wireless power transmission

Wireless Power Transmission through Inductive Resonance Coupling REPORT OF MINOR PROJECT-I – BAEP-611 SUBMITTED IN THE PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF

Master of Technology In (Engineering Physics) By Rohit yadav 01240809712 Under the Supervision of Dr. Kriti Batra Assistant Professor /Associate Professor /Professor University School of Basic And Applied Sciences Guru Gobind Singh Indraprastha University Sector 16-C, Dwarka, Delhi-110075

University School of Basic and Applied Sciences

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Guru Gobind Singh Indraprastha University Sector 16-C, Dwarka, Delhi-110075 (Batch 2012-2014)

CERTIFICATE This is to certify that the report, entitled " Wireless Power Transmission through Inductive Resonance Coupling" is a record of the minor project presentation (BAEP-611, Minor Project-I, First Semester) done by Rohit Yadav for the fulfillment of the M.Tech Engineering Physics degree course in the School of Basic and Applied Science, GGS Indraprastha University under my guidance and supervision.

(Dr.Kriti Batra ) Assistant Professor /Associate Professor /Professor University School Of Basic And Applied Sciences Guru Gobind Singh Indraprastha University Sector 16-C, Dwarka, Delhi-110075

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ACKNOWLEDGEMENT I would like to articulate my profound gratitude and indebtedness to my project guide, Dr. Kriti Batra, who has always been a constant motivation and guiding factor throughout the project duration. It has been a great pleasure for me to get an opportunity to work under her and complete the minor project successfully. An undertaking of this nature could never have been attempted without reference to and inspiration from the works of others whose details are mentioned in references section. I acknowledge my indebtedness to all of them.

ROHIT YADAV (01240809712)

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INDEX 1. Introduction 2. Problem Statement 3. Research • Nikolai Tesla • Space Satellite System • Microsystems and Micro sensor Power Supply 4. Possible Solutions • Antenna • Inductive Coupling • Laser Power Transmission 5. Operating Frequency • Very High and Greater Frequency Ranges • Very Low to Extremely Low Frequency Ranges • Low, Medium and High Frequency Ranges 6. Theoretical Background 7. Safety and FCC regulations 8. Conclusion 9. References

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I. INTRODUCTION

Wireless power transmission is the means to power devices without a built in power source such as a generator or battery. There are multiple needs and uses for such technology. One initial use of such technology is found in powering small devices where much of the size of the device is in the battery itself. By eliminating the battery in a small device it would be possible to compact the device even further. Furthermore, on a larger scale as consumable energy sources on the planet are dwindling in number it remains an important task to look to the future. If it was possible to transmit power wirelessly it would be economical to retrieve power from outer space and simply transmit it back to the planet’s surface as an endless power source. In my initial research i have that discovered many have looked into the feasibility of wireless power transmission and there are many solutions that all offer promise. I chose to research the feasibility of wireless power transmission through inductive coupling. This consists of using a transmission and receiving coils as the coupling antennas. Although the coils do not have to be solenoid they must be in the form of closed loops to both transmit and receive power. To transmit power an alternating current must be passed through a closed loop coil. The alternating current will create a time varying magnetic field. The flux generated by the time varying magnetic field will then induce a voltage on a receiving coil closed loop system. This seemingly simple system outlines the major principle that my research investigated. The primary benefits to using inductive coupling are the simplicity of the transmission and receiving antennas, additionally for small power transmission this is a much safer means of conveyance.

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II. Problem Statement

For the completion of this project I was asked to study the mechanism of wireless transfer of power of an AC oscillating waveform into a DC voltage on the receiving end which will be used to light a bulb to demonstrate instantaneous power transfer.

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III. HISTORY

Nikolai Tesla Nikolai Tesla was the first to develop the designs for wireless power transmission. Tesla was famed for his work in the research and work with alternating current. His wireless research began with his original transformer design and though a series of experiments that separated the primary and the secondary coils of a transformer. Tesla performed many wireless power transmission experiments near Colorado Springs. InTesla’s experimentation, Tesla was able to light a filament with only a single connection to earth. Tesla’s findings lead him to design the Wardenclyffe plant as a giant mushroom shaped wireless power transmitter. Tesla was never able to complete construction of this project.

