Mechanical–electrical analogies are the representation of
mechanical systems as
electrical network
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sou ...
s. At first, such analogies were used in reverse to help explain
electrical phenomena
This is a list of electrical phenomena. Electrical phenomena are a somewhat arbitrary division of electromagnetic phenomenon, electromagnetic phenomena.
Some examples are:
*Atmospheric electricity
*Biefeld–Brown effect — Thought by the pe ...
in familiar mechanical terms.
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
introduced analogies of this sort in the 19th century. However, as
electrical network analysis matured it was found that certain mechanical problems could more easily be solved through an electrical
analogy. Theoretical developments in the electrical domain
that were particularly useful were the representation of an electrical network as an abstract topological diagram (the
circuit diagram
A circuit diagram (or: wiring diagram, electrical diagram, elementary diagram, electronic schematic) is a graphical representation of an Electrical network, electrical circuit. A pictorial circuit diagram uses simple images of components, whil ...
) using the
lumped element model and the ability of network analysis to
synthesise a network to meet a prescribed
frequency function.
This approach is especially useful in the design of
mechanical filters—these use mechanical devices to implement an electrical function. 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. Electrical analogies are particularly used by
transducer
A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, M ...
designers, by their nature they cross energy domains, and in
control system
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial ...
s, whose
sensors and
actuator
An actuator is a machine element, component of a machine that produces force, torque, or Displacement (geometry), displacement, when an electrical, Pneumatics, pneumatic or Hydraulic fluid, hydraulic input is supplied to it in a system (called an ...
s will typically be domain-crossing transducers. A given system being represented by an electrical analogy may conceivably have no electrical parts at all. For this reason domain-neutral terminology is preferred when developing network diagrams for control systems.
Mechanical–electrical analogies are developed by finding relationships between variables in one domain that have a mathematical form identical to variables in the other domain. There is no one, unique way of doing this; numerous analogies are theoretically possible, but there are two analogies that are widely used: the
impedance analogy and the
mobility analogy. The impedance analogy makes force and voltage analogous while the mobility analogy makes force and current analogous. By itself, that is not enough to fully define the analogy, a second variable must be chosen. A common choice is to make pairs of power
conjugate variables
Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation— ...
analogous. These are variables which when multiplied together have units of power. In the impedance analogy, for instance, this results in force and velocity being analogous to voltage and current respectively.
Variations of these analogies are used for rotating mechanical systems, such as in
electric motor
An electric motor is a machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a electromagnetic coil, wire winding to gene ...
s. In the impedance analogy, instead of force,
torque
In physics and mechanics, torque is the rotational analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...
is made analogous to voltage. It is perfectly possible that both versions of the analogy are needed in, say, a system that includes rotating and
reciprocating parts, in which case a force-torque analogy is required within the mechanical domain and a force-torque-voltage analogy to the electrical domain. Another variation is required for acoustical systems; here pressure and voltage are made analogous (impedance analogy). In the impedance analogy, the ratio of the power conjugate variables is always a quantity analogous to
electrical impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit.
Quantitatively, the impedan ...
. For instance force/velocity is
mechanical impedance. The mobility analogy does not preserve this analogy between impedances across domains, but it does have another advantage over the impedance analogy. In the mobility analogy the topology of networks is preserved, a
mechanical network diagram has the same topology as its analogous electrical network diagram.
Applications
Mechanical–electrical analogies are used to represent the function of a mechanical system as an equivalent electrical system by drawing analogies between mechanical and electrical parameters. A mechanical system by itself can be so represented, but analogies are of greatest use in
electromechanical systems where there is a connection between mechanical and electrical parts. Analogies are especially useful in analysing
mechanical filters. These are filters constructed of mechanical parts but designed to work in an electrical circuit through
transducer
A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, M ...
s. Circuit theory is well developed in the electrical domain in general and in particular there is a wealth of filter theory available. Mechanical systems can make use of this electrical theory in mechanical designs through a mechanical–electrical analogy.
Mechanical–electrical analogies are useful in general where the system includes
transducer
A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, M ...
s between different energy domains.
[An energy domain pertains to a system or subsystem in which the energy and forces are all of a particular kind such as electrical, mechanical, acoustical, thermal, and so on.] Another area of application is the mechanical parts of
acoustic systems such as the
pickup and
tonearm of
record player
A phonograph, later called a gramophone, and since the 1940s a record player, or more recently a turntable, is a device for the mechanical and analogue reproduction of sound. The sound vibration Waveform, waveforms are recorded as correspond ...
s. 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. Early phonographs suffered badly from unwanted
resonance
Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
s in the mechanical parts. 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
A passband is the range of frequency, frequencies or wavelengths that can pass through a Filter (signal processing), filter. For example, a radio receiver contains a bandpass filter to select the frequency of the desired radio signal out of all t ...
