Wireless Energy Transfer

Minor Project Report

on

‘WIRELESS ENERGY TRANSFER’

Submitted by Sriram Venkateshan (B. Tech EE IV)

Sreshtha Mohan (B. Tech EE IV)

Submission Date: 06.12.2010

Wireless energy transfer

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Acknowledgements

We are greatly indebted to Prof Pramod Agarwal for accepting to guide us in

such an unorthodox topic, that we chose for this project and for providing us full

support in all respects. We thank Prof Vipul Rastogi for referring us to the

appropriate material and helping us understand the concepts involved. We thank

Mr. Gautam, for assisting us with the lab work, procuring us the needed

components, instruments, and allowing us to work in the lab. We also thank our

close classmate Mohit Choradia for sharing/spending time with us throughout the

time we worked on this project.


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Table of contents

Acknowledgements 1

Table of contents 2

List of figures and tables 3

1. Abstract 4

2. Introduction 5

3. The Evanescent Magnetic Field

3.1. The far field 7

3.2. The near field 7

3.2.1. The radiative near field 8

3.2.2. The reactive near field 8

3.3. Summary 9

3.4. Alternative explanation for the method of coupling 9

4. Theory 11

4.1. Analysis of the scheme 11

4.2. Theoretical model for self-resonant coils 15

4.3. Simulation and results 17

5. Design and description of the experimental setup 21

5.1. Design of the coils 22

5.2. Design of the supply 22

5.3. Design of the load 23

6. Experimental observations and results 24

6.1. Frequency characteristics 24

6.2. Distance characteristics 25

6.3. Observational remarks 26

7. Conclusions 27

References 28


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List of Figures and tables

Fig. 1 Theoretical frequency characteristics

Fig. 2 Theoretical distance characteristics

Fig. 3 Schematic of the experimental setup

Fig. 4 Non-inverting amplifier circuit using OPA 548

Fig. 5 Experimental frequency characteristics

Fig. 6 Experimental distance characteristics

Fig. 7 Scheme for implementation of the discussed scheme in DC load

applications

Table. 1 Experimental readings for frequency characteristics

Table. 2 Experimental readings for distance characteristics


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1. Abstract

Wireless energy transfer based on coupled magnetic resonances is a new technology which

energy can be transferred via coupled magnetic resonances in the non-radiative near field. A

simple energy transfer system structure is analyzed in this project. Based on the power and

distance specifications of the energy transfer in question, the experimental setup is designed

and with available resources, realized. The back electromotive force (back-EMF) in the receiving

coil and the efficiency of the transfer related with different transfer distance and with driving

frequency is observed with the realized apparatus. These results, along with the theoretical

predictions for the same, can be used to prove that the scheme used is appropriate for energy

transfer over midrange distances. Some basic modifications which could be done to improve

the scheme’s performance, but could not implemented due to lack of time and resources, are

also suggested.


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2. Introduction

In the early days of electromagnetism, before the electrical wire grid was deployed, serious

interest and effort was devoted (most notably by Nikola Tesla) towards the development of

schemes to transport energy over long distances without any carrier medium (i.e. wirelessly).

These efforts appear to have met with little success. Radiative modes of omni-directional

antennas (which work very well for information transfer) are not suitable for such energy

transfer, because a vast majority of energy is wasted into free space.

Directed radiation modes, using lasers or highly-directional antennas, can be efficiently used for

energy transfer, even for long distances (transfer distance LTRANS >> LDEV, where LDEV is the

characteristic size of the device), but require existence of an uninterruptible line-of-sight and a

complicated tracking system in the case of mobile objects. The use of such schemes in layman

applications is very complex and thus limited.

However, unlike the time of Tesla, now we are faced with an entirely different challenge. Since

the existing electrical-wire grid carries energy almost everywhere, transmission of power over

long distances for power wheeling, is not at all in the question. Even a medium-range (LTRANS ≈

few LDEV) wireless energy transfer would be quite useful for many applications. Rapid

development of autonomous electronics of recent years (e.g. laptops, cell-phones, house-hold

robots, that all typically rely on chemical energy storage) which has led to invention of various

gadgets, justifies revisiting investigation of this issue.