Space Satellite System The concept of wireless power transmission has been an area of research that the U.S. Department of Energy (D.O.E.) and the National Aeronautical Space Administration (NASA) have been working to develop. NASA has been looking into research to develop a collection of satellites with the capability to collect solar energy and transmit the power to earth. The current design for project by NASA and DOE is to use microwaves to transfer power to rectifying antennas on earths. Similar to this system, NASA and DOE have put research into using laser technology to beam power to earth. Japan’s National Space Development Agency (NASDA) has also been performing this variety of research to use satellite and laser technology to beam power to earth. Japan is expected to have the laser technology developed by 2025. The use of laser technology would theoretically eliminate many of the problems that could occur with the use of 7

microwaves. This laser satellite system is unlikely to be devolved by the United States due to current treaties with Russia preventing either nation from having satellites with high power laser technology. This treaty was created to prevent either nation from completing President Regan’s “Star Wars” project.

Microsystems and Micro sensor Power Supply Currently, the use of inductive coupling is in development and research phases. There several different projects that use inductive coupling to create alternatives for batteries. One developed at the Tokyo Institute of Technology is to develop a power supply for a medical sensor while it is left inside the human body. In this system, power was transmitted by both electromagnetic waves when at close distance to the transmitter an also by magnetic flux when at farther distances. The receiver portion utilizes a cascade voltage booster to charge capacitors within the device to provide the necessary power to the system. Another similar project, done at Louisiana State University in Baton Rouge, uses inductive coupling in a similar method recharge an internal small battery in a small bio-implanted microsystem.

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IV. POSSIBLE SOLUTIONS In my research, as well as practical knowledge, i knew of three possibilities to design a device. There are the use of antennas, inductive coupling, and laser power transfer. In addition, i had to be aware of how antennas and inductive coupling would be affected by the frequency we select.

Antenna Antennas are the traditional means of signal transmission and would likely work. In initial research, it appears that system utilizing antennas can receive power gains based upon the shape and design of the antenna. This would allow more power actually being sent and received while also have a small input power. The difficulty comes in the trade off of antenna size versus frequency. In attempting to stay in a lower frequency, one would be require using antennas of very large size.

Inductive Coupling Inductive coupling does not have the need for large structures transfer power signals. Rather, inductive coupling makes use of inductive coils to transfer the power signals. Due to the use of coils rather than the antenna, the size of the actual transmitter and receiver can be made to fit the situation better. The tradeoff is for the benefit of customize, there will be a poor gain on the solenoid transmitter and receiver.

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Laser Power Transmission The concept of laser power transmission is addressed in the research of NASA and NASDA solar programs. Lasers would allow for a very concentrated stream of power to be transferred from one point to another. Based upon available research material, it appears that this solution would be more practical for space to upper atmosphere or terrestrial power transmission. This option would not be valid to accomplish tasks because light wavelengths are higher than the specified allowable operational frequencies.

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V. OPERATING FREQUENCY

Very High and Greater Frequency Ranges High frequency transmissions are common in several devices including cell phones and other wireless communications. Higher frequencies can be made to transmit in very specific directions. In addition, these antennas can be rather small. This set of frequency ranges includes microwave frequency bands. Very High Frequencies to Extremely High frequencies are described as being in the range of 30 MHz to 300 GHz and Microwave frequencies are described as being the range of 3 GHz to 300 GHz. The safety issues of using the high end of the spectrum are not completely known. There is currently research looking into the safety of microwave and higher frequencies. However, many of the devices in this frequency range are not permissible due to the frequency limitations placed on our research.

Very Low to Extremely Low Frequency Ranges Antennas of these frequencies would need to be of sizes that are very impractical to build and would be better suited for power transmission over wire. Several of these frequencies are specifically used for submarine communication transmission. Extremely low frequencies and possibly other frequencies in the band up to 3 KHz have the uncertain risk of being potentially hazardous the humans and the environment. There is still ongoing research on the dangers on very low to extremely low range frequencies.

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Low, Medium, and High Frequency Ranges Radio Frequencies in these bands seem to have few hazardous concerns given by the FCC. In addition, these frequencies are commonly used as the primary frequency bands of radio transmission. The high frequency band is typically used in short range communications due to the ease of the reflection of these waves off the ionosphere. This range is described as being from 3 MHz to 30 MHz. In addition, this frequency range includes two experimental frequency bands. The major disadvantage of working in this frequency range is the inability to properly test in the design phase due to effects parasitic capacitance in breadboards . Medium Frequency includes the AM broadcast band. Medium frequencies are described as being from300 KHz to 3 MHz This band includes one band used for testing purposes. The Low frequency band is primarily used for aircraft, navigation, information and weather systems. In addition, this frequency includes a band commonly used for testing purposes. The low frequency band is described as being from30 KHz to 300 KHz.

