wireless powering of maritime satellite transceiveretd.dtu.dk/thesis/ihk-11327962/wpt_report.pdf ·...

Copenhagen University College of Engineering Center for Information Technology & Electronics (CITE) Lautrupvang 15 2750 Ballerup Denmark Tel.: +45 4480 5130 Fax: +45 4480 5140 www.ihk.dk

Bachelor Project for: Spring 2012

070286, Kasper Krogh Hansen

Wireless Powering of Maritime Satellite Transceiver

Abstract:

An analysis of wireless power transfer with an assessment of its practical applicability in terms of

efficiency. This assessment is obtained through the design and construction of a resonant inductive

wireless powering system suited to supply a satellite transceiver with 30 W of power at 24 V, over a 10

mm air gap.

I accept that the report is available at the library of CITE.

Student: Kasper Krogh Hansen Sign.: …………………………………….

Supervisor: Søren Hougård Jensen Sign.: …………………………………….

Company: Thrane & Thrane A/S

Coordinator: Lars Maack Sign.: …………………………………….

Ext. examiner Jan Møller Hansen Sign.: …………………………………….

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Contents

1. Preface ....................................................................................................................................................... 4

2. Introduction ............................................................................................................................................... 5

2.1 Technological background ................................................................................................................. 5

2.2 Project background ........................................................................................................................... 7

2.3 Problem statement ............................................................................................................................ 8

3. Problem analysis ........................................................................................................................................ 9

3.1 System types ...................................................................................................................................... 9

3.2 Inductive power transfer ................................................................................................................. 10

3.3 Employing Resonance ...................................................................................................................... 13

4. Project delimitation ................................................................................................................................. 16

4.1 Solution strategy .............................................................................................................................. 16

4.2 Requirements specification ............................................................................................................. 16

4.3 Methods and Resources .................................................................................................................. 17

Two methods of measuring coupling coefficient .................................................................................... 17

Finite element simulations using FEMM 4.2 ........................................................................................... 18

Winding structure for multilayered planar coil ....................................................................................... 18

Planar coil bobbins .................................................................................................................................. 19

Resources................................................................................................................................................. 19

5. Problem solution ..................................................................................................................................... 20

4.4 Block diagram .................................................................................................................................. 20

4.5 Power Train...................................................................................................................................... 21

Transmitter and receiver coils ................................................................................................................. 21

Inverter .................................................................................................................................................... 27

Matching circuitry .................................................................................................................................... 33

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5.1 System simulations .......................................................................................................................... 36

Secondary power regulation ................................................................................................................... 37

5.2 Control Loop .................................................................................................................................... 39

Microcontroller Boards............................................................................................................................ 40

Rx & Tx coils ............................................................................................................................................. 42

5.3 Efficiency .......................................................................................................................................... 43

6. Conclusion ............................................................................................................................................... 44

5.4 Project conclusion ........................................................................................................................... 44

5.5 Process oriented conclusion ............................................................................................................ 45

7. Works Cited ............................................................................................................................................. 46

8. List of figures ........................................................................................................................................... 48

9. Appendice ................................................................................................................................................ 50

11.1 Initial project outline ....................................................................................................................... 50

12.1 Overall project plan ......................................................................................................................... 51

12.2 Milestone plan ................................................................................................................................. 52

12.3 Project diary..................................................................................................................................... 54

12.4 Network model of coupled coils ...................................................................................................... 56

12.5 Original figure “Pole-splitting Effect” .............................................................................................. 61

12.6 Series resonant capacitor differential voltage figure ...................................................................... 61

12.7 MATLAB script LLC calculations ....................................................................................................... 62

12.8 Schematic, Transmitter ................................................................................................................... 63

12.9 Schematic, Receiver ......................................................................................................................... 64

12.10 Schematic, AT88V piggyboard ..................................................................................................... 65

12.11 Simulation circuits, section 5.1 .................................................................................................... 66

12.12 Pictures of the proposed system ................................................................................................. 67

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1. Preface

This report serves as the documentation of the focused efforts of a single person during the period from

the 1st

of February to the 31st

of May 2012. An extensive amount of time and energy has been put in to the

finding, studying and deciphering of results from research facilities across the world, and the content of this

report reflects an intention of clarifying the concepts in practical terms. The explanatory form of this report

offers a great introduction to the concepts of Wireless Power Transfer, and further investigations are

encouraged by an extensive list of cited works.

I would like to address a big thanks to Thrane & Thrane for welcoming me in their organization by providing

both an exciting project outline as well as the resources necessary to pursue it. It has been a great pleasure

to work in a professional environment with a pleasant atmosphere, while enjoying the advice of highly

competent colleagues whenever needed.

Especially I would like to thank Søren Hougård, who has been a great help in narrowing an otherwise very

wide project proposition down to a manageable size and form. In spite of a tight schedule and a heavy

workload, he has taken the time to provide me with technical advice and guidance along the way, and I

owe a great deal of the project’s successful outcome to his goodwill.

A final thanks to Lars Maack for providing feedback and good advice, as well as taking the time to

participate in technical discussions which have helped me tremendously in tying down some of the more

elusive technical aspects of this subject.

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2. Introduction

2.1 Technological background

Throughout the history of science and technology, the possibility of supplying power wirelessly has held a

prominent place in the mindset of scientists as well as the general public. The concept of wireless electrical

power is far from new and has been heavily exploited throughout the 20th

century, e.g. in applications

employing electromagnetic waves as means of transporting very low power over vast distances for

communication purposes (radio transmission).

Although the prospect of transmitting high power levels over similarly great distances has been subject to a

lot of scientific research over the course of the last 121 years1, a practically implementable and

commercially viable solution has yet to be presented due to the losses associated with the large distances

of interest. Recent year’s technological advances have however led to the introduction of battery powered

portable equipment with different logistical requirements in terms of power and distances than have

previously been the case. The subsequent change in use, from long range powering to short range charging

has altered the premise on which Wireless Power Transfer (WPT) was previously discarded as a non-

feasible solution. Furthermore the prospect of gaining valuable early shares of emerging markets, has re-

sparked interest from the scientific community and led to serious commercial efforts towards bringing

forward a solution to wireless charging of products ranging from smaller portable devices to electric

vehicles.

Some of the more notable recent contributors in the growing field of WPT include MIT and Intel, whose

R&D efforts [1] have led to the coining of nifty terms such as WiTricity and WREL2 respectively. Currently

none of their efforts have led to commercially available products, but their demonstrations have inspired a

large group of commercial players to investigate for WPT’s applicability in their own field of work. An

industry driven effort towards standardization is led by the Wireless Power Consortium (WPC) to secure

compatibility under the shared platform Qi3, intended to guarantee compatibility as have previously been

the case with shared platforms such as WiFi, Bluetooth and USB. The limitations4 inherent to platforms with

guaranteed interoperability means that a lot of proprietary solutions are still being maintained and

1 starting with Nikola Tesla’s experiments and 1891 demonstration

2 Wireless Resonant Energy Link

3 Pronounced ”chee”, one directly competing standard is Powermat.

4 the Qi is among other restrictions limited to 5W

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developed to accommodate power needs not covered by the standard. “eCoupled” and “Plugless Power”

are examples of such proprietary solutions, where the former addresses medium power needs for home

appliances and the latter targets the high power segment.

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2.2 Project background

Thrane & Thrane A/S develops advanced mobile satellite terminals and MF/VHF handsets for use in land,

maritime and aviation contexts across the globe. The unfavorable operating conditions of such rugged

environments impose the need for very high IP classifications of equipment (typically IP66 and IP67).

A recurring problem is the power connector feed through, which compromises the ability to keep moisture

and water out. In terminals equipped with Wi-Fi, an obvious solution would be to utilize “Wireless Power

Transfer”, allowing the unit to be kept hermetically sealed throughout the entire product life cycle, thus

eliminating the risk of failure due to water exposure.

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2.3 Problem statement

The goal of this project is to:

- design a circuit realizing Wireless Power Transfer, suited to power a maritime satellite transceiver

while providing general insight towards: power limitations, maximum efficiency, environmental

influence in terms of EMI and manufacturability.

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3. Problem analysis

3.1 System types

WPT systems are generally characterized by the physical property on which their transfer is based. By this

standard, any system can initially be distinguished by belonging to either the radiative5 or non-radiative

6

category. For radiative systems such as radio transmitters, the power density decays rapidly as the waves

scatter in all directions. While it works well for information transmission, it is unacceptably inefficient from

a power perspective. For directed waves such as laser, the distances involved are much greater, but the

transfer requires an uninterrupted line of sight. Common to both types of systems are the damages they

inflict on tissue which disqualifies them for use in all but a few very specific environments, such as space

and automated industrial processing lines.

In the category of non-radiative transfer systems, a further distinction between capacitive and inductive is

made. While capacitive transfer is possible, it is generally only considered practical over the range of a few

millimeters [2, p. 28] and for low power levels. The capacitive type of transfer is however subject to

ongoing academic research7, and may in the future prove practical for certain applications.

The different link type characteristics are summarized in table 1 for ease of comparison and overview.

