Unterschiede
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Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
electrical_engineering_2:magnetic_circuits [2023/06/12 11:40] ott |
electrical_engineering_2:magnetic_circuits [2024/05/03 16:02] (aktuell) mexleadmin [Magnetic Circuit with two Sources] |
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- | ====== 5. Magnetic Circuits ====== | + | ====== 5 Magnetic Circuits ====== |
< | < | ||
Zeile 405: | Zeile 405: | ||
$k_{21}$ describes how much of the flux from coil $1$ is acting on coil $2$ (similar for $k_{12}$): | $k_{21}$ describes how much of the flux from coil $1$ is acting on coil $2$ (similar for $k_{12}$): | ||
- | \begin{align*} k_{21} = {{\Phi_{21} \cdot \Phi_{22} }\over{|\Phi_{21} \cdot \Phi_{22}|}} {{\Phi_{21}}\over{\Phi_{11}}} \\ \end{align*} | + | \begin{align*} k_{21} = \pm {{\Phi_{21}}\over{\Phi_{11}}} \\ \end{align*} |
+ | |||
+ | The sign of $k_{21}$ depends on the direction of $\Phi_{21}$ relative to $\Phi_{22}$! If the directions are the same, the positive sign applies, if the directions are oposite, the minus sign applies. | ||
When $k_{21}=+100~\%$, | When $k_{21}=+100~\%$, | ||
Zeile 422: | Zeile 424: | ||
& | & | ||
\end{align*} | \end{align*} | ||
+ | |||
+ | Note, that also $M_{21}$ and $M_{12}$ can be either positiv or negative, depending on the sign of the coupling coefficients. | ||
The formula is finally: | The formula is finally: | ||
Zeile 486: | Zeile 490: | ||
* the mutual inductances are equal: $M_{12} = M_{21} = M$ | * the mutual inductances are equal: $M_{12} = M_{21} = M$ | ||
* the mutual inductance $M$ is: $M = \sqrt{M_{12}\cdot M_{21}} = k \cdot \sqrt {L_{11}\cdot L_{22}}$ | * the mutual inductance $M$ is: $M = \sqrt{M_{12}\cdot M_{21}} = k \cdot \sqrt {L_{11}\cdot L_{22}}$ | ||
- | * The resulting *total coupling* $k$ is given as \begin{align*} k = \rm{sgn}(k_{12}) \sqrt{k_{12}\cdot k_{21}} \end{align*} | + | * The resulting |
==== Effects in the electric Circuits ==== | ==== Effects in the electric Circuits ==== |