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Area Circuit theory / Circuit elements and their characteristics

IEV ref131-12-32

Symbol
C

en
capacitance matrix
for a linear capacitive n-terminal element, matrix m × m, where m = n − 1, used to express the electric charges qi (131-12-11) at m terminals as functions of the voltages (131-11-56) ujn between these terminals and the remaining nth terminal:

( q 1 q 2 q i q m )=( C 11 C 12 C 1j C 1m C 21 C 22 C 2j C 2m C i1 C i2 C ij C im C m1 C m2 C mj C mm )( u 1n u 2n u jn u mn ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meGabaGacmGadiWaaiWabaabaiaafaaake aadaqadaqaauaabeqageaaaaqaaiaadghadaWgaaWcbaqcLboacaaI XaaaleqaaaGcbaGaamyCamaaBaaaleaajug4aiaaikdaaSqabaaake aacqWIUlstaeaacaWGXbWaaSbaaSqaaiaadMgaaeqaaaGcbaGaeSO7 I0eabaGaamyCamaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPa aacqGH9aqpdaqadaqaauaabeqagyaaaaaabaGaam4qamaaBaaaleaa jug4aiaaigdacaaIXaaaleqaaaGcbaGaam4qamaaBaaaleaajug4ai aaigdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaam4qamaaBaaaleaa jug4aiaaigdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaam4qamaaBa aaleaajug4aiaaigdaliaad2gaaeqaaaGcbaGaam4qamaaBaaaleaa jug4aiaaikdacaaIXaaaleqaaaGcbaGaam4qamaaBaaaleaajug4ai aaikdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaam4qamaaBaaaleaa jug4aiaaikdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaam4qamaaBa aaleaajug4aiaaikdaliaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7 I0eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eaba Gaam4qamaaBaaaleaacaWGPbqcLboacaaIXaaaleqaaaGcbaGaam4q amaaBaaaleaacaWGPbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGdb WaaSbaaSqaaiaadMgacaWGQbaabeaaaOqaaiabl+Uimbqaaiaadoea daWgaaWcbaGaamyAaiaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7I0 eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eabaGa am4qamaaBaaaleaacaWGTbqcLboacaaIXaaaleqaaaGcbaGaam4qam aaBaaaleaacaWGTbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGdbWa aSbaaSqaaiaad2gacaWGQbaabeaaaOqaaiabl+Uimbqaaiaadoeada WgaaWcbaGaamyBaiaad2gaaeqaaaaaaOGaayjkaiaawMcaaiabgwSi xpaabmaabaqbaeqabyqaaaaabaGaamyDamaaBaaaleaajug4aiaaig daliaad6gaaeqaaaGcbaGaamyDamaaBaaaleaajug4aiaaikdaliaa d6gaaeqaaaGcbaGaeSO7I0eabaGaamyDamaaBaaaleaacaWGQbGaam OBaaqabaaakeaacqWIUlstaeaacaWG1bWaaSbaaSqaaiaad2gacaWG UbaabeaaaaaakiaawIcacaGLPaaaaaa@C1A5@

Note 1 – A capacitance matrix is always symmetric and positive definite.

Note 2 – A capacitance matrix can also be determined for a set of electric circuit elements having capacitive couplings between any pair of them.


fr
matrice des capacités, f
pour un multipôle capacitif linéaire à n bornes, matrice m × m, où m = n − 1, servant à exprimer les charges électriques qi (131-12-11) en m bornes, en fonction des tensions électriques (131-11-56) ujn entre ces bornes et la borne restante notée n:

( q 1 q 2 q i q m )=( C 11 C 12 C 1j C 1m C 21 C 22 C 2j C 2m C i1 C i2 C ij C im C m1 C m2 C mj C mm )( u 1n u 2n u jn u mn ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgaruWqVvNCPvMCG4uz 3bqee0evGueE0jxyaibaieYdi9WrpeeC0lXdi9qqqj=hEeeu0lXdbb a9frFj0xb9Lqpepeea0xd9s8qiYRWxGi6xij=hbba9q8aq0=yq=He9 q8qiLsFr0=vr0=vr0db8meGabaGacmGadiWaaiWabaabaiaafaaake aadaqadaqaauaabeqageaaaaqaaiaadghadaWgaaWcbaqcLboacaaI XaaaleqaaaGcbaGaamyCamaaBaaaleaajug4aiaaikdaaSqabaaake aacqWIUlstaeaacaWGXbWaaSbaaSqaaiaadMgaaeqaaaGcbaGaeSO7 I0eabaGaamyCamaaBaaaleaacaWGTbaabeaaaaaakiaawIcacaGLPa aacqGH9aqpdaqadaqaauaabeqagyaaaaaabaGaam4qamaaBaaaleaa jug4aiaaigdacaaIXaaaleqaaaGcbaGaam4qamaaBaaaleaajug4ai aaigdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaam4qamaaBaaaleaa jug4aiaaigdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaam4qamaaBa aaleaajug4aiaaigdaliaad2gaaeqaaaGcbaGaam4qamaaBaaaleaa jug4aiaaikdacaaIXaaaleqaaaGcbaGaam4qamaaBaaaleaajug4ai aaikdacaaIYaaaleqaaaGcbaGaeS47IWeabaGaam4qamaaBaaaleaa jug4aiaaikdaliaadQgaaeqaaaGcbaGaeS47IWeabaGaam4qamaaBa aaleaajug4aiaaikdaliaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7 I0eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eaba Gaam4qamaaBaaaleaacaWGPbqcLboacaaIXaaaleqaaaGcbaGaam4q amaaBaaaleaacaWGPbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGdb WaaSbaaSqaaiaadMgacaWGQbaabeaaaOqaaiabl+Uimbqaaiaadoea daWgaaWcbaGaamyAaiaad2gaaeqaaaGcbaGaeSO7I0eabaGaeSO7I0 eabaGaeSy8I8eabaGaeSO7I0eabaGaeSy8I8eabaGaeSO7I0eabaGa am4qamaaBaaaleaacaWGTbqcLboacaaIXaaaleqaaaGcbaGaam4qam aaBaaaleaacaWGTbGaaGOmaaqabaaakeaacqWIVlctaeaacaWGdbWa aSbaaSqaaiaad2gacaWGQbaabeaaaOqaaiabl+Uimbqaaiaadoeada WgaaWcbaGaamyBaiaad2gaaeqaaaaaaOGaayjkaiaawMcaaiabgwSi xpaabmaabaqbaeqabyqaaaaabaGaamyDamaaBaaaleaajug4aiaaig daliaad6gaaeqaaaGcbaGaamyDamaaBaaaleaajug4aiaaikdaliaa d6gaaeqaaaGcbaGaeSO7I0eabaGaamyDamaaBaaaleaacaWGQbGaam OBaaqabaaakeaacqWIUlstaeaacaWG1bWaaSbaaSqaaiaad2gacaWG UbaabeaaaaaakiaawIcacaGLPaaaaaa@C1A5@

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

Note 2 – Une matrice des capacités peut aussi être déterminée pour un ensemble d’éléments de circuit électrique comportant des couplages capacitifs entre chaque paire d’éléments.


de
Kapazitätsmatrix, f

es
matriz de capacidades

ja
キャパシタンス行列

no
nb kapasitansmatrise

nn kapasitansmatrise

pl
macierz pojemności

pt
matriz de capacidades

zh
电容矩阵

Publication date: 2008-09
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