# Capacitive Accelerometers with Beams Based on Alternated Segments of Different Widths

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Capacitive Accelerometers

#### 2.1. Some Basic Concepts

^{2}). A differential equation governing the motion is given by [22]:

_{E}= 0, is given by Equation (3), which was obtained by the use of Laplace transformations, and considering the quality factor given by $Q={\omega}_{0}m/\gamma $, where ${\omega}_{0}$ is the mechanical resonant frequency [15,22].

#### 2.2. Static Performance

_{0}), the behavior of the accelerometer is determined by the proof mass and the stiffness of the suspension beam [21]:

^{3}/12 is the second moment of inertia. The boundary conditions are x (0) = 0 and $\frac{\partial x(0)}{\partial y}=0$. From the moment–curvature relationship, the beam displacement, or the equation of the elastic curve, is obtained:

## 3. Design and Simulation of Devices

#### 3.1. Characteristic Equations for ¼ of Accelerometer with Symmetrical Beams

_{b}

_{1}and L

_{b}

_{2}(Equations (8) and (9)), multiplied by an adjustment factor (Δ). The equation of the maximum value of bending stress is given by Equation (13), where, again, it is given by the contributions of L

_{b}

_{1}and L

_{b}

_{2}, multiplied by a correction factor (1.τ), in accordance with the section of accelerometer under consideration (¼ or, ½,); 1.τ corresponds to 1.25 or 1.5, respectively.

_{b}

_{1}and L

_{b}

_{2}. Analysis of the ¼ accelerometer with uniform beam is performed [22].

#### 3.2. Characteristic Equations for 1/2 of Accelerometer with Uniform Beams

#### 3.3. Characteristic Equations for 1/2 of Accelerometer with Symmetrical Beams

_{max}calculation:

#### 3.4. Characteristic Equations for the Complete Accelerometer with Uniform Beams

_{ACC}) can be obtained directly using Hooke’s Law. T

_{max}is given by:

#### 3.5. Characteristic Equations for Complete Accelerometer with Symmetrical Beams

_{b1}) in the accelerometer, Δ is the adjustment factor = 10, I

_{Wb1}and I

_{Wb2}are the inertial moments of the corresponding beam width and g is the gravity acceleration unit. T

_{max}and the force F of this accelerometer are calculated with Equations (2) and (18), respectively. Displacement is also obtained from Hooke’s Law.

_{Tmax}). For the complete accelerometer, the largest error is 3.81% and corresponds to T

_{max}. In Figure 4, the average percentage of errors are also shown. For recurrence in two cases, an additional adjustment in T

_{max}could be performed to decrease the error value. Differences between data from analytical and simulation are under an acceptable range. For the case of new analytical approximations, errors are obtained at larger values [22].

## 4. Harmonic Response and Explicit Dynamic Analysis of the Devices

#### 4.1. Harmonic Response Analysis

#### 4.2. About the Damping Factor

#### 4.3. Explicit Dynamic Analysis

#### 4.4. Comparison with Other Arm’s Shapes

#### 4.5. Determination of Thinner Width Segments of Symmetrical Arms to Reduce the Natural Frequencies Decrement

_{b2}, as was previously defined, equal to the uniform arm width. As can be observed, for the first two cases, the increment in the displacement of the proof mass corresponds to increments from the reference by 24.82% and 39.57%, while the decrements in natural frequency are low, corresponding to 10.45% and 15.30%. Then these proportions are recommended for frequency values near to the case of uniform arms accelerometers, but with larger displacements. The changes in force are negligible, but the stress increases considerably, but far from critical values.

_{b1}= (1/3) (W

_{b2})) are shown in Table 14. The effect of angle changes on the main parameters is negligible. This fact represents an advantage for fabrication process selection.

_{bu}= W

_{b2}/3, with angle θ = 1°. The simulation of stress is given in Figure 8 for both cases. The zoom-in allows us to observe the place of the bigger stress in each case. The stress distribution is observed on all the thin guided segments of the symmetric beam (Figure 8b), with the bigger value near to the proof mass. For the simplified case (uniform beams arrangement), the bigger stress values are located near to the proof mass (Figure 8d), and on its corner, producing a small deformation on it. In this test, the lower effect on the corner of the proof mass is given with the symmetric beam. The advantage of the symmetric beam is the stress distribution, reducing its effect on the proof mass.

