Table 2.

Electromechanical properties of the exemplary magnetic field sensor referred to in this article and resulting numerical values for the derived equations.

Property	Value for AM	Value for PM
Static capacitance	$C_0=44 \mathrm{pF}$
Loss factor	$tan{\delta }_0=5·{10}^{-3}$
Loss resistance	$R_0\left(f_{\mathrm{res}}\right)=97.5 \mathrm{M}\mathsf{\Omega }$
Resonance frequency	$f_{\mathrm{res}}=7421.1 \mathrm{Hz}$
Quality factor	$Q=887.1$
Motional resistance	$R_{\mathrm{m}}=476.67 \mathrm{k}\mathsf{\Omega }$
Motional capacitance	$C_{\mathrm{m}}=50.71 \mathrm{fF}$
Motional inductance	$L_{\mathrm{m}}=9.07 \mathrm{kH}$
Magnetic operating point	$B_{\mathrm{bias}}=0.65 \mathrm{mT}$
Magnetic sensitivity	$S_{\mathrm{mag}}=80 \mathrm{Hz}/\mathrm{mT}$
Excitation amplitude	${\widehat{V}}_{\mathrm{ex}}=1 \mathrm{V}$
Feedback capacitance	$C_{\mathrm{f}}=10 \mathrm{pF}$
Transimpedance	$\left|T\right(f_{\mathrm{res}}\left)\right|=2.145 \mathrm{M}\mathsf{\Omega }$
Excitation frequency	$f_{\mathrm{ex}}^{\mathrm{AM}}=f_{\mathrm{res}}\mp 0.352 \mathrm{Hz}$	$f_{\mathrm{ex}}^{\mathrm{PM}}=f_{\mathrm{res}}$
Electrical sensitivity	$S_{\mathrm{elec}}^{\mathrm{AM}}=\pm 112.7·{10}^{-3}1/\mathrm{Hz}$	$S_{\mathrm{elec}}^{\mathrm{PM}}=-239·{10}^{-3}\mathrm{rad}/\mathrm{Hz}$
Sensitivity cutoff frequency ($-3 \mathrm{dB}$)	$f_{\mathrm{cs}}^{\mathrm{AM}}=4.35 \mathrm{Hz}$	$f_{\mathrm{cs}}^{\mathrm{PM}}=4.18 \mathrm{Hz}$
Overall sensitivity	$|S_{\mathrm{AM}}\left(1\mathrm{Hz}\right)|=8.9 1/\mathrm{mT}$	$|S_{\mathrm{PM}}\left(1\mathrm{Hz}\right)|=18.6 \mathrm{rad}/\mathrm{mT}$
Thermal electrical voltage noise density	$E_{\mathrm{d}0}\left(f_{\mathrm{res}}\right)=27.5 \mathrm{nV}/\sqrt{\mathrm{Hz}}$
Thermal mechanical voltage noise density	$E_{\mathrm{dm}}\left(f_{\mathrm{res}}\right)=393\mathrm{nV}/\sqrt{\mathrm{Hz}}$
Overall noise power spectral density	$S_{\alpha }\left(1 \mathrm{Hz}\right)=1.55·{10}^{-14}1/\mathrm{Hz}$	$S_{\phi }\left(1 \mathrm{Hz}\right)=1.45·{10}^{-14}{\mathrm{rad}}^2/\mathrm{Hz}$
Noise cutoff frequency ($-3 \mathrm{dB}$)	$f_{\mathrm{cn}}^{\mathrm{AM}}=7.0 \mathrm{Hz}\ne f_{\mathrm{cs}}^{\mathrm{AM}}$	$f_{\mathrm{cn}}^{\mathrm{PM}}=4.18 \mathrm{Hz}=f_{\mathrm{cs}}^{\mathrm{PM}}$
Overall detectivity	${\mathrm{LOD}}_{\mathrm{AM}}\left(1\mathrm{Hz}\right)=140.1 \mathrm{pT}/\sqrt{\mathrm{Hz}}$	${\mathrm{LOD}}_{\mathrm{PM}}\left(1\mathrm{Hz}\right)=64.8 \mathrm{pT}/\sqrt{\mathrm{Hz}}$
Overall detectivity cutoff frequency ($+3 \mathrm{dB}$)	$f_{\mathrm{cd}}^{\mathrm{AM}}=5.1 \mathrm{Hz}$	$f_{\mathrm{cd}}^{\mathrm{PM}}=60.0 \mathrm{Hz}$