Principle of transfer Parameter of dependence Applicability/Reason

RF Permeability µ & dielectric constant

ε

None/Harmful to human tissue, very low

power range

Optical (laser, x-rays, UV) Refraction index None/ Harmful to human tissue

Ultra sound (Acoustics) Compressibility and specific mass of

matter

None/Impractical due to acoustic damping of

air and the need of an air tight seal.

Capacitive dielectric constant ε None at the moment/Low power levels, short

distances

Inductive Permeability µ Applicable, but needs special considerations

and techniques to compensate for poor

coupling

table 1: Applicability of different transfer schemes

5 Commonly referred to as ”far field”-region

6 Commonly referred to as ”near field”-region

7A capacitive WPT reference is included for general interest [11]

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Though each of the methods mentioned above could be subject to much more investigation, the

characteristics mentioned in column 3 of table 1 are sufficient to justify their disqualification in relation to

the problem at hand. This leaves inductive power transfer as the best option in the context of the projects

scope.

Induction is the principle of operation in a common power transformer, where the mutual inductance of

tightly coupled coils allows great amounts of power to be transferred at high efficiencies. Tight coupling is

achieved through the use of high permeability materials such as iron or ferrite, but such materials offer

only galvanic isolation rather than true physical separation. For WPT applications it is therefore necessary

to omit the flux-guiding material in order to achieve full separation between the primary and secondary

coil. The omission of magnetic material is a necessary compromise that introduces some problems that

must be properly dealt with in order to achieve a practically viable solution. In the following section, a

qualitative analysis of coupled coils will provide an understanding of the fundamental challenges involved

with inductive power transfer.

3.2 Inductive power transfer

The electrical models used in this section are thoroughly derived in section 12.4: “Network model of

coupled coils”. A quick review of this section prior to further reading is advised.

As inductive power transfer is widely utilized in common power transformers, it makes sense to view a

wireless inductive power transfer system in relation to a transformer. Basically, a transformer is just a pair

of coils which share a large portion of their magnetic flux through a magnetically well-conducting material.

Omitting the magnetic material does not change the fundamental physics of the system, only the amount

of shared flux and hence the coupling factor k. Recognizing this, allows for the modeling of a wireless power

transfer system through the well-established physics and mathematics of transformers.

A network model of a pair of coupled coils (i.e. a transformer) is shown in fig. 1, where the coupling factor

k is ≠ 1, and series winding resistances have been included on both sides. Since the model is analogous to

that of a transformer, the terms “transmitter and receiver” will be freely substituted with the terms

“primary and secondary” as seen fit in the immediate context of explanation.

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fig. 1: Network model of coupled coils

To get a perspective of the critical issues regarding efficient transfer of power from the source to the

equivalent load resistor, this model needs to be thoroughly understood. In section 12.4 it was established

that an ideal transformer has infinite primary and secondary inductances, as well as a coupling factor of 1.

The practical model depicted in fig. 1 above utilizes an ideal transformer and models the non-ideal behavior

by inclusion of external inductors with relative values governed by the coupling factor k. The objective of

the circuit is to transfer power from the AC source to the load RL , but the efficiency is to some extend

obstructed by the non-ideal properties of a real life transformer with its finite inductances and non-unity

coupling. In any case, a good practical transformer has most of its inductances placed in parallel with the

ideal transformer, whereas a bad one in terms of coupling has most of its inductance placed in series. The

effects of this coupling-determined inductance division are better examined by revising the circuit to two

different perspectives of observation, namely the transmitters and the receivers.

Seen in fig. 2 is the equivalent network model8 of these coupled coils, when the circuit is reduced to just the

primary side as proposed in [2, p. 47]. For the time being, the reduced model shall serve as an investigative

example of the influence of a low coupling coefficient seen from the transmitter’s perspective.

fig. 2: Equivalent primary circuit

For the model provided, a k close to 1 causes the term 1 to almost disappear, and the term

to reduce to roughly . This is the case in a good transformer, where the

8 A descriptive development of the model is provided in appendix 12.4: “Network model of coupled coils”.

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impedance of is large compared to the series resistance and inductance. In practical terms, this

means that a large and dominant portion of the driving voltage is present on the terminals of the

transformer, and the parasitic inductance can be neglected. If, however the coupling factor is low, the

values of the two inductors change in favor of the spread inductance, while the magnitude of the reflected

load decreases. This effectively causes the formation of a voltage divider where the parallel

connection || looks very small. To get any power to the load, the current thus has to

increase which leads to increased power dissipation in R. In this scenario, the load is regarded the

term. On the receiving end, only the portion delivered to the load resistor is effective

power, hence the efficiency degradation is not limited to the transmitting side. The model in fig. 3 depicts

the circuit reduced to the secondary side:

fig. 3: Equivalent secondary circuit

It is obvious that only a portion of the induced voltage will be presented at the load resistors

terminals due to the dividing action of the series impedances of RS, 1 and RL. The inherent

parasitic inductances of poorly coupled coils must be properly dealt with to achieve any serious efficiency,

as any coupling compensation in the form of increased primary voltage alone would call for impractically

high voltages.

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3.3 Employing Resonance

Resonance is the enabling factor when it comes to transferring power through the common magnetic field

of air wound coils. The level of coupling is however very determinative for the degree of resonant

operation that is achievable in practice. This will become apparent later in this section, but first the

positive effects of resonance shall be presented.

According to Faradays law of induction, an emf induced in a single coil loop is dependent in magnitude on

the first time derivative of the magnetic flux it encloses. As demonstrated in 12.4, as well as [3, p. 96],

Faradays law can be rewritten to: = = = !"

The rewritten equation indicates that the induced secondary voltage is dependent on both the coupling

factor k, and the rate of change for the current of the primary coil. Rewriting the latter in terms of

frequency yields the expression: = !" = !"#$ cos#( in which it becomes obvious that the induced secondary voltage is proportional to coupling, frequency and

amplitude of the primary current. Since the coupling of coils is a locked entity dependent on the system

geometry, this cannot be used to optimize for better performance. Frequency should be as high as possible,

but will to some extend always be bound by the finite switching speeds of the driving circuit as well as

radiation loss considerations9. What remains is the maximization of primary coil driving current, which to

this point of analysis has been hindered by the spread inductance. To overcome the current limitations

imposed by this inductance, a resonant transfer scheme is usually employed. In practice this means that

capacitors are added to both the primary and secondary coils, which cause resonant LC tanks to form on

either side.

Although the spread inductances are still present, the added capacitance allows for energy to oscillate

between E- and B-field states of energy storage respectively10

. Provided that the driving force matches the

oscillations in phase and frequency, a large current is allowed to gradually build11

up and thus overcome

the obstructive presence of the spread inductances.

9 Radiation losses become significant as the coil and wave lengths become comparable.

10 Analogous to the potential and kinetic energy states of a swinging pendulum.

11 Referred to as “Current Magnification”

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fig. 4: Inductive system with resonant capacitors

In fig. 4, the coupled coils are shown with resonant capacitors Cr and Cp added. The choice of either series

or parallel connection of capacitors has a significant impact on the systems characteristics, but for this

particular explanation the primary resonant capacitor is connected in series while the secondary resonant

capacitor is connected in parallel. Looking at the primary side, two LC networks can be seen, namely the

series connection of Cp and Lrp as well as the series connection of Cp and (Lrp+kLp) respectively. For medium

levels of coupling the magnitude of the spread inductance Lrp and the magnetizing inductance kLp are

comparable, which means that the resonant frequencies of the two possible LC networks are different, that

is:

1!)"*" + 1!)"*" "

For low coupling, the spread inductance dominates, which means that the resonant frequency of the two

LC networks do not differ as much from each other. That is:

1!)"*" 1!)"*" "

This simple property means that a single coinciding resonant transfer frequency only exists for systems with

very low coupling, whereas medium coupled systems must rely solely on the current magnification scheme

described earlier in this section. The phenomenon is formally called pole-splitting, and it is very well

illustrated by fig. 5 below, which is an adaptation of figure 2.29 in [2, p. 66]. It depicts the gain vs. frequency

vs. coupling for a comparable series-parallel system12

operating at 20 MHz.

12

The system in mention consists of identical coils of 1.96 uH, 5.18 Ω with a load of 1 kΩ

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fig. 5: Pole splitting effect, figure adapted from [2, p. 66]

The cross-sectional face at k=0.4 has respectfully been added to emphasize the characteristic

gain/frequency plot (dotted) one should expect for a similar series-parallel system in a fixed load condition

at medium coupling. The original figure with caption is included in section 12.5.

In very low coupled systems such as the ones suggested by MIT and Intel, a wide variation in coupling is

part of the typical use case scenario as they aim at supplying numerous portable devices throughout large

spaces. The challenge of achieving true resonant operation throughout the full range of distance and

loading is a matter of continuously adapting the primary and secondary to the immediate level of coupling.

The complexity of this tuning and the difficulties involved with dynamically measuring the coupling

coefficient is likely the reason that these systems have not yet been launched commercially.

