BE. Electronic and Computer Engineering Final Year Project Report

BE. Electronic and Computer Engineering Final Year Project Report Title: Development of electrical models for inductive coils used in wireless power systems Paul Burke 09453806 3 rd April 2013 Supervisor: Dr. Maeve Duffy Co-Supervisor: Dr Edward Jones

Abstract This main aim of the project was to develop Matlab programs to do calculations for inductive coils used in wireless power transfer and compare results with those obtained using FEA software. AS FEA software is very expensive and impractical; the Matlab programs development would be a cost effective and efficient alternative. The programs could also be used instead of testing the coils in the lab as this is very time-consuming. i P a g e

Acknowledgements I would like to thank my supervisor Dr Maeve Duffy for her continued support and advice through-out the project. I would also like to thank my co-supervisor Dr Eddie Jones for the advice and guidance given in relation to the project during the year. ii P a g e

Table of Contents Abstract... i Acknowledgements... ii Glossary... v List of Figures... vi Nomenclature... viii Chapter 1-Introduction... 1 1.1 Project Overview... 2 1.2 Wireless power transfer... 3 1.3 Applications of Wireless power transfer... 3 1.4 Electromagnetic Shielding... 4 1.5 Ansys Maxwell... 4 1.5.1 Procedure to setting up model... 5 Chapter 2 Calculation and Measurements... 7 2.1 Inductance of a single plane coil (air core)... 7 2.1.1 Calculation of inductance of prototype (Figure 6)... 7 2.1.2 Simulation of prototype (Figure 6) using Ansys Maxwell... 10 2.2 Electromagnetic shielding... 12 2.2.1 Calculation of Inductance with a Shielding Layer (Figure 13)... 13 2.2.2 Simulation of prototype (Figure 13) using Ansys Maxwell... 16 2.3 AC resistance calculation due to eddy current effect... 20 2.3.1 Calculation of Impedance using Matlab... 20 2.3.2 Simulation of single turn coil (Figure 20) using Ansys Maxwell... 24 Chapter 3 - Conclusion... 28 3.1 Discussion... 28 iii P a g e

Bibliography... 30 Appendices... 31 iv P a g e

Glossary FEA Finite Element Analysis SE Shielding Effectiveness AC Alternating Current DC Direct Current v P a g e

List of Figures Figure 1 Wireless Power Transmission... 3 Figure 2 Nokia Lumia phone with wireless charging plate... 3 Figure 3 Typical power transfer system... 4 Figure 4 Flowchart for setup of Ansys model... 5 Figure 5 Solution Setup for Ansys... 6 Figure 6 Cross sectional view of 3 turn coil being used in testing (IEEE)... 7 Figure 7 Flowchart of Matlab code... 8 Figure 8 While loop representing integrating to infinity... 9 Figure 9 Algorithm to calculate radii... 9 Figure 10 Final Step in calculating Inductance... 9 Figure 11 Table of results for Ansys simulation... 10 Figure 12 Zoomed in version of Figure 12... 11 Figure 13 Prototype built and magnetic field applied... 11 Figure 14 Cross section of coil with shielding layer (IEEE)... 12 Figure 15 Flowchart for Matlab program to calculate Inductance of coil with shielding layer... 14 Figure 17 Table of Results for Matlab code... 15 Figure 16 Users inputs prototype specification into Matlab... 15 Figure 18 Graph of results for Matlab code... 16 Figure 19 Magnetic field layer applied to prototype without shielding layer... 17 Figure 20 Magnetic field layer applied to prototype without shielding layer... 17 Figure 21 Table of results from Ansys simulation... 18 Figure 22 Graph of results for Ansys simulation... 18 Figure 23 Comparison of results for Matlab and Ansys... 19 Figure 24 Cross section of single turn coil... 20 Figure 25 Cross section of coil split into 10 sections... 20 Figure 26 Flowchart for Matlab program to calculate Impedance for prototype... 22 Figure 27 User input to program... 22 Figure 28 Table of results from Matlab... 23 vi P a g e

