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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
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Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Transfer function and Bode Plots-II01:23

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In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
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Wavelet excited measurement of system transfer function.

H Olkkonen1, J T Olkkonen

  • 1Department of Physics, University of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland. hannu.olkkonen@uku.fi

The Review of Scientific Instruments
|June 21, 2007
PubMed
Summary

A new wavelet excitation method (WEM) accurately measures system transfer functions using sequential wavelets. This technique allows for reduced sampling rates, enabling high-speed sensor applications.

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Area of Science:

  • Electrical Engineering
  • Signal Processing
  • Measurement Science

Background:

  • System transfer function measurement is crucial for analyzing system dynamics.
  • Traditional methods like impulse or sine wave excitation have limitations, especially in high-speed systems.
  • High-quality impulse excitation is not always feasible in certain testing scenarios.

Purpose of the Study:

  • To introduce a novel method, the wavelet excitation method (WEM), for system transfer function measurement.
  • To demonstrate the advantages of WEM over conventional excitation techniques.
  • To explore the potential of WEM in enabling new high-speed sensor applications.

Main Methods:

  • The wavelet excitation method (WEM) utilizes sequential excitation by biorthogonal symmetric wavelets.
  • System transfer functions are reconstructed from the measured outputs.
  • WEM allows for a reduction in the analog-to-digital converter's sampling rate to f/N when N excitation sequences are used at rate f.

Main Results:

  • WEM provided consistent results in transfer function measurements of multistage amplifiers.
  • Performance was comparable to established methods like linear circuit analysis (SPICE) and sine wave excitation.
  • The method proved effective even where high-quality impulse excitation is not applicable.

Conclusions:

  • The wavelet excitation method (WEM) is a viable and effective technique for system transfer function measurement.
  • WEM offers significant advantages in terms of reduced sampling rates and applicability to systems unsuitable for impulse excitation.
  • This method opens possibilities for new high-speed sensor applications with lower sampling rates relative to system bandwidth.