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4. Project delimitation

4.1 Solution strategy

The pioneering nature of this project limits the degree of maturity the product can possibly reach during

the allocated time window. This strongly suggests that the proposed circuit, in case Thrane & Thrane wishes

to pursue the technology commercially, will be subject to further development and testing. To

accommodate such needs, this projects aim will be to provide a development platform through which the

initial steps of a commercial project’s delimitation can be taken with less effort than would have otherwise

been the case.

4.2 Requirements specification

• Input Voltage: 24 VDC

• Output Voltage: 24 VDC

• Output Power: 0-30 W

• System Efficiency: As high as possible – preferable >80% @ maximum load (30W)

• Must not interfere with the Transceiver Rx frequency band at 1525-1545 MHz.

• Must comply with mechanical outline of the 3027 Transceiver as shown below.

• Distance between transmitter and receiver: max. 10 mm (assuming perfect axial alignment)

fig. 6: Mechanical outline of transceiver, bottom view

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4.3 Methods and Resources

Two methods of measuring coupling coefficient

To evaluate the coupling of different coil designs, two different methods were used based on inductance

and gain measurements respectively. The inductance method utilizes the fact that coupled coils connected

in series phase will exhibit an inductance equal to: =" 2, while the same two coils

connected in series counter-phase will exhibit and inductance equal to: =" 2. Solving for

M yields: = - .-/0 , which is related to the coupling k by: = 1!23 , where LA and LB refers to the

inductances of either coil when measured alone. The code snippet below is an excerpt from MATLAB

calculating a coupling of 0.36 between coil A and B.

L_A=17.91e-6;

L_B=17.75e-6;

L_series1=48.9e-6; % L_series1=Lp+Ls+2M

L_series2=21.6e-6; % L_series2=Lp+Ls-2M

M=(L_series1-L_series2)/4

k=M/sqrt(L_A*L_B)

This method of determining the coupling takes 4 impedance measurements and some reconfiguring of the

coils in between each, which was found to be a bit tedious.

A much faster method of determining coupling is to measure the forward and reverse gain of the coil set,

and directly read out the gain value from the flat section above the gain curves lower pole and below the

resonance point. As proposed in [2, p. 192], the forward gain will be k*n while the reverse will be k/n, and

thus the coupling k equal to: = !454* while the turns ratio n is calculated: = 67879

In case of a unit turns ratio, the coupling can be directly read out as the gain value of the flat section. This

allows for a much simpler evaluation of coil coupling, requiring only 1 or 2 measurements. In the case of

coils A and B, the gain measurement resulted in a coupling of 0.38, - well within an acceptable margin of

the more tedious inductance-based measurement form. The measurements are graphically depicted as a

function of coil to coil distance in section 5.

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Finite element simulations using FEMM 4.2

During the coil design phase, the free simulation tool FEMM 4.2 13

was of tremendous aid in predicting the

magnetic properties of the different coil configurations of interest. The design process relied partly on

practical experiments and calculations, but just as much on these simulations. For the possible further

development of this project, the modeling of magnetic properties in terms of magnetic field strength,

inductance and losses could be assessed with great accuracy through the use of this tool.

Winding structure for multilayered planar coil

To obtain a high level of winding uniformity during the construction of each designated planar coil, a

winding station fit for such coil geometries was designed.

fig. 7: Winding structure with planar coil inserted (left); Coil viewed through glue-application slit (right)

It has proven extremely helpful in obtaining wound structures with a high degree of uniformity and great

repeatability in terms of electrical parameters. The structure consists of a massive base with a circular rod

fixed by means of a bolt mounted from below. The rod has a helical incision to accommodate the un-

wound wire as the bottom layer is being glued. A disc slides on the circular rod to apply uniform pressure

all over the winding plane, while allowing for the application of glue through a slit, as depicted in fig. 7

above.

13

Finite Element Method Magnetics

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Planar coil bobbins

To maintain a fixed coil distance during measurements and tests, a set of planar coil bobbins have been

constructed in a non-magnetic and non-conducting polymer. These bobbins each consist of two

interlocking discs with a threaded hole in the axial center point for assembly with a 5 mm nylon bolt.

fig. 8: CAD rendition of a single disassembled bobbin

At an outer wall thickness of 5 mm, stacking two bobbins results in a fixed distance of 10 mm between the

closest edges of the coils, allowing for measurements to be compared on a consistent ground.

Resources

During the project, a “Qi” evaluation board14

has been made available for inspirational purposes. The kit

consists of a transmitter and receiver as depicted in fig. 9 below for general interest.

fig. 9: BQTESLA100LP evaluation kit.

Besides this, a full set of lab equipment has been at my disposal and I have been granted “parts-ordering”

privileges to accommodate my every need in terms of components.

14

Part no. BQTESLA100LP

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5. Problem solution

4.4 Block diagram

The diagram in fig. 10 serves to clarify the distinction between the WPT systems two main functional parts,

namely the Power train and the Control loop. Throughout the development phase, the control loop has

been replaced by manual tuning of the operating frequency based on power readings from multimeters

and an electronic DC load. As such, a greater part of the development effort has gone in to analysis and

design of the Power train, which in the context of maximizing efficiency is by far the most critical

component.

fig. 10: System Block diagram

The “Power Train” block constitutes the magnetic link from source to load, while the “Control Loop” senses

the supply and load scenario and adjusts the operating frequency accordingly15

. The detailed block diagram

in fig. 11 below depicts the system blocks of both the power train (upper segment) and the control loop

(lower segment), and accordingly distinguishes between the two isolated system components

“Transmitter” and “Receiver”

fig. 11: Detailed block diagram distinguishing Transmitter and Receiver

15

This is the intended function of the control loop. In the systems present form, the control loop only senses

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The power train and control loop shall in the following section be described individually by means of each

system’s sub-blocks in consecutive order. Note that the control loop, in the systems present iteration, is not

influencing the operation since the power train has been sufficiently matched throughout the load range.

The control loop has however been implemented and will for further development present a critical aid in

accommodating other load scenarios as well as safety precautions. This will be revisited in section 5.2.

4.5 Power Train

The diagram in fig. 12 depicts the functional blocks of the power train which on the transmitting side

consists of an inverter, matching capacitors and the transmitter coil. The secondary side similarly consists of

a receiver coil and matching capacitors, along with rectification/smoothing and a DC-DC converter for

output voltage regulation.

fig. 12: Block diagram of system Power train

These are the essential parts of the Power Train which shall in the following be described by each of its

functional blocks.

Transmitter and receiver coils

Considering that WPT system performance is critically dependent on the merits of the coil pair, they mark a

sensible starting point for both design and evaluation purposes. As have previously been established,

designing coils for optimum performance is a matter of increasing the coupling and decreasing the

resistance. Both considerations aim to reduce the losses, since good coupling allows for lowering the

circulating primary current, and less resistance translates to lower I2 losses for the required magnitude of

primary current.

Since the coupling of coils is related to their size and distance, the limited available space of the intended

application imposes constraints on the solution diversity. Though coupling is highly dependent on the coils

axial distance, different coil geometries have different merits in terms of inductance and coupling. Since the

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project is targeted the Mini-C transceiver depicted in fig. 13 below, the mechanical outline of this unit

defines the basic shape and size of coils.

fig. 13: Mini C transceiver, figure adapted from T&T’s Sailor 6110 Installation Manual

The transceiver is intended for pole mounting, and the bottom of the shell has an indentation to

accommodate the pole mounting kit. In most space sensitive enclosures, a planar geometry is the least

intrusive in terms of space consumption and this consideration along with the tempting presence of a snug

mounting opportunity lead to deciding on exploring the abilities of a planar coil configuration. A rendition

of the configurations mechanical outline alongside the transceiver in its current wired configuration is

presented in fig. 14.

fig. 14: Possible coil situation, figure adapted from T&T’s Sailor 6110 Installation Manual

The drawing (right side) shows the coils at a 10 mm spacing as required according to the original project

description.

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Although the properties of coils are easily explained, the prediction of performance is much more

complicated. Usually the design process relies on theoretical calculations, qualified assumptions and

practical measurements, and this design process was no different. This means that the superior

performance of the proposed coil design cannot be fully appreciated without knowledge of the work

preceding their construction.

Basically the iterations followed a stepwise procedure of winding and testing with a gradual shift towards

the end of using finite element simulations to verify and predict performance. In this manner, experiments

with both helical and planar coils were conducted and a good experience base was founded. In fig. 15

below, a photographic selection consisting of the coils “A”, “C”, “D” and “F” have been included for

reference.

fig. 15: Selection of experimental planar coils

The coils “A”, “D” and “E” share their basic geometry (planar) as well as their turns ratio and layering.

Experiments with helical coils were conducted but have been left out of this documentation in order to

maintain focus on the chosen planar geometry.

The first coil set consisting of coils “A” and “B” (not pictured, but identical to A) were used to assess what

coupling range to expect for the particular distance to diameter relation. The graph in Fig. 16 depicts the

measured relation between their coupling and the distance between each coils midpoint when they are

coaxially aligned. The specified distance is from edge to edge, which in the graph has been marked at 13.2

mm.

