Substituting Equation (3) into Equation (6), the capacitance of air gap can be evaluated as:Cgap={?��a2dox,p=04?��Dd0pln(d0+a2p64Dd0?a2p64D),p>0(7)The capacitive pressure sensor is constructed by 16 sensing cells, so the capacitance, Cs, of the pressure sensor can be expressed as:Cs=161Cox+1Cgap+1Cox(8)According to Equation (7), we know that the variation of capacitance Cgap depends on the pressure p. In Equation (8), the capacitances Cox are constant, and the variation of capacitance Cs relies on the capacitance Cgap. Thus, the capacitance Cs of the pressure sensor changes as the pressure p varies. In this design, the radius and thickness of the plate in the sensing cell are 50 ��m and 2.
6 ��m, respectively. The material of the metal layers in Figure 2(b) is aluminum.
The Young’s moduli of aluminum and silicon oxide are 70 GPa and 69 GPa, respectively [12]. Thereby, suppose that the Young’s modulus of the plate is 69.5 GPa, and the Poisson’s ratio of the plate is 0.25. Substituting E = 69.5 GPa, �� = 0.25, h = 2.6 ��m, a = 50 ��m, dox = 1 ��m, d0 = 0.64 ��m, �� = 8.85 �� 10?12 F/m and ��ox = 3.54 �� 10?11 F/m into Equations (2), (5), (7) and (8), the variation of capacitance AV-951 Cs in the pressure sensor related to the pressure p can be obtained, and the results are shown in Figure 3. The results reveal that the capacitance of the pressure sensor changes from 0.97 pF to 1.18 pF as the pressure increases from 0 to 500 kPa.
Figure 3.Relation between capacitance and pressure in the pressure sensor.The capacitance variation of the pressure sensor is converted into the output voltage using the ring oscillator circuit.
The professional circuit simulation software, HSPICE, is Drug_discovery used to simulate the output signal of the ring oscillator circuit. As shown in Figure 1, M1, M3 and M5 are PMOS; M2, M4 and M6 are NMOS, where the capacitance of C1 and C2 is 0.5 pF. Figure 4 displays the simulated results of the ring oscillator. In this simulation, the input voltage Vdd of 3.3 V is adopted. The simulated results depict that the oscillation frequency of the ring oscillator changes from 486 to 476 MHz as the capacitance of the pressure sensor increases from 0.97 to 1.
18 PF.Figure 4.Oscillation frequency of the ring oscillator.Combining the data in Figures 3 and and4,4, we can obtain the relation between the output frequency and the pressure in the pressure sensor with ring oscillator circuit, and the results are plotted in Figure 5. The results present that the output frequency of the pressure sensor changes from 486 to 476 MHz as the pressure varies from 0 to 500 kPa.