The dynamic linearity of the sensor is a measure of its ability to follow rapid changes in the input parameter. Amplitude distortion characteristics, phase distortion characteristics, and response time are important in determining dynamic linearity. Given a system of low hysteresis (always desirable), the amplitude response is represented by:
F(X) = aX + bX2 + cX3
+ dX4 + ••• + K (6-2)
In Equation 6-2, the term F(X) is the output signal, while the X terms represent the input parameter and its harmonics, and K is an offset constant (if any). The harmonics become especially important when the error harmonics generated by the sensor action fall into the same frequency bands as the natural harmonics produced by the dynamic action of the input parameter. All continuous waveforms are represented by a Fourier series of a fundamental sinewave and its harmonics. In any nonsinusoidal waveform (including time-varying changes of a physical parameter). Harmonics present will be that can be affected by the action of the sensor.
Figure 6. Output versus input signal curves showing (a) quadratic error; (b) cubic error. Source: J.J. Carr, Sensors and Circuits Prentice Hall.
The nature of the nonlinearity of the calibration curve (Figure 6) tell something about which harmonics are present. In Figure 6a, the calibration curve (shown as a dotted line) is asymmetrical, so only odd harmonic terms exist. Assuming a form for the ideal curve of F(x) = mx + K, Equation 6-2 becomes for the symmetrical case:
F(X) = aX + bX2 + cX4 + ••• + K (6-3)
In the other type of calibration curve (Figure 6b), the indicated values are symmetrical about the ideal mx + K curve. In this case, F(X) = -F(-X), and the form of Equation 6-2 is:
F(X) = aX + bX3 + cX5 + ••• + K (6-4)
Excerpt from the book, Introduction to Biomedical Equipment Technology, Third Edition, published by Prentice Hall Professional (http://www.phptr.com). Copyright Prentice Hall Inc. 2006. All rights reserved.