- Lumped element model
In general, the

**lumped component model**is a way of simplifying the behaviour of spatially distributed systems into atopology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions. It is useful inelectronics ,heat transfer ,mechanics andacoustics **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 thewire s connecting elements are perfect conductors.The lumped element model is valid whenever $L\_c<\mapsto math>,\; where$ L\_c$denotes\; the\; circuit\text{'}s\; characteristic\; length,\; and$ lambda$denotes\; the\; circuit\text{'}s\; operatingwavelength.Otherwise,\; we\; must\; consider\; more\; general\; models,\; such\; as\; theDistributed\; element\; model.$

Real-world components exhibit non-ideal characteristics. To account for leakage in

capacitor s for example, we can visualize the capacitor as having a largeresistor connected in-parallel. Similarly to account forinductive reactance , we can visualize component leads as smallinductor s.**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 aninductor 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 anend 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 awoofer orsubwoofer drive unit may be approximated as a series connection of a zero-impedancevoltage source, aresistor , acapacitor and aninductor . The values depend on the specifications of the unit. The approximation depends on the specifications of the unit and the wavelength of interest.**ee also***

Distributed element model **External links*** [

*http://www.jat.co.kr/eda/saber/mpp.pdf Advanced modelling and simulation techniques for magnetic components*]

* [*http://www.imtek.uni-freiburg.de/simulation/mathematica/IMSweb/ IMTEK Mathematica Supplement (IMS)*] , the Open Source IMTEK Mathematica Supplement (IMS) for lumped modelling

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