Mechanical–electrical analogies
At first, such analogies were used in reverse to help explain electrical phenomena in familiar mechanical terms.
However, the technique can be used to solve purely mechanical problems, and can also be extended into other, unrelated, energy domains.
Nowadays, analysis by analogy is a standard design tool wherever more than one energy domain is involved.
It has the major advantage that the entire system can be represented in a unified, coherent way.
For this reason domain-neutral terminology is preferred when developing network diagrams for control systems.
These are filters constructed of mechanical parts but designed to work in an electrical circuit through transducers.
[note 1] Another area of application is the mechanical parts of acoustic systems such as the pickup and tonearm of record players.
This was of some importance in early phonographs where the audio is transmitted from the pickup needle to the horn through various mechanical components entirely without electrical amplification.
It was found that these could be eliminated by treating the mechanical parts as components of a low-pass filter which has the effect of flattening out the passband.
These are network diagrams that describe the topology of the electrical system using a specialised graph notation.
The circuit diagram does not try to represent the true physical dimensions of the electrical components or their actual spatial relationship to each other.
For instance, traditional mechanical filters are only made up to around 600 kHz[11] (although MEMS devices can operate at much higher frequencies due to their very small size).
[12] In some cases it is possible to continue using a topological network diagram even when components needing a distributed element analysis are present.
[13] The transmission line is a special case because it is invariant along its length and hence the full geometry need not be modelled.
[16] However, these effects can often be modelled by introducing some virtual lumped elements called strays or parasitics.
In the electrical domain the power conjugate variables chosen are invariably voltage (v) and current (i).
[25] Different fundamental variables are chosen for mechanical translation and rotational systems leading to two variants for each of the analogies.
Analogies between all three domains − electrical, mechanical and acoustical − are required to fully represent electromechanical audio systems.
Power conjugate variables in the analog domain are chosen that bear some resemblance to force and velocity.
Oscillating voltages and currents give rise to the concept of electrical impedance when there is a phase difference between them.
The benefit of the through and across analogy is that when the through Hamiltonian variable is chosen to be a conserved quantity, Kirchhoff's node rule can be used, and the model will have the same topology as the real system.
The following table gives a summary of the most common power conjugate variables used to form analogies.
[45] On the other hand, a transducer converting non-analogous power conjugate variables cannot be represented by a transformer.
By analogy, a transducer that converts non-analogous variables between energy domains is also called a gyrator.
[48] James Clerk Maxwell developed very detailed mechanical analogies of electrical phenomena.
[52] Maxwell's purpose in constructing this analogy was not to represent mechanical systems in terms of electrical networks.
[53] When George Ashley Campbell first demonstrated the use of loading coils to improve telephone lines in 1899, he calculated the distance needed between coils by analogy with the work of Charles Godfrey on mechanical lines loaded with periodic weights.
[55] The application of electrical network analysis, most especially the newly developed field of filter theory, to mechanical and acoustic systems led to huge improvements in performance.
Remarkably, the conversion efficiency was improved at the same time (the usual situation with amplifying systems is that gain can be traded for bandwidth such that the gain-bandwidth product remains constant).
Firestone introduced the concept of across and through variables in this paper and presented a structure for extending the analogy into other energy domains.