Wireless energy transfer involves the second major difficulty as the radiation of the energy into

space. This is due to two primary problems: one, which is the efficiency. For radiation of energy,

a significant amount of energy could get radiated into free space and thus wasted. This would

drastically decrease the efficiency. The second is the concern on the safety of the scheme, and

its effects with respect to life and health. Because of the above reasons, normally non-radiative

schemes are preferred.

There are several currently used schemes, which rely on non-radiative modes (magnetic

induction), but they are restricted to very close-range (LTRANS << LDEV). In contrast to all the

above schemes, an experiment conducted at the Massachusetts Institute of Technology

investigated the feasibility of using oscillatory resonant electromagnetic modes, with localized

evanescent field patterns, for efficient wireless non-radiative mid-range energy transfer. The

proposed method is based on the well known principle of resonant coupling (the fact that two

same-frequency resonant objects tend to couple, while interacting weakly with other off-

resonant environmental objects) and, in particular, resonant evanescent coupling (where the


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coupling mechanism is mediated through the overlap of the non- radiative near fields of the

two objects). This well known physics leads trivially to the result that energy can be efficiently

coupled between objects in the extremely near field (e.g. in optical waveguide or cavity

couplers and in resonant inductive electric transformers). Detailed theoretical analysis shows

that even an efficient mid-range wireless energy exchange can actually be achieved, while

suffering only modest transfer and dissipation of energy into other off-resonant objects,

provided the exchange system is carefully designed to operate in a regime of ‘‘strong coupling’’

compared to all intrinsic loss rates. The physics of ‘‘strong coupling’’ is also known but in very

different areas, such as those of light-matter interactions. In this favorable operating regime,

the following question can be addressed quantitatively: up to which distances can such a

scheme be efficient and how sensitive is it to external perturbations? The omni-directional but

stationary nature of the near field makes this mechanism suitable for mobile wireless receivers.

It could therefore have a variety of possible applications including for example, placing a source

(connected to the wired electricity network) on the ceiling of a factory room, while devices

(robots, vehicles, computers, or similar) are roaming freely within the room. Other possible

applications include electric engine buses, RFIDs, and perhaps even nano-robots.


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3. The evanescent magnetic field

The coupling of the two systems used in transmission, can be done in any manner, until the

resonant modes of the oscillation in both the systems match. However, if the coupling occurs

with every object, no efficient transfer would occur. Thus, reactive magnetic fields are being

used in the scheme considered. The field surrounding a transmitting system can be categorized

as follows:

3.1. The far field

The far-field region is the region in space around the oscillator, where the angular field

distribution is essentially independent of distance from the source. In the far field, the shape of

the angular energy distribution is independent of distance from the transmitting oscillator. If

the source has a maximum overall dimension ‘D’ that is large compared to the wavelength ‘λ’,

the far-field region is commonly taken to exist at distances from the source, greater than

Fresnel parameter S = D2/(4λ), S > 1.

3.2. The near field

The near-field, which is inside about one wavelength distance from the transmitter, is a region

in which there are strong inductive and capacitive effects from the currents and charges in the

transmitter, which do not behave like far-field radiation. These effects decrease in power far

more quickly with distance, than does the far-field radiation power. Also, absorption of radiated

power in this region does have effects which feedback to the transmitter, increasing the load on

the transmitter that feeds the transmitter by decreasing the system impedance that the

transmitter sees. Thus, the transmitter can sense that power has been absorbed from the near-

field zone, and if this power is not absorbed, the transmitter does not draw as much power. The

transition zone between these regions is the distance from one to two wavelengths from the

source, in which both near and far field effects are important, and in which near field behavior

dies out and ceases to become important, leaving far-field effects as the dominant interaction.

The near field is further divided into two sub parts, as below:


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3.2.1. The radiative near field

This field is seen where the effects of the feedback cannot be clearly seen due to significant lag

in phase between the feedback and generated fluxes. This field does not contribute to any extra

power input from the source as its effect is not detected at the transmitter at all.