.
Electrical analogies of mechanical systems can be used just as a teaching aid, to help understand the behaviour of the mechanical system. In former times, up to about the early 20th century, it was more likely that the reverse analogy would be used; mechanical analogies were formed of the then little understood electrical phenomena.
Forming an analogy
Electrical systems are commonly described by means of a
circuit diagram
A circuit diagram (or: wiring diagram, electrical diagram, elementary diagram, electronic schematic) is a graphical representation of an Electrical network, electrical circuit. A pictorial circuit diagram uses simple images of components, whil ...
. 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. This is possible because the electrical components are represented as ideal lumped elements, that is, the element is treated as if it is occupying a single point (lumped at that point). Non-ideal components can be accommodated in this model by using more than one element to represent the component. For instance, a
coil intended for use as an
inductor has
resistance as well as
inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
. This can be represented on the circuit diagram as a
resistor in series with an inductor. Thus, the first step in forming an analogy of a mechanical system is to describe it as a mechanical network in a similar way, that is, as a topological graph of ideal elements. Alternatively, more abstract representations to the circuit diagram are possible, for instance the
bond graph.

In an electrical network diagram, limited to
linear systems, there are three
passive elements: resistance, inductance, and
capacitance
Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
; and two active elements: the
voltage generator, and the
current generator.
[The five-element scheme can be extended to active devices such as transistors by the use of two-port networks containing dependent generators provided the transistor is operating in a substantially linear region.] The mechanical analogs of these elements can be used to construct a
mechanical network diagram. What the mechanical analogs of these elements are depends on what variables are chosen to be the fundamental variables. There is a wide choice of variables that can be used, but most commonly used are a power
conjugate pair of variables (described below) and the pair of Hamiltonian variables derived from these.
There is a limit to the applicability of this
lumped element model. The model works well if the components are small enough that the time taken for a wave to cross them is insignificant, or equivalently, if there is no significant
phase difference in the wave either side of the component. What amounts to significant depends on how accurate the model is required to be, but a common
rule of thumb
In English language, English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associat ...
is to require components to be smaller than one sixteenth of a
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
. Since wavelength decreases with frequency, this puts an upper limit on the frequency that can be covered in this kind of design. This limit is much lower in the mechanical domain than the equivalent limit in the electrical domain. This is because the much higher propagation speeds in the electrical domain lead to longer wavelengths (mechanical vibrations in steel propagate at about 6,000 m/s, electromagnetic waves in common cable types propagate at about ). For instance, traditional mechanical filters are only made up to around 600 kHz (although
MEMS devices can operate at much higher frequencies due to their very small size). In the electrical domain, on the other hand, the transition from the lumped element model to the
distributed element model occurs in the hundreds of megahertz region.
In some cases it is possible to continue using a topological network diagram even when components needing a distributed element analysis are present. In the electrical domain, a
transmission line
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
, a basic distributed element component, can be included in the model with the introduction of the additional element of
electrical length
In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through t ...
. The transmission line is a special case because it is invariant along its length and hence the full geometry need not be modelled. Another way of dealing with distributed elements is to use a
finite element analysis
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of structural ...
whereby the distributed element is approximated by a large number of small lumped elements. Just such an approach was used in one paper to model the
cochlea
The cochlea is the part of the inner ear involved in hearing. It is a spiral-shaped cavity in the bony labyrinth, in humans making 2.75 turns around its axis, the modiolus (cochlea), modiolus. A core component of the cochlea is the organ of Cort ...
of the human ear. Another condition required of electrical systems for the application of the lumped element model is that no significant
fields exist outside the component since these can
couple to other unrelated components. However, these effects can often be modelled by introducing some virtual lumped elements called strays or
parasitics. An analog of this in mechanical systems is vibration in one component being coupled to an unrelated component.
Power conjugate variables
The
power conjugate variables are a pair of variables whose product is power. In the electrical domain the power conjugate variables chosen are invariably
voltage
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
(''v'') and
current (''i''). Thus, the power conjugate variables in the mechanical domain are analogs. However, this is not enough to make the choice of mechanical fundamental variables unique. The usual choice for a
translational mechanical system is force (''F'') and velocity (''u'') but it is not the only choice. A different pair may be more appropriate for a system with a different geometry, such as a rotational system.
