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Concept# Lumped-element model

Summary

The lumped-element model (also called lumped-parameter model, or lumped-component model) is a simplified representation of a physical system or circuit that assumes all components are concentrated at a single point and their behavior can be described by idealized mathematical models. The lumped-element model simplifies the system or circuit behavior description into a topology. It is useful in electrical systems (including electronics), mechanical multibody systems, heat transfer, acoustics, etc. This is in contrast to distributed parameter systems or models in which the behaviour is distributed spatially and cannot be considered as localized into discrete entities.
The simplification reduces the state space of the system to a finite dimension, and the partial differential equations (PDEs) of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations (ODEs) with a finite number of parameters.
The lumped-matter discipline is a set of imposed assumptions in electrical engineering that provides the foundation for lumped-circuit abstraction used in network analysis. The self-imposed constraints are:
The change of the magnetic flux in time outside a conductor is zero.
The change of the charge in time inside conducting elements is zero.
Signal timescales of interest are much larger than propagation delay of electromagnetic waves across the lumped element.
The first two assumptions result in Kirchhoff's circuit laws when applied to Maxwell's equations and are only applicable when the circuit is in steady state. The third assumption is the basis of the lumped-element model used in network analysis. Less severe assumptions result in the distributed-element model, while still not requiring the direct application of the full Maxwell equations.
The lumped-element model of electronic circuits makes the simplifying assumption that the attributes of the circuit, resistance, capacitance, inductance, and gain, are concentrated into idealized electrical components; resistors, capacitors, and inductors, etc.

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