Figure 29 Graph of inductance results for Matlab... 23 Figure 30 Table of results for Resistance calculation... 23 Figure 31 Graph of resistance results for Matlab... 24 Figure 32 Table of results for Ansys simulation (Inductance)... 24 Figure 33 Graph of results (Inductance)... 25 Figure 34 Table of Results for Ansys Simulation (Resistance... 25 Figure 35 Graph of Results (Resistance)... 26 Figure 36 Graph of comparison of results (Inductance)... 26 Figure 37 Graph of comparison of results (Resistance)... 27 vii P a g e

Nomenclature Internal radii of each turn in coil External radii of each turn in coil Height of each winding Thickness of track ( ) ( ) Bessel function of first kind M Mutual inductance between two turns in coil in air Q, S Defined in (5) and (6) Thickness of substrate Inductance Z Mutual impedance between two turns in coil Additional mutual impedance due to the substrates added to the system Angular frequency (rad/s) Conductivity of substrate Relative permeability of substrate Permeability of free space(4 * 10-7 H/m) ( ) Defined in (7) ( ) ( ) Defined in (8) and (9), ( ) Defined in (10) and (11) Defined in (12) and (13) viii P a g e

Chapter 1-Introduction Wireless power transfer is being investigated further by companies. For the smaller companies, it is not feasible to purchase FEA software (Ansys Maxwell) used to simulate the magnetic fields produced by the inductive coils used in wireless power transfer. The Matlab programs developed in the project have produced an alternative way of providing accurate calculations for inductance and resistance of the inductive coil. The inductive coils used for wireless power transfer can also be expensive, so before purchasing a coil, testing could be carried out using the Matlab programs to check the coil in question is sufficient for the project. 1 P a g e

1.1 Project Overview The first part of the project was to develop a Matlab program to calculate the inductance of a single plane coil. These results are given in a matrix format showing self and mutual inductances. The next stage of the project is to add in a magnetic and copper shielding layer. The shielding layer is added to prevent the magnetic field inducing a voltage to objects (Inductors) which are close by but have nothing to do with the system. The final stage of the project is to develop a program to allow for eddy current effects caused in the coil. The program divides the coil into a number of smaller sections and calculates the inductance and resistance which provides a more accurate result. For each stage in the project, the user enters the specification of the coil and the calculations are carried out using the algorithms implemented in the code. 2 P a g e

1.2 Wireless power transfer Wireless power transfer works by induction. An electrical current flowing through a primary coil creates a magnetic field. This magnetic field interacts with a secondary coil which in turn induces a voltage across the coil (Figure 1). One of the most important aspects of wireless power transfer is the efficiency. The closer the coils are together the more efficient the transmission is and the less energy used. Wireless power transfer is very convenient in situations where wiring is unpractical, hazardous or impossible. Figure 1 Wireless Power Transmission 1.3 Applications of Wireless power transfer One of the latest developments in wireless power transfer consumer products is in the new range of nokia lumia mobile phones that allow wireless charging. The phone can be placed on a charging plate designed by nokia for their range of phones (Figure 2). Figure 2 Nokia Lumia phone with wireless charging plate [1] 3 P a g e

A transmitter coil is positioned at the bottom (L1) and the receiver coil (L2) is situated at the top and these coils are embedded into different electrical devices. L1 would be the Nokia Wireless Charging Plate and L2 would be the Nokia Lumia 920 (Figure 3). [1] Figure 3 Typical power transfer system As these coils have to fit in the modern day Smartphone, the coils are very small which mean the transmitter and receiver coil have to be very close together for it to work. 1.4 Electromagnetic Shielding Electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. It has been shown that a double-layer shielding comprising of a magnetic material and a conductive material provides a much higher shielding effectiveness than a single layer substrate of finite thickness, where SE is defined as the ratio between the field strength at a given distance from the source without the shield in the prototype and the field strength with the shield introduced into the prototype [2]. The shielding layers added under the primary coil and above the secondary coil are important for the safe operation of wireless power transfer. The absence of shielding layers, could lead to the following problems: the magnetic field may interfere with the device or other objects the battery could overheat current might circulate in metallic objects within the magnetic field [3] 1.5 Ansys Maxwell 4 P a g e

