page_title: Mechanical filter
section_title: Elements
hierarchical_section_title: Mechanical filter / Elements
caption_attribution_description: Deutsch: Filterbaustein mit der Bezeichnung MF 200 + E Bauart: mechanisches Filter mit Torsions-Resonatoren für eine Trägerfrequenzanlage.
context_page_description: A mechanical filter is a signal processing filter usually used in place of an electronic filter at radio frequencies. Its purpose is the same as that of a normal electronic filter: to pass a range of signal frequencies, but to block others. The filter acts on mechanical vibrations which are the analogue of the electrical signal. At the input and output of the filter, transducers convert the electrical signal into, and then back from, these mechanical vibrations.
  The components of a mechanical filter are all directly analogous to the various elements found in electrical circuits. The mechanical elements obey mathematical functions which are identical to their corresponding electrical elements. This makes it possible to apply electrical network analysis and filter design methods to mechanical filters. Electrical theory has developed a large library of mathematical forms that produce useful filter frequency responses and the mechanical filter designer is able to make direct use of these. It is only necessary to set the mechanical components to appropriate values to produce a filter with an identical response to the electrical counterpart.
context_section_description: The elements of a passive linear electrical network consist of inductors, capacitors and resistors which have the properties of inductance, elastance (inverse capacitance) and resistance, respectively. The mechanical counterparts of these properties are, respectively, mass, stiffness and damping. In most electronic filter designs, only inductor and capacitor elements are used in the body of the filter (although the filter may be terminated with resistors at the input and output). Resistances are not present in a theoretical filter composed of ideal components and only arise in practical designs as unwanted parasitic elements. Likewise, a mechanical filter would ideally consist only of components with the properties of mass and stiffness, but in reality some damping is present as well.
  The mechanical counterparts of voltage and electric current in this type of analysis are, respectively, force (F) and velocity (v) and represent the signal waveforms. From this, a mechanical impedance can be defined in terms of the imaginary angular frequency, jω, which entirely follows the electrical analogy.
  Notes:
  The symbols x, t, and a represent their usual quantities; distance, time, and acceleration respectively.
  The mechanical quantity compliance, which is the inverse of stiffness, can be used instead of stiffness to give a more direct correspondence to capacitance, but stiffness is used in the table as the more familiar quantity.
  The scheme presented in the table is known as the impedance analogy. Circuit diagrams produced using this analogy match the electrical impedance of the mechanical system seen by the electrical circuit, making it intuitive from an electrical engineering standpoint. There is also the mobility analogy, in which force corresponds to current and velocity corresponds to voltage. This has equally valid results but requires using the reciprocals of the electrical counterparts listed above. Hence, M → C, S → 1/L, D → G where G is electrical conductance, the inverse of resistance. Equivalent circuits produced by this scheme are similar, but are the dual impedance forms whereby series elements become parallel, capacitors become inductors, and so on. Circuit diagrams using the mobility analogy more closely match the mechanical arrangement of the circuit, making it more intuitive from a mechanical engineering standpoint. In addition to their application to electromechanical systems, these analogies are widely used to aid analysis in acoustics.
  Any mechanical component will unavoidably possess both mass and stiffness. This translates in electrical terms to an LC circuit, that is, a circuit consisting of an inductor and a capacitor, hence mechanical components are resonators and are often used as such. It is still possible to represent inductors and capacitors as individual lumped elements in a mechanical implementation by minimising (but never quite eliminating) the unwanted property. Capacitors may be made of thin, long rods, that is, the mass is minimised and the compliance is maximised. Inductors, on the other hand, may be made of short, wide pieces which maximise the mass in comparison to the compliance of the piece.
  Mechanical parts act as a transmission line for mechanical vibrations. If the wavelength is short in comparison to the part then a lumped-element model as described above is no longer adequate and a distributed-element model must be used instead.  The mechanical distributed elements are entirely analogous to electrical distributed elements and the mechanical filter designer can use the methods of electrical distributed-element filter design.
caption: Mechanical filter from a telephone carrier system using torsional resonator elements
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