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VI. Theoretical Background The power transmission system utilizes the concepts of transformer theory. In a basic single phase transformer as shown in figure 1, when the primary coil is connected to an AC source, a time varying flux is produced in the core. This flux is confined within the magnetic core. If another coil is added on the same core, the flux links the second coil inducing voltage at its terminals given by the equation ,where N is the number of turns of the secondary coil and φ is the flux generated. Furthermore if a load is connected across the terminals of the coil, current flows across the load. V = -N (∂φ/∂t)

The system follows the same concepts of Faraday’s law of electromagnetic induction, but with two major differences. The system is an air core transformer i.e. there is no solid magnetic core 13

that confines the flux produced at the primary. This means that there is high flux leakage and only a portion of the flux generated induces an emf across the secondary coil. Moreover in our system the primary and secondary coils are two feet apart, which results in low flux linkage, low coupling, and even lower power transfer. Therefore the biggest challenge in this project is to maximize the flux linkage between the primary and secondary coils to be able to transfer enough power to light a bulb at the given distance.

Self-Inductance and Inductive Reactance The property of self-inductance is a particular form of electromagnetic induction. Self inductance is defined as the induction of a voltage in a current-carrying wire when the current in the wire itself is changing. In the case of self-inductance, the magnetic field created by a changing current in the circuit itself induces a voltage in the same circuit. Therefore, the voltage is self-induced.

The term inductor is used to describe a circuit element possessing the property of inductance and a coil of wire is a very common inductor. In circuit diagrams, a coil or wire is usually used to indicate an inductive component. Taking a closer look at a coil will help understand the reason that a voltage is induced in a wire carrying a changing current. The alternating current running through the coil creates a magnetic field in and around the coil that is increasing and decreasing as the current changes. The magnetic field forms concentric loops that surround the wire and join to form larger loops that surround the coil as shown in the image below. When the current increases in one loop the expanding magnetic field will cut across some or all of the neighboring loops of wire, inducing a voltage in these loops. This causes a voltage to be induced in the coil when the current is changing.

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By studying this image of a coil, it can be seen that the number of turns in the coil will have an effect on the amount of voltage that is induced into the circuit. Increasing the number of turns or the rate of change of magnetic flux increases the amount of induced voltage. Therefore, Faraday's Law must be modified for a coil of wire and becomes the following.

Where: VL = induced voltage in volts N = number of turns in the coil dø/dt = rate of change of magnetic flux in Webers/second The equation simply states that the amount of induced voltage (VL) is proportional to the number of turns in the coil and the rate of change of the magnetic flux (dø/dt). In other words, when the frequency of the flux is increased or the number of turns in the coil is increased, the amount of induced voltage will also increase. 15

In a circuit, it is much easier to measure current than it is to measure magnetic flux, so the following equation can be used to determine the induced voltage if the inductance and frequency of the current are known. This equation can also be reorganized to allow the inductance to be calculated when the amount of inducted voltage can be determined and the current frequency is known.

Where: VL = the induced voltage in volts L = the value of inductance in henries di/dt = the rate of change of current in amperes per second Lenz's Law Soon after Faraday proposed his law of induction, Heinrich Lenz developed a rule for determining the direction of the induced current in a loop. Basically, Lenz's law states that an induced current has a direction such that its magnetic field opposes the change in magnetic field that induced the current. This means that the current induced in a conductor will oppose the change in current that is causing the flux to change. Lenz's law is important in understanding the property of inductive reactance, which is one of the properties measured in eddy current testing.

Inductive Reactance The reduction of current flow in a circuit due to induction is called inductive reactance. By taking a closer look at a coil of wire and applying Lenz's law, it can be seen how inductance reduces the flow of current in the circuit. In the image below, the direction of the primary current is shown in red, and 16

the magnetic field generated by the current is shown in blue. The direction of the magnetic field can be determined by taking your right hand and pointing your thumb in the direction of the current. Your fingers will then point in the direction of the magnetic field. It can be seen that the magnetic field from one loop of the wire will cut across the other loops in the coil and this will induce current flow (shown in green) in the circuit. According to Lenz's law, the induced current must flow in the opposite direction of the primary current. The induced current working against the primary current results in a reduction of current flow in the circuit.