Ansys Maxwell is FEA software used by engineers when designing and analyzing 3-D and 2-D electromagnetic and electromechanical devices, including motors, transformers and coils [4]. Ansys is a key component of the project as it is used to verify all results obtained by the code developed in Matlab. There are a number of steps involved in stepping up a model in Ansys. Figure 4 Flowchart for setup of Ansys model 1.5.1 Procedure to setting up model 5 P a g e

After selecting the 2-D design model, a solution type is chosen. Throughout the project the same setup is used. The geometry is set as Cylindrical about Z and the specific area is the magnetic fields (Eddy Currents), (Figure 5). Figure 5 Solution Setup for Ansys The next step is to draw the prototype in question. After the prototype is drawn the workspace/region also needs to be drawn. The height of the workspace is typically 70% of the outer radius of the prototype and the width is ideally twice the outer radius. The boundaries are then applied to this workspace. A balloon boundary is used through-out the project. Current needs to be applied to the coil. This is done by adding an excitation to the coil. The next step is to define the analysis setup specifications (e.g. frequency). The model is ready to be solved. Additional fields can be added before solving. The magnetic field is of the most interest, it is added before generating the solution. Once the solution has been generated, the results can be viewed and analysed in the solution data. 6 P a g e

Chapter 2 Calculation and Measurements 2.1 Inductance of a single plane coil (air core) The air-cored inductor is the simplest design for a planar magnetic component. This is the basis for more advanced structures using magnetic substrates. Figure 6 Cross sectional view of 3 turn coil being used in testing [5] The prototype being used is a single plane air-cored inductor which consists of 3 turns. This was chosen as the starting point as it is a very basic design and fairly straight forward for modelling in both Matlab and Ansys Maxwell. 2.1.1 Calculation of inductance of prototype (Figure 6) The calculation of inductance for the prototype in Figure 6 was completed using Matlab and the results were compared to the results given in [5]. The prototype was also modelled in Ansys Maxwell and the results were compared to those obtained from the Matlab program developed. Matlab was chosen as the desired software because the equation (1) needed to calculate the mutual inductance is very complex and would not be practical to compute by hand. ( ) ( ) ( ) z = 0; (1) 7 P a g e

The program layout is as follows: Figure 7 Flowchart of Matlab code The user enters the coil specifications: Number of turns Inner radius of first turn in coil Outer radius of first turn in coil Distance between each turn in coil 8 P a g e

To calculate the rest of the radii of each turn, an algorithm was developed (Figure 8). Figure 8 Algorithm to calculate radii Depending on the number of turns in the coil, it will calculate the inner and outer radii for each turn based on the specifications entered by the user at the start. This data then is inputted into (1). Since integrating to infinity is impossible, a while loop (Figure 9) is used to keep integrating and comparing answers until the results is accurate up until 12 decimal places. Figure 9 While loop representing integrating to infinity The final part then is to the integral part by the rest of M (Figure 10). Figure 10 Final Step in calculating Inductance Since the prototype has 3 turns, a total of 9 inductance values are expected and an overall total inductance for the system. The results are shown in a matrix: ( ) Where L 11 is the self inductance of the first turn in the coil, L 12 is the mutual inductance between the first turn and the second turn in the coil and so on. ( ) 9 P a g e

Total Inductance (L) is equal to the sum of the matrix L = 4.597e-8 Henries 2.1.2 Simulation of prototype (Figure 6) using Ansys Maxwell To verify the result given from the developed Matlab code, Ansys Maxwell was used to simulate the results. Following the steps given in section 1.5, the model was drawn in Ansys. The solution setup was the same throughout the project; select magnetic eddy currents and the geometry were to be Cylindrical around the Z axis (as shown above). Once this was done, a model of the prototype in Figure 6 was built. The next step is to draw to workspace/region. The size of the workspace depended on the size of the prototype. The height of the workspace was typically 70% the radius and the width would ideally be about twice the radius of the prototype. The next step was to apply the boundary to the workspace and the excitation to the coil itself. The boundary used was the balloon boundary and was applied to each edge of the workspace. Apply an excitation to each turn of the coil (A current of 1 Amp). The final step to setting up the model was to select a frequency or a range of frequencies in which to run the model. To coincide with the [5] a frequency of 10 khz was selected. The final design is shown in Figure 11 below. A magnetic field layer has also been applied to show the magnetic fields created when current is flowing through the coil. Ansys does not directly output a result for inductance. The following are the results from simulating the prototype in Ansys. Total Energy(J) Frequency(Hz) Inductance(H) 1.079e-9 10000 4.316e-8 Figure 11 Table of results for Ansys simulation 10 P a g e