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Fig. 16: Coupling of coils A & B over increasing coaxial distance

The coupling was measured using the two different methods described in 4.3, and the result of both is

included on the plot. The observed decay over increasing distance is in accordance with Gauss’ Law as well

as the mathematical model proposed in [4] where the coupling decays by the third power of the distance.

The value of the coupling for coil A and B is readout as somewhere between 0.36 and 0.38 (depending on

the method used), which puts the system in what is formally called the strong coupled regime. Due to the

individual insulation of each strand, the final coil set “E” and “F” had a larger circumference, which led to a

coupling of 0.42.

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

coup

ling

distance from coplanar position [mm]

Coupling of coils A & B

Measured by inductance

Measured by gain

Edge to edge distance of 10 mm.

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Regarding the ESR of the coils, fig. 17 shows both the simulated and measured results.

fig. 17: ESR of planar coils, simulated & measured

As seen, both the 1.65 mm solid copper conductor (red) as well as the 10 stranded 0.5 mm litz (blue) have

ESR’s in the region of 850 mΩ. However, the multi-stranded coil D does have a region of low ESR in the

range from just a few kHz to about 170 kHz, where the lines intersect. The tendency of such low ESR in the

lower frequency range is due to the much larger effective cross sectional area of a multi-stranded wire due

to the skin effect. As frequency increases, the skin depth of the conductor becomes increasingly thin until a

point where the eddy current losses start to dominate. If however, the diameter of the conductor is less

than 1.5 times the skin depth (and preferable much smaller), the eddy current losses are negligible [5].

Assuming that the reduction in strand thickness is countered by a similar increase in strand count, a certain

wire configuration exists, which will keep the ESR low in the frequency region of interest. The skin depth d

is calculated by

: = ; <=>? = ; 1.68 ∗ 10^ − 8

=? ∗ 1.256 ∗ 10^ − 6= 145>H

By finite element simulations of strand thicknesses smaller than the calculated skin depth, an optimum and

industrially available configuration was found at an individual strand thickness of 71 µm and a count of 405

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 105

0

0.5

1

1.5

2

2.5

Frequency [Hz]

Re

sis

tance [

Ohm

]

AC resistance of coils

Coil A measured

Coil A simulated (1.6 mm solid)

Coil D measured

Coil D simulated (10x0.500 mm litz)

Coil E simulated (405x0.071 mm litz)

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strands. The simulated characteristics in terms of ESR is included as the black graph in fig. 17 where it is

clear that the wire indeed has a much lower ESR.

The transmitter and receiver coils are constructed identical, since this is expected to simplify the matching

operation, at least from an analytical perspective.

fig. 18: Planar coil in place

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Inverter

The primary coil is driven by a class-D half bridge inverter which, due to its switching nature does not

compromise the overall efficiency of the entire system. The intended resonant operating region allows for

zero-current-switching, - thus eliminating the losses usually associated with the state transitions of

MOSFETs. The resonant network is effectively a band pass filter which attenuates all but the fundamental

component of the driving square wave. This translates to near perfect sinusoidal circulating currents, which

from an EMI perspective is desirable. As a side note, the class-D inverter can drive resistive, inductive and

capacitive loads; a feature which is practical in relation to the possible further development of a frequency

controlled16

wireless power system.

Knowing that the inverter is operating at (or close to) the loaded resonance, the design analysis can be

greatly simplified by assuming only the fundamental frequency of the driving square wave is present as

proposed in [6]. This approach is known as the “first harmonic assumption” and was applied to the design

process of the inverter to get rough estimates of current and voltage magnitudes. As the system evolved in

complexity, the estimates were substituted with Spice simulations which have been observed to be a more

viable solution due to the need for “tuning” the circuit to a certain power level. The inverter is

schematically depicted in fig. 19, along with all the loading circuitry.

fig. 19: Inverter and influential system, schematic overview

The magnitude of the current provided by the power stage is strongly tied to the total power dissipation of

the secondary side. This dissipation consists of both losses and the power drawn through the load resistor.

At an effective power output of 30 W at 1.25 A (according to the specification), the secondary side

rectification, conversion and load resistor is approximated by a single equivalent resistance incorporating

16

Since operation above and below resonance corresponds to having a system dominated by either an inductive or

capacitive reactance.

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all the losses. The efficiency of the converter and rectification are for the time being assumed to be 0.9, and

the equivalent resistance which resulted in a 33 W dissipation was found by iterating the resistor value until

the power dissipation was equal to 30/0.9 = 33 W.

fig. 20: Secondary resonant equivalent

As fig. 20 suggests, the secondary circuit (assuming resonance) looks purely ohmic, thus justifying the

substitution with an equivalent resistor. Referring the secondary circuit to the primary sides’ FHA

equivalent with the driving signal replaced with a sinusoid yields the circuit depicted in fig. 21 below:

fig. 21: FHA equivalent, primary referred

This circuit resembles that of an LLC converter, which is the subject of interest in [6] and thus allows for the

comparison between simulations and manually calculated electrical variables. The MATLAB script

containing these calculations have been appended in 12.7, and only the resulting current calculations have

been included here for comparison with the simulations. According to [6] the RMS load current Is of the

circuit is: $ = I√ ∗ $KL MNOPQQQR$S3.34U1

where Iout is the specified 1.25 A, and n=1 as well as k = 0.42 stems from the coil design section. The

magnetizing current im is calculated as : $V = W-_YZ[I5-\ = 1.94U1 and it thus follows that the oscillating

current Ir is equal to $* = 6$V $ = 3.84U1. This sinusoidal current of 5.3 Apeak is what the lower

MOSFET has to conduct when it is on for a half cycle, while the upper only conducts to compensate for

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what is removed by either parasitic losses or the load. During startup however, a large current spike will

occur as the magnetizing field is built up, and therefore both transistors have been chosen with the

resonant mesh current ir in mind. The chosen transistors are a pair of Infineon Optimos Power transistors17

with a continuous drain current rating of 45 A, and a drain-source breakdown voltage of 80 V to

accommodate both the 24 V supply as well as any spikes generated from dead-time between switch

transitions. The MOSFETS are not critical to the overall performance, as long as the on-resistance is low.

These transistors have on-resistance in the range of 15 mΩ, which is negligible compared to the ESR of the

designed coils, and while they are switching at the zero current transition, the switching losses can be

neglected.

Regarding the gate driver, the choice was very much affected by the desire to have an adaptively controlled

dead-time since the possible shoot-through of the transistors when operated at undamped resonance

would lead to a lot of hassle during practical measurements. In the context of this application it makes

sense to accommodate a typical “test-scenario” where some unwanted spikes may arise due to a sudden

load dump or whatever may be the fault. The proposed system consists of high Q coils driven at resonance,

so it is obvious that some large voltage amplitudes may build up if the circuit is not sufficiently damped by

losses and load. The TPS28225 synchronous driver from TI delivers adaptive dead-time control by sensing

the state of both transistors and not allowing either to switch on before the other is asserted to be off. This

feature has proven immensely practical, and dramatically lowered the count of MOSFET casualties during

the development. The waveform in fig. 22 below depicts the simulated system switching node voltage and

resonant mesh current with a secondary load resistor tuned to an RMS power dissipation of 33 W,

equivalent to the nominal loading power times (Pout*1/nBUCK)

17

IPD135N08N3 to be exact

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fig. 22: Switching node current and voltage, SPICE simulation

The node voltage (red) has been scaled down by a factor 5 to better compare the timing between the two

waveforms. As the system is running at the resonant frequency of the primary LC tank, the driving

waveform switching coincides with the zero crossing of the mesh current, effectively eliminating switching

losses. This operation is highly desirable since it not only eliminates the switching losses, but also reduces

the EMI radiation normally associated with switched currents. This mode of operation is verified by the

measurement depicted in fig. 23 below, where the RMS current is readout at 3.4 A.

fig. 23: Switching node current and voltage, measured

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The slight curvature of the switching waveforms “high” half-period comes from the voltage drop imposed

by the on-resistance of the upper MOSFET as it conducts to account for the losses and load power

dissipation. The zero current switching on both transitions is possible since the duty cycle of the waveform

is fixed at 50 %. As previously explained, it is a criteria for such lossless switching that the system is driven

at the resonant frequency of the immediate load, - that is the primary resonant tank. This means that the

possible further development of a frequency controlled control loop must take switching losses and EMI

originating from this point in to account.

In fig. 24 below, the simulated voltage and current of the primary coil is depicted. The current

magnification inherent to the resonant operation enables the voltage over the primary coil to increase to

120 VAC (Peak), thus overcoming the obstructive presence of the spread inductance as explained in 3.3.

(Note that the coil voltage has been scaled by a factor of 10)

fig. 24: Primary coil current and voltage, SPICE simulation

The simulation is in accordance with the measurement depicted in fig. 25 below. Measurement bars have

been added on the voltage graph (yellow) to mark the 24 V increase as the upper MOSFET turns on.

