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Unified Inductance Calculations for On-Chip Planar Nonuniform Spirals
  • Shuangwen Xie ,
  • Jie Cui ,
  • Jun Fu
Shuangwen Xie
Tsinghua University

Corresponding Author:[email protected]

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We present several calculations for the DC inductance of planar polygonal nonuniform spiral inductors, including common layout shapes of square, hexagon, octagon, and circle. The term “nonuniform” is a novel classification proposed in this paper to characterize the turn-to-turn variable metal width inductors. We take three extreme cases into consideration, according to the spiral coil from inside to outside: type 1 with the increasing width, type 2 with the fixed width and space (conventional inductors), and type 3 with the decreasing width. Five unified calculations are first proposed for the conventional inductors (type 2 inductors), which are only layout dependent with different coefficients, and then we successfully further three of the five calculations, with a simple modification on some calculation parameters, for all nonuniform types. Fractional inductors are treated as “integer plus fraction” parts, both of which can be easily determined by derived calculations. Automatic scripts are employed to generate over a million inductor layouts for electromagnetic (EM) simulation. Our calculations match the EM inductance values typically within around 3%. Comparison with both measured and published experimental results also shows good agreement.