3.2.2. The reactive near field

In a close range to the source, (the terminology just implies that the range is small compared to

the far field transmission distances used in radio communications) the relationship between the

strengths of the E and H fields is often too complex to predict. Both field component (E or H)

may dominate at one point, and the opposite relationship dominate at a point only a short

distance away. This makes finding the true power density in this region problematic. This is

because to calculate power, not only E and H both have to be measured, but the phase

relationship between E and H must also be known. In this reactive region, not only is an

electromagnetic wave being radiated outward into far-space, but there is a "reactive"

component to the electromagnetic field, meaning that the nature of the field around the

transmitter is sensitive to, and reacts to, EM absorption in this region (this is not true of

absorption far from the transmitter, which has no effect on the transmitter or the near-field).

Very close to the transmitter, in the reactive region, energy of certain amount, if not absorbed

by a receiver is held back and is stored very near the transmitter surface. This energy is carried

back and forth from the transmitter to the reactive near-field by electromagnetic radiation of

the type that slowly changes electrostatic and magneto-static effects. For example, current

flowing in the transmitter creates a purely magnetic component in the near-field, which then

collapses as the transmitter current begins to reverse, causing transfer of the field's magnetic

energy back to electrons in the transmitter as the changing magnetic field causes a self-

inductive effect on the transmitter that generated it. This returns energy to the transmitter in a

regenerative way, so that it is not lost. A similar process happens as electric charge builds up in

one section of the transmitter under the pressure of the signal voltage, and causes a local

electric field around that section of transmitter, due to the transmitter's self-capacitance. When

the signal reverses so that charge is allowed to flow away from this region again, the built-up

electric field assists in pushing electrons back in the new direction of their flow, as with the

discharge of any uni-polar capacitor. This again transfers energy back to the transmitter

current.

Because of this energy storage and return effect, if either of the inductive or electrostatic

effects in the reactive near-field does transfer energy to electrons in a different (nearby)

conductor, this energy is lost to the primary source, and thus an extra drain is seen on the


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transmitter circuit, resulting from the reactive near-field energy which is not returned. This

constitutes the coupling that is required in the Coupled Mode Theory (CMT) equations.

3.3. Summary

Solving Maxwell's equations for the electric and magnetic fields for a localized oscillating

source, such as an antenna, surrounded by a homogeneous material (typically vacuum or air),

yields fields that, far away, decay in proportion to ‘1/r’ where r is the distance from the source.

These are the radiating fields, and the region where r is large enough for these fields to

dominate is the far field. More generally, the fields of a source in a homogeneous isotropic

medium can be written as a multi-pole expansion. The terms in this expansion are spherical

harmonics (which give the angular dependence) multiplied by spherical Bessel functions (which

give the radial dependence). For large r, the spherical Bessel functions decay as 1/r, giving the

radiated field above. As one gets closer and closer to the source (smaller r), approaching the

near field, other powers of r become significant. The next term that becomes significant is

proportional to 1/r2 and is sometimes called the induction term. It can be thought of as the

primarily magnetic energy stored in the field, and returned to the transmitter in every half-

cycle, through self-induction. For even smaller r, terms proportional to 1/r3 become significant;

this is sometimes called the electrostatic field term and can be thought of as stemming from

the electrical charge in the transmitter element.

Very close to the source, the multipole expansion is less useful (too many terms are required

for an accurate description of the fields). Rather, in the near field, it is sometimes useful to

express the contributions as a sum of radiating fields combined with evanescent fields, where

the latter are exponentially decaying with r.

3.4. Alternate explanation for the method of coupling

The fields around a transmitter can be thought of as due to two main reasons. They are given

below.

The transmitter itself, when visualized as a waveguide, gives rise to several modes of

oscillations within it. Some modes, due to indices of the material of the transmitter and the

surrounding medium, portray themselves as leaky, and thus the radiative fields originate in the

space around the transmitter. Also due to TIR at the surface of the so called waveguide, the

incident wave is totally manifested as the reflected wave inside the material. This gives rise to a

non travelling wave solution in free space, which decays in the direction perpendicular to

wavefronts of the solution, which are called evanescent waves.


