文档介绍：Fundamentals of Measurement Technology (7)
Prof. Wang Boxiong
Both the transfer function and the frequency response function describe the response of a measuring instrument or system to sinusoidal excitation.
But the frequency response describes only the transfer characteristics of a system with steady-state input and output.
A transient output will reduce gradually to zero, and the system will then reach the steady-state stage. For describing the whole process of the two stages, the transfer function must be employed, and the frequency response is only a special case of the transfer function.
Responses of measuring system to typical excitations
The dynamic response of a measuring system can be also obtained through applying other excitations to the system.
The monly used excitation signals are: unit impulse, unit step, and ramp signals.
Responses of measuring system to typical excitations
Unit impulse response
For a unit impulse function δ(t), its Fourier transform Δ(jω)=1 and the Laplace transform of δ(t): Δ(s)=L[δ(t)]=1. The output of a measuring instrument with δ(t) as its excitation: Y(s)=H(s)X(s)=H(s)Δ(s)=H(s). Making inverse Laplace transform of Y(s), then
h(t) is referred to as the impulse response function or weighting function of a measuring system.
Responses of measuring system to typical excitations
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The first-order system
its impulse response h(t)
where time constant.
Responses of measuring system to typical excitations
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Fig. Impulse response of first-order system
A second-order system
(assuming its static sensitivity K=1)
Responses of measuring system to typical excitations
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Responses of measuring system to typical excitations
Fig. Impulse responses for second-order system with different dampimgs
The unit impulse does not exist in reality. Often in engineering, an approximation is made by use of a pulse signal with very short time duration for the impulse