The sensing element plays a crucial role in converting physical quantities into electrical signals. For instance, a Wheatstone bridge can be employed to transform pressure into an electrical output. However, many sensing elements exhibit inherent non-linear behavior, meaning their output does not vary proportionally with the physical quantity being measured. Instead, the output changes in a non-linear fashion as the input varies.
To address this non-linearity, a sensor signal conditioner is used. This component helps correct the irregularities in the output of the sensing element, ensuring more accurate and reliable data. In this article, we explore two common techniques for linearizing sensor outputs: 1) look-up tables (LUTs) or interpolation; and 2) polynomial fitting or curve modeling. We will compare these methods and discuss their respective advantages and limitations.
A complete sensor system typically consists of a sensing element and a signal conditioner. The sensing element, such as a Wheatstone bridge or a hot wire anemometer, converts physical parameters like pressure or air mass flow into electrical signals. The signal conditioner then processes these signals, correcting issues like non-linearity, temperature drift, and dynamic response. Figure 1 illustrates the overall structure of the sensor system.
Figure 1: A block diagram showing the relationship between the input physical quantity (x), the sensing element output (y), and the conditioned output (z). The signal conditioner is responsible for improving the quality of the signal by addressing non-ideal characteristics such as non-linearity and temperature effects.
This article focuses on how to handle non-linearity in sensor outputs using signal conditioning techniques. Although various forms of non-linearity exist, we will focus specifically on second-order non-linearity to demonstrate the process of linearization. These principles can be extended to other types of non-linear behavior as well.
If the relationship between the input (x) and output (y) of a sensing element follows the equation shown in Equation 1, it can be classified as having second-order non-linearity:
In this equation:
- a = offset of the sensing element, representing the output when the physical quantity is at its minimum value
- b = span of the sensing element, calculated as the difference between the maximum and minimum outputs
- c = coefficient representing the second-order non-linearity
- x = the measured physical quantity
- y = the output of the sensing element, which depends on x
For example, consider a nonlinear sensing element with the following parameters:
- x ranges from 0 to 1 (normalized, no units)
- a = 0
- b = 1
- c = 10% full scale (FS), where FS = b
With these values, the functional relationship becomes Equation 2. Figure 2 shows the graph of this function for x ranging from 0 to 1. As seen in the figure, when x = 0.5, the output y is 0.6 instead of the expected 0.5 if the system were perfectly linear. This deviation represents a 10% non-linearity at the midpoint, resulting in a bulge in the output curve.
Figure 2: Output of a nonlinear sensing element. Note the bulging shape of the curve, indicating second-order nonlinearity.
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