BE. Electronic and Computer Engineering Final Year …. Electronic and Computer Engineering Final Year Project Report Title: Development of electrical models for inductive coils used

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

3rd April 2013

Supervisor: Dr. Maeve Duffy

Co-Supervisor: Dr Edward Jones

DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING

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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.


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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.


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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


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Bibliography ............................................................................................................. 30

Appendices .............................................................................................................. 31


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Glossary

FEA – Finite Element Analysis

SE – Shielding Effectiveness

AC – Alternating Current

DC – Direct Current


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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


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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


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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)


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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.


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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.


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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.

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 1 Wireless Power Transmission

Figure 2 Nokia Lumia phone with wireless charging plate [1]


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“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]

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

Figure 3 Typical power transfer system


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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.

1.5.1 Procedure to setting up model

Figure 4 Flowchart for setup of Ansys model


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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).

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.

Figure 5 Solution Setup for Ansys


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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.

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)

Figure 6 Cross sectional view of 3 turn coil being used in testing [5]


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The program layout is as follows:

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

Figure 7 Flowchart of Matlab code


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To calculate the rest of the radii of each turn, an algorithm was developed (Figure 8).

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.

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 L11 is the self inductance of the first turn in the coil, L12 is the mutual inductance

between the first turn and the second turn in the coil and so on.

(

)

Figure 8 Algorithm to calculate radii

Figure 9 While loop representing integrating to infinity


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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


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Figure 12, shows a closer image of the coil. The magnetic activity of the coil itself can be

seen clearly.

Figure 12 Zoomed in version of Figure 12

Figure 13 Prototype built and magnetic field applied


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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).

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)

Figure 14 Cross section of coil with shielding layer [2]


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( ) {

(

)

[

]

(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.


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The program layout was as follows:

Figure 15 Flowchart for Matlab program to calculate Inductance of coil with shielding layer


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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).

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.

Figure 17 Table of Results for Matlab code

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 16 Users inputs prototype specification into Matlab


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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.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

10000 100000 1000000 10000000

L/Lo

Frequency(Hz)

Inductance with Shielding

Inductance


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Figure 19 Magnetic field layer applied to prototype without shielding layer

Figure 20 Magnetic field layer applied to prototype without shielding layer


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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

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.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

10000 100000 1000000 10000000

L/Lo

Frequency(Hz)

Inductance with Shielding

Inductance


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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.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

10000 100000 1000000 10000000

L/Lo

Frequency(Hz)

Inductance with sheilding

Ansys

Matlab


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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.

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.

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 ro = outer radius of section ri = inner radius of section

Figure 24 Cross section of single turn coil

Figure 25 Cross section of coil split into 10 sections


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Impedance is equal to

, therefore using the equation (15), the current was calculated when

= 1 Volt,

The program layout was as follows:


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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.

Figure 26 Flowchart for Matlab program to calculate Impedance for prototype


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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).

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.

Figure 30 Table of results for Resistance calculation

0

5E-10

1E-09

1.5E-09

2E-09

2.5E-09

3E-09

3.5E-09

4E-09

4.5E-09

5E-09

100000 1000000 10000000

Ind

uct

ance

(H)

Frequency(Hz)

Inductance(H)

Inductance

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


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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.

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)

0

0.005

0.01

0.015

0.02

0.025

0.03

100000 1000000 10000000

Re

sist

ance

(oh

m)

Frequency(Hz)

Resistance(Ohm)

Resistance


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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.

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.

0.00E+00

5.00E-10

1.00E-09

1.50E-09

2.00E-09

2.50E-09

3.00E-09

3.50E-09

4.00E-09

4.50E-09

5.00E-09

100000 1000000 10000000

Ind

uct

ance

(H)

Frequency(Hz)

Inductance(H)

Inductance(H)

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


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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.

Figure 36 Graph of comparison of results (Inductance)

0

0.005

0.01

0.015

0.02

0.025

100000 1000000 10000000

Re

sist

ance

(oh

m)

Frequency(Hz)

Resistance(Ohm)

Resistance(Ohm)

0.00E+00

5.00E-10

1.00E-09

1.50E-09

2.00E-09

2.50E-09

3.00E-09

3.50E-09

4.00E-09

4.50E-09

5.00E-09

100000 1000000 10000000

Ind

uct

ance

(H)

Frequency(Hz)

Inductance(H)

Ansys

Matlab


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The results for the resistance calculation show that the Matlab code developed is quite

accurate up to about 1MHz.

Figure 37 Graph of comparison of results (Resistance)

0

0.005

0.01

0.015

0.02

0.025

100000 1000000 10000000

Re

sist

ance

(oh

m)

Frequency(Hz)

Resistance(Ohm) Ansys/Matlab

Ansys

Matlab


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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.


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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.


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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].


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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.

Documents

BE. Electronic and Computer Engineering Final Year …. Electronic and Computer Engineering Final Year Project Report Title: Development of electrical models for inductive coils used