Simple accurate expressions for planar spiral inductances

Abstract

We present several new simple and accurate expressions for the DC inductance of square, hexagonal, octagonal, and circular spiral inductors. We evaluate the accuracy of our expressions, as well as several previously published inductance expressions, in two ways: by comparison with three-dimensional field solver predictions and by comparison with our own measurements, and also previously published measurements. Our simple expression matches the field solver inductance values typically within around 3%, about an order of magnitude better than the previously published expressions, which have typical errors around 20% (or more). Comparison with measured values gives similar results: our expressions (and, indeed, the field solver results) match within around 5%, compared to errors of around 20% for the previously published expressions. (We believe most of the additional errors in the comparison to published measured values is due to the variety of experimental conditions under which the inductance was measured.) Our simple expressions are accurate enough for design and optimization of inductors or of circuits incorporating inductors. Indeed, since inductor tolerance is typically on the order of several percent, "more accurate" expressions are not really needed in practice.

Continuous wireless pressure monitoring and mapping with ultra-small passive sensors for health monitoring and critical care

“…The use of a microstructured elastomer as the dielectric layer enhances pressure sensitivity in the low pressure range due to an increase in effective permittivity on top of the reduction in separation distance between the spiral layers under compression. The 5-turn 1 Â 1 mm 2 design with 50 mm metal traces and spacing outperforms the most sensitive passive wireless pressure previously reported 33 . At pressures above 100 mm Hg, the microstructures are fully deformed and, hence, only the separation distance reductions act to increase the variable capacitance under applied pressure, resulting in a lower sensitivity.…”

“…The greatest deviation between analytical calculations, electromagnetic simulations and measured resonant frequencies is observed with the smallest sensor. This is probably due to an overestimation of inductances at high spiral fill ratio by analytical models 33 . Effective spiral length is desirable for improved mutual coupling to the readout antenna in the near field.…”

Planar Inductor Design for High Power Applications

“…The inductance of the spiral inductor is calculated using Greenhouse-based formulation is given in [14][15][16]. Other methods such as empirical formulation in calculation of the inductance of the spirals are outlined in [17]. The inductance of the spiral using a mathematical model with Kramers-Kronig relations are proposed in [18].…”

Digital Circuit Optimization via Geometric Programming

“…Other problems in digital circuit design where GP plays a role include buffering and wire sizing Wong 1999, 2001a), sizing and placement (Chen et al 2000), yield maximization , Patil et al 2005, parasitic reduction (Qin and Cheng 2003), clock tree design (Vittal and Marek-Sadowska 1997), and routing (Borah et al 1997). Geometric programming has also been used for the design of nondigital circuits, e.g., analog circuits (Dawson et al 2001, Hershenson 2003, Hershenson et al 1998, Mandal and Visvanathan 2001, Vanderhaegen and Brodersen 2004, mixed-signal circuits (Colleran et al 2003, Hassibi and Hershenson 2002, Hershenson 2002, and RF (radio frequency) circuits Mohan et al 1999Mohan et al , 2000Xu et al 2004). Geometric programming has also been used in floorplanning, for both analog and digital circuits (Moh et al 1996).…”