Reflected impedance
= Reflected impedance
{title2=$Z_{\mathrm{ref}}=\omega^2M^2/Z_s$}
The <reflected impedance> is the contribution of a coupled secondary load to a primary winding's <input impedance>. For two ideal mutually coupled <inductors>, choose winding signs so that positive <electric currents> reinforce their <magnetic fluxes>. If the secondary loop has <complex impedance> $Z_s$, its <Kirchhoff's voltage law> gives $\widetilde I_s=-i\omega M\widetilde I_p/Z_s$. Substitution in $\widetilde V_p=i\omega L_p\widetilde I_p+i\omega M\widetilde I_s$ gives $Z_{\mathrm{in}}=i\omega L_p+\omega^2M^2/Z_s$. For $Z_s=R+i\omega L_s$, the reflected real part is $\omega^2M^2R/[R^2+(\omega L_s)^2]$, and primary mean input <power> equals secondary mean <Joule heating>.