EERI 313-PRACTICAL 1
JP BURGER 37309056
Kobus Burger
Contents
Introduction: .......................................................................................................................... 2
FDM: ..................................................................................................................................... 2
Analytical calculations: .......................................................................................................... 3
FEMM Simulation: .................................................................................................................. 4
Comparison and conclusion: ................................................................................................. 4
References: ........................................................................................................................... 5
Figure 1: FDM from excel ........................................................................................................ 2
Figure 2: Analytical calculations ............................................................................................. 3
Figure 3: Shape of the capacitor.............................................................................................. 4
Figure 4: The results from FEMM ............................................................................................. 4
1
Introduction:
In this practical we will analyze and design a capacitor with a square inside of a triangle. This
practical is to compare different methods and see their similarities. We will be using analytical
calculations, FDM (Finite difference method) and computer simulations in FEMM. The use of
supercapacitors is very common in large electric structures such as electric cars.
Supercapacitors are very similar to normal capacitors, but they can store much larger amounts
of electrical charge than any other capacitor. A supercapacitor is in some uses a substitute for a
battery. The supercapacitor uses the same dielectric as any capacitor, but it is a combination of
the working of a capacitor and a battery.
The shape of the capacitor in this practical is a small square inside of a big triangle. The square
has the positive load, ad the triangle the negative. The squares sides has lengths of 1.44 , 1.42 ,
1.43 and 1.42 respectively. The triangles sides has lengths of 10 , 11.74 and 9.57 respectively.
FDM:
Figure 1: FDM from excel
The finite difference method was used to calculate the differences between the nodes. This was
manually done in excel and the results are shown in Figure 1 above. The first column shows the
first iteration of the FDM that I moved from the FEMM diagram to excel. From the second column
the iterations were calculated in excel until the 23rd iteration.
2
Analytical calculations:
Figure 2: Analytical calculations
3
FEMM Simulation:
Figure 3: Shape of the capacitor
Figure 4: The results from FEMM
Comparison and conclusion:
From the analytical calculations and the FEMM simulation we have some similarities. In the
analytical calculations we have that the potential difference at a specific point is equal to the
4
potential difference given by the graph in the FEMM simulation at that point. The FEMM
simulation and the FDM in excel is very similar with little to none differences in values. The excel
sheet does not show the shape of the figure as in FEMM, but knowing that we can easily
compare the two sketches. Therefore the FDM, FEMM and analytical calculations are so similar
that either of the three methods can be used to simulate a capacitor. The values of all three
methods are therefore applicable for practical use.
From this practical we learned a lot about capacitors and how they work. We also worked with
the FEMM software and we now know exactly how it works. The FDM in excel was a challenge at
first, but the more we worked with it the easier it got to do the calculations. Another challenge
was the analytical calculations, because of the odd shapes the formulas had to be changed in
order to find the correct values.
References:
https://www.researchgate.net/publication/317951391_High_Dielectric_Materials_for_Superca
pacitor
https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Boo
k%3A_University_Physics_II_-
_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/08%3A_Capacitance/8.02%3A_Ca
pacitors_and_Capacitance
https://eepower.com/capacitor-guide/types/supercapacitor/#
