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The derivative element (D element)

The relationship between the input and output of a derivative element is described by

 (4.26)

This element differentiates the input signal and therefore is called a derivative element, or in short D element. The associated transfer function is

 (4.27)

and with it follows that the frequency response

 (4.28)

from which the magnitude

 (4.29)

and the phase response

 (4.30)

follow. It can easily be seen, that the I and D elements are related by an inversion. Therefore the curves of the magnitude and phase response of the D element can be found - as shown above - by mirroring those of the I element at the 0- line and line, respectively. This is obvious from Eqs. (4.29) and (4.30). Figure 4.8 shows the Bode diagram and the Nyquist plot of the frequency response of the D element. The slope of the line is +20 /decade and the phase response is independent of the frequency.

The D element discussed here is - as already mentioned in section 3.3 - an idealisation and therefore not a physically realisable element. For practical applications the D element will be approximated by the element (see section 4.4.6).

Next: The 1st-order lag element Up: Some important transfer function Previous: The integrator (I element)   Contents
Christian Schmid 2005-05-09