#### 4.6. Nonlinearities

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Typical capacitive accelerometer with uniform flexures. (

**b**) Basic mechanical mass–spring damper model.

**Figure 4.**Simulated parameter values of the complete accelerometers with uniform and symmetrical beams, respectively, considering a sweep on applied acceleration from 1 to 50 g. (

**a**,

**b**) Displacement of guided ends. (

**c**,

**d**) Maximum stress at clamped ends of beams. (

**e**,

**f**) Force applied to the guided end.

**Figure 5.**Harmonic response of devices: (

**a**) ¼ of ACC_UNIF and ¼ of ACC_SYMM, (

**b**) ½ of ACC_UNIF and ½ of ACC_SYMM and (

**c**) Complete ACC_UNIF and Complete of ACC_SYMM.

**Figure 6.**Harmonic response of devices with damping factor (γ): (

**a**) ¼ of ACC_SYMM and ¼ of ACC_UNIF. (

**b**) ½ of ACC_SYMM and ½ of ACC_UNIF. (

**c**) Complete ACC_SYMM and Complete ACC_UNIF.

**Figure 7.**Explicit dynamic analysis. Velocity applied to (

**a**) ¼ of ACC_SYMM, 3D view. (

**b**) Complete ACC_SYMM, 3D view. Displacement of (

**c**) ¼ of ACC_SYMM and ¼ of ACC_UNIF, (

**d**) Complete ACC_SYMM and Complete ACC_UNIF. Performance with velocity load at (

**e**) 155 m/s for Complete ACC_UNIF, and (

**f**) 640 m/s for Complete ACC_SYMM. Performance of (

**g**) complete ACC_UNIF at 250 m/s and (

**h**) Complete ACC_SYMM at 1 km/s.

**Figure 8.**Simulation of stress for (

**a**) the accelerometer with symmetric beams, (

**b**) zoom in at one of the symmetric beams, (

**c**) accelerometer with simplified beams and (

**d**) zoom in at the one of the simplified beams.

Ref. | Year | Shape of Beams | Material | Larger Displacement and Conditions | Stress | Natural Freq. |
---|---|---|---|---|---|---|

Authors | Beam Size (µm × µm × µm) | |||||

[7] | 2015 | E, pi and T | Silicon/PZT-5H. | 0.6078 µm, E-shaped beam (applied force: 0.5 µN). | N/A | N/A |

P. Graak et al. | 60 × 10 × (1.5/0.5) | |||||

[8] | 2014 | Trapezoid and rectangular, double- and single-legged | Silicon | 6.93 × 10^{−4} µm, one legged-rectangular beam (constant force applied). | 20.361 MPa | 11.58 MHz |

H. F. Hawari et al. | 110 × 50 × 40 | |||||

[9] | 2017 | Basic, T and circular | Si, Ge, Ni, SiO2, PMMA, polymide | Disk-shaped cantilever of silicon (load of 1 kg/m^{2}). It is followed by T-shaped. | N/A | Max. Eigenfrequency = 0.498.94 MHz |

Siddaiah et al. | 80 × 20 | |||||

[10] | 2014 | Trapezoidal, trapezoidal with square step at fixed end, length-wise symmetry | SiO_{2} over Si | 0.231 × 10^{−9} m, Trapezoidal with square step at fixed end (pressure 19.2 Pa, equal to surface stress 0.05 N/m). | N/A | N/A |

Parsediya et al. | 50, 50 and 150, t = 50. Trapezoidal with square step at fixed end |

Ref. | Year | Shape of Beams | Material | Larger Displacement | Stress | Natural Freq. |
---|---|---|---|---|---|---|

Authors | Mass and Beam Sizes (µm × µm × µm) | |||||

Capacitive Sandwiched Accelerometers | ||||||

[11] | 2015 | Fully symmetrical double-sided H-shaped | 3 silicon wafers | N/A | N/A | 1.954 kHz |

Xiaofeng Zhou et al. | Mass: 3200 × 3200 × 560 Beam: 380 × 20 × 30 | |||||

[15] | 2016 | Symmetrical double-sided serpentine | Glass–silicon–glass | 0.574 μm on Z-axis, at 1 g | N/A | N/A |

