Fundamentals of Instrumentation and Measurement

Chapter 9¹

Elaboration of Models for the Interaction Between the Sensor and its Environment

9.1. Modeling a sensor’s interactions with its environment

The focus of this chapter will be to describe the relation between a sensor’s output variables and the physical variable applied to its input, called the measurand.

This relation can also take into account the role played by other variables, a priori external, that can cause variations in the output signal (some examples are the sensor’s feed tension and the temperature).

9.1.1. Physical description of the model

The best approach is first to analyze what a sensor does and then to understand and completely describe the physical processes of transduction. We then convert these into mathematical forms by using physical laws. The result is an equation that links output variables to input variables (creating a knowledge model).

This is a difficult task, requiring a complete understanding of all the phenomena involved. In general, this process is long, especially for complex phenomena, but this approach does have the advantage of being easily transposable to other, similar systems.

9.1.2. Phenomenological approach

This is an experimental method that consists of collecting data. The values of the output signals are compared to the values taken by the input variables under a set of given conditions. The study of the structure of these data helps us collect results in the form of mathematical relations (dependency models) that explain the ...