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Mathematically,

…3.1

represents the real power of the wave. As all the power of the incident wave is seen at the

reflected wave, assuming lossless reflection, the wave at the transmitter surface has either

…3.2

or

As, the medium outside need not be lossless, the first case is impossible. So, by second case,

the wave ceases to be a travelling wave. However, the conclusion from the fact that the

absorbed energy is zero is from the fact that, if there was a coupling through these evanescent

waves, and power was consumed by them, the source would just feed in the extra power to

maintain the power in the transmitter waveguide unchanged. So, a coupling with these waves

can produce an energy transfer as needed.

Also, as these waves do not die out with time, they can be stable and thus maintain the energy

transfer method with any attenuation with time. These waves, for a coil as the transmitter, are

predominantly magnetic and thus do not harm people and life. So, they can be used without

any difficulties. Moreover, normal substances, which may block the line of sight between

transmitter and receiver, are diamagnetic and thus do not change the field, thus producing no

effect on the power transferred.


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4. Theory

4.1. Analysis of the scheme

Using the above discussions, we can start analyzing the scheme. The range and rate of the

proposed wireless energy-transfer scheme are the first subjects of examination, without

considering yet energy drainage from the system for use into work.

Efficient midrange power transfer occurs in particular regions of the parameter space

describing resonant objects strongly coupled to one another. An appropriate analytical

framework for modeling this resonant energy-exchange is that of the well-known coupled-

mode theory (CMT). Using coupled-mode theory to describe this physical system, we obtain

the following set of linear equations:

…4.1

where F1,2(r) are the eigenmodes of 1 and 2 alone, and then the field amplitudes a1(t) and a2(t)

can be shown to satisfy, to lowest order:

…4.2

where

where the indices denote the different resonant objects. The variables am(t) are defined so that

the energy contained in object m is |am(t)|2, ωm is the resonant angular frequency of that

isolated object, and Γm is its intrinsic decay rate (e.g. due to absorption and radiated losses). In

this framework, an uncoupled and undriven oscillator with parameters ω0 and Γ0 would evolve

in time.


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This is given by

…4.3

The κmn = κnm are coupling coefficients between the resonant objects indicated by the

subscripts, and Fm(t) are driving terms.

We limit the treatment to the case of two objects, denoted by source and device, such that the

source (identified by the subscript S) is driven externally at a constant frequency, and the two

objects have a coupling coefficient κ. Work is extracted from the device (subscript D) by means

of a load (subscript W) that acts as a circuit resistance connected to the device, and has the

effect of contributing an additional term ΓW to the unloaded device object’s decay rate ΓD. The

overall decay rate at the device is therefore Γ’D = ΓD + ΓW. The work extracted is determined by

the power dissipated in the load, that

…4.4

Taking the case of two objects as above, the equations are

…4.5

…4.6

Here, the source has a forcing term, which is the supply. But the receiver side has no source,

but on the other hand, has an extra loss term representing the load on the receiver coil.

Differentiating the two equations, we get

…4.7


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…4.8

Using the equations 4.7, 4.8 and substituting 4.5 and 4.6 in them, we get

…4.9

…4.10

Multiplying by appropriate terms and adding 4.9 and 4.10 to eliminate aD(t), we get

…4.11

This can be solved in the frequency realm to yield a result, through Laplace transforms as

…4.12

…4.13

In frequency domain, s = iω, so

…4.14


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The efficiency is given by

…4.15

Substituting 4.14 in 4.15 and maximizing G by putting ω=ωD, we get

…4.16

To maximize this efficiency, differentiate 4.16 with respect to ΓW, and equate to 0. Then we get

…4.17

Substituting 4.17 into 4.16, we get

…4.18

This increases when the term,

So, this is chosen as the figure of merit for the scheme.

This is commonly referred to as the strong coupling regime. Resonance plays an essential role in

this power transfer mechanism, as the efficiency is improved by approximately ω2/ΓD2 (≈106 for

typical parameters) relative to the case of inductively coupled non-resonant objects.


