b61d18625573e432110a734cfdf692ac pmc_11819867.pdf 318b770be6521729289276f0046685df3964404f pmc_11819867.pdf aa788f9c5e70803124fe4c39661310fbee2d017a844c97b2ce2e4b9913c328d0 pmc_11819867.pdf Title: A Discussion on Sensitivity Optimization in Reflective-Mode Phase-Variation Permittivity Sensors Based on Semi-Lumped Resonators Subject: Typically, the operating frequency in single-frequency reflective-mode phase-variation permittivity sensors based on semi-lumped resonators (e.g., step-impedance resonators—SIRs) is set to the resonance frequency of the sensing resonator when it is loaded with the so-called reference (REF) material, f0,REF. For the case of an SIR-based sensor, if the ratio between the inductance and the capacitance is high (corresponding to a high-Q resonator), the sensitivity in the limit of small perturbations of the dielectric constant (in the vicinity of that of the REF material) is also high. However, the optimum frequency for sensitivity optimization in the limit of small perturbations neither corresponds to the resonance frequency nor coincides with the frequency of maximum phase slope. Such frequencies are calculated in this paper, and it is shown that the optimum frequency for sensitivity optimization is located between the frequency of maximum phase slope and the resonance frequency, although such frequencies tend to coincide for high-Q sensing resonators. This aspect is validated in this paper from electromagnetic simulation and experiment. Keywords: microwave sensors; permittivity sensors; phase-variation sensors; step-impedance resonator (SIR); high-Q resonators Author: Lijuan Su, Paris Vélez, Pau Casacuberta, Xavier Canalias, Nazmia Kurniawati and Ferran Martín Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25 CreationDate: Sat Jan 25 11:09:02 2025 CET ModDate: Sat Jan 25 11:23:24 2025 CET Custom Metadata: no Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 14 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 1974625 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- MIKRSI+VnURWPalladioL Type 1 Custom yes yes yes 10 0 EBMMAL+URWPalladioL-Roma Type 1 Custom yes yes yes 16 0 ZZGCPN+URWPalladioL-Bold Type 1 Custom yes yes yes 22 0 PICRKI+URWPalladioL-Ital Type 1 Custom yes yes yes 27 0 GRDIOW+PazoMath-Italic Type 1 Builtin yes yes yes 53 0 LWYFXZ+CMEX10 Type 1 Builtin yes yes yes 61 0 FSYJUW+PazoMath Type 1 Builtin yes yes yes 66 0 GIGFZE+CMR10 Type 1 Builtin yes yes yes 71 0 MTGWKX+CMSY10 Type 1 Builtin yes yes yes 76 0 JJNJLK+TimesNewRoman,Italic CID TrueType Identity-H yes yes yes 88 0 JJNJLL+TimesNewRoman,Italic TrueType WinAnsi yes yes no 94 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 97 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 100 0 JJNIAB+TimesNewRoman CID TrueType Identity-H yes yes yes 103 0 QIELJB+CMMI10 Type 1 Builtin yes yes yes 118 0 EBLVEP+EURM10 Type 1 Builtin yes yes yes 126 0 JJNJLK+TimesNewRoman,Italic CID TrueType Identity-H yes yes yes 138 0 JJNJLL+TimesNewRoman,Italic TrueType WinAnsi yes yes no 144 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 147 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 150 0 JJNIAB+TimesNewRoman CID TrueType Identity-H yes yes yes 153 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 167 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 170 0 JJNKIH+Symbol Type 1C Custom yes yes yes 184 0 JJNJLL+TimesNewRoman,Italic TrueType WinAnsi yes yes no 189 0 JJNNKF+Arial CID TrueType Identity-H yes yes yes 192 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 198 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 201 0 JJNIAB+TimesNewRoman CID TrueType Identity-H yes yes yes 204 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 215 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 218 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 238 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 241 0 JJNKIH+Symbol Type 1C Custom yes yes yes 257 0 JJNJLL+TimesNewRoman,Italic TrueType WinAnsi yes yes no 262 0 JJNNKF+Arial CID TrueType Identity-H yes yes yes 265 0 JJOGIB+Arial,Italic TrueType WinAnsi yes yes no 271 0 JJNGPB+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 274 0 JJNGPD+PalatinoLinotype TrueType WinAnsi yes yes no 277 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-02-26 02:08:24 CET RepresentationInformation: pmc_11819867.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-02-26 02:04:03 CET Size: 1974625 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 431 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: section.1 Item: Title: Analysis Destination: section.2 Item: Title: Validation Destination: section.3 Item: Title: Conclusions Destination: section.4 Item: Title: References Destination: section.5 Info: Title: A Discussion on Sensitivity Optimization in Reflective-Mode Phase-Variation Permittivity Sensors Based on Semi-Lumped Resonators Author: Lijuan Su, Paris Vélez, Pau Casacuberta, Xavier Canalias, Nazmia Kurniawati and Ferran Martín Subject: Typically, the operating frequency in single-frequency reflective-mode phase-variation permittivity sensors based on semi-lumped resonators (e.g., step-impedance resonators SIRs) is set to the resonance frequency of the sensing resonator when it is loaded with the so-called reference (REF) material, f0,REF. For the case of an SIR-based sensor, if the ratio between the inductance and the capacitance is high (corresponding to a high-Q resonator), the sensitivity in the limit of small perturbations of the dielectric constant (in the vicinity of that of the REF material) is also high. However, the optimum frequency for sensitivity optimization in the limit of small perturbations neither corresponds to the resonance frequency nor coincides with the frequency of maximum phase slope. Such frequencies are calculated in this paper, and it is shown that the optimum frequency for sensitivity optimization is located between the frequency of maximum phase slope and the resonance frequency, although such frequencies tend to coincide for high-Q sensing resonators. This aspect is validated in this paper from electromagnetic simulation and experiment. 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