It should be noted that the inductive reactance will increase if the number of winds in the coil is increased since the magnetic field from one coil will have more coils to interact with.

Similarly to resistance, inductive reactance reduces the flow of current in a circuit. However, it is possible to distinguish between resistance and inductive reactance in a circuit by looking at the timing between the sine waves of the voltage and current of the alternating current. In an AC circuit that contains only resistive components, the voltage and the current will be in-phase, meaning that the peaks and valleys of their sine waves will occur at the same time. When there is inductive 17

reactance present in the circuit, the phase of the current will be shifted so that its peaks and valleys do not occur at the same time as those of the voltage.

Mutual Inductance The magnetic flux through a circuit can be related to the current in that circuit and the currents in other nearby circuits, assuming that there are no nearby permanent magnets. Consider the following two circuits.

The magnetic field produced by circuit 1 will intersect the wire in circuit 2 and create current flow. The induced current flow in circuit 2 will have its own magnetic field which will interact with the magnetic field of circuit 1. At some point P, the magnetic field consists of a part due to i1 and a part due to i2. These fields are proportional to the currents producing them.

The coils in the circuits are labeled L1 and L2 and this term represents the self inductance of each of the coils. The values of L1 and L2 depend on the geometrical arrangement of the circuit (i.e. number of turns in the coil) and the conductivity of the material. The constant M, called the mutual inductance of the two circuits, is dependent on the geometrical arrangement of both circuits. In particular, if the circuits are far apart, the magnetic flux through circuit 2 due to the current i1 will be small and the mutual inductance will be small. L2 and M are constants. 18

We can write the flux,

B

through circuit 2 as the sum of two parts. B2

= L2i2 + i1M

An equation similar to the one above can be written for the flux through circuit 1. B1

= L1i1 + i2M

Though it is certainly not obvious, it can be shown that the mutual inductance is the same for both circuits. Therefore, it can be written as follows:

M1,2 = M2,1 Series RLC circuit

In this circuit, the three components are all in series with the voltage source. The governing differential equation can be found by substituting into Kirchhoff's voltage law (KVL) the constitutive equation for each of the three elements. From KVL,

where

are the voltages across R, L and C respectively and

from the source. Substituting in the constitutive equations,

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is the time varying voltage

For the case where the source is an unchanging voltage, differentiating and dividing by L leads to the second order differential equation:

This can usefully be expressed in a more generally applicable form:

and

are both in units of angular frequency. is called the neper frequency, or attenuation, and is

a measure of how fast the transient response of the circuit will die away after the stimulus has been removed. Neper occurs in the name because the units can also be considered to be nepers per second, neper being a unit of attenuation.

is the angular resonance frequency.

For the case of the series RLC circuit these two parameters are given by:

and

A useful parameter is the damping factor, which is defined as the ratio of these two,

In the case of the series RLC circuit, the damping factor is given by,

The value of the damping factor determines the type of transient that the circuit will exhibit. Some authors do not use and call the damping factor. 20

Transient response The differential equation for the circuit solves in three different ways depending on the value of . These are under damped (

), over damped (

) and critically damped (

). The differential

equation has the characteristic equation.

The roots of the equation in s are,

The general solution of the differential equation is an exponential in either root or a linear superposition of both,

The coefficients A1 and A2 are determined by the boundary conditions of the specific problem being analysed. That is, they are set by the values of the currents and voltages in the circuit at the onset of the transient and the presumed value they will settle to after infinite time.

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Overdamped response The over damped response (

) is,

The over damped response is a decay of the transient current without oscillation. Underdamped response The under damped response (

) is,

By applying standard trigonometric identities the two trigonometric functions may be expressed as a single sinusoid with phase shift,

The under damped response is a decaying oscillation at frequency

. The oscillation decays at a

rate determined by the attenuation . The exponential in describes the envelope of the oscillation. B1 and B2 (or B3 and the phase shift in the second form) are arbitrary constants determined by boundary conditions. The frequency

is given by,

This is called the damped resonance frequency or the damped natural frequency. It is the frequency the circuit will naturally oscillate at if not driven by an external source. The resonance frequency, which is the frequency at which the circuit will resonate when driven by an external oscillation, may often be referred to as the undamped resonance frequency to distinguish it.

