Coilsolver is a PHP port of MATLAB code written to optimize planar spiral inductors with respect to quality factor. This code was developed to optimize an LC resonant tank for wireless implantation. The capacitor in question is a capacitive pressure sensor with fixed construction and the optimal inductor geometric parameters are sought to maximize quality factor. The details of the implementation can be found in the paper cited below.[1]

The capacitive pressure sensor is treated as an ideal capacitor and the inductor parasitics are included. The tank is treated as an RLC series circuit with the capacitance being the sum of the ideal sensor capacitance and the inductor self-capacitance. The basic version of this solver enforces the lumped element constraint, but the advanced version allows you to disable it. Under these conditions it can be shown that the only free parameters are the coil trace width and the number of turns.[1]

The top-down photograph (top right figure) and cross-sectional diagram (bottom right figure) detail the construction of the coil and capacitor for the purposes of this optimization. The important thing to note is the presence of a return line underneath the coil going to the capacitor. This is the key parasitic self-capacitance that is generated. The advanced version of the solver allows you to modify the fabrication parameters to suit your process.

[1] Shah, N. et al. "Inductor Optimization for Passive Wireless Implantable Capacitive Sensors". *IEEE Sensors*, vol. 14, pp. 2452-2460, Aug 2014.

Also see: Shah, N. *Inductor Optimization for Passive Wireless Implantable Capacitive Sensors.* Master's thesis, University of California Berkeley. [PDF]