Area Circuit theory / Circuit elements and their characteristics

IEV ref 131-12-34

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:

$\left(\begin{array}{c}{\Psi }_{1}\\ {\Psi }_{2}\\ ⋮\\ {\Psi }_{i}\\ ⋮\\ {\Psi }_{m}\end{array}\right)=\left(\begin{array}{cccccc}{L}_{11}& {L}_{12}& \cdots & {L}_{1j}& \cdots & {L}_{1m}\\ {L}_{21}& {L}_{22}& \cdots & {L}_{2j}& \cdots & {L}_{2m}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ {L}_{i1}& {L}_{i2}& \cdots & {L}_{ij}& \cdots & {L}_{im}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ {L}_{m1}& {L}_{m2}& \cdots & {L}_{mj}& \cdots & {L}_{mm}\end{array}\right)\cdot \left(\begin{array}{c}{i}_{1}\\ {i}_{2}\\ ⋮\\ {i}_{j}\\ ⋮\\ {i}_{m}\end{array}$

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:

$\left(\begin{array}{c}{\Psi }_{1}\\ {\Psi }_{2}\\ ⋮\\ {\Psi }_{i}\\ ⋮\\ {\Psi }_{m}\end{array}\right)=\left(\begin{array}{cccccc}{L}_{11}& {L}_{12}& \cdots & {L}_{1j}& \cdots & {L}_{1m}\\ {L}_{21}& {L}_{22}& \cdots & {L}_{2j}& \cdots & {L}_{2m}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ {L}_{i1}& {L}_{i2}& \cdots & {L}_{ij}& \cdots & {L}_{im}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ {L}_{m1}& {L}_{m2}& \cdots & {L}_{mj}& \cdots & {L}_{mm}\end{array}\right)\cdot \left(\begin{array}{c}{i}_{1}\\ {i}_{2}\\ ⋮\\ {i}_{j}\\ ⋮\\ {i}_{m}\end{array}$

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

ko
인덕턴스 행렬

ja
インダクタンス行列

 no nb induktansmatrise nn induktansmatrise

pl
macierz indukcyjności

pt
matriz de indutâncias