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Critically Damped Response The critically damped response (

) is,

The critically damped response represents the circuit response that decays in the fastest possible time without going into oscillation. This consideration is important in control systems where it is required to reach the desired state as quickly as possible without overshooting. D1 and D2 are arbitrary constants determined by boundary conditions

Resonant coupling Non-resonant coupled inductors, such as typical transformers, work on the principle of a primary coil generating a magnetic field and a secondary coil subtending as much as possible of that field so that the power passing though the secondary is as close as possible to that of the primary. This requirement that the field be covered by the secondary results in very short range and usually requires a magnetic core. Over greater distances the non-resonant induction method is highly inefficient and wastes the vast majority of the energy in resistive losses of the primary coil.

Using resonance can help improve efficiency dramatically. If resonant coupling is used, each coil is capacitively loaded so as to form a tuned LC circuit. If the primary and secondary coils are resonant at a common frequency, it turns out that significant power may be transmitted between the coils over a range of a few times the coil diameters at reasonable efficiency. Resonance occurs because energy is stored in two different ways: in an electric field as the capacitor is charged and in a magnetic field as current flows through the inductor. Energy can be transferred 23

from one to the other within the circuit and this can be oscillatory. A mechanical analogy is a weight suspended on a spring which will oscillate up and down when released. This is no passing metaphor; a weight on a spring is described by exactly the same second order differential equation as an RLC circuit and for all the properties of the one system there will be found an analogous property of the other. The mechanical property answering to the resistor in the circuit is friction in the spring/weight system. Friction will slowly bring any oscillation to a halt if there is no external force driving it. Likewise, the resistance in an RLC circuit will "damp" the oscillation, diminishing it with time if there is no driving AC power source in the circuit. The resonance frequency is defined as the frequency at which the impedance of the circuit is at a minimum. Equivalently, it can be defined as the frequency at which the impedance is purely real (that is, purely resistive). This occurs because the impedance of the inductor and capacitor at resonance are equal but of opposite sign and cancel out. Circuits where L and C are in parallel rather than series actually have maximum impedance rather than minimum impedance. For this reason they are often described as anti resonators, it is still usual, however, to name the frequency at which this occurs as the resonance frequency.

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The sharpness of the peak in the resonance response curve for a particular physical system is often expressed in terms the “quality factor” or “quality” of the resonance, given by the Q value of the resonance (not to be confused with the charge Q on the capacitor). This number can be read directly from the resonance curve. If we call ω1 the frequency where the current has risen, at the left of the peak, to 1/√2 times the peak current, and ω2 the frequency where it has fallen to this same value at the right of the peak, then if ω0 is the peak frequency, the Q value is

with the result that, for R/L >> ω0, the Q value is given in terms of the inductance and 25

resistance of the RLC circuit by

As seen from Eq. the Q value is determined in part by the damping. Weaker damping corresponds to smaller resistance, therefore to larger Q, and hence to a sharper resonance peak. Mechanical systems have Q values below 100, while electromagnetic resonators can reach Q values of 104or 106, and atomic systems can have Q values as high as 1010.

The quantity δ expressing the relative phase of the current and driving voltage in Eqs. and varies with frequency in the manner shown in Fig. 3. Right at resonance, δ = 0, so that the current and voltage are in phase. At very low frequencies, the capacitor is seen in Eq. to be the dominant hindrance to the flow of current, and δ is positive. The 26

current then “leads the voltage” as shown in Fig. 4 (meaning that the current reaches its maximum values before the voltage). At frequencies higher than ω0 the inductor dominates. The phase is negative and “the current lags the voltage” as shown in Fig. 5. The higher the Q(corresponding to small Rand weak damping) the more abruptly δ shifts from positive to negative values as the frequency varies across the resonance peak. A change in phase of the sort shown in Fig. 3 is also a unique signature of a resonating system.

Series Resonance Frequency

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Impedance in a Series Resonance Circuit

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Series RLC Circuit at Resonance

Series Circuit Current at Resonance

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The frequency response curve of a series resonance circuit shows that the magnitude of the current is a function of frequency and plotting this onto a graph shows us that the response starts at near to zero, reaches maximum value at the resonance frequency when IMAX = IR and then drops again to nearly zero as ƒ becomes infinite. The result of this is that the magnitudes of the voltages across the inductor, L and the capacitor, C can become many times larger than the supply voltage, even at resonance but as they are equal and at opposition they cancel each other out.

