Lumped Element Model - Examples - Lumped Element Model in Electrical Systems

Lumped Element Model in Electrical Systems

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. joined by a network of perfectly conducting wires.

The lumped element model is valid whenever, where denotes the circuit's characteristic length, and denotes the circuit's operating wavelength. Otherwise, when the circuit length is on the order of a wavelength, we must consider more general models, such as the distributed element model (including transmission lines), whose dynamic behaviour is described by the Maxwell equations. Another way of viewing the validity of the lumped element model is to note that this model ignores the finite time it takes signals to propagate around a circuit. Whenever this propagation time is not significant to the application the lumped element model can be used. This is the case when the propagation time is much less than the period of the signal involved. However, with increasing propagation time there will be an increasing error between the assumed and actual phase of the signal which in turn results in an error in the assumed amplitude of the signal. The exact point at which the lumped element model can no longer be used depends to a certain extent on how accurately the signal needs to be known in a given application.

Real-world components exhibit non-ideal characteristics which are, in reality, distributed elements but are often represented to a first-order approximation by lumped elements. To account for leakage in capacitors for example, we can model the non-ideal capacitor as having a large lumped resistor connected in-parallel even though the leakage is, in reality distributed throughout the dielectric. Similarly a wire-wound resistor has significant inductance as well as resistance distributed along its length but we can model this as a lumped inductor in series with the ideal resistor.

Read more about this topic:  Lumped Element Model, Examples

Other articles related to "model, system, systems, models":

Grand Unified Theory - Ingredients
... A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection ... The Lie group contains the Standard Model group and the Higgs fields acquire VEVs leading to a spontaneous symmetry breaking to the Standard Model ...
IBM System/360 - Remaining Machines
... sold or leased in very large numbers for a mainframe system of its era, only a few System/360 computers are known to exist today, none of which is in ... from competing with IBM's newer computers, such as the System/370 ... As with all classic mainframe systems, complete System/360 computers were prohibitively large to be held in storage, and too expensive to maintain ...
Model Organism
... A model organism is a non-human species that is extensively studied to understand particular biological phenomena, with the expectation that discoveries made in the organism model will provide insight into the ... Model organisms are in vivo models and are widely used to research human disease when human experimentation would be unfeasible or unethical ... Studying model organisms can be informative, but care must be taken when extrapolating from one organism to another ...
Database Management System - Modeling Language
... in the DBMS, according to the DBMS database model ... Database management systems (DBMS) are designed to use one of five database structures to provide simplistic access to information stored in databases ... The five database structures are the hierarchical model, the network model, the relational model, the multidimensional model the object relational model, the object oriented model,and the object model ...

Famous quotes containing the words systems, electrical, element and/or model:

    Our little systems have their day;
    They have their day and cease to be:
    They are but broken lights of thee,
    And thou, O Lord, art more than they.
    Alfred Tennyson (1809–1892)

    Few speeches which have produced an electrical effect on an audience can bear the colourless photography of a printed record.
    Archibald Philip Primrose, 5th Earl Rosebery (1847–1929)

    What was any art but an effort to make a sheath, a mould in which to imprison for a moment the shining, elusive element which is life itself—life hurrying past us and running away, too strong to stop, too sweet to lose?
    Willa Cather (1873–1947)

    The Battle of Waterloo is a work of art with tension and drama with its unceasing change from hope to fear and back again, change which suddenly dissolves into a moment of extreme catastrophe, a model tragedy because the fate of Europe was determined within this individual fate.
    Stefan Zweig (18811942)