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fig. 25: Primary coil current and voltage, measured

The great correspondence between the simulations and measurements allow for the differential voltage

over the series resonant capacitor to be assessed without conducting a practical measurement. This

simulated differential voltage was readout as 130 VAC (Peak), and is, along with the resonant current a

critical parameter in the selection of resonant capacitors. The simulated graph is included in section 12.6

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Matching circuitry

The matching capacitors are crucial to the efficiency of the system, and must be chosen in accordance with

the estimated voltages and currents of either tank. Furthermore the configuration as either series or

parallel capacitance influences the characteristics of the resulting resonant network and therefore the

choice of configuration must be made to compliment the driving/loading circuitry.

It is a complex task to provide an exact mathematical model of the equivalent network when all parasitic

capacitances are taken into account, and trying to do so has taken up vast amounts of time throughout this

projects development. To this point one such exact model has not been successfully developed, but a lot of

practical experience have been acquired while trying to do so.

The output capacitance of the driving MOSFETs, as well as the reflected capacitance of the smoothing

capacitor after the secondary full bridge rectifier, have been observed to influence the resulting resonant

frequency of the primary tank, and thus the proposed method of matching is a combination of practical

measurements and SPICE simulations.

First off, the value of primary capacitor was chosen in relation to a desired resonant frequency of 200 kHz.

For the primary side, the coupling of coils as well as their inductance determines the spread inductance

with which the capacitor should resonate. For convenience, fig. 2 from section 3.2 has been reprinted

below:

Recalling that the spread inductance on the primary side is: *" = 1 !" , which in the case of

identical coils is equal to: *" = 1 " = 1 = 1 0.42 ∗ 23.83^_ 19.63^_

the matching capacitor at 200 kHz is calculated by: )*

I5/9

I∗``ab/∗c.deLa 32.25f

The voltage type output of the chosen Class-D inverter calls for a series resonant capacitor, resulting in the

primary equivalent network of fig. 21. In recognition of the need for the capacitor to withstand both a large

series current and differential voltage, a type based on metallized polypropylene dielectric was chosen. The

WIMA FKP1 capacitor series is designed particularly for high pulsed current action, and the exact capacitor

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of 33 nF18

nominal value was chosen with a voltage rating of 630 VAC, since a large voltage margin translates

to less relative degradation, and thus lower series resistance (ESR). Obviously a large ESR of the primary

resonant capacitor would compromise the carefully designed low-ESR coil set, so this is an important thing

to attend to.

In relation to the secondary tank capacitance, the figure below is an adaptation of fig. 3 from section 3.2. It

depicts the secondary tank with a capacitor placed in parallel with the secondary side inductance to yield a

voltage type output with a purely ohmic output impedance (Ideally).

fig. 26: Parallel secondary capacitor

Initially, this secondary tank was thought of as having just as critical impact on the overall performance as

the primary in terms of resonant behavior. Practical experiments have however shown that this is not

entirely the case. As the coupling of these particular coils is strong, the overall performance doesn’t rely on

a single resonant operating point, but rather on the current magnification scheme of the primary circuit (as

explained in section 3.3 by means of fig. 5 “Pole Splitting Effect”). However, the current induced in the

secondary inductor will result in very large voltage (kV) amplitudes in a no load situation. As this application

has to accommodate loading in the range from 0 to 30 W, the parallel capacitor closes the circuit and

allows for the induced secondary current to oscillate, rather than generating voltage spikes. The secondary

capacitance was deliberately degraded by adding a small loss by means of a resistance. Doing so ensures

that a no load situation, from a secondary coil perspective, can no longer occur, as the ESR of the capacitor

causes a small dissipation under low external load conditions. At full load, almost all of the induced

secondary current is drawn from the circuit, and thus the oscillating through the capacitance is at a

minimum, with a minimum ESR-dissipation to follow.

18

Measured at 36.8 nF by impedance, resulting in an optimal operating frequency of I√c.dN.d∗ed.gN.c = 187.3_i

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The prospect of devising a clever feedback communications channel led to the rather unorthodox

secondary capacitor arrangement depicted in fig. 27 below:

fig. 27: Adaptive secondary capacitance

By separating the secondary capacitance in to a fixed and an “adaptive” part by means of a pair of

MOSFETS, as is done by the Wireless Power Consortiums “Qi”-standard, - the immediate load current can

be modulated and thus a communication backchannel established19

. The proposed systems hardware is

implemented with this possibility in mind, and thus features the arrangement depicted above with the

capacitance split into a single 22 nF, and two 4.7 nF WIMA capacitors. The deliberate degradation of

capacitance in terms of ESR is accomplished by selecting the FDS9945 N-channel MOSFET pair which has an

on resistance of 200 mΩ @ VGS=5 V. Even though the arrangement is not utilized for communication

purposes, its inclusion is justified by the declared goal of devising a versatile development platform for

further development.

19

Known as “Back-scatter modulation” - in the “Qi” standard, the transmitting side detects this modulation by sensing

and filtering the current in the primary coil.

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5.1 System simulations

To provide insight on the overall system behavior, the system is simulated with the actual component

values and depicted in fig. 28 below:

fig. 28: Circuit Thévenin equivalent simulated

The upper plot shows the output voltage which appears to have two peaks. As predicted in section 3.3, the

voltage gain function thus exhibits the same characteristic “pole –splitting” as depicted by the added face in

fig. 5. This phenomenon manifests itself as these two resonant peaks which are situated above and below

the intended operating frequency respectively. Based on the open-circuit voltage and the short circuit

current, the output impedance is calculated and depicted by the third graph in fig. 28.

If the load is assumed to be a pure resistance of a fixed value, the maximum output power is calculated by:

|kl| ∗ |ml|/4 , which is depicted by the bottom graph.

As a consequence of the characteristics of both the open circuit output voltage and the short circuit loading

current, three interesting peaks occur in the maximum power plot. The two outer peaks are generated by

the large voltage gain of the system at these points. Utilizing either of these frequencies for efficient power

transfer is problematic in terms of secondary side regulation, as a step down converter exhibits a behavior

similar to a negative resistance. For a constant loading power this means that an increase in secondary

voltage leads to a decrease in current draw. Similarly, a drop in secondary voltage leads to an increase in

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current draw, and consequently the system becomes unstable. Operation at these frequencies is thus only

possible through a fast closed loop regulation between primary and secondary, or by means of a linear

regulator which would sacrifice efficiency by shunting excess current to ground.

In the context of well coupled systems such as the one being proposed here, the proper operating

frequency is that of the primary circuit’s resonance, which appears as the max power peak at 187 kHz as

designed for.

fig. 29: Secondary voltage and power for different loads

Above, fig. 29 depicts the secondary voltage and loading power for different load resistors. The red line

marks 33 W, the equivalent power needed for an effective load power of 30 W if an efficiency of 0.9 is

assumed for the rectifier and converter. As noted, the 33 W equivalent resistor is somewhere in between

25 Ω and 40 Ω, and tracing the secondary voltages on the upper plot for these two values gives a secondary

loaded voltage ranging from 32 to 36 V, which leads to the conclusion that the output voltage regulation

can be managed by a step-down converter which shall be accounted for in the following section.

Secondary power regulation

The regulation of output voltage is obtained by means of a step-down converter. Since the scope of this

project is to determine the feasibility of the Wireless Power Transfer concept, the chosen converter

solution is based on TI’s LM25116 evaluation board. The LM5116 controller was particularly chosen due to

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its wide input range which is specified from -0.3 to 100 V, - a span that easily accommodates (almost) any

possible future system configuration. The evaluation board was repopulated for an output voltage of 24 V,

and the compensation was adjusted accordingly. The converter is in this context used as a component, and

shall not be subject to further explanation.

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5.2 Control Loop

As have been mentioned earlier in this document, the control loop is at the present stage of development

not influencing the operation of the system. Since the control loop has great significance for the further

development, it shall however be presented and some prospective functions explained.

As was depicted in fig. 29, the power transfer function exhibits a peak around the 187 kHz operating

frequency where the transfer is at its highest point. The equivalent circuit of the circuit, when reduced to

the primary side bears a striking resemblance to that of an LLC converter. Such a converter modulates the

operating frequency rather than the duty cycle for voltage regulation, and it is likely that such a scheme

could be utilized in order to omit the secondary side buck converter, by regulating the operating frequency

around the power transfer functions peak. For this to be possible, a feedback channel would be necessary.

Another useful feature of such a feedback channel would be to be able to distinguish between an actual

receiver coil loading the circuit, and not just a peace of conducting material which happened to be in the

vicinity of the driving coil. By implementing a simple hand-shake routine between the transmitter and the

intended load, the transmitting system could detect whether to turn off immediately (in case of

unintentional coupling to foreign matter), or to continue driving the primary coil (in case of a “legal” load).

The control loop’s functional blocks are depicted in fig. 30 below.

fig. 30: Block diagram of system Control loop

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Microcontroller Boards

Both MCU1 and MCU2 have been implemented by means of the same PCB layout. The simple schematic is

shown for reference in fig. 31 below.

fig. 31: ATmega88V piggy-board schematic

The microcontroller has two of it’s ADC’s, the UART’s Rx and Tx, a PWM and 3 general purpose IO’s pinned

out. These ports are necessary to accommodate the intended operation on either of the system sides.

