An Improved Calculation of Copper Losses in Integrated Power Inductors on Silicon

Thin-film Si-integrated inductors with closed cores have different magnetic field distributions in the winding window space compared to the inductors with unclosed cores. One-dimensional methods are no longer applicable for these inductors to calculate the ac resistance. Based on the analysis of the magnetic field distribution of the devices, a 2-D field solution was developed, which leads to an improved 2-D method to calculate the ac resistance of the device. High accuracy of this new approach has been verified by finite-element analysis, while 1-D methods can lead to significant errors.