EE3901/EE5901 Sensor Technologies

Week 8 Tutorial

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).

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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.

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