Regarding MCU1, its intended operation is to receive messages via it’s UART Rx port, and perform

corrections on the PWM output which is connected to the PWM input of the TPS28225 gate driver of the

inverter. A control routine would be implemented in software to calculate the proper correction in terms of

operating frequency.

For the secondary side, the MCU2 senses the voltage output of a MAX4172 High Side Current Sense

Amplifier which is depicted in fig. 30 as the “Current sense”-block. After A/D converting the output voltage

(which is proportional to the load current), MCU2 transmits the value via its UART Tx port. At the present

stage of development, the system is sensing and transmitting the value via a wired UART. Through the

wired connection, MCU1 receives the message and simply re-transmits it via its own UART Tx which is

hooked up to a PC running a terminal window. Though the simple functionality is not influencing the

operation, the possibility of implementing an “intelligent” system, able to detect a proper load is ready at

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hand, once again – for future development. One of the populated microcontroller PCB’s is are shown for

reference in fig. 32 below.

fig. 32: ATmega88V PCB

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Rx & Tx coils

A set of auxiliary coils was designed to accommodate the feedback channel wirelessly. By winding the coils

in a shape of eights, they are indifferent to flux which is common to both of the loops of either coil. In this

way, they can be placed directly on top of both of the power coils without picking up the power transfer

signal. By aligning the coils to have each of the two individual loops aligned, only the flux generated by one

of the coils would cause a net-flux change of the other. The coils are tuned to a mutually coupled resonant

frequency of 5 MHz, and it is the intention that the UART signal of MCU2 shall act as an enable signal for a

carrier wave, thus effectively transmitting an OOK modulated signal, which could easily be decoded on the

primary side. A drawing of the coil shapes are included in fig. 33 below.

fig. 33: Auxiliary coils for feedback communication

As mentioned elsewhere, the OOK modulated feedback channel has not been implemented.

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5.3 Efficiency

The proposed system has been evaluated in terms of efficiency, and fig. 34 below depicts the result of the

measurements.

fig. 34: System efficiency, measured

The load was gradually increased while the input and output power of both the buck converter as well as

the overall system was monitored. The three graphs above depict the efficiencies of both the buck

converter, and the coils including the full bridge rectifier, as well as the overall efficiency. It is noteworthy

that the coils have a somewhat flat characteristic throughout the load range, only dropping by a slight

amount as the current increases. The overall efficiency is thus primarily dominated by the buck converter

characteristics which has a great impact in the lower region. The overall efficiency at maximum power is

readout as 82.8 %.

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Eff

icie

ncy P

out/

Pin

Loading power [W]

Efficiency of sub-systems

Total efficiency

Buck Efficiency

Coils and rectifier efficiency

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6. Conclusion

5.4 Project conclusion

A wireless power transfer system capable of transferring the required amount of power has successfully

been constructed. The system is supplied by 24 VDC as required, and delivers a regulated 24 VDC at the

output which is also in accordance with the requirement specification. The system accommodates the

entire load range from 0 to 30 W at a max load efficiency of 82.8 % over the required distance of 10 mm. By

employing zero current switching, the system can rightly be assumed to not generate any significant level

of EMI, and does as such not interfere with the transceivers reception band. The system has been designed

with the mechanical properties of the transceiver in mind, and the assessment of its applicability in relation

to this particular product can thus be made with confidence that the technology’s requirements in terms of

space consumption is within reason.

Through the development of this system, a noteworthy realization was made. The similarity to an LLC

converter suggests that the secondary side converter can be omitted by devising a feedback channel

through a pair of auxiliary coils. A scheme for such a feedback channel was proposed, but only partly

implemented. This possibility should be investigated, since this would make possible the omission of the

secondary side converter and the losses it inflicts on the overall performance.

Regarding the maximum transferrable power, it comes down to the coil pair, as the ESR of these is the

limiting factor. The maximum transferrable power is thus only a matter of the tolerable level of resistive

losses.

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5.5 Process oriented conclusion

Writing this report has been a tremendous challenge. I prefer to justify every decision in a design by exact

mathematical expressions which are usually based on available textbook examples and application notes.

The pioneering nature of this project meant that no directly comparable examples have been at my

disposal, and that all the necessary material has had to be sourced from higher learning/research facilities

across the globe. A lot of time was spent interpreting scientific papers and trying to mold the results into

something useful in this particular context. As a result, no exact mathematical expressions were ready at

hand for the immediate justification of every step along the way. Throughout the entire project duration, a

great effort has been made towards obtaining an exact mathematical representation of the system, but

without luck. As a consequence, much of this report relies on simulations, assumptions and empirical work.

When all this is said, I am also very satisfied with the result, both in terms of learning outcome as well as

the developed product and methods, and I am confident that I have done the best I could possibly do.

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7. Works Cited

[1] A. Kurs, A. Karalis, R. Moffatt, J. Joannopoulos, P. Fisher and M. Soljacic, "Wireless Power Transfer via

Strongly Coupled Magnetic Resonances," Sciencemag, vol. 317, no. July 6, pp. 83-86, 2007.

[2] K. V. Schuylenbergh and R. Puers, Inductive Powering, Basic Theory and Application to Biomedical

Systems, Leuven, Belgium: Springer Science + Business Media B.V. 2009, 2009.

[3] K. Y. Kim, Wireless Power Transfer - Principles and Engineering Explorations, Intech Open Access

Publisher, 2012.

[4] S. J. Mazlouman, A. Mahanfar and B. Kaminska, "Mid-range Wireless Energy Transfer Using Inductive

Resonance for Wireless Sensors," Simon Fraser University, Burnaby, Canada, 2009.

[5] H. Chen and A. P. Hu, "Power Loss Analysis of a TET System for High Power Implantable Devices," in

Second IEEE Conference on Industrial Electronics and Applications, 2007.

[6] H. Huang, "Designing an LLC Half Bridge Converter," in 2010 Texas Instruments Power Supply Design

Seminar SEM1900 TI ref. no: SLUP256, 2010.

[7] G. Vandevoorde and R. Puers, "Wireless energy transfer for stand alone systems: a comparison

between low and high power applicability," Elsevier Science B.V, Heverlee, 2000.

[8] H. Sasaki, "Wireless Power Transfer of Magnetic Resonances," Agilent Technologies, 2010.

[9] J. Ross, The essence of Power Electronics, Prentice Hall Europe, 1997.

[10] A. Karalis, J. Joannopoulos and M. Soljacic, "Efficient wireless non-radiative mid-range energy

transfer," Annals of Physics, 2008.

[11] T. Chuan Beh, T. Imura, M. Kato and Y. Hori, "Wireless Power Transfer System via Magnetic Resonant

Coupling at Restricted Frequency Range," University of Tokyo, Tokyo, 2010.

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[12] A. Bodrov and S.-K. Sul, "Analysis of Wireless Power Transfer by Coupled Mode Theory (CMT) and

Practical Considerations to Increase Power Transfer Efficiency," Intech, 2012.

[13] Wireless Power Consortium, "Wireless Power Technology," WPC, [Online]. Available:

http://www.wirelesspowerconsortium.com/technology/. [Accessed Feb 2012].

[14] M. Kline, I. Izyumin, B. Boser and S. Sanders, "Capacitive Power Transfer for Contactless Charging,"

University of California, Berkeley, Berkeley, CA, 2011.

[15] C. Alexander and M. Sadiku, "Magnetic Circuits," in Fundamentals of Electric Circuits, 5th edition,

McGraw Hill, pp. 555-580.

[16] J. W. Nillson and S. A. Riedel, Electric Circuits, 8th edition, Pearson Education, 2008.

[17] R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, New York: Springer, 2001.

[18] W. P. Consortium, "Qi" System Description, Wireless Power Transfer, version 1.0.3, WPC, 2011.

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8. List of figures

fig. 1: Network model of coupled coils ............................................................................................................ 11

fig. 2: Equivalent primary circuit ..................................................................................................................... 11

fig. 3: Equivalent secondary circuit .................................................................................................................. 12

fig. 4: Inductive system with resonant capacitors ........................................................................................... 14

fig. 5: Pole splitting effect, figure adapted from [2, p. 66] .............................................................................. 15

fig. 6: Mechanical outline of transceiver, bottom view................................................................................... 16

fig. 7: Winding structure with planar coil inserted (left); Coil viewed through glue-application slit (right) ... 18

fig. 8: CAD rendition of a single disassembled bobbin .................................................................................... 19

fig. 9: BQTESLA100LP evaluation kit. ............................................................................................................... 19

fig. 10: System Block diagram .......................................................................................................................... 20

fig. 11: Detailed block diagram distinguishing Transmitter and Receiver ....................................................... 20

fig. 12: Block diagram of system Power train .................................................................................................. 21

fig. 13: Mini C transceiver, figure adapted from T&T’s Sailor 6110 Installation Manual ............................... 22

fig. 14: Possible coil situation, figure adapted from T&T’s Sailor 6110 Installation Manual .......................... 22

fig. 15: Selection of experimental planar coils ................................................................................................ 23

