Analytical calculation for DC inductances of rectangular spiral inductors with finite metal thickness in the PEEC formulation

Abstract

Inductances of rectangular spiral inductors with finite metal thickness are evaluated by the partial element equivalent circuit (PEEC) technique. The six fold partial self and mutual inductance integrals resulting from the PEEC partitions are found to have analytical expressions, so that the singularities of the integrands can be overcome and the theoretical or "exact" results can be obtained very efficiently. Via and underpath required for input/output connection can also be included in the calculation. Calculated inductance values for 20 square spiral inductors are checked against measured data published in open literature. Dependence of inductance values on metal thickness is investigated for two specific spiral structures.

Characterization of on‐chip miniature multi‐layer spiral inductors for RFICs

“…The self inductance is the summation of DC inductance of each spiral in different layer, which can be determined using some closed-form equations proposed by Kuo et al [3], Asgaran [4], and Jenei et al [5], respectively. However, we need to compare their accuracies so as to pick out the most accurate equation among them.…”

“…To further examine three sets of equations presented in [3][4][5], the average relative errors (E aver ), as defined by (2), are calculated and they are E aver ϭ 5.54%, 2.87%, and 6.25%, respectively. It is found that the equation in [4] has the smallest average relative error.…”

“…Several models have been proposed for determining the inductor's parameters [1,2]. In particular, some closed-form equations have been derived to calculate DC inductance of single-spiral inductors efficiently [3][4][5]. However, it is difficult to use these equations for multi-layer spiral geometries [6], which can be also employed in radio frequency integrated circuits (RFICs) with high integration density.…”

“…The fundamental methods to realize circular polarization by use of microstrip antenna are: (1) single layer orthogonally-fed circularly polarized microstrip antenna [1]; (2) single layer or multilayer singly-fed or multiply-fed circularly polarized microstrip antenna [2,3]; (3) broadband circularly polarized microstrip antenna composed of curved microstrip; (4) circularly polarized microstrip antenna composed of microstrip antenna array [4,5]. The theory of multiple radiating elements combination circular polarization and single layer multiply-fed circular polarization is similar.…”

Analytical Calculation of the Inductance of Planar Zig-Zag Spiral Inductors

“…Their relative easy layout requires extensive computation if modelled numerically using full-wave electromagnetic methods [2]; the solution may be indeed accurate, however run times may be long and the analysis may be limited to inductors of just a few turns only. The inductance of planar rectangular spiral inductors can be more efficiently calculated with analytical procedures, as in [3,4]. For more complex geometries of inductors, such as square, hexagonal, octagonal and circular shapes, approximate expressions are given [5].…”