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4.2. Theoretical model for self-resonant coils

The experimental realization of the scheme consists of two self-resonant coils. One coil (the

source coil) is coupled inductively to an oscillating circuit; the other (the device coil) is coupled

inductively to a resistive load. (Fig. 5.1, page 21). Self-resonant coils rely on the interplay

between distributed inductance and distributed capacitance to achieve resonance. The coils are

made of an electrically conducting wire of total length ‘l’ and cross-sectional radius a wound

into a helix of n turns, radius r, and height h. Assuming the simple quasi-static model,

calculations are made for the field distributions of the helical coils. It can be observed that the

current must be zero at the ends of the coil, and we can make the educated guess that the

resonant modes of the coil are well approximated by sinusoidal current profiles along the

length of the conducting wire. We are interested in the lowest mode, so if we denote by s the

parameterization coordinate along the length of the conductor, such that it runs from −l/2 to

+l/2, then the time-dependent current profile has the form I0 cos(πs/l) exp(iωt).

It follows from the continuity equation for charge that the linear charge density profile is of the

form l0 sin(πs/l) exp(iωt), so that one-half of the coil (when sliced perpendicularly to its axis)

contains an oscillating total charge (of amplitude q0=λl/π) that is equal in magnitude but

opposite in sign to the charge in the other half. As the coil is resonant, the current and charge

density profiles are π/2 out of phase from each other, meaning that the real part of one is

maximum, when the real part of the other is zero. Equivalently, the energy contained in the coil

is at certain points in time completely due to the current, and at other points it is completely

due to the charge. Using electromagnetic theory, we can define an effective inductance L and

an effective capacitance C for each coil as follows:

…4.19

where

N=number of turns

R=radius of the coil

μr=relative permeability

μ0=permeability of free space

a=cross-sectional radius of the wire


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…4.20

Where the formula is just empirical and gives an approximate of the capacitance, in conjunction

with the geometry of the object. As defined, L and C have the property that the energy U

contained in the coil is given by

…4.21

Given this relation and the equation of continuity, the resulting resonant frequency is

…4.22

We can now treat this coil as a standard oscillator in coupled-mode theory by defining

…4.23

We can estimate the power dissipated by noting that the sinusoidal profile of the current

distribution implies that the spatial average of the peak current squared is |I0|2/2. For a coil

with n turns and made of a material with conductivity σ, we modify the standard formulas for

Ohmic (Ro) and radiation (Rr) resistance accordingly:

…4.24

…4.25


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The first term in Eq. is a magnetic dipole radiation term (assuming r << 2πc/ω, where c is the

speed of light); the second term is due to the electric dipole of the coil and is smaller than the

first term for our experimental parameters. The coupled-mode theory decay constant for the

coil is therefore Γ = (Ro + Rr)/2L, and its quality factor is Q = ω/2Γ.

We find the coupling coefficient κDS by looking at the power transferred from the source to the

device coil, assuming a steady-state solution in which currents and charge densities vary in time

as exp(iωt):

…4.26

where M is the effective mutual inductance, the subscript S indicates the current in the source.

We can then conclude from standard coupled-mode theory arguments that

…4.27

When the distance D between the centers of the coils is much larger than their characteristic

size, κ scales with the D−3 dependence characteristic of dipole-dipole coupling. Both κ and Γ are

functions of the frequency, and κ/Γ and the efficiency are maximized for a particular value of f.

Thus, picking an appropriate frequency for a given coil size, as we do in this experimental

demonstration, plays a major role in optimizing the power transfer.

4.3. Simulation and results

The above equations are used to calculate the performance of the setup theoretically. Using

the solution of the differential equations mentioned above, and the parameters given below,

we get the plots which are shown later.

MATLAB is used for the calculation and plotting of results. The code implemented and the

resulting plots are shown below. Here, the values of the setup dimensions and parameters are

taken the same as the values for which the experimental apparatus is designed, for the sake of

clear comparison of the results.