As a series resonance circuit only functions on resonant frequency, this type of circuit is also known as an Acceptor Circuit because at resonance, the impedance of the circuit is at its minimum so easily accepts the current whose frequency is equal to its resonant frequency. The effect of resonance in a series circuit is also called "voltage resonance".

You may also notice that as the maximum current through the circuit at resonance is limited only by the value of the resistance (a pure and real value), the source voltage and circuit current must 30

therefore be in phase with each other at this frequency. Then the phase angle between the voltage and current of a series resonance circuit is also a function of frequency for a fixed supply voltage and which is zero at the resonant frequency point when: V, I and VR are all in phase with each other as shown below. Consequently, if the phase angle is zero then the power factor must therefore be unity.

Phase Angle of a Series Resonance Circuit

Notice also, that the phase angle is positive for frequencies above ƒr and negative for frequencies 31

below ƒr and this can be proven by,

Bandwidth of a Series Resonance Circuit If the series RLC circuit is driven by a variable frequency at a constant voltage, then the magnitude of the current, I is proportional to the impedance, Z, therefore at resonance the power absorbed by the circuit must be at its maximum value as P = I2Z. If we now reduce or increase the frequency until the average power absorbed by the resistor in the series resonance circuit is half that of its maximum value at resonance, we produce two frequency points called the half-power points which are -3dB down from maximum, taking 0dB as the maximum current reference.

These -3dB points give us a current value that is 70.7% of its maximum resonant value as: 0.5( I2 R ) = (0.707 x I)2 R. Then the point corresponding to the lower frequency at half the power is called the "lower cut-off frequency", labeled ƒL with the point corresponding to the upper frequency at half power being called the "upper cut-off frequency", labeled ƒH. The distance between these two points, i.e. ( ƒH - ƒL ) is called the Bandwidth, (BW) and is the range of frequencies over which at least half of the maximum power and current is provided as shown.

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The frequency response of the circuits current magnitude above, relates to the "sharpness" of the resonance in a series resonance circuit. The sharpness of the peak is measured quantitatively and is called the Quality factor, Q of the circuit. The quality factor relates the maximum or peak energy stored in the circuit (the reactance) to the energy dissipated (the resistance) during each cycle of oscillation meaning that it is a ratio of resonant frequency to bandwidth and the higher the circuit Q, the smaller the bandwidth, Q = ƒr /BW.

As the bandwidth is taken between the two -3dB points, the selectivity of the circuit is a measure of its ability to reject any frequencies either side of these points. A more selective circuit will have a narrower bandwidth whereas a less selective circuit will have a wider bandwidth. The selectivity of a series resonance circuit can be controlled by adjusting the value of the resistance only, keeping all the other components the same, since Q = (XL or XC)/R.

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Two inductively coupled RLC circuits Two inductively coupled RLC circuits are shown in Figure 6. Having 2 circuits gives 2 resonant frequencies whose separation depends on the value of the mutual inductance M (the ratio of the voltage in the secondary to the rate of change of primary current with time, and the unit is the henry. This has a reactance at the operating frequency Xm= ωM)

The mutual inductance coupling between primary and secondary can be related to their selfinductance by means of the coupling constant k:

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Notice, that since k is defining the relationship between magnetic flux linkages in the circuit, it can never be greater than 1. A value of 1 means that all the flux produced by the primary is linked with the secondary and vice versa. A value of k greater than 1 would mean that more than all of the flux produced by the primary is linked with the secondary. The coupling constant is independent of the number of turns in a coil. The number of turns in a coil determines the magnetic field, which will be produced for a given current. The coupling constant is concerned with how the lines of magnetic force produced by one coil interact with another coil, and hence the coupling constant between two air spaced coils depends only on their physical size and disposition in space. Hence to obtain the best coupling between primary and secondary in an aircored transformer we can only change the size and spatial relationships of the coils.

