On the relationship of quality factor and hollow winding structure of coreless printed spiral winding (CPSW) inductor

The principle of using hollow spiral winding is not novel, but the study on this topic is far from complete. In this paper, how hollow the central region of the coreless printed spiral winding (CPSW) inductor should be for a given footprint area in order to achieve the maximal quality factor Q_max and to maintain high inductance value is explored. A hollow factor based on the ratio of the inner hollow radius and the outer winding radius τ = R_in/R_out, is proposed as for optimization and quantifying how hollow a spiral winding is. The relationship between τ and Q_max, which depends on the operating frequency and the dimensional parameters of CPSW inductor, is established. For a specific operating frequency, it is discovered that if the conductor width is comparable with the skin depth, or the conductors are placed relatively far away from each others, the hollow design of the CPSW inductor has little improvement on Q but reduces the inductance. If the conductor width is much larger than the skin depth and the conductors are closely placed, the hollow spiral design is recommended. The optimal range of τ with which the Q_max can be achieved is found to be around 0.45-0.55.