Radio Frequency Circuit Design, 2nd Edition

APPENDIX BAnalytical Spiral Inductor Model

Modeling equations for spiral inductors given in [1, 2] are collected here for convenience. A straight line of length l, width w, thickness t, resistivity ρ, and in a material of permeability μ₀ has the following inductance:

(B.1)

where

(B.2)

(B.3)

If inhomogeneous current density across the conductor cross section is to be considered, an additional expression is found in [1].

The single-loop inductor is illustrated in Fig. B.1 where the total angular rotation, ϕ₀, is somewhat less than 360°. The inductance is found by numerical integration of the following equation:

(B.4)

where

(B.5)

FIGURE B.1 Single-loop inductor.

The values for r₁ and r₂ below are replaced by r_i and r_o as specified by Eq. (B.5):

(B.6)

(B.7)

The inductance of a circular ...