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%INIT.m:

%Constants

j=sqrt(-1);

MU0=4*pi*1e-7;

EPSILON0=8.8541878e-12;

c=3e8;

%Source specifications

Vs=8;

%OMEGA=2*pi*2e5;

%Apparatus dimensions and materials

%D=.1; %Distance

RL=5000; %Load resistance

%Source end:

ap=.8e-3; %Cross sectional radius of

the source coil

Rp=4.55e-2; %Radius of the source coil

Np=53; %Number of turns in source

coil

N=13; %Cross sectional radius of

the transmitter coil

a=1.8e-3; %Radius of the transmitter

coil

R=5.64e-2; %Number of turns in

transmitter coil

SIGMA=5.8e7; %Conductivity of transmitter

coil

%Circuit parameters


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L=(N^2)*R*MU0*(log(8*R/a)-2);

C=1e-8;

OMEGA1=1/sqrt(L*C);

R0=(sqrt(MU0*OMEGA/(2*SIGMA)))*N*R/2/a;

Rr=(sqrt(MU0/EPSILON0))*pi*(N^2)*((OMEGA*R/c)^4)/12;

%Performance analysis

GAMMA=(R0+Rr)/(2*L);

M=pi*MU0*N*N*((R*R)^2)/(4*(D^3));

KAPPA=OMEGA*M/(2*sqrt(L*L));

GAMMAw=RL*((N/Np)^2)/2/L;

F=(N/Np)*Vs/sqrt(L/2);

Gds=j*KAPPA/(j*OMEGA-j*OMEGA1+GAMMA+GAMMAw);

AmpGds=abs(Gds);

ETA=GAMMAw*(AmpGds^2)/(GAMMA+(GAMMA+GAMMAw)*(AmpGds^2));

%END

%MAIN CODE:

D=0.12;

for i=400:1000

OMEGA=2*pi*i*1e3;

freq(i)=OMEGA/2/pi;

INIT

eff(i)=ETA;

end

OMEGA=2*pi*612e3;

for i=1:100

D=i*2e-3;

dis(i)=D;

INIT

eff(i)=ETA;

end


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The plots using the simulation are shown below:

Frequency Characteristics

Fig. 1

Distance Characteristics

Fig. 2


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5. Design and description of the experimental

setup

With respect to the specifications of power and distance of the power transfer, the system is

designed as shown below. The equations used, which are also shown side by side, are all

derived from the basic equations of 3.

Specifications:

Supply voltage = 10 V amplitude.

Maximum power transfer distance = 20 cm

Maximum power that may be transferred ≈ 10 W

Maximum current through the input or output side = 2 A

The schematic of the experimental setup is shown in the figure below

Fig 3

A is a thin copper coil of radius 4.64 cm that is part of the driving circuit, which outputs a sine

wave with frequency 100-1000 kHz. S and D are respectively the source and device coils

referred to in the text. B is a loop of wire attached to the load (light bulb). The first coupling

from the source is inductive, as the distance is very small and the frequencies do not match

very well. The same can be said on the load end as well, where the load and the receiver coil do

not have matching resonant frequencies. The middle coupling is made strongly resonant by

careful construction of the two coils, which are completely similar. However, a weak direct

coupling also occurs from the source to load coil due to similarity in their construction.


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5.1. Design of the coils

As the evanescent field propagation is upto 1 to 1.5 times the device size, for 20 cm, let the

diameter of the coils be 10 cm.

So, R = 5 cm

Resonant frequency of the coil is dependent on both the inductance and the capacitance, which

would yield the resonant frequency near a midrange of the supply capacity i.e. 500 kHz, if we

choose a cross-sectional diameter of 1.626 mm (from the standard wire gauge to support

maximum 2A with copper having tolerance 4A /mm2), we would have to take on

C = 0.98463 nF

So, for a given resonant frequency as 500 kHz,

L = 0.10504 mH

Then the value of N is

N ≈ 14 turns

The experimental values of inductance agree with the theoretical prediction. So the resonant

frequency would come in the required range. Now, for the source and load coils, if we design

both with the same dimensions for the ease of construction,

as the maximum driving current of the supply is 100 mA, the no load current should be 1

percent of this, making the inductance of the coil as

L = 0.31 mH, designing at 50 kHz

Then for a small diameter, which yields higher inductance, the value of N can be calculated as

N > 32

A large value of N is chosen to make to safe for low frequencies as well. Thus, N ≈ 50

5.2 Design of the supply

The supply provided was capable of handling 100 mA at a high frequency, and should give a

true sine wave at this frequency. The primary idea would be to construct a power oscillator.

