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Area Circuit theory / Circuit elements and their characteristics

IEV ref131-12-34

Symbol
L

en
inductance matrix
for a linear inductive m-terminal-pair element, matrix m × m used to express the linked fluxes Ψi (131-12-17) between the terminals of each pair, as a function of the electric currents ij at the first terminal of each pair:

( Ψ 1 Ψ 2 Ψ i Ψ m )=( L 11 L 12 L 1j L 1m L 21 L 22 L 2j L 2m L i1 L i2 L ij L im L m1 L m2 L mj L mm )( i 1 i 2 i j i m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meGabaGacmGadiWaaiWabaabaiaafaaake aadaqadaqaauaabeqageaaaaqaaiaadI6adaWgaaWcbaqcLboacaaI XaaaleqaaaGcbaGaamiQdmaaBaaaleaajug4aiaaikdaaSqabaaake aacqWIUlstaeaacaWGOoWaaSbaaSqaaiaadMgaaeqaaaGcbaGaeSO7 I0eabaGaamiQdmaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPa aacqGH9aqpdaqadaqaauaabeqagyaaaaaabaGaamitamaaBaaaleaa jug4aiaaigdacaaIXaaaleqaaaGcbaGaamitamaaBaaaleaajug4ai aaigdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaamitamaaBaaaleaa jug4aiaaigdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaamitamaaBa aaleaajug4aiaaigdaliaad2gaaeqaaaGcbaGaamitamaaBaaaleaa jug4aiaaikdacaaIXaaaleqaaaGcbaGaamitamaaBaaaleaajug4ai aaikdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaamitamaaBaaaleaa jug4aiaaikdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaamitamaaBa aaleaajug4aiaaikdaliaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7 I0eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eaba GaamitamaaBaaaleaacaWGPbqcLboacaaIXaaaleqaaaGcbaGaamit amaaBaaaleaacaWGPbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGmb WaaSbaaSqaaiaadMgacaWGQbaabeaaaOqaaiabl+UimbqaaiaadYea daWgaaWcbaGaamyAaiaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7I0 eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eabaGa amitamaaBaaaleaacaWGTbqcLboacaaIXaaaleqaaaGcbaGaamitam aaBaaaleaacaWGTbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGmbWa aSbaaSqaaiaad2gacaWGQbaabeaaaOqaaiabl+UimbqaaiaadYeada WgaaWcbaGaamyBaiaad2gaaeqaaaaaaOGaayjkaiaawMcaaiabgwSi xpaabmaabaqbaeqabyqaaaaabaGaamyAamaaBaaaleaajug4aiaaig daaSqabaaakeaacaWGPbWaaSbaaSqaaKqzGdGaaGOmaaWcbeaaaOqa aiabl6UinbqaaiaadMgadaWgaaWcbaGaamOAaaqabaaakeaacqWIUl staeaacaWGPbWaaSbaaSqaaiaad2gaaeqaaaaaaOGaayjkaiaawMca aaaa@BF21@

Note 1 – An inductance matrix is always symmetric and positive definite.

Note 2 – An inductance matrix can also be determined for a set of electric circuit elements having inductive couplings between any pair of them.


fr
matrice des inductances, f
pour un élément inductif linéaire à m paires de bornes, matrice m × m servant à exprimer les flux totalisés Ψi (131-12-17) entre les bornes de chaque paire en fonction des courants électriques ij à la première borne de chaque paire:

( Ψ 1 Ψ 2 Ψ i Ψ m )=( L 11 L 12 L 1j L 1m L 21 L 22 L 2j L 2m L i1 L i2 L ij L im L m1 L m2 L mj L mm )( i 1 i 2 i j i m ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meGabaGacmGadiWaaiWabaabaiaafaaake aadaqadaqaauaabeqageaaaaqaaiaadI6adaWgaaWcbaqcLboacaaI XaaaleqaaaGcbaGaamiQdmaaBaaaleaajug4aiaaikdaaSqabaaake aacqWIUlstaeaacaWGOoWaaSbaaSqaaiaadMgaaeqaaaGcbaGaeSO7 I0eabaGaamiQdmaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPa aacqGH9aqpdaqadaqaauaabeqagyaaaaaabaGaamitamaaBaaaleaa jug4aiaaigdacaaIXaaaleqaaaGcbaGaamitamaaBaaaleaajug4ai aaigdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaamitamaaBaaaleaa jug4aiaaigdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaamitamaaBa aaleaajug4aiaaigdaliaad2gaaeqaaaGcbaGaamitamaaBaaaleaa jug4aiaaikdacaaIXaaaleqaaaGcbaGaamitamaaBaaaleaajug4ai aaikdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaamitamaaBaaaleaa jug4aiaaikdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaamitamaaBa aaleaajug4aiaaikdaliaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7 I0eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eaba GaamitamaaBaaaleaacaWGPbqcLboacaaIXaaaleqaaaGcbaGaamit amaaBaaaleaacaWGPbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGmb WaaSbaaSqaaiaadMgacaWGQbaabeaaaOqaaiabl+UimbqaaiaadYea daWgaaWcbaGaamyAaiaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7I0 eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eabaGa amitamaaBaaaleaacaWGTbqcLboacaaIXaaaleqaaaGcbaGaamitam aaBaaaleaacaWGTbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGmbWa aSbaaSqaaiaad2gacaWGQbaabeaaaOqaaiabl+UimbqaaiaadYeada WgaaWcbaGaamyBaiaad2gaaeqaaaaaaOGaayjkaiaawMcaaiabgwSi xpaabmaabaqbaeqabyqaaaaabaGaamyAamaaBaaaleaajug4aiaaig daaSqabaaakeaacaWGPbWaaSbaaSqaaKqzGdGaaGOmaaWcbeaaaOqa aiabl6UinbqaaiaadMgadaWgaaWcbaGaamOAaaqabaaakeaacqWIUl staeaacaWGPbWaaSbaaSqaaiaad2gaaeqaaaaaaOGaayjkaiaawMca aaaa@BF21@

Note 1 – Une matrice des inductances est toujours symétrique et définie positive.

Note 2 – Une matrice des inductances peut aussi être déterminée pour un ensemble des éléments électriques comportant des couplages inductifs entre chaque paire d’éléments.


de
Induktivitätsmatrix, f

es
matriz de inductancias

ja
インダクタンス行列

no
nb induktansmatrise

nn induktansmatrise

pl
macierz indukcyjności

pt
matriz de indutâncias
matriz de indutividades

zh
电感矩阵

Publication date: 2008-09
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