D. B. Xiao et al. | Proof Mass: 4 × 4mm × Beam: total length 8.4 mm w of each beam: 0.14 mm, t = 25 µm | |||||

[16] | 2017 | Slanted beams | Glass–silicon–glass | 0.632 μm at 50 g | N/A | 3.9 kHz |

Wei Xu et al. | Proof mass: 2100 × 1800 × 380 Slanted beam: 1000 × 380 × 120 | |||||

Capacitive Accelerometers | ||||||

[17] | 2015 | Straight-, crab-leg, serpentine and folded | Silicon | 0.3 μm | N/A | 6.842 MHz Crab-leg flexure |

Avinash and Siddheshwar | Proof mass: 540 × 400 × 2.1 Crab-leg Beam: 300 × 150. All structure thickness: 3.5 | |||||

[18] | 2013 | L-shaped beams | Proof mass of Cu, beams of Si | In z, 50.55 nm at 10 m/s^{2} | N/A | In z, 1st eigenfreq 2254.42 Hz |

Vincas Benevicius et al. | Proof mass: 100 × 100 × 100 Beams, cross size: 5 × 8.25 Overall size 1.23 × 1.23 mm | |||||

[19] | 2006 | Spiral beams | Parylene | N/A | <5 MPa (spiral structure) | 0.5 kHz |

S. Aoyagi et al. | Proof mass r = 1000, t = 5 Beam 1800 × 100 × 5 | |||||

[13] | 2019 | Multilayer metal serpentine springs | Au proof mass, Si beams | N/A | N/A | 202 Hz at 0.5 V (DC Vias V) |

Daisuke Yamane et al. | Mass 4000 × 4000 × 20 Beam (L _{b} × L_{a} × W × t): 200 × 10 × 6 × 15 | |||||

[12] | 2020 | Folded beams | Silicon | 148 μm at 1 g, in X-axis, Beam t = 5 μm | 100 Hz | |

Kannan Solai et al. | Proof mass with parallel plates: 3000 × 5000 × 80 Beams (L _{b} × W_{b} × L_{a}): 1800 × 4 × 100 | |||||

[14] | 2018 | π-shaped springs (fully differential capacitive MEMS accelerometer) | Silicon | 29.8 nm at 1 g, 300 nm at 10 g | N/A | 2870 Hz (1st frequency mode) |

Keshavarzi and Hasani | Differential sensor (L × W) 1 × 1mm Beam (L × W × t) 160 × 2 × 10 | |||||

[20] | 2013 | Folded beams with turns (comb accel.) | PolySi | 0.5 μm at 1 g and Wb = 2 μm | N/A | N/A |

Benmessaoud M. et al. | Mass: 80 × 200 Beam: 270 × 3 Variation of thickness |

Parameters and Units | Silicon [24,25] |
---|---|

Density, ρ (kg/m^{3}) | 2329 |

Young’s modulus, E (GPa) | 130.1 |

Coefficient of thermal expansion, α ((1/°K)) | 2.568 × 10^{−6} |

Poisson ratio, ν (dimensionless) | 0.33 |

Tensile yield strength (MPa) | 250 |

ID | Description | Dimensions (µm) |
---|---|---|

L_{m} | Length of the roof mass of the ¼ accelerometer | 200 |

W_{m} | Width of the proof mass of the ¼ accelerometer | 270 |

L_{b} | Length of the uniform cantilever | 300 |

W_{b} | Width of the uniform cantilever | 2.1 |

t | Device thickness | 3.5 |

L_{m}/2 | Center of the gravity for the mass | 100 |

L_{b1} | Length of the 1st, 3rd, 4th and 6th sections of the proposed beam | L_{b}/8 = 37.5 |

L_{b2} | Length of the 2nd and 5th sections of the proposed beam | 2 (L_{b}/8) =75 |

θ | Inclination angle | 1° |

W_{b2} | Width of sections with L_{b2} | W_{b} = 2.1 |

W_{b1} | Width of sections with L_{b1} | W_{b}/3 = 0.7 |

Parameters | Analytical Value | Value ANSYS | Avg. Error% | Analytical Value | Value ANSYS | Avg. Error% |
---|---|---|---|---|---|---|

¼ of accelerometer, uniform beams (ACC_UNIF) | ¼ of accelerometer symmetrical beams (ACC_SYMM) | |||||

x(y_{τ}) = x(y_{1/4}) Deformation, (µm) | 0.1659 | 0.166 | 0.03 | 2.372 | 2.382 | 0.421 |

