Lumped-element model: Difference between revisions

Revision as of 00:00, 31 January 2022

Revision as of 04:21, 26 February 2022

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=== Lumped-matter discipline===

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 (electrical circuits)|network analysis]].<ref>Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare ([http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf PDF]), [[Massachusetts Institute of Technology]].</ref> The self-imposed constraints are:

# The change of the magnetic flux in time outside a conductor is zero. <math display="block">\frac{\partial \phi_B} {\partial t} = 0</math>

1.# The change of the magnetic fluxcharge in time outsideinside aconducting conductorelements is zero. <math display="block">\frac{\partial q} {\partial t} = 0</math>

3.# Signal timescales of interest are much larger than propagation delay of [[electromagnetic waves]] across the lumped element.

::<math>\frac{\partial \phi_B} {\partial t} = 0</math>

2. The change of the charge in time inside conducting elements is zero.

::<math>\frac{\partial q} {\partial t} = 0</math>

3. 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 (electronics)|steady state]]. The third assumption is the basis of the lumped-element model used in [[Network analysis (electrical circuits)|network analysis]]. Less severe assumptions result in the [[distributed-element model]], while still not requiring the direct application of the full Maxwell equations.