EE3901/EE5901 Sensor Technologies
Week 8 Tutorial

College of Science and Engineering, James Cook University

Last updated 21 February 2022

Question 1

Download this STL file, which is a classic parallel plate capacitor. When setting up a numerical method, it is essential to benchmark its performance on a problem for which you already know the answer. The geometry is a 2D slice through the plates. The plates are 20mm high and have 0.01mm separation.

Load the geometry into Matlab and examine its structure.

(a) Predict the capacitance using the equation for plane parallel capacitors. Note that you do not know the surface area (because the 2D model is only a slice through the real geometry). However, you can write the surface area as a height times an unknown width, and then divide by the width to get the capacitance in F/m. The meaning of this unit is the capacitance per metre of extrusion of this geometry.

(b) Numerically calculate the capacitance using the methods discussed in this week’s notes. Compare your answer to that in part (a).

Answer

(a) 17.71 nF/m

(b) You should obtain a value close to that in part (a), depending upon the size of your finite element mesh. Your relative error should be less than 0.5%. A more precise answer is obtained with a finer mesh.

Note that the answer from part (a) is an approximation that neglects edge effects, and therefore is subject to some uncertainty in its own right.

Question 2

Using the coplanar geometry considered in lectures, analyse the impact of the high permittivity region. Calculate the capacitance when the relative permittivity of this region is varied from 1 to 30. Produce a plot of this capacitance.

Answer

Figure A2:
The impact of the permittivity of the sensing region for the geometry used in lectures.
Zoom:

Next steps

You are now ready to begin work on Assignment 2.