https://www.wirelesspowerwiki.com/ 2026-04-08T09:47:16+00:00 https://www.wirelesspowerwiki.com/ https://www.wirelesspowerwiki.com/lib/exe/fetch.php?media=wiki:logo.png text/html 2024-04-04T17:07:42+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.wirelesspowerwiki.com/doku.php?id=ipt:basics:resonancefrequency&rev=1712250462&do=diff Coupled coils with series resistance Circuit Consider two coils with inductances $L_1$ and $L_2$, coupled by mutual inducance $M$. The inductors have series resistance $R_1$ and $R_2$. Equivalent circuit This circuit can be represented by the following equivalent circuit:\begin{align} Z = \begin{bmatrix} z_{11} & z_{12} \\ z_{21} & z_{22} \\ \end{bmatrix}= \begin{bmatrix} R_1+j\omega L_1 & j \omega M \\ j \omega M & R_2+j\omega L_2 \\ \end{bmatrix} \end{align}$\omeg…