Unterschiede
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Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
electrical_engineering_2:magnetic_circuits [2023/06/13 09:35] 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 407: | Zeile 407: | ||
\begin{align*} k_{21} = \pm {{\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. | + | 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 $k_{21}=+100~\%$, | ||
When $k_{21}=-100~\%$, | When $k_{21}=-100~\%$, | ||
Zeile 423: | 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 487: | 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 ==== |