Tuesday, April 14, 2009

Mechanical And Electrical Filters

At the turn of the 20th century, it was proven that the propagation of electric waves along electric lines was analogous to the propagation of elastic waves along mechanical lattices. Vincent’s model of a mechanical filter and Campbell’s equivalent electrical circuit are shown above. A mechanical and its equivalent electrical low-pass filter are shown below

Low Pass Mechanical System and Electrical Circuit

Text excerpt from L. Brillouin, Wave Propagation in Periodic Structures, 1946, pg 42 The mechanical low-pass filter consists of point masses joined by elastic elements that we might visualize as springs. The elastic elements each have two ends, one connected to one mass and one to another mass, while the masses are represented by single points. An electric line having all its condensers shunting the high frequencies may be regarded as a single line with the condensers connected between the line and ground at regular intervals. Then the inductances appear as having two ends connected to different condensers and the condensers are essentially points in the structure. Another way of looking at the problem is to regard the elastic forces as coupling forces in the electric line, while the masses and condensers are thought of as supplying inertial forces to their respective systems. End Excerpt

Mathematically too, the equations for the propagation of electric waves along low-pass, high-pass and band-pass electric filters are identical to the equations for the propagation of elastic waves along similarly constructed mechanical lattices.
The question can thus be asked: Are the mechanical and electrical sciences then analogous to each other and formulating the same principles with two different sets of laws and equations when in fact one set of laws is sufficient to express all that there is to be expressed.

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