Figure 12, shows a closer image of the coil. The magnetic activity of the coil itself can be seen clearly. Figure 13 Prototype built and magnetic field applied Figure 12 Zoomed in version of Figure 12 11 P a g e

2.2 Electromagnetic shielding For this example, an electromagnetic shield is only applied under the primary coil. This is typical for a charging platform as shown in Chapter 1. The secondary coil for this system would be placed in the phone. The shield used here consists of 2 layers. The first-layer is a magnetic material (ferrite) and the second-layer is a layer of conductive material (Copper). Figure 14 Cross section of coil with shielding layer [2] To calculate the inductance of the new prototype a new equation will have to be used to factor in the double layer substrate used for shielding. By calculating the impedance (Z) of the system we are able to obtain the inductance. The inductance is equal to imaginary part of Z. (2) where M is the mutual inductance of the coil when the substrate is absent(3); is the impedance of the coil taking into account the shielding layer which can be calculated using (4) ( ) ( ) ( ) (3) ( ) ( ) ( ) ( ) (4) 12 P a g e

( ) { ( ) [ ] (5) ( ) ( ) ( ) ( ) (6) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (7) ( ) (8) ( ) (9) (10) ( ) ( ) ( ) (11) (12) (13) 2.2.1 Calculation of Inductance with a Shielding Layer (Figure 13) The calculation of Inductance for the prototype in Figure 13 was once again developed using Matlab. The prototype was also modelled in Ansys Maxwell and the results were compared to those given from the Matlab program developed. The equations ((3) and (4)) that were used in this section are variations of the equation (1) used in Section 2.1. The code developed in Section 2.1 was modified to allow for a shielding layer. Matlab was chosen to do the calculations as the foundation for the program has already been developed in Section in 2.1. 13 P a g e

The program layout was as follows: Figure 15 Flowchart for Matlab program to calculate Inductance of coil with shielding layer 14 P a g e

The user enters the coil specification as above in section 2.1.1, but in addition to these specifications the user will also need to enter the range of frequencies in which to run the program through and also the conductivity value, permeability value and thickness of both substrate layers (Figure 15). Figure 16 Users inputs prototype specification into Matlab Once the User entered the data above, the program calculates M (3) and (4). This was the same process used in section 2.1 to calculate inductance. With M and calculated, they were entered into (2). This then produces Impedance (Z) of the prototype where (14) The following table shows the results from the program running over a wide range of frequencies (10kHz to 10MHz). To allow comparison with the paper [2], the inductance L is divided by Lo, where Lo =1.312µH. Inductance(H) Frequency(Hz) L/Lo 0.00000229914692 10000 1.752398565 0.00000229906062 20000 1.752332792 0.00000229901407 40000 1.752297308 0.00000229899910 70000 1.7522859 0.00000229899495 100000 1.752282737 0.00000229899182 200000 1.752280351 0.00000229899102 400000 1.752279739 0.00000229899084 700000 1.752279601 0.00000229899079 1000000 1.752279566 0.00000229899076 2000000 1.75227954 0.00000229899074 4000000 1.752279529 0.00000229899073 7000000 1.752279516 0.00000229899070 10000000 1.7522795 Figure 17 Table of Results for Matlab code 15 P a g e

L/Lo DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING Inductance with Shielding 2 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1 10000 100000 1000000 10000000 Frequency(Hz) Inductance Figure 18 Graph of results for Matlab code The graph (Figure 17) shows the inductance of the prototype over a range of frequencies. As the frequency increases there is a slight decrease in inductance value (As expected). 2.2.2 Simulation of prototype (Figure 13) using Ansys Maxwell To verify the results given by the Matlab code, the prototype was built and simulated for the same range of frequencies used in the Matlab program. To set up the prototype in Figure 13 in Ansys, the same process was followed as in section 2.1.2. Once the prototype was built, the results were taken and compared to the results above (Figure 17). The prototype without the substrate is shown below in Figure 18 and with the substrate in Figure 19. A magnetic field layer was also applied to show the effects the double layer substrate has on the magnetic fields created by the copper coil. The results from Figure 18 and Figure 19 show when a double layer substrate of ferrite and copper is added to the system it reflects the magnetic field back up, which increases the magnetic field strength and prevents the magnetic field from going below the substrate. 16 P a g e