Kirchhoff’s voltage law equations for the primary and secondary loops are given by

(it is assumed that R1+RL1= R2+RL2=R and L1= L2). We can write these eqs. in the matrix form as follows

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Thus, the solution from which the frequency response can be obtained is:

Resonance occurs at the 2 frequencies given by the following equations:

Here, the coupling coefficient k = M/L (for L1=L2). The behavior of the circuit can be understood qualitatively on the basis of the reflected impedance(or coupled impedance). A transformer (or inductively coupled circuit) is said to "reflect" impedance in the secondary into the primary circuit. Consider the coupled circuits shown in Fig6. The positive direction of the currents is chosen into the polarity mark on the generator representing the induced voltages, so that Kirchhoff's equations are

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ZMis the mutual impedance jωM, Z1includes the source impedance, and Z2the secondary load. These equations may be solved for the equivalent primary impedance

At resonance, the reflected impedance is resistive, and acts to lower the Q of the primary, and thereby to reduce the output. This is counteracted by the increased coupling, which increases the output. The lower Q gives a wider passband. At frequencies lower than exact resonance, the reflected impedance is inductive, which adds to the inductance of the primary and resonates at a lower frequency, producing a peak in the output. At frequencies higher than exact resonance, the reflected impedance is capacitive, which cancels part of the inductance and causes the circuit to resonate at a higher frequency, producing the other peak. As the coupling is reduced, the response becomes single-peaked at critical coupling, and then decreases as the coupling is made even looser.

The critical coupling coefficient is given by

in terms of the Q's of the individual tuned circuits. Frequently it is assumed that optimum coupling occurs for k ≈1.5kc. In this case, the response is double-peaked, but does not dip much between the peaks and the response is close to what is ideally required. The bandwidth can be estimated as BW = kfo, where k is the coefficient of coupling and fo is the resonant frequency of each circuit.

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VII. Safety and FCC regulations The FCC regulations are put in place first to limit the use of particular frequency bandwidths. In doing so, the FCC prevents multiple users from occupying the same frequency band and interfering with one another. In addition, the FCC also regulates power emissions of a variety of different devices. The project is an intentional radiator as well as working with radio frequency (RF) energy. The FCC defines an intentional radiator as: A device that intentionally generates and emits radio frequency energy by radiation or induction. The FCC defines radio frequency energy as: Electromagnetic energy at any frequency in the radio spectrum between 9 kHz and 3,000,000 MHz. For this project, the frequency band of 160-190 KHz was selected. The frequency of 160-190 KHz is an open test band that does not require any special permission to work in the frequency range. This frequency range contains three limiting factors. The limitations of this frequency are the following: • Total input power into the final radio frequency stage shall not exceed 1 watt. • The total length of transmission line, antenna, and ground lead shall not exceed 15 meters. • All emissions below 160 kHz and above 190 kHz shall be attenuated at least 20 dB below the level of the unmodulated carrier.

Radiation in the frequency band of 160 KHz to 190 KHz does not seem particularly hazardous at such low power levels. In general, it is suggested to remain a distance radius of 6 inches away from the transmitter and not standing in the direction of transmission. Additionally avoid exposure to children under a body weight of 50 lbs. 38

During the testing procedure, radiation from the transmitter did not affect cell phones, calculators, and digital watches. Direct effects of the radiation of the system on medical devices, such as pace makers, are unknown. It is recommended that people with medical implants remain a distance of 1 meter away from the transmitter as a precaution.

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VIII. CONCLUSIONS

The feasibility of wireless power transfer through inductive resonance coupling is the definite aim of my project. While it is possible to transmit and receive power using inductive coupling it has some finite drawbacks. The maximum distance is of 2 meters where we can receive power effectively.

The efficiency between transmitted power and received power decreases with increase in distance.

At a distance greater than 2 meters inductive coupling is far inefficient in its current state.

However inductive coupling still has a definite future in short range transmission distance. This particularly has medical implementations to transmit a few inches to power a remote sensor implanted in human body. Now a days inductive resonance coupling is used by many industries to power their products like cell phones, inductive cooker, wireless television and many more.

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IX. REFRENCES.

1. Wireless power transmission utilizing a phased array of tesla coil by Joseph C. Stark III, Thesis for M.E in electrical engg. , MIT. 2. Wikipedia 3. Feynman lectures Vol.1 & 2 4. Video lectures from you tube website 5. C L Arora , S Chand publications 6. Code of Federal Regulations, Title 47, Volume1,Revised as of October 1, 2003 ,Fromthe 7. U.S. Government Printing Office via GPO Access, CITE: 47CFR15.3, Page 686-689 8. “Category:Radio spectrum-Wikipedia, the free encyclopedia,” [online document], 2004 Aug 9.

26 [cited 12/11/04], http://en.wikipedia.org/wiki/Category:Radio_spectrum.

10.U.S. Department of Energy, “Energy Savers: Solar Power Satellites,” [online document] rev 11. 200

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