Lumped element model

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In general, the lumped component model is a way of simplifying the behaviour of spatially distributed systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions. It is useful in electronics, mechanics and acoustics

1 Lumped component model in electronics
2 Lumped component model in acoustics
3 See also
4 External links

[edit] Lumped component model in electronics

The lumped element model of electronic circuits makes the simplifying assumption that each element is finite point in space, and that the wires connecting elements are perfect conductors.

The lumped element model is valid whenever $L c < < λ$ , where $L c$ denotes the circuit's characteristic length, and $λ$ denotes the circuit's operating wavelength. Otherwise, we must consider more general models, such as the Distributed element model.

Real-world components exhibit non-ideal characteristics. To account for leakage in capacitors for example, we can visualize the capacitor as having a large resistor connected in-parallel. Similarly to account for inductive reactance, we can visualize component leads as small inductors.

[edit] Lumped component model in acoustics

In this context, the lumped component model extends the distributed concepts of Acoustic theory subject to approximation. In the acoustical lumped component model, certain physical components with acoustical properties may be approximated as behaving similarly to standard electronic components or simple combinations of components.

A rigid-walled cavity containing air (or similar compressible fluid) may be approximated as a capacitor whose value is proportional to the volume of the cavity. The validity of this approximation relies on the shortest wavelength of interest being significantly (much) larger than the longest dimension of the cavity.

A reflex port may be approximated as an inductor whose value is proportional to the effective length of the port divided by its cross-sectional area. The effective length is the actual length plus an end correction. This approximation relies on the shortest wavelength of interest being significantly larger than the longest dimension of the port.

Certain types of damping material can be approximated as a resistor. The value depends on the properties and dimensions of the material. The approximation relies in the wavelengths being long enough and on the properties of the material itself.

A loudspeaker drive unit (typically a woofer or subwoofer drive unit may be approximated as a series connection of a zero-impedance voltage source, a resistor, a capacitor and an inductor. The values depend on the specifications of the unit. The approximation depends on the specifications of the unit and the wavelength of interest.