Figure 20 Magnetic field layer applied to prototype without shielding layer Figure 19 Magnetic field layer applied to prototype without shielding layer 17 P a g e

L/Lo DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING The following table shows the results from Ansys for the same range of frequencies as above. Total Energy(J) Frequency(Hz) Inductance(H) L/Lo 5.77E-07 10000 0.00000230608 1.75768292682927 5.75E-07 20000 0.00000230148 1.75417682926829 5.74E-07 40000 0.00000229752 1.75115853658537 5.74E-07 70000 0.00000229496 1.74920731707317 5.73E-07 100000 0.00000229352 1.74810975609756 5.73E-07 200000 0.00000229084 1.74606707317073 5.72E-07 400000 0.00000228728 1.74335365853659 5.70E-07 700000 0.00000228196 1.73929878048780 5.69E-07 1000000 0.00000227616 1.73487804878049 5.66E-07 2000000 0.00000226204 1.72411585365854 5.62E-07 4000000 0.00000224956 1.71460365853659 5.61E-07 7000000 0.00000224272 1.70939024390244 5.60E-07 10000000 0.00000223952 1.70695121951219 Figure 21 Table of results from Ansys simulation Inductance is calculated by multiplying the Total Energy by 4. To allow comparison with the paper [2], the inductance L is divided by Lo, where Lo =1.312µH Inductance with Shielding 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 10000 100000 1000000 10000000 Frequency(Hz) Inductance Figure 22 Graph of results for Ansys simulation The graph (Figure 21) above again shows the inductance over a range of frequencies. This also shows a slight decrease in inductance as the frequency increases. 18 P a g e

L/Lo DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING 2.0 Inductance with sheilding 1.9 1.8 1.7 1.6 1.5 1.4 1.3 Ansys Matlab 1.2 1.1 1.0 10000 100000 1000000 10000000 Frequency(Hz) Figure 23 Comparison of results for Matlab and Ansys The graph above shows Matlab results with the results taken from Ansys superimposed on each other. The results are quite accurate up to 1MHz. 19 P a g e

2.3 AC resistance calculation due to eddy current effect Eddy currents are currents induced in conductive materials cause by changing magnetic fields. When current flows in a coil it flows in a cylindrical fashion due to these effects (Figure 23). This causes a higher intensity magnetic field around the edges of the coil. Figure 24 Cross section of single turn coil To allow for these effects and to get a more accurate result when calculating the resistance, the coil was split up into a number of sections (Figure 24). This allows us to calculate the resistance and inductance for a number of smaller sections which in turn gives a more accurate result. Figure 25 Cross section of coil split into 10 sections 2.3.1 Calculation of Impedance using Matlab To calculate the impedance for each section of the single turn coil in Figure 21, a new formula is needed. ( ) (15), (16) where δ = 1/conductivity of coil r o = outer radius of section r i = inner radius of section 20 P a g e

Impedance is equal to, therefore using the equation (15), the current was calculated when = 1 Volt, The program layout was as follows: 21 P a g e

Figure 26 Flowchart for Matlab program to calculate Impedance for prototype The user enters the coil specification as above in section 2.1.1, but in addition the user entered the number of sections to split the coil up into for both the x-axis and y-axis. The user also enters the range of frequencies in which to run the program. Figure 27 User input to program Once the user enters the data above, the program first of all calculates resistance for each section. For this example, there were 10 sections which resulted in 10 resistances stored on the diagonal of a 10*10 matrix. The next step was calculating the self and mutual inductance for each section in the coil using (2). The results were stored in a 10*10 matrix. Using these results, the impedance (Z) of each section of the coil was calculated for the range of frequencies entered by the user at the start. With Z calculated, the current can be calculated by using the formula when is equal to 1 volt. The result is in a complex number format where the real part is the AC resistance of the coil and the imaginary part is equal to ωl. The following tables show the results for both results and the inductance for the single turn coil prototype. 22 P a g e

