The Construction of a Wireless Power Supply System using Planar Spiral Inductors

A Fast and Precise Tool for Multi-Layer Planar Coil Self-Inductance Calculation

“…However, this simplicity brings some limitations regarding the coil geometries that the approximation applies for, as well as the precision of the model results. Based on the literature [1,8,[20][21][22][23][24][25][26]30], there are several approximation formulas for calculating the inductance of planar coils, some are application specific [18,[30][31][32], or are only valid for one type of geometry such as the research works from Bryan, Terman, Olivei, Gleason, Dill and others [1,26,33,34], some remain valid for several regular geometries like the Data Fitted Monomial, the Current Sheet Approximation and the Modified Wheeler [1,24,26,35]. These last ones, due to their higher versatility and precision in the results, when compared to others proposed in the literature, are the ones most commonly used.…”

“…According to the literature [ 1 , 8 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ], to define the design of a coil for an application, two types of methodologies stand out, the numerical methods, e.g., finite element method (FEM), and the approximation formulas. Although FEM simulation is the most accurate methodology, it requires expensive simulation programs, high computational resources, and the FEM model development itself is a meticulous and complex process.…”

“…Currently, to perform these calculations, the combination of the coupling coefficient with the self-inductance values obtained by the previously mentioned approximation formulas is being used [ 37 , 40 ]. Typically, this coefficient is either calculated analytically [ 24 ] or using a numerical model [ 25 ], or it can even be measured experimentally [ 41 ]. Equation ( 6 ) is the analytical expression that is commonly used to calculate the coupling coefficient between coils [ 20 , 21 , 24 ].…”

“…The design and optimization of planar coils is a complex, costly and time consuming process, usually based on finite element modeling (FEM) methods and experimental measurements [ 17 , 18 , 19 ]. Fast, closed form analytical methods can also be found in the literature [ 1 , 8 , 20 , 21 , 22 , 23 , 24 , 25 , 26 ] for coil optimization. However, these methods are limited to the calculation of the self-inductance of regular coils with specific geometries.…”

Miniaturized lumped quadrature hybrid using inductance‐ and integration‐enhanced inductors for VHF band applications

“…[4][5][6][7][8] Conventional planar spiral inductors with high inductance take up large planar dimensions because they are implemented on single layer. 9 By virtue of the three-dimensional (3D) layout capability, low-temperature co-fired ceramic (LTCC) technology has better flexibility to implement highly integrated circuits, which can achieve a much more compact size than planar circuits. Although a 3D spiral inductor etched 1.5 more planar turns inside the spiral, 10 it does not take advantage of the multilayered structure to enhance inductance and integration, which thus gives rise to both low inductance and low Q-factor.…”