“…The magnetic inductance is assigned to the CNTs and the substrate. Magnetic inductance depends on the current loops formed by the bundles and, therefore, is highly dependent on the geometry of the BMWCNT-based power inductor [7]- [12], as shown (2)-(4), at the top of the next page, where n is the number of turns, d o the outer diameter of the spiral, d i the inner diameter of the spiral, d BMWCNT the overall diameter of the bundled cylindrical tubes, s the spacing between the segments, n the number of turns, ρ CNT the resistivity of the CNTs (0.34 × 10 −6 Ω·cm [9]), d BMWCNT the diameter of the CNT-bundle, a and b the rectangular dimensions of the cross section, L s the self-inductance, l SWCNT the length of the spiral as expressed in (4), and γ is the geometric mean distance (GMD), which is 0.46 times a side for a square or rectangular cross section and 0.25 times the length for a straight-line cross section. Since the skin depth phenomenon has little effect on CNTs power inductor, τ should be considered to have a value of 1 for high frequencies (greater than 50 MHz).…”