Inductance(H) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING ωl Frequency(Hz) Inductance(H) 0.00274307 100000 4.36398E-09 0.005485291 200000 4.3633E-09 0.010963954 400000 4.36066E-09 0.019157222 700000 4.35391E-09 0.027309495 1000000 4.34469E-09 0.054154985 2000000 4.30778E-09 0.106824815 4000000 4.24871E-09 0.185014663 7000000 4.20488E-09 0.263101931 10000000 4.18571E-09 Figure 28 Table of results from Matlab Inductance is given by dividing ωl by 2*π*frequency (ω). Inductance(H) 5E-09 4.5E-09 4E-09 3.5E-09 3E-09 2.5E-09 2E-09 1.5E-09 1E-09 5E-10 0 100000 1000000 10000000 Frequency(Hz) Inductance Figure 29 Graph of inductance results for Matlab The graph (Figure 28) shows the results for the inductance calculation from the Matlab code developed. As the frequency increases the inductance decreases slightly, which is as expected. Frequency(Hz) Resistance(Ohm) 100000 0.017203976 200000 0.01721592 400000 0.017262718 700000 0.017383996 1000000 0.017553232 2000000 0.018275132 4000000 0.019589594 7000000 0.020708807 10000000 0.021255759 Figure 30 Table of results for Resistance calculation 23 P a g e

Resistance(ohm) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING The results are as expected. As the frequency increases the resistance increases. The graph below shows the resistance plotted versus the frequency which clearly demonstrates the gradual increase in the resistance. 0.03 Resistance(Ohm) 0.025 0.02 0.015 0.01 Resistance 0.005 0 100000 1000000 10000000 Frequency(Hz) Figure 31 Graph of resistance results for Matlab 2.3.2 Simulation of single turn coil (Figure 20) using Ansys Maxwell To verify the results given by the Matlab code, a single turn coil was modeled and simulated for the same range of frequencies used in the Matlab program. The tables and graphs below show the results taken from the simulation on Ansys. Total Energy(J) Frequency(Hz) Inductance(H) 1.10E-09 100000 4.38E-09 1.10E-09 200000 4.39E-09 1.10E-09 400000 4.38E-09 1.09E-09 700000 4.38E-09 1.09E-09 1000000 4.37E-09 1.08E-09 2000000 4.32E-09 1.06E-09 4000000 4.26E-09 1.05E-09 7000000 4.20E-09 1.04E-09 10000000 4.17E-09 Figure 32 Table of results for Ansys simulation (Inductance) 24 P a g e

Inductance(H) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING The table (Figure 31) above shows the results from the simulation of the single turn coil in Ansys. The results prove that inductance decreases as the frequency increases which is as expected. The graph (Figure 32) below displays the results clearly. 5.00E-09 Inductance(H) 4.50E-09 4.00E-09 3.50E-09 3.00E-09 2.50E-09 2.00E-09 Inductance(H) 1.50E-09 1.00E-09 5.00E-10 0.00E+00 100000 1000000 10000000 Frequency(Hz) Figure 33 Graph of results (Inductance) Ansys does not give a value for resistance directly. Ansys gives power loss in watts, using this we can calculate resistance as it is equal to twice the power loss. The table below shows the power loss over a range of frequencies. Using this result, the resistance of the coil was calculated. Loss(W) Frequency(Hz) Resistance(Ohm) 0.0086034 100000 0.0172068 0.008612 200000 0.017224 0.0086401 400000 0.0172802 0.008713 700000 0.017426 0.0088151 1000000 0.0176302 0.0092556 2000000 0.0185112 0.010124 4000000 0.020248 0.011082 7000000 0.022164 0.011788 10000000 0.023576 Figure 34 Table of Results for Ansys Simulation (Resistance 25 P a g e