Tmax (stress, MPa) | 0.5036 | 0.501 | 0.47 | 4.09 | 4.058 | 0.82 |

Force (nN) | 4.32 | 4.34 | 0.58 | 4.318 | 4.359 | 0.94 |

1/2 ACC_UNIF | 1/2 ACC_SYMM | |||||

x(y_{τ}) = x(y_{1/2}) Deformation, (µm) | 0.0311 | 0.0279 | 10.04 | 0.4447 | 0.4538 | 2.04 |

Tmax (stress, MPa) | 0.1888 | 0.1664 | 11.89 | 2.4 | 2.31 | 3.41 |

Force (nN) | 8.6364 | 8.6865 | 0.58 | 8.636 | 8.6699 | 0.94 |

Complete ACC_UNIF | Complete ACC_SYMM | |||||

x(y_{complete}) Deformation, (µm) | 0.0277 | 0.0278 | 0.65 | 0.441 | 0.451 | 2.16 |

Tmax (stress, MPa) | 0.1259 | 0.1642 | 2.19 | 2.38 | 2.29 | 3.81 |

Force (nN) | 17.27 | 17.42 | 0.87 | 17.27 | 17.38 | 0.38 |

Device | Solver Target | Element Type/Mesh | Convergence | Total Mass (kg) | ||
---|---|---|---|---|---|---|

No. of Total Nodes | No. of Total Elements | Change % | ||||

¼ of accelerometer, uniform beams (ACC_UNIF) | Mechanical APDL | SOLID 187/Refinement Controlled program (Tet10) | 12,241 | 5920 | 0.20869 | 0.44532 × 10^{−9} |

¼ of accelerometer symmetrical beams (ACC_SYMM) | 11,825 | 5562 | 0.28611 | 0.4436 × 10^{−9} | ||

1/2 ACC_UNIF | 16,821 | 7978 | 0.3232 | 0.89063 × 10^{−9} | ||

1/2 ACC_SYMM | 22,807 | 11,275 | 0.20715 | 0.88721 × 10^{−9} | ||

Complete ACC_UNIF | 23,737 | 11,739 | 0.49405 | 1.7813 × 10^{−9} | ||

Complete ACC_SYMM | 46,237 | 24,129 | 0.54386 | 1.7744 × 10^{−9} |

**Table 7.**Stiffness constant of uniform and symmetrical beams and operation frequency of the ¼, ½ and complete accelerometers.

Parameters | Fraction of UNIF Beam ACC, ANSYS | Fraction of SYMM Beam ACC, ANSYS | Decrement % |
---|---|---|---|

¼ of ACC_UNIF | ¼ of ACC_SYMM | ||

Stiffness constant of the spring, N/m | 2.62 × 10^{−2} | 1.83 × 10^{−3} | 6.98 |

Natural frequency, Hz | 841.37 | 223.84 | 26.6 |

½ of ACC_UNIF | ½ of ACC_SYMM | ||

Stiffness constant of spring, N/m | 0.31043 | 0.0192 | 6.18 |

Natural frequency, Hz | 2982.2 | 740.44 | 24.8 |

Complete ACC_UNIF | Complete ACC_SYMM | ||

Stiffness constant of spring, N/m | 0.62474 | 0.0192 | 3.07 |

Natural frequency, Hz | 2990.5 | 742.3 | 24.8 |

Device | Displacement (x), (m) | Displacement (y), (m) | Displacement (z), (m) | Cross Axis Sensitivity, X-axis, % | Cross Axis Sensitivity, Z-axis, % |
---|---|---|---|---|---|

ACC_SYMM | 4.6598 × 10^{−9} | 4.5702 × 10^{−7} | 1.4079 × 10^{−11} | 1.0196 | 0.0030 |

ACC_UNIF | 1.4739 × 10^{−10} | 2.8053 × 10^{−8} | 1.8296 × 10^{−12} | 0.5253 | 0.0065 |

Modal Form | Frequency (kHz) | |||||
---|---|---|---|---|---|---|

¼ of ACC_UNIF | ¼ of ACC_SYMM | ½ of ACC_UNIF | ½ of ACC_SYMM | Complete of ACC_UNIF | Complete of ACC_SYMM | |