Even after the mechanical fundamental variables have been chosen, there is still not a unique set of analogs. There are two ways that the two pairs of power conjugate variables can be associated with each other in the analogy. For instance the associations ''F'' with ''v'' and ''u'' with ''i'' can be made. However, the alternative associations ''u'' with ''v'' and ''F'' with ''i'' are also possible. This leads to two classes of analogies, the impedance analogies and the mobility analogies. These analogies are the
dual of each other. The same mechanical network has analogs in two different electrical networks. These two electrical networks are the
dual circuits of each other.
Hamiltonian variables
The Hamiltonian variables, also called the energy variables, are those variables , which are conjugate according to
Hamilton's equations:
Further, the time derivatives of the Hamiltonian variables are the power conjugate variables.
The Hamiltonian variables in the electrical domain are
charge (''q'') and
flux linkage (λ) because,
:
(
Faraday's law of induction) and,
In the translational mechanical domain the Hamiltonian variables are distance
displacement
Displacement may refer to:
Physical sciences
Mathematics and physics
*Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...
(''x'') and
momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...
(''p'') because,
:
(
Newton's second law of motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows:
# A body re ...
) and,
There is a corresponding relationship for other analogies and sets of variables. The Hamiltonian variables are also called the energy variables. The
integrand of a power conjugate variable with respect to a Hamiltonian variable is a measure of energy. For instance,
:
and,
are both expressions of energy. They can also be called ''generalised momentum'' and ''generalised displacement'' after their analogs in the mechanical domain. Some authors discourage this terminology because it is not domain neutral. Likewise, the use of the terms ''I-type'' and ''V-type'' (after current and voltage) is also discouraged.
Classes of analogy
There are two principal classes of analogy in use. The impedance analogy (also called the Maxwell analogy) preserves the analogy between mechanical, acoustical and electrical impedance but does not preserve the topology of networks. The mechanical network is arranged differently to its analogous electrical network. The mobility analogy (also called the Firestone analogy) preserves network topologies at the expense of losing the analogy between impedances across energy domains. There is also the ''through and across'' analogy, also called the Trent analogy. The through and across analogy between the electrical and mechanical domain is the same as in the mobility analogy. However, the analogy between the electrical and acoustical domains is like the impedance analogy. Analogies between the mechanical and acoustical domain in the through and across analogy have a dual relationship with both the impedance analogy and mobility analogy.
Different fundamental variables are chosen for mechanical translation and rotational systems leading to two variants for each of the analogies. For instance, linear distance is the displacement variable in a translational system, but this is not so appropriate for rotating systems where
angle
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...
is used instead. Acoustical analogies have also been included in the descriptions as a third variant. While acoustical energy is ultimately mechanical in nature, it is treated in the literature as an instance of a different energy domain, the fluid domain, and has different fundamental variables. Analogies between all three domains − electrical, mechanical and acoustical − are required to fully represent electromechanical audio systems.
Impedance analogies
Impedance analogies, also called the Maxwell analogy, classify the two variables making up the power conjugate pair as an ''effort'' variable and a ''flow'' variable. The effort variable in an energy domain is the variable analogous to force in the mechanical domain. The flow variable in an energy domain is the variable analogous to velocity in the mechanical domain. Power conjugate variables in the analog domain are chosen that bear some resemblance to force and velocity.
In the electrical domain, the effort variable is voltage and the flow variable is electrical current. The ratio of voltage to current is
electrical resistance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paral ...
(
Ohm's law
Ohm's law states that the electric current through a Electrical conductor, conductor between two Node (circuits), points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of ...
). The ratio of the effort variable to the flow variable in other domains is also described as resistance. Oscillating voltages and currents give rise to the concept of
electrical impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit.
Quantitatively, the impedan ...
when there is a phase difference between them. Impedance can be thought of as an extension to the concept of resistance. Resistance is associated with energy dissipation. Impedance encompasses energy storage as well as energy dissipation.
The impedance analogy gives rise to the concept of impedance in other energy domains (but measured in different units). The translational impedance analogy describes mechanical systems moving in a single linear dimension and gives rise to the idea of
mechanical impedance. The unit of mechanical impedance is the mechanical ohm; in SI units this is N-s/m, or Kg/s. The rotational impedance analogy describes rotating mechanical systems and gives rise to the idea of rotational impedance. The unit of rotational impedance in the SI system is N-m-s/rad. The acoustical impedance analogy gives rise to the idea of
acoustic impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The International System of Units, SI unit of acoustic impeda ...