Inductance(H) Resistance(ohm) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING 0.025 Resistance(Ohm) 0.02 0.015 0.01 Resistance(Ohm) 0.005 0 100000 1000000 10000000 Frequency(Hz) Figure 35 Graph of Results (Resistance) The results show that as the frequency increases the resistance of the single turn coil increase which is as expected. Below the results of the simulation of the coil in Ansys and Matlab are compared. The results are very accurate for the inductance calculation. Inductance(H) 5.00E-09 4.50E-09 4.00E-09 3.50E-09 3.00E-09 2.50E-09 2.00E-09 1.50E-09 1.00E-09 5.00E-10 0.00E+00 100000 1000000 10000000 Frequency(Hz) Ansys Matlab Figure 36 Graph of comparison of results (Inductance) 26 P a g e

Resistance(ohm) DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING The results for the resistance calculation show that the Matlab code developed is quite accurate up to about 1MHz. 0.025 Resistance(Ohm) Ansys/Matlab 0.02 0.015 0.01 0.005 Ansys Matlab 0 100000 1000000 10000000 Frequency(Hz) Figure 37 Graph of comparison of results (Resistance) 27 P a g e

Chapter 3 - Conclusion 3.1 Discussion The main objective of the project was to develop Matlab programs which could replace the need to use FEA software to calculate inductance, resistance and the effects of different shielding layers of coils used in wireless power transfer. In Section 2.1, inductance of a 3 turn, single layer coil was investigated. The result gave the self and mutual inductances for the prototype in Figure 6. The results were compared to the results in the paper [5].Not all results were given in the paper but the results compared were very accurate. The overall system result was not as accurate to the results taken from Ansys. The Matlab program developed in this section could be used as a replacement for FEA software as the results were very accurate. In section 2.2, inductance of a coil with a double layer substrate was investigated. The results of Ansys and Matlab were compared and demonstrated that the results were accurate up to about 1MHz. From reviewing the paper [2], the results show a very similar trend to the results shown above (Figure 23). Therefore it is assumed that the equation used is only very accurate up to approximately 1MHz. The program developed to calculate the effects of shielding layers could be used to replace FEA software. In section 2.3, AC resistance and inductance of a coil was investigated. The coil was split into a number of sections (5 along the x-axis, 2 along the y-axis) to allow for eddy current effects in the coil. The results from both Ansys and Matlab for inductance and resistance were taken and graphed above. The results were very accurate for the inductance calculation (Figure 36). The resistance calculation was quite accurate again up to approximately 1MHz (Figure 37). The program developed in this section could be used as a replacement for FEA software for frequencies up to approximately 1MHz. 28 P a g e

Overall, the developed programs have their limitations. The results are quite accurate for a band of frequencies up to approximately 1MHz, once the frequency goes above this the results taken from Ansys and Matlab start to vary. Prior to the commencement of this project, I had limited knowledge in Matlab programming and was inexperienced in FEA software. I have gained a great knowledge of both Matlab and Ansys. I now feel confident developing models in Ansys and programming in Matlab. This project has been an invaluable introduction to the emerging area of Wireless power transfer. It was very interesting project as wireless power transfer is beginning to appear in modern applications. 29 P a g e

Bibliography [1 "Nokia Conversations," [Online]. Available: ] http://conversations.nokia.com/2012/10/01/wireless-charging-explained/. [Accessed 30 March 2013]. [2 "Extended Theory on the Inductance Calculation of Planar Spiral Windings Including the ] Effect of Double-layer Electromagnetic Shield," [Online]. Available: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4342506. [Accessed 30 March 2013]. [3 "Wireless Power Consortium," [Online]. Available: ] http://www.wirelesspowerconsortium.com/technology/shielding-effectiveness.html. [Accessed 30 March 2013]. [4 "Ansys," [Online]. Available: ] http://www.ansys.com/products/simulation+technology/electromagnetics/electromech anical+design/ansys+maxwell. [Accessed 30 March 2013]. [5 "Calculation of self and mutual impedances in planar magnetic structures," [Online]. ] Available: http://www.nuigalway.ie/power_electronics/documents/ieee_trans_magnetics_1995.pd f. [Accessed 30 March 2013]. 30 P a g e

Appendices The entire folder used throughout the development of this project is included in the CD attached. All Matlab code, graphs and Ansys project simulations are divided into folders accordingly. 31 P a g e