Certified Inductance and RLC Extraction for HF RFID Resonators: From Guaranteed Magnetic-Energy Bounds to a Certified Resonance Band

Abstract

A 13.56 MHz HF RFID or NFC tag is a magnetically driven RLC resonator, and its resonance frequency and quality factor follow from the inductance, the loss and the capacitance of its coil. These are usually obtained from field solvers that return a single number with no certificate on the discretisation error, or from closed-form formulas valid only for canonical shapes. This paper applies the complementary-energy machinery of the dual discrete geometric method to the resonant HF tag and carries the resulting guaranteed intervals through to the quantities a tag designer signs. The inductance is enclosed by a two-sided bracket built from a primal nodal solve and a complementary flux solve; a field-circuit coupled eddy-current solve returns the series loss resistance with skin and proximity effects; and the coil self-capacitance is extracted electrostatically and bracketed as well, so L, R and C are all field-based and all certified. Propagated through a chip-loaded circuit model, they give a guaranteed band on the resonance frequency and the loaded quality factor. An axisymmetric formulation is introduced for coils whose turns are closed loops of finite cross-section: it removes both the filament regularisation of an edge-element engine and the overestimation of a Cartesian cross-section, and reproduces the exact circular-loop self and mutual inductance to better than one percent. Against a printed four-layer spiral measured on fifteen samples with an impedance analyser, the certified interval sits 0.6 to 1.4 percent below the measured inductance, depending on the copper foil thickness that the source does not state, and closer to it than any of the three analytical methods published with that measurement, while the numerical certificate itself is 0.15 percent wide, an order of magnitude tighter than the coil-to-coil manufacturing spread. The separation between what is certified, the discretisation error, and what is not, the geometric and material data, is stated explicitly throughout.