Fig. 16: Coupling of coils A & B over increasing coaxial distance .................................................................... 24

fig. 17: ESR of planar coils, simulated & measured ......................................................................................... 25

fig. 18: Planar coil in place ............................................................................................................................... 26

fig. 19: Inverter and influential system, schematic overview ......................................................................... 27

fig. 20: Secondary resonant equivalent ........................................................................................................... 28

fig. 21: FHA equivalent, primary referred........................................................................................................ 28

fig. 22: Switching node current and voltage, SPICE simulation ....................................................................... 30

fig. 23: Switching node current and voltage, measured .................................................................................. 30

fig. 24: Primary coil current and voltage, SPICE simulation ............................................................................ 31

fig. 25: Primary coil current and voltage, measured ....................................................................................... 32

fig. 26: Parallel secondary capacitor ................................................................................................................ 34

fig. 27: Adaptive secondary capacitance ......................................................................................................... 35

fig. 28: Circuit Thévenin equivalent simulated ................................................................................................ 36

fig. 29: Secondary voltage and power for different loads ............................................................................... 37

fig. 30: Block diagram of system Control loop ................................................................................................. 39

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fig. 31: ATmega88V piggy-board schematic .................................................................................................... 40

fig. 32: ATmega88V PCB .................................................................................................................................. 41

fig. 33: Auxiliary coils for feedback communication........................................................................................ 42

fig. 34: System efficiency, measured ............................................................................................................... 43

fig. 35: Ideal transformer ................................................................................................................................. 56

fig. 36: Ideal transformer with state variables ................................................................................................ 56

fig. 37: Ideal transformer with load resistor .................................................................................................... 57

fig. 38: Load transformed to primary side ....................................................................................................... 57

fig. 39: Source transformed to secondary side................................................................................................ 57

fig. 40: Flux enclosing a wound conducting wire, Courtesy of NDT Resource Center .................................... 58

fig. 41: Flux interception by coil in the vicinity ................................................................................................ 59

fig. 42: Non-ideal transformer ......................................................................................................................... 60

fig. 43: Original figure: ”Pole Splitting Effect” ................................................................................................. 61

fig. 44: V-I characteristics of primary series capacitor .................................................................................... 61

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9. Appendice

11.1 Initial project outline

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12.1 Overall project plan

Project week Dates Phase Task

From -∞ to 0 -- Project conception

1

01-02-12 – 03-02-2012

(Calendar week 5)

Research Project plan, overall. (this

table)

Research

2 06-02-12 – 12-02-2012 Research Research

Meeting w. SHJ 10/2:

-project scope,

3 13-02-12 – 17-02-2012 Project definition and

planning

Meeting with LMA & SHJ

Produce project

description.

4 20-02-12 – 24-02-2012 Problem analysis - Hand in project

description.

- Finish problem analysis

and delimitation.

- Decision on system

specs

5 27-02-12 – 02-03-2012 - Milestone plan

6 05-03-12 – 09-03-2012 Project execution starts

- see milestone plan for

objective driven time

plan

7 12-03-12 – 16-03-2012

8 19-03-12 – 23-03-2012 Mid-term evaluation

Set up meeting w.

LMA/SHJ

9 26-03-12 – 30-03-2012

10 02-04-12 – 04-04-2012

(Holiday from 5th

to 9th

)

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11 10-04-12 – 13-04-2012

12 16-04-12 – 20-04-2012

13 23-04-12 – 27-04-2012

14 30-04-12 – 03-04-2012

(Holiday the 4th)

Report

15 07-05-12 – 11-05-2012

16 14-05-12 – 18-05-2012

17 21-05-12 – 24-05-2012

(Vacation from 25th

to 28th

)

Close project Finalize report 24-05-12

18 29-05-12 - 31-05-2012 Final read through Hand in 01-06-12 at

12.00

12.2 Milestone plan

Task Milestone

Inductive link rev.1 05-03-12 – 09-03-2012 Design the coupled coils, and

perform measurements.

Finite element simulation of

resistive losses.

Resonant inverter 12-03-12 – 16-03-2012 Design and simulate the

primary driver circuit.

Boost converter 19-03-12 – 23-03-2012 Design converter for

secondary side regulation.

Matching 26-03-12 – 30-03-2012

Measuring efficiency 02-04-12 – 04-04-2012

(Holiday from 5th

to

9th

)

10-04-12 – 13-04-2012

16-04-12 – 20-04-2012

Testing 23-04-12 – 27-04-2012

Testing 30-04-12 – 03-04-2012

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(Holiday the 4th)

Report work 07-05-12 – 11-05-2012

Report work 14-05-12 – 18-05-2012

Report work 21-05-12 – 24-05-2012

(Vacation from 25th

to

28th

)

Close project,

Finalize report 24-05-12

29-05-12 - 31-05-2012 Final read through

Hand in 01-06-12 at 12.00

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12.3 Project diary

Date;Activities;Hours

01022012;PC setup, Studied Faradays law, Lentz' Law, Overview of concept, Initial thoughts on

structure, printed app notes;8.0

02022012;Studied MIT paper, researched CMT(Coupled-mode theory), Sketched time plan;7.5

03022012;Project description started, studied A.KAR paper, EMpro software, WPC site,7.0

Weekend, total: 22,5

06022012;WPC site cont'd, work on notes, studied Intech chp1, Metamaterials?;8.0

07022012;Intech chp2,Alan Yates website,Installed MATLAB;8.0

08022012;Work on presentation for fridays meeting,8.0

09022012;Presentation work, investigated ways of modeling coupled coils as a transformer,

investigated ways of evaluating coil coupling using VNA;6.5

10022012;study, meeting with SHJ, helical coil on POM experiment, Impedance measurement; 9.0

Weekend, total:62

13022012;Research, meeting w. LMA;8

14022012;Research inductive charging, modeling coupled coils, simulations, found Schuylenbergh;9.0

15022012;Studied Schuylenbergh, measured Qi coil coupling and calculated turns ratio on behalf of

gain/phase measurements!;9.0

16022012;Studied Schuylenbergh, got report started w. formatting and headlines,Milestone plan,

Transformer modeling; 7.5

17022012;Schuylenbergh, Matlab calculation of maximum theoretical efficiency between coils; 4


20022012;Worked on Problem analysis (needs to be done in order to make detailed time plan);8

21022012;Problem analysis, got the planar-coil bobbins from proto, wound planar coils for testing

later, stuck on problem analysis; 8

22022012;Worked on analysis (home); 5.0

23022012;Analysis continued;8

24022012;Work on equivalent network model of loosely coupled coils to be used in problem analysis;9


27022012;work on network model of loosely coupled coils;8



01032012;Finished network model of loosely coupled coils;8

02032012;Analysis continued;7


05032012;Analysis continued; 8.5

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06032012;Started coil design rev1; 4

07032012;rev1 coil design;8

08032012;rev1 coil design, measuring rev1 coils;7

09032012;Measuring rev1 coils(AB), FEMM simulations;7+4=11

Weekend, total:210,5

12032012;Specified loose requirements for resonant inverter and boost converter;8

13032012;Worked on resonant inverter;7

14032012;Resonant inverter/power stage;8

15032012;Half bridge & LLC study; 8

16032012;LLC cicuit calculations;7

Weekend, total:248,5

19032012;MOSFET selection, gate driver ic;8

20032012;Breadboarded half bridge inverter;8

21032012;Half bridge inverter measurements with coils A&B, transmitted 6 W at roughly 50 % eff; 8

22032012;Measurement of AC-resistance for AB coils, design of new multi strand coils; 8

23032012;Constructed and measured multistrand coil, calc. AC res. Compared to AB in MATLAB; 8

Weekend, total:289

26032012;Poor performance on multistrand coil due to eddy current losses. Designed 405*0.071 Litz,

FEMM Simulations; 8

27032012;Sourced litz wire, contact w. FLUX & Matech systems. Designed coil winding stand; 8

28032012;Ordered 12 m litz, simulations in Spice, DTU messe;8

29032012;Very inefficient day;8

30032012;Constructed coils EF, measured coupling and ESR, hooked up to inverter; 8

Weekend, total:329

02042012 to 27042012: further development and test (lost track of diary);

01052012 to 01062012: worked on report

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12.4 Network model of coupled coils

The ideal transformer

In fig. 35 below, an ideal transformer consisting of two perfectly coupled coils of inductances Lp and Ls is

depicted.

fig. 35: Ideal transformer

A basic property of the ideal transformer is its voltage and current changing ability which is governed

entirely by the turns-ratio as described by the relations: opo- = qpq- = -p

These relations are based on the lossless property of the ideal transformer along with the conservation of

energy principle since p- = 1 MNOPQQQR ^"m" = ^m

For an open secondary circuit, is =0, which leads to the conclusion that the ip must also be zero and thus

independent of the driving voltage vp. As a consequence, the ideal transformer is said to have infinite

primary and secondary inductances.

In fig. 36 the transformers state variables are shown:

fig. 36: Ideal transformer with state variables

The impedance on either side can be expressed in terms of the voltage and currents:

r" = opp and r = o-- which after rearrangement leads to the expression sps- = tqpq-u

Hence the impedances seen from either side looking in to the transformer are proportional to the square of

the turns ratio, which thus entirely determines the ideal transformers properties.

