Simple and accurate radio frequency inductance expression for on-chip planar spiral inductors

A simple and accurate expression for calculating radio frequency (RF) inductance of square, hexagonal, octagonal and circular on-chip planar spiral inductors is presented in this paper. The expression presented shows a functional relationship between RF inductance (L
RF
) and some certain electrical parameters of inductors, which are low frequency inductance (L
0
), self resonant frequency (ƒ
R
), work frequency (ƒ
W
) and substrate material correlation coefficient (β). Compared with both three-dimensional field solver simulation data and experiment data, the RF inductance data obtained by the presented expression matched both of them typically within around 5%. So it is worth expecting that this expression would be very useful for designing and optimizing of inductors, especially for applying inductors to RF ICs.