1 | 0.8414 | 0.2238 | 1.598 | 0.7404 | 2.991 | 0.7423 |

2 | 1.2050 | 0.4843 | 2.982 | 1.1230 | 4.774 | 3.2941 |

3 | 4.1642 | 1.3795 | 8.310 | 5.6787 | 8.397 | 5.7063 |

4 | 5.5462 | 2.300 | 22.025 | 15.339 | 14.831 | 10.264 |

5 | 23.335 | 16.246 | 92.581 | 39.987 | 78.889 | 40.027 |

6 | 178.720 | 45.948 | 149.99 | 44.729 | 92.200 | 43.652 |

7 | 270.030 | 197.680 | 178.48 | 92.484 | 174.68 | 77.858 |

8 | 325.670 | 226.170 | 178.69 | 149.24 | 179.17 | 92.184 |

9 | 368.980 | 311.970 | 255.21 | 197.64 | 179.18 | 173.73 |

10 | 491.740 | 368.690 | 273.84 | 197.76 | 179.23 | 177.97 |

Parameters | ¼ of ACC_UNIF | ¼ of ACC_SYMM | ½ of ACC_UNIF | ½ of ACC_SYMM | Complete ACC_UNIF | Complete ACC_SYMM |
---|---|---|---|---|---|---|

Frequency (Hz) | 840 | 223 | 2980 | 740 | 2995 | 741 |

γ = 0 | ||||||

Equivalent von Mises stress (MPa) | 194.59 | 771.34 | 180 | 1897.2 | 86.57 | 654.7 |

γ = 0.05 | ||||||

Equivalent von Mises stress (MPa) | 0.887 | 16.82 | 0.1614 | 1.13 | 0.309 | 3.19 |

γ = 0.1 | ||||||

Equivalent von Mises stress (MPa) | 0.268 | 4.61 | 0.0406 | 0.283 | 0.077 | 0.802 |

γ = 0.5 | ||||||

Equivalent von Mises stress (MPa) | 0.0623 | 0.589 | 0.00186 | 0.0124 | 0.00305 | 0.0326 |

**Table 11.**Technical details about the FEA simulations for frequencies of modal and harmonic response.

Device | Solver Target | Element Type/Mesh | Convergence | |||
---|---|---|---|---|---|---|

No. of Total Nodes | No. of Total Elements | No. of Total Nodes | No. of Total Elements | |||

Modal | Harmonic Response | |||||

¼ of (ACC_UNIF) | Mechanical APDL | SOLID 187/Refinement Controlled program (Tet10) | 47,128 | 27,303 | 10,373 | 4796 |

¼ of (ACC_SYMM) | 51,295 | 29,656 | 11,825 | 5562 | ||

1/2 ACC_UNIF | 56,433 | 31,992 | 13,617 | 6107 | ||

1/2 ACC_SYMM | 65,074 | 36,899 | 17,856 | 8286 | ||

Complete ACC_UNIF | 52,074 | 28,840 | 16,471 | 7455 | ||

Complete ACC_SYMM | 63,359 | 34,551 | 23,583 | 10,678 |

Device | Displacement (nm) | Force (µN) | Stress von Misses (kPa) | Natural Frequency (kHz) | Sensitivity $\left|\mathbf{x}\left(\mathbf{y}\right)\right|/\left|\mathbf{g}\right|$$\mathbf{or}(\mathbf{m}/\mathbf{k})$ | Images of Devices |
---|---|---|---|---|---|---|

Accelerometer 1 UNIF [31] | 2.24 | 3.88 | 116.07 | 18.376 | 2.28 × 10^{−10} | |

Accelerometer 1 SYMM without angles | 13.49 | 3.87 | 751.2 | 4.144 | 1 × 10^{−9} | |

Accelerometer 1 SYMM with angles | 15.67 | 3.87 | 767.73 | 2.835 | 2 × 10^{−9} | |

Accelerometer 2 UNIF [17] | 27.8 | 1.74 × 10^{−2} | 259.4 | 2.995 | 3 × 10^{−9} | |

Accelerometer 2 SYMM without angles | 451.89 | 1.734 × 10^{−2} | 2.281 × 10^{3} | 0.741 | 4.6 × 10^{−8} | |

Accelerometer 2 SYMM with angles | 451.51 | 1.734 × 10^{−2} | 2.294 × 10^{3} | 0.741 | 4.6 × 10^{−8} | |

