MEMS

ECE 5134

Summer 2019

Homework 1

Due July 10, Wednesday

1. (20) Literature survey.

Write a mini report introducing a MEMS device and its typical applications.

2. (25) In calibration of the static response of an accelerometer, the device was mounted on a rotary table that has a resolution of 0.002º. It was mounted in such a way that at -90º, the device was

subjected to a -1.0 g gravitational acceleration; and at +90º, a +1.0 g. The recorded data from the

characterization tests are shown in the following table.

1) In the same coordinate, plot the results showing going up and coming down measurements, with acceleration (in g) as x-axis.

2) Find the measurement range, full scale output, output offset in the tests.

3) Use the least square regression method, estimate the linearity of the response.

4) Find hysteresis and accuracy of the device based on the results in the above step(s).

5) What’s the sensitivity of the accelerometer?

Measured output voltage (V)

Device position on the

rotary table (Angle relative

to the horizon, θ)

Going Coming

-90 0.8271 0.8283

-85 0.8362 0.8386

-80 0.844 0.8467

-75 0.8646 0.8657

-70 0.8891 0.8875

-65 0.9136 0.917

-60 0.9437 0.9472

-55 0.9812 0.9791

-50 1.0224 1.0188

-45 1.0671 1.0667

-40 1.1186 1.1141

-35 1.1687 1.172

-30 1.2314 1.2267

-25 1.2923 1.2871

-20 1.3541 1.3514

-15 1.4208 1.4174

-10 1.4852 1.4832

-5 1.5523 1.5507

0 1.6184 1.6168

5 1.6878 1.6844

10 1.7562 1.7524

15 1.8246 1.8203

20 1.8906 1.8866

25 1.955 1.9511

30 2.0174 2.0126

35 2.075 2.0708

40 2.1273 2.1124

45 2.1774 2.1732

50 2.2204 2.2162

55 2.2587 2.2536

60 2.2951 2.2893

65 2.3225 2.3148

70 2.3425 2.3394

75 2.3608 2.3559

80 2.3712 2.3674

85 2.3771 2.3746

90 2.3792 2.3752

Hint: In the device mounting given in the table, -90° corresponds -1.0 g; +90° corresponds +1.0 g.

In between, acceleration a is given by 1.0 sin( )a   . In Matlab, radian is the default unit for

angles. So,  = d/180· in calculations

3. (10) A set of measurement data follows the Normal distribution. Step by step, estimate the possibility

of finding a data point falling in the range of 2.5 (: standard deviation) around the mean value µ of

the data set. You may use the Error function table given in the lecture note.

4. (15) The following figure shows noise spectrum of a MEMS accelerometer over a bandwidth of 400 Hz. In static characterization tests, the sensor exhibits a sensitivity of 0.24 V/g. In dynamic tests, the

device responds up to 5 g of acceleration with satisfied error specifications.

1) Estimate the peak-peak noise floor from the spectrum;

2) What is the input-referred noise floor in g/√Hz?

3) Calculate the resolution and dynamic range of the device if used in the given bandwidth.