 times better than the short stroke LVDT calibrated with a micrometer.

Another important factor to consider is the measure of linearity associated with the signal in response to a truly linear displacement. If a device is truly linear, it will produce signals in strict proportion to smaller and smaller subdivisions of the displacement. For example, if an LVDT moved by a micrometer screw produces a 1 volt signal for a 1cm displacement, then it is expected to produce a 0.5 volt for a 0.5cm displacement, and so on. As the subdivisions are taken to be smaller and smaller, the corresponding output voltages may begin to differ slightly from the expected value. This is due to the inherent nonlinearity every device possesses. When the smallest division of the micrometer is reached, however, one can no longer ascertain that a further subdivision would produce a corresponding proportional output or not. Conversely, any electrical output that falls between the two values corresponding to the two adjacent smallest subdivisions of the micrometer can not be assumed to be a result of a displacement proportional to it. It is scientifically incorrect to postulate that a device is more accurate, or has a better linearity than what can be verified or calibrated. Consequently, to ascribe accuracy and linearity to an LVDT that is beyond that of the micrometer screw (or any other similar device) which was used to calibrate it is simply meaningless. Claims of "infinite resolution" imply perfect linearity which simply does not exist.

For LVDTs, this claim is even more frivolous, as short range nonlinearities caused by winding-to-winding magnetic field variations are inherent to the device due to its construction.

Adding further amplification to the output of a transducer may seemingly resolve the electrical output to a higher degree, but such a process is nothing more than a magnification of noise in terms of the distance resolution, and therefore it is meaningless.

In the case of the digital transducer, the inherent accuracy and linearity within the stated limits was built in during production when accuracies in producing exact displacements are a lot more possible than out in the field with the use of a micrometer screw. By nature, the device can not distinguish any displacement signals that fall between the finest subdivisions, and therefore the resolution is fixed but very well-defined.

Summary

In dilatometry digital displacement transducer is far superior to analog devices, because:

• it requires no periodic calibration.
• its accuracy, resolution, and linearity does not change with time.
• it is minimally temperature sensitive, requiring no special environmental controls.
• it has an inherently long range while maintaining high resolution and linearity.
• it has very high ABSOLUTE accuracy and defined resolution.

Specifically, LVDTs are inferior to digital displacement transducers because:

• an LVDT can either provide a long range or high resolution, but not both.
• an LVDT requires frequent calibration.
• an LVDT is more sensitive to temperature changes, especially from the pushrod which is directly connected to it, and therefore requires a more stringent environment control than digital transducers in demanding applications. But even with the use of constant temperature circulation the heat up of the iron core cannot be eliminated.
• an LVDT is a relative, gain sensitive device, with overall performance dependent on the stability and linearity of the signal conditioning network.