. The unit of acoustic impedance is the
acoustic ohm; in SI units this is N-s/m
5.
Mobility analogies
Mobility analogies, also called the Firestone analogy, are the
electrical duals of impedance analogies. That is, the effort variable in the mechanical domain is analogous to current (the flow variable) in the electrical domain, and the flow variable in the mechanical domain is analogous to voltage (the effort variable) in the electrical domain. The electrical network representing the mechanical system is the
dual network of that in the impedance analogy.
The mobility analogy is characterised by
admittance
In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the multiplicative inverse, reciprocal of Electrical impedance, impedance, analogous to how Electrical resistanc ...
in the same way that the impedance analogy is characterised by impedance. Admittance is the algebraic inverse of impedance. In the mechanical domain, mechanical admittance is more usually called ''mobility''.
Through and across analogies
Through and across analogies, also called the Trent analogy, classify the two variables making up the power conjugate pair as an ''across'' variable and a ''through'' variable. The across variable is a variable that appears across the two terminals of an element. The across variable is measured relative to the element terminals. The through variable is a variable that passes through, or acts through an element, that is, it has the same value at both terminals of the element. 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.
Thus, in the electrical domain the across variable is voltage and the through variable is current. In the mechanical domain the analogous variables are velocity and force, as in the mobility analogy. In the acoustic system, pressure is an across variable because pressure is measured relative to the two terminals of an element, not as an absolute pressure. It is thus not analogous to force which is a through variable, even though pressure is in units of force per area. Forces act through an element; a rod with a force applied to the top will transmit the same force to an element connected to its bottom. Thus, in the through and across analogy the mechanical domain is analogous to the electrical domain like the mobility analogy, but the acoustical domain is analogous to the electrical domain like the impedance analogy.
Other energy domains
The electrical analogy can be extended to many other energy domains. In the field of
sensors and
actuator
An actuator is a machine element, component of a machine that produces force, torque, or Displacement (geometry), displacement, when an electrical, Pneumatics, pneumatic or Hydraulic fluid, hydraulic input is supplied to it in a system (called an ...
s, and for
control systems using them, it is a common method of analysis to develop an electrical analogy of the entire system. Since sensors can be sensing a variable in any energy domain, and likewise outputs from the system can be in any energy domain, analogies for all energy domains are required. The following table gives a summary of the most common power conjugate variables used to form analogies.
It is perhaps more common in the thermal domain to choose temperature and thermal power as the fundamental variables because, unlike entropy, they can be measured directly. The concept of
thermal resistance is based on this analogy. However, these are not power conjugate variables and are not fully compatible with the other variables in the table. An integrated electrical analogy across multiple domains that includes this thermal analogy will not correctly model energy flows.
Similarly, the commonly seen analogy using mmf and magnetic flux as the fundamental variables, which gives rise to the concept of
magnetic reluctance, does not correctly model energy flow. The variable pair mmf and magnetic flux is not a power conjugate pair. This reluctance model is sometimes called the reluctance-resistance model since it makes these two quantities analogous. The analogy shown in the table, which does use a power conjugate pair, is sometimes called the
gyrator–capacitor model.
Transducers
A
transducer
A transducer is a device that Energy transformation, converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, M ...
is a device that takes energy from one domain as input and converts it to another energy domain as output. They are often reversible, but are rarely used in that way. Transducers have many uses and there are many kinds, in electromechanical systems they can be used as actuators and sensors. In audio electronics they provide the conversion between the electrical and acoustical domains. The transducer provides the link between the mechanical and electrical domains and thus a network representation is required for it in order to develop a unified electrical analogy. To do this the concept of
port
A port is a maritime facility comprising one or more wharves or loading areas, where ships load and discharge cargo and passengers. Although usually situated on a sea coast or estuary, ports can also be found far inland, such as Hamburg, Manch ...
from the electrical domain is extended into other domains.
Transducers have (at least
[ Piezoelectric transducers are frequently modelled as three-port devices, one electrical and two mechanical, because mechanical vibrations are induced on both sides of the crystal (Cheeke, pp. 213-214).]) two ports, one port in the mechanical domain and one in the electrical domain, and are analogous to electrical
two-port networks. This is to be compared to the elements discussed so far which are all one-ports. Two-port networks can be represented as a 2×2 matrix, or equivalently, as a network of two
dependent generators and two impedances or admittances. There are six canonical forms of these representations:
impedance parameters,
chain parameters,
hybrid parameters and their
inverses. Any of them can be used. However, the representation of a passive transducer converting between analogous variables (for instance an effort variable to another effort variable in the impedance analogy) can be simplified by replacing the dependent generators with a
transformer.
