“…The prong length l , width w , thickness t , and prong spacing g of the custom QTF are 9.4 mm, 2 mm, 0.25 mm, and 0.8 mm, respectively, as shown in Figure A, which were determined based on the following design consideration. According to the Euler–Bernoulli model, ,, the fundamental resonance frequency f of the QTF is related to its geometric parameters, which is given by the following: where E is the elastic Young modulus of the quartz (0.72 × 10 11 N/m 2 ) and ρ is the density of the quartz (2,650 kg/m 3 ).…”