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Connecting a load to the secondary side yields the circuit in fig. 37 below:

fig. 37: Ideal transformer with load resistor

The equivalent circuit is modeled from the source’s perspective by using the derived expression for the

reflected impedance (fig. 38) The apparent load seen from the source side is transformed by the square of

the turns ratio n = N:1 = N1/N2

fig. 38: Load transformed to primary side

For the load side, the apparent source is the primary voltage divided by the turns-ratio:

fig. 39: Source transformed to secondary side

The circuit parameters are transformed across the transformer, but the power supplied from the source

equals the power delivered to the load since: v = o/U hence v"* = op/Uw∗/ = op//Uw =vNx If a series

resistance is present in the primary source, this resistance will of course influence the secondary with an

apparent value of ′ = t /u

Mutual inductance

Based on: Riedel p. 208; Schuyl. P46, Uni.Phys. p. 11xx.

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A wound wire exhibits an interesting electrical property known as self-inductance. The phenomenon can be

expressed through Faradays Law: = , which states that the induced EMF in a single electrical loop is

equal to the time derivative of the magnetic flux that penetrates it. Furthermore, Faradays Law for an N-

turn coil states that the induced emf is equal to the number of loops multiplied by the time derivative of

the magnetic flux that penetrates a single loop: = z p9|p The magnetic analogy to electrical conductivity is called the permeance, defined as: ~ = q = 7O .

The flux φ can thus be expressed: = ~zm and it hereby follows that the voltage over a coil due to a

changing current is equal to: = z = z ~q =z~ =z 7O = It is apparent that the self-inductance of a coil is proportional to the squared number of turns, and the

expression holds under the assumption that all flux penetrates all loops (the flux through each loop is

common to all loops) which is the ideal case. Observing just the terms: z = of the equation above

it is also apparent that the inductance is linearly proportional to the portion of enclosed flux as:

z = = z = $ MNOPQQQR = q

In practice, coils exhibit an amount of flux leakage, which means that some flux escapes between the

windings, and takes the short path enclosing the immediate wire as depicted in fig. 40

fig. 40: Flux enclosing a wound conducting wire, Courtesy of NDT Resource Center20

The flux leakage results in an inductance lower than predicted by the expression above for varying coil

dimensions and spacing.

Now, having established that the self-inductance of a single coil is dependent on the amount of flux that is

common to all loops, we can move to the concept of coupled coils. If we imagine two coils in each other’s

20

http://www.ndted.org/EducationResources/CommunityCollege/EddyCurrents/Physics/selfinductance.htm

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vicinity, they will share a portion of whatever flux is present. To get an overview, we categorize the

different flux portions in accordance with a situation where coil 1 is being energized by a time varying

current source that generates the current i1 in coil 1. The flux penetrating coil 1 is thus equal to = where the subscript 11 denotes flux penetrating coil 1 due to i1, and subscript 21 denotes flux

penetrating both coils due to i1 as depicted in fig. 41

fig. 41: Flux interception by coil in the vicinity

The coils current/flux relationship has previously been established as = ~zm. It follows that the voltage

over coil 1 is equal to: = z~ ~ = where L1 is the self-inductance of coil 1. For coil 2

the voltage v2 can be calculated on behalf of coil 2’s flux =~zm leading to the expression:

= zz~ where the entity zz~ is the called mutual inductance of the coils. Hence the

voltage induced in coil 2 is related to the current in coil 1 through the mutual inductance M: =

The mutual induction acts both ways, meaning that either coil’s voltage will be the sum of voltages due to

the mutual inductance as well as the self-inductance. This means that if we close the loop on the secondary

side, the induced current will act back thus changing the network equations to:

= :m:( :m:(

= :m:( :m:(

In the case of coupled air coils the mutual inductances M12 and M21 are equal and only denoted M.

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The fraction of flux generated by the first coil that flows through the second coil (and vice versa) is denoted

k and it is related to M in the following manner: = !"

Normally we assume a coupling factor k of 1 for a transformer to simplify computations. This however does

not hold true for coupled air coils, which means that the network model for such a system must take this

into account. We will now quickly revisit the ideal transformer equations, prior to addressing the coupling

factor’s impact on the network equations.

Influence of low k

For the consideration of a transformer with a coupling lower than 1, a real transformer with a coupling

between 0 and 1 is shown in fig. 42.

fig. 42: Non-ideal transformer

We have some finite inductances Lp and Ls, but the non-ideal coupling means that only a fraction of these

inductances will contribute to the transforming action. Intuitively we can make the abstraction that the

apparent inductances Lp and Ls consist of a wanted as well as an unwanted part, namely the primary,

secondary and two leakage inductances.

Recalling that we previously established that: 1. the coupling coefficient k denotes the fraction of flux

generated by the primary that is intercepted by the secondary (and vice versa) and 2. the inductance is

proportional to the coils ability to capture its own flux we can extend the model above by assuming that

the inductances can be distinguished by multiplication with the entities k and (1-k) .

Continue by developing T model (Sadiko; Charles p.539), then the adding of ideal transformer (riedel p.

792-795) and finally reduce to primary side (schuyl p.47) See handwritten notes

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12.5 Original figure “Pole-splitting Effect”

As copied from “The Concepts of Inductive Powering” page 66

fig. 43: Original figure: ”Pole Splitting Effect”

12.6 Series resonant capacitor differential voltage figure

fig. 44: V-I characteristics of primary series capacitor

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12.7 MATLAB script LLC calculations

close all;

clear all;

clc;

format short eng;

set(0,'DefaultFigureWindowStyle','docked');

% Hong Huang calculations

V_DC=24; % 10-32 V

f_0=200e3;

f_sw=linspace(f_0/10,f_0*10,1000);

w_0=2*pi*f_0;

f_n=f_sw/f_0;

n=1; % turns ratio Ns/Np

V_out=24; %[V] DC

I_out=1.25; %[A] DC

k=0.42; % from EF measurements

theta_v=0; % phase angle between v_oe and v_ge

t=linspace(0,10/f_0,1001);

R_load=V_out/I_out;

Rs=0.150; % [Ohm] approx. from FEMM

L_A=23.83e-6; % from EF measurements

L_B=23.86e-6;

Lr=(1-k^2)*sqrt(L_A*L_B);

Lm=k^2*sqrt(L_A*L_B);

Cr=1/((2*pi*f_0)^2*Lr) % matching cap at load 0 0 Ohm, should be at 19.2 (2.473)

Ln=Lm/Lr

fp=1/(2*pi*sqrt((Lr+Lm)*Cr)) % resonant frequency at no load

% Relationship of electrical variables

v_ge=2/pi*V_DC*sin(2*pi*f_0*t); % fundamental component of the square wave

v_ge_RMS=sqrt(2)/pi*V_DC; % RMS of fundamental frequency

v_oe=(k/n)*(4/pi)*V_out*sin(2*pi*f_0*t-theta_v);

v_oe_RMS=(2*sqrt(2))/pi*(k/n)*V_out;

i_oe_RMS=pi/(2*sqrt(2))*(n/k)*I_out;

i_oe_ex=1.11*((1.25/0.9)/0.42)

R_e=v_oe_RMS/i_oe_RMS % three ways of calculating the same

R_e2=(8/pi^2)*(k/n)^2*(V_out/I_out) % --||--

R_e3=(8/pi^2)*(k/n)^2*(R_load)%+Rs) % --||--

Qe=sqrt(Lr/Cr)/(R_e+Rs) % Q of loaded coil (transmitter?)

%Qe2=

X_Cr=1./(i.*2.*pi.*f_sw.*Cr);

X_Lr=i.*2.*pi.*f_sw.*Lr;

X_Lm=i.*2.*pi.*f_sw.*Lm;

I_m_RMS=v_oe_RMS/(2*pi*f_0*Lm); % two ways of calculating RMS magnetizing current

I_m_RMS2=(2*sqrt(2))./pi.*(k/n).*(V_out./(2*pi*f_0*Lm)); % --||--

I_r=sqrt(I_m_RMS.^2+i_oe_RMS.^2);

% Voltage-Gain function for LCC driven coils, based on Hong Huang

Mg_DC=(k/n)*(V_out/V_DC)*(1/2);

% approximating Mg_DC ~ Mg_sw = V_so/V_sq

% substituting V_so & V_sq with their fundamental components v_ge & v_oe:

Mg_AC=v_oe/v_ge;

% now Mg_AC will be denoted Mg only

% The transfer function is the voltage division between (Cr+Lr) and (Lm||Re)

Lm_par_R_e=1./(X_Lm.^-1+R_e^-1);

Mg=Lm_par_R_e./(Lm_par_R_e+(X_Lr+X_Cr));

% hence V_out = Mg*n*(V_in/2)

semilogx(f_sw/f_0,abs(Mg));

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12.8 Schematic, Transmitter

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12.9 Schematic, Receiver

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12.10 Schematic, AT88V piggyboard

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12.11 Simulation circuits, section 5.1

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12.12 Pictures of the proposed system

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wireless powering of maritime satellite transceiveretd.dtu.dk/thesis/ihk-11327962/wpt_report.pdf ·...

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