Impedance analogy

The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters.

The roles of voltage and current are reversed in these two methods, and the electrical representations produced are the dual circuits of each other.

The impedance analogy is widely used to model the behaviour of mechanical filters.

These are filters that are intended for use in an electronic circuit but work entirely by mechanical vibrational waves.

Transducers are provided at the input and output of the filter to convert between the electrical and mechanical domains.

A very early application of this type was to make significant improvements to the abysmal audio performance of phonographs.

The mechanical system is broken down into a number of ideal elements each of which can then be paired with an electrical analogue.

Analogies can also be developed for distributed elements such as transmission lines but the greatest benefits are with lumped-element circuits.

Mechanical analogies are required for the three passive electrical elements, namely, resistance, inductance and capacitance.

[6] The mechanical analogy of electrical resistance is the loss of energy of a moving system through such processes as friction.

A mechanical component analogous to an inductor is a large, rigid weight.

The analogous equation in the mechanical domain is Newton's second law of motion,

The analogy of stiffness in the electrical domain is the less commonly used elastance, the inverse of capacitance.

The analogous equation in the mechanical domain is a form of Hooke's law,

Mechanical resonators are analogous to electrical LC circuits consisting of inductance and capacitance.

This is analogous to a real voltage source, such as a battery, which remains near constant-voltage with load provided that the load resistance is much higher than the battery internal resistance.

An example of a practical constant velocity generator is a lightly loaded powerful machine, such as a motor, driving a belt.

[18] Electromechanical systems require transducers to convert between the electrical and mechanical domains.

They are analogous to two-port networks and like those can be described by a pair of simultaneous equations and four arbitrary parameters.

is the open circuit mechanical impedance, that is, the impedance presented by the mechanical side of the transducer when no current (open circuit) is entering the electrical side.

They are both analogous to transfer impedances and are hybrid ratios of an electrical and mechanical quantity.

[19] The mechanical analogy of a transformer is a simple machine such as a pulley or a lever.

[21] The circuit diagram shows an impedance analogy model of the human ear.

This example thus demonstrates the power of electrical analogies in bringing together three domains (acoustic, mechanical and fluid flow) into a single unified whole.

The cochlea portion of the circuit uses a finite element analysis of the continuous transmission line of the cochlear duct.

An ideal representation of such a structure would use infinitesimal elements, and there would thus be an infinite number of them.

[5] The principal disadvantage of the impedance analogy is that it does not preserve the topology of the mechanical system.

Elements that are in series in the mechanical system are in parallel in the electrical equivalent circuit and vice versa.

However, many practical transducers, especially at audio frequencies, work by electromagnetic induction and are governed by just such a relationship.

[28] Henri Poincaré in 1907 was the first to describe a transducer as a pair of linear algebraic equations relating electrical variables (voltage and current) to mechanical variables (force and velocity).

The mechanical symbol for a damper (left) and its electrical analogy (right). [ 7 ] The symbol is meant to be evocative of a dashpot . [ 8 ]
The mechanical symbol for a mass (left) and its electrical analogy (right). [ 7 ] The square angle below the mass is meant to indicate that movement of the mass is relative to a frame of reference. [ 9 ]
The mechanical symbol for a stiffness element (left) and its electrical analogy (right). [ 7 ] The symbol is meant to be evocative of a spring. [ 11 ]
The mechanical symbol for a constant force generator (left) and its electrical analogy (right) [ 15 ]
The mechanical symbol for a constant velocity generator (left) and its electrical analogy (right) [ 16 ]
Simple mechanical resonator (left) and its impedance analogy equivalent circuit (right)
One equivalent circuit of the human ear using the impedance analogy
Anatomy of the ear.
Brown is outer ear .
Red is middle ear .
Purple is inner ear .