But, as this involves a lot of high frequency components (as is the case with any power amplifier

for the high frequency), we use a power Opamp, OPA 548.


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The basic non-inverting amplifier circuit using the OPA 548 is shown below

Fig. 4

Without the capacitances, the opamp can still function properly without, any damage and

fluctuation in the output. So, the above circuit is used without the capacitors shown. The supply

signal to the power opamp is given by a function generator with peak amplitude as 15 V. The

regulated dc supply is used for biasing the opamp. Gain is set at 10 by putting R1 = 1 kΩ and R2 =

10 kΩ. Supply in put is adjusted for a faithful output without clipping at saturation levels.

5.3 Design of the load

Though a more suitable load could be chosen, a simple resistance in series with small LED’s

could serve the same purpose without any hindrances. The values of ΓW calculated for optimum

efficiency is 5-10.

So, for the above inductance of the load coil, the resistance is 10-30 kΩ.

Waveforms for measurement of efficiency are all observed through a cathode ray oscilloscope.


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6. Experimental observations and results:

6.1. Frequency characteristics

The setup is supplied with various frequencies at a fixed distance, and the frequency response of the scheme is

checked. As expected theoretically, the resonance can be observed. The readings are shown below

Supply voltage = 7.625 V Supply resistance = 100 Ω Load resistance =10 kΩ Distance = 10 cm Time lag between the current and voltage = 434 ns Time period of the input voltage = 1.738 μs So, pf = 1.807 × 10-3

Frequency (kHz)

Input Voltage(mV)

Load Voltage(mV)

Input power(μW)

Load power(μW)

Efficiency (%)

500 303 186 41.7 3.459 8.29

520 316 237.25 43.55 5.628 12.92

540 327 269.75 45.07 7.276 16.14

560 334 266.25 46.03 7.088 15.39

580 347 241 47.82 5.8081 12.14

600 358 208.25 49.34 4.336 8.788 620 366 183 50.44 3.349 6.639

640 380 161.75 52.37 2.616 5.00

660 389 144.5 53.61 2.088 3.89

680 400 132.75 55.13 1.762 3.196

700 411 123.75 56.64 1.531 2.703

Table 1

Fig. 5


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6.2. Distance characteristics

Frequency = 552 kHz

Supply voltage = 7.19 V

Supply resistance = 100 Ω

Time lag between the current and voltage waveforms of the input = 434 ns

Time period of the supply voltage = 1.811 μs

Power factor angle = 89.8˚

Distance (cm)

Supply Voltage(mV)

Load Voltage(mV)

Supply power(μW)

Load power(μW)

Efficiency (%)

3 331 586 83.07 34.34 41.34

4 325 535 81.57 28.62 35.09

5 327 439 82.07 19.27 23.48

6 329 379 82.57 14.36 17.39

7 327 337 83.07 11.36 13.68

8 327 308 83.07 9.49 11.42

9 325 286 81.57 8.18 10.03

12 327 275 82.07 7.56 9.21

15 333 273 83.58 7.45 8.91

Table 2

Fig. 6


26

6.3 Observational remarks

Characteristics of the scheme shows that the efficiency is maximum at a specific

frequency, proving that this is not the ordinary inductive coupling, through which the

energy transfer is taking place.

The efficiency of the scheme decreases as the cube of the distance due to the variation

of the mutual inductance of the two coils in consideration.

The difference in theoretical and experimental observations is apparent, and can be

explained in the following ways

o Tuning is intrinsic and the exact matching of resonant frequencies has not been

achieved. This is due to the fact that tuning would require variable inductances

or capacitances to fine tune the resonance of the two coils.

o The system realized, though easy in analyzing, consists of two inductive coupled

systems (one at the source and the transmitting coil, the other at the load and

receiving coil). This causes considerable leakage and leads to low power factors.

