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 in order to achieve the maximal quality factor value Q
_max
is explored. A new parameter, namely the ratio of the inner hollow radius and the outer winding radius ¿ = R
_in
/ R
_out
, is proposed as an indicator for optimization and used to quantify how hollow a spiral winding is. With the aid of Finite Element Analysis (FEA), the relationship between ¿ 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. On the contrary, if the conductor width is much larger than the skin depth and the conductors are placed relatively close, the hollow spiral design is recommended. The optimal range of ¿ with which the Q
_max
can be achieved is found to be around 0.45 to 0.55.