Accelerometer 3 UNIF [32] | 0.146 | 1.78 × 10^{−3} | 6.24 | 41.5 | 1.48 × 10^{−}^{11} | |

Accelerometer 3 SYMM without angles | 4.9 | 1.73 × 10^{−3} | 108.57 | 7.33 | 4.99 × 10^{−10} | |

Accelerometer 3 SYMM with angles | 4.91 | 1.73 × 10^{−3} | 106.45 | 7.33 | 4.99 × 10^{−10} |

Device | Displacement (µm) | Increment (%) | Force (nN) | Increment (%) | Stress (MPa) | Increment (%) | Natural Frequency (Hz) | Increment (%) | |
---|---|---|---|---|---|---|---|---|---|

ACC_UNIF | 0.0278 | Reference | 17.42 | Reference | 0.1642 | Reference | 2990.5 | Reference | |

ACC_SYMM | Wb_{1} = (8/10) (Wb_{2}) | 0.0347 | 24.82 | 17.36 | −0.34 | 0.328 | 99.76 | 2678 | −10.45 |

Wb_{1} = (5/7) (Wb_{2}) | 0.0388 | 39.57 | 17.35 | −0.40 | 0.421 | 156.40 | 2532.9 | −15.30 | |

Wb_{1} = (4/6) (Wb_{2}) | 0.0487 | 75.18 | 17.35 | −0.40 | 0.538 | 227.645 | 2260.5 | −24,41 | |

Wb_{1} = (2/4) (Wb_{2}) | 0.082 | 194.97 | 17.34 | −0.46 | 0.863 | 425.58 | 1737.1 | −41.91 | |

Wb_{1} = (1/3) (Wb_{2}) | 0.452 | 1525.90 | 17.34 | −0.46 | 2.29 | 1294.64 | 742.3 | −75.18 |

**Table 14.**Parameters of symmetric beam accelerometer (W

_{b1}= W

_{b2}/3), at different angle values.

ACCEL SYMM Inclination Angle θ | x(y) Displacement (µm) | Stress (MPa) | Force (nN) | Natural Frequency (Hz) | Sensitivity $\left|\mathbf{x}(\mathbf{y})\right|/\left|\mathbf{g}\right|$$\mathbf{or}(\mathbf{m}/\mathbf{k})$ 1/s ^{2} |
---|---|---|---|---|---|

0.5° | 0.446 | 2.34 | 17.3 | 746.56 | 4.5 × 10^{−10} |

1° | 0.452 | 2.29 | 17.3 | 745.3 | 4.6 × 10^{−10} |

1.5° | 0.449 | 2.16 | 17.3 | 744.16 | 4.6 × 10^{−10} |

2° | 0.449 | 2.19 | 17.3 | 743.7 | 4.6 × 10^{−10} |

2.5° | 0.451 | 2.27 | 17.3 | 742.62 | 4.6 × 10^{−10} |

3° | 0.450 | 2.27 | 17.3 | 743.16 | 4.6 × 10^{−10} |

3.5° | 0.451 | 2.28 | 17.3 | 742.94 | 4.6 × 10^{−10} |

4° | 0.451 | 2.3 | 17.3 | 742.57 | 4.6 × 10^{−10} |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tecpoyotl-Torres, M.; Vargas-Chable, P.; Sandoval-Reyes, J.O.; Rodriguez-Fuentes, S.F.; Cabello-Ruiz, R. Capacitive Accelerometers with Beams Based on Alternated Segments of Different Widths. *Actuators* **2020**, *9*, 97.
https://doi.org/10.3390/act9040097

**AMA Style**

Tecpoyotl-Torres M, Vargas-Chable P, Sandoval-Reyes JO, Rodriguez-Fuentes SF, Cabello-Ruiz R. Capacitive Accelerometers with Beams Based on Alternated Segments of Different Widths. *Actuators*. 2020; 9(4):97.
https://doi.org/10.3390/act9040097

**Chicago/Turabian Style**

Tecpoyotl-Torres, Margarita, Pedro Vargas-Chable, Josue Osvaldo Sandoval-Reyes, Sahiril Fernanda Rodriguez-Fuentes, and Ramon Cabello-Ruiz. 2020. "Capacitive Accelerometers with Beams Based on Alternated Segments of Different Widths" *Actuators* 9, no. 4: 97.
https://doi.org/10.3390/act9040097