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Radio Frequency Circuit Design, 2nd Edition by W. Alan Davis

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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) bapp02e001

where

(B.2) bapp02e002

(B.3) bapp02e003

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) bapp02e004

where

(B.5) bapp02e005

FIGURE B.1 Single-loop inductor.

bapp02f001

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

(B.6) bapp02e006

(B.7)

The inductance of a circular ...

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