Patent ID: 7451415

Claim:
A method for predicting inductance and self-resonant frequency of a spiral inductor, characterized by the steps of: (1). determining the material parameters and dimensions of a spiral inductor; (2). calculating magnetic factor α for determining paramagnetic and diamagnetic characteristic constrained by material and geometry of the spiral inductor determined in step (1); (3). evaluating kinetic energy (E L ), quasi-electrostatic electric field ( (r)) constrained in corners in the inductor, and scattering energy (E C ) due to the electric field in the corners; (4). determining the self-resonant frequency ω r of the two-port freely suspended spiral inductor; according to the material parameters and dimensions of the inductor determined in step (1); (5). relying on the result in step (4) to calculate the frequency-dependent inductance of the two-port freely suspended spiral inductor; (6). relying on the results of steps (1) and (4) to determine the inductance; thus, the self-resonant frequency and inductance can be obtained wherein said kinetic energy (E L ), said quasi-electrostatic electric field (r), and said scattering energy (E C ) can be calculated as: E L ⁢ 3 / 5 ⁢ η 2 m e ⁢ ( 3 ⁢ ⁢ π 2 ⁢ n e ) 1 / 3 ⁢ π l total , where l total represents the total length of the inductor; and E ρ ⁡ ( r ) = 1 4 ⁢ ⁢ π ⁢ ⁢ ɛ 0 ⁢ q ⁡ [ π + 8 ⁢ ⁢ sin ⁡ ( π 2 / 4 ⁢ ⁢ β ) ] 2 8 ⁢ ⁢ ϖ ⁢ ⁢ h ⁢ ⁢ β ⁡ [ csc ⁡ ( β / 2 ) - 1 ] ⁢ ( π + β ) ⁢ r ^ , where q is elementary charge, ω and h are width and height of the spiral inductor, respectively and ε 0 is vacuum permittivity; then, β is corner angle, and the electric field is centered at the outer apex of each corner; and E C = πɛ 0 ⁢ ϖ ⁢ ⁢ h ⁡ [ csc ⁡ ( β / 2 ) - 1 ] ⁢  E μ  ⁢ q NV 2 / 3 ⁢ σ eff ⁡ [ ( 1 + 2 ⁢ ∫ - ∞ ∞ ⁢ ⁢ ⅆ r r 3 + … ) ⁢ csc ⁡ ( π - β 2 ) ] 2 = { q 2 4 ⁢ NV 2 / 3 ⁢ σ eff ⁢ ( π + 8 ⁢ sin ⁢ π 2 4 ⁢ β ) 2 8 ⁢ β ⁡ ( π + β ) ⁢ csc 2 ⁡ ( π - β 2 ) , for ⁢ ⁢ β < π q 2 4 ⁢ NV 2 / 3 ⁢ σ eff ⁢ ( π + 4 ⁢ 2 ) 2 4 ⁢ π ⁢ π 2.7 , for ⁢ ⁢ β = π ⁢ ⁢ ( circular ⁢ ⁢ inductor ) where r, N, V, and σ eff are electronic incident path, number of corners, volume of polygon spiral inductor, and effective cross section of the inductor, respectively.