On the other hand, a transducer converting non-analogous power conjugate variables cannot be represented by a transformer. The two-port element in the electrical domain that does this is called a
gyrator. This device converts voltages to currents and currents to voltages. By analogy, a transducer that converts non-analogous variables between energy domains is also called a gyrator. For instance, electromagnetic transducers convert current to force and velocity to voltage. In the impedance analogy such a transducer is a gyrator. Whether a transducer is a gyrator or a transformer is analogy related; the same electromagnetic transducer in the mobility analogy is a transformer because it is converting between analogous variables.
History
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish physicist and mathematician who was responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism an ...
developed very detailed mechanical analogies of electrical phenomena. He was the first to associate force with voltage (1873) and consequently is usually credited with founding the impedance analogy. This was the earliest mechanical–electrical analogy. However, the term ''impedance'' was not coined until 1886, long after Maxwell's death, by
Oliver Heaviside. The idea of
complex impedance was introduced by
Arthur E. Kennelly in 1893, and the concept of impedance was not extended into the mechanical domain until 1920 by Kennelly and
Arthur Gordon Webster.
Maxwell's purpose in constructing this analogy was not to represent mechanical systems in terms of electrical networks. Rather, it was to explain electrical phenomena in more familiar mechanical terms. 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. As electrical phenomena became better understood the reverse of this analogy, using electrical analogies to explain mechanical systems, started to become more common. Indeed, the lumped element abstract topology of electrical analysis has much to offer problems in the mechanical domain, and other energy domains for that matter. By 1900 the electrical analogy of the mechanical domain was becoming commonplace. From about 1920 the electrical analogy became a standard analysis tool.
Vannevar Bush was a pioneer of this kind of modelling in his development of
analogue computers, and a coherent presentation of this method was presented in a 1925 paper by
Clifford A. Nickle.
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. According to
Warren P. Mason the efficiency of ship electric foghorns grew from less than one per cent to 50 per cent. The
bandwidth of mechanical
phonograph
A phonograph, later called a gramophone, and since the 1940s a record player, or more recently a turntable, is a device for the mechanical and analogue reproduction of sound. The sound vibration Waveform, waveforms are recorded as correspond ...
s grew from three to five
octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...
s when the mechanical parts of the sound transmission were designed as if they were the elements of an electric filter (''see also ''). 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).
In 1933
Floyd A. Firestone proposed a new analogy, the mobility analogy, in which force is analogous to current instead of voltage. Firestone introduced the concept of across and through variables in this paper and presented a structure for extending the analogy into other energy domains. A variation of the force-current analogy was proposed by
Horace M. Trent in 1955 and it is this version that is generally meant by the through and across analogy. Trent used a linear graph method of representing networks which has resulted in the force-current analogy historically being associated with linear graphs. The force-voltage analogy is historically used with bond graph representations, introduced in 1960 by
Henry Paynter, however, it is possible to use either analogy with either representation if desired.
[Bishop, p. 8.8]
See also
*
Analogical models
*
Elastance contains information on
Oliver Heaviside's role in analogies
*
Teledeltos
*
Hydraulic analogy
Electronic–hydraulic analogies are the representation of electronic circuits by hydraulic circuits. Since electric current is invisible and the processes in play in electronics are often difficult to demonstrate, the various electronic compon ...
Notes
References
Bibliography
* Agarwal, Anant; Lang, Jeffrey, ''Foundations of Analog and Digital Electronic Circuits'', Morgan Kaufmann, 2005 .
* Barron, Randall F., ''Industrial Noise Control and Acoustics'', CRC Press, 2002 .
* Beranek, Leo Leroy; Mellow, Tim J., ''Acoustics: Sound Fields and Transducers'', Academic Press, 2012 .
* Bishop, Robert H., ''Mechatronics: An Introduction, ''CRC Press, 2005 .
* Borutzky, Wolfgang, ''Bond Graph Methodology, ''Springer, 2009 .
* Busch-Vishniac, Ilene J., ''Electromechanical Sensors and Actuators'', Springer Science & Business Media, 1999 .
