Inductor on PCB-1

Inductor on print circuit board (PCB) is a complicated. In Figure.1, it shows some factors, which may influence the inductance and q factor. W is the width of trace line. S is the space between two different trace lines. D is outer diameter, N is number of windings, x is the difference of the sides of the square, and d is inner diameter. The formula in this spiral inductor is

\[L=K_1u_0\frac{N^2 D_avg}{1+K_2p}\]

\[D_{avg}=\frac{(D-d)}{(D+d)}\]

Figure. 1 Factor of Inductor

Figure. 2 (a) is the 3D view of inductor design. This design can provide high inductance and magnetic field. Figure. 2(b) is the equivalent circuit of Figure. 2 (a). Thus, the maximum inductance value by stacking two spirals. The thickness may influence the inductance slightly. On the other hand, thickness would influence parasitic capacitor and change the q factor.  

Figure. 2 3D view of inductor design(a) and circuit(b)