Cole-Cole/FDSC Co-Design of a Robust Compact Dual-Band Implantable Biosensor Antenna in Dispersive Multilayer Tissue
Keywords:
Cole-Cole model, Electric-energy participation, Field filling factor, Frequency-dependent Smith chart, Implantable antenna, Specific absorption rate, Uncertainty propagationAbstract
Implantable biosensor antennas are sensitive to the dispersive electromagnetic properties of surrounding tissue and to implantation variability. This study presents an uncertainty-aware co-design framework combining a band-constrained Cole-Cole tissue model, a multilayer field-filling approximation, a dual-resonance impedance surrogate, and a frequency-dependent Smith-chart (FDSC) representation. A field-integral derivation distinguishes the weights in an arithmetic complex-permittivity mixture from electric-energy participation factors. The derivation also identifies the frozen-field, tissue-loading, and dispersion assumptions behind the resonance approximation; it does not establish an exact stored-energy model for lossy tissue. The reported computational study propagates tissue, filling-factor, depth, encapsulation, feed, and fabrication uncertainty through 12,000 fixed-seed Monte Carlo samples. Relative to nominal tuning, uncertainty-aware electrical targets increase the proportion satisfying S₁₁ ≤ −10 dB at every evaluated frequency from 36.5% to 85.8% in the MedRadio band, from 33.0% to 79.8% in the 2.45-GHz band, and from 12.2% to 68.6% jointly. Median worst in-band S₁₁ changes from −7.67 to −15.39 dB and from −7.96 to −13.59 dB, respectively. These are reused-ensemble, grid-based estimates rather than independent validation or continuous-frequency guarantees. A conductivity-and-matching-scaled SAR proxy is approximately 0.20 W/kg at its 95th percentile for 1 mW input, but is neither a proven upper bound nor a permissible-power calculation. The framework supports selection of electrical targets for subsequent full-wave and phantom investigation; exact numerical reproduction additionally requires the original fitted coefficients and computational configuration.
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