* Care, Charles, ''Technology for Modelling: Electrical Analogies, Engineering Practice, and the Development of Analogue Computing'', Springer, 2010 .
* Carr, Joseph J. ''RF Components and Circuits'', Oxford: Newnes, 2002 .
* Chan, Shu-Park, "Circuits: Introduction", pp. 2–4, in Dorf, Richard C. (ed), ''The Electrical Engineering Handbook, ''CRC Press, 1997 .
* Cheeke, David N., ''Fundamentals and Applications of Ultrasonic Waves'', CRC Press, 2012 .
* Darlington, S
"A history of network synthesis and filter theory for circuits composed of resistors, inductors, and capacitors" ''IEEE Transactions on Circuits and Systems'', vol. 31, pp. 3–13, 1984.
* de Silva, Clarence W., ''Vibration: Fundamentals and Practice'', CRC Press, 2006 .
* Eargle, John, ''Loudspeaker Handbook'', Kluwer Academic Publishers, 2003 .
* (2 pages)
* Firestone, Floyd A., "A new analogy between mechanical and electrical system elements", ''The Journal of the Acoustical Society of America, ''vol. 3, pp. 249–267, 1933.
* Froehlich, Fritz E.; Kent, Allen, ''The Froehlich/Kent Encyclopedia of Telecommunications'', CRC Press, 1991 .
* Fukazawa, Tatsuya; Tanaka, Yasuo, "Evoked otoacoustic emissions in a cochlear model", pp. 191–196 in Hohmann, D. (ed), ''ECoG, OAE and Intraoperative Monitoring: Proceedings of the First International Conference, Würzburg, Germany, September 20–24, 1992'', Kugler Publications, 1993 .
* Hamill, David C.
"Lumped equivalent circuits of magnetic components: the gyrator-capacitor approach" ''IEEE Transactions on Power Electronics'', vol. 8, iss. 2, pp. 97–103.
* Hunt, Frederick V., ''Electroacoustics: the Analysis of Transduction, and its Historical Background'', Harvard University Press, 1954 .
* Jackson, Roger G., ''Novel Sensors and Sensing'', CRC Press, 2004 .
* Janschek, Klaus, ''Mechatronic Systems Design'', Springer, 2011 .
* Joines, William T.; Palmer, W. Devereux; Bernhard, Jennifer T., ''Microwave Transmission Line Circuits'', Artech House, 2013 .
* Kleiner, Mendel, ''Electroacoustics'', CRC Press, 2013 .
* Lenk, Arno; G. Ballas, Rüdiger; Werthschützky, Roland; Pfeifer, Günther, ''Electromechanical Systems in Microtechnology and Mechatronics'', Springer, 2010 .
* Lurie, Boris; Enright, Paul, ''Classical Feedback Control'', CRC Press, 2011 .
* Martinsen, Orjan G.; Grimnes, Sverre, ''Bioimpedance and Bioelectricity Basics'', Academic Press, 2011 .
* Mason, Warren P.
"Electrical and mechanical analogies" ''Bell System Technical Journal'', vol. 20, no. 4, pp. 405–414, October 1941.
* Myers, Rusty L., ''The Basics of Physics'', Greenwood Publishing Group, 2006 .
* Paynter, Henry M.,'' Analysis and Design of Engineering Systems'', MIT Press, 1961 .
* Radmanesh, Matthew M., ''Electronic Waves & Transmission Line Circuit Design'', Author House, 2011 .
* Regtien, Paul P. L., ''Sensors for Mechatronics'', Elsevier, 2012 .
* Seely, Samuel; Tarnoff, Norman H.; Holstein, David, ''Digital Computers in Engineering'', Holt, Rinehart and Winston, 1970 .
* Semmlow, John, ''Signals and Systems for Bioengineers'', Academic Press, 2012 .
* Sen, S. N., ''Acoustics, Waves and Oscillations'', New Age International, 1990 .
* Smith, Malcolm C.,
Synthesis of mechanical networks: the inerter, ''IEEE Transactions on Automatic Control'', vol. 47, iss. 10, pp. 1648–1662, October 2002.
* Trent, Horace M.
"Isomorphisms between oriented linear graphs and lumped physical systems" ''The Journal of the Acoustical Society of America'', vol. 27, pp. 500–526, 1955.
* White, Curt, ''Data Communications and Computer Networks'', Cengage Learning, 2012 .
{{DEFAULTSORT:Mechanical-electrical analogies
Electrical analogies
Electromechanical engineering
Electronic design