The input power measurement, which has been primarily done through

measurement of voltages, currents and time lag between them, gets adversely

affected by the low pf, as even a small error in the measurement of the time lag,

causes a considerable change in the pf, and thus the input power. (Output power

is measured just by the square of the output voltage).

The low power involved in the experiment is mainly due to lack of an appropriate power

supply. This could be solved by use of high frequency power oscillators.


27

7. Conclusions

Mid range energy transfer is observed to be possible by evanescent magnetic field

coupling, and the efficiency is significant enough for low power (upto a few watts)

applications.

The range of transfer, as determined by the characteristic size of the devices, could be

maintained unchanged even when decreasing the size of the receiver, by making the

product of the sizes of both devices constant. Hence, although the two coils are

currently of identical dimensions, it is possible to make the device coil small enough to

fit into portable devices without decreasing the efficiency.

Though in our considered apparatus, tuning has been inherent and required no external

tuning, we can still conclude that the matching of the resonant modes of both the coils

plays the most important role in the energy transfer. A slight detuning would cause the

system to deliver near zero power.

External objects have a noticeable effect only when they are within a few centimeters

from either one of the coils. Some materials (such as aluminum foil, Styrofoam, and

humans) mostly just shift the resonant frequency, which can in principle be easily

corrected with a feedback circuit; other materials (cardboard, wood, and polyvinyl

chloride) lower Q when placed closer than a few centimeters from the coil, thereby

lowering the efficiency of the transfer.

Using appropriate drive circuitry for the supply side could facilitate the derivation of the

high frequency supply needed for the transfer, and a high frequency rectifier on the

load end, would enable the scheme to power dc loads and devices. Such a scheme is

shown below.

Fig. 7


28

References

[1] André Kurs, Aristeidis Karalis, Robert Moffatt, J. D. Joannopoulos, Peter Fisher, Marin Soljacic “Wireless Power Transfer via Strongly Coupled Magnetic Resonances”

SCIENCE, Volume 317, 6 July 2007. (www.sciencemag.org)

[2] Aristeidis Karalis, J.D. Joannopoulos, Marin Soljacic “Efficient wireless non-radiative mid-range energy transfer”

Annals of Physics 323, (2008) 34-48. (Accepted 17 April 2007)

[3] www.wikipedia.org

[4] Herman A.Haus, Weiping Huang “Coupled Mode Theory”

Proceedings of the IEEE, Vol. 79, No. 10 October 1991 – Invited Paper.

[5] B. E. Little and W. P. Huang “Coupled Mode Theory for optical waveguides”

Progress in Electromagnetics Research, PIER 10, 217-270, 1995.

[6] Chunbo Zhu, Kai Liu , Chunlai Yu, Rui Ma, Hexiao Cheng, “Simulation and Experimental Analysis on Wireless Energy Transfer Based on Magnetic Resonances”

IEEE Vehicle Power and Propulsion Conference, September 3-5, 2008, Harbin.

[7] Henk F. Arnoldus “Evanescent waves in the magnetic field of an electric dipole”

Journal of Modern Optics, No. 9, 15 June 2005, 1215-1241.

[8] David W. Knight “The self-resonance and self-capacitance of solenoid coils”

Version 0.01, 9 May 2010. (www.g3ynh.info).

[9] Shahrzad Jalali Mazlouman, Alireza Mahanfar, Bozena Kaminska “Mid-range Wireless Energy Transfer Using Inductive Resonance for Wireless Sensors”

Proceedings of IEEE, Vol. 978, 517-522, 2009.

[10] Ajoy K. Ghatak, K. Thyagarajan “An introduction to fiber optics”

Cambridge University Press, 1998.

[11] Carlo G Someda “Electromagnetic waves”

CRC Press, January 2006.

[12] Texas Instruments - high-voltage, high-current operational amplifier OPA548T datasheet.

http://www.wikipedia.org/

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