RAVI KUMAR. A & RAMA CHANDRA. M

--The Wireless Electricity.

By

1) History of Wireless power.

2) Need of Witricity.

3) Basic Principle.

4) Range & Rate of Coupling.

5) Design of Parameters and Simulation.

6) Pros and Cons.

History of Wireless Power: In 1899, Sir Nikola Tesla Proposed a method of Wireless Power Transmission.

As it is in Radiative mode, most of the Power was wasted and has less efficiency.

The efficient midrange power transfer concept is Witricity. In this model source and load are in Magnetic resonance so there is no power loss.

Need of Witricity:Now a days there is a Rapid development of autonomous

electronics like Laptops, Cell-phones, House-hold robots and all those devices typically rely on chemical energy storage(Battery) As they are becoming daily needs to present generation, Wire less energy transfer would be useful for many applications as above and they need midrange energy.

Basic Principle:The basic principle involved in Witricity concept is,

Two objects having same resonating frequency and in Magnetic resonance at Strongly coupled regime tend to exchange energy , while dissipating relatively little energy to the extraneous off-resonant objects.

Experimental Design:Our experimental scheme consists of two Self-resonant

coils. One coil (source coil) is coupled inductively to an oscillating circuit; the other (device coil) is coupled inductively to a resistive load. Self-resonant coils rely on the interplay between distributed inductance and distributed capacitance to achieve resonance.

Range & Rate of Coupling:

Using Coupled Mode Theory (CMT), we can give some frame work to the system. The field system of the two resonant objects 1, 2 is

F(r,t)=a1(t)F1(r)+a2(t)F2(r)

Where F1,2(r) are the resonating modes of 1 and 2 alone, and then the field amplitudes a1(t) and a2(t).The lower order representation of the system is given by :

Where ω1, 2 are the individual frequencies, Γ1, 2 are the Resonance widths (Decay rates) due to the objects’ intrinsic (absorption, radiation etc.) losses, and ‘κ’ is the coupling coefficient .

The solution of the equation show that at exact resonance at

ω1=ω2 and Γ1=Γ2

the normal modes of the combined system are split by 2κ.

The energy exchange between the two objects takes place in time Pi/κ and is nearly perfect, apart for losses, which are minimal when the coupling rate is much faster than all loss rates (κ>> Γ1, 2).

It is exactly this ratio {κ /sqrt (Γ1, 2)} shows that, it will set as figure-of-merit for any system under consideration for wireless energy-transfer, along with the distance over which this ratio can be achieved.

The desired optimal regime {κ/sqrt (Γ1,2)>>1} is called “Strong-Coupling” regime. There is No change in Energy, unless κ/Γ>>1 is true.

Design of parameters:The coupled mode theory plays a vital role in solving the lower

order equations of the system. Using perturbation technique of x(t)=A cos(ω 0t)+ B sin(ω 0t)

The solution of this equation is by including decay rate due to loss Γ0X(t)=C exp(-i ω 0t)exp(-t/ Γ0)

Why the Perturbation technique??All these fields are by Damped oscillator. The details of the

damping mechanism is unknown to us, but the rate of energy loss due to damping known and it is small. So perturbation technique is the approach to solve these equations when the details is unknown to us. To solve the above equation considered a laser cavity and loss rates due to absorption and radiation is taken into account and finally found that κ/Γ ratio is proportional to the quality factor.

Consider two loops at distance D between their centers, radius r1 and r2 of conducting wire with circular cross-section of radius ‘a’ and diameter ‘d’.via a dielectric of relative permittivity ε and everything surrounded by air.

To calculate the RLC parameters used the method called Finite-Element Frequency-Domain (FEFD) simulations (for Maxwell’s equations solving purpose) and Perturbation methods, we get the following formulae.

Formulation for Simulation:

κ= ωM/2*sqrt(L1L2)

L= μ0 r[ln(8r/a)] C= ε0ε a/D η=sqrt(μ0/ ε0)

M={(Pi/2)* μ0* ( r1r2)^2}/D^3Rabs≈ {(Pi/6)η r/a} Rrad≈{(Pi/6)η r/a } Qabs≈ωL/ Rabs Qrad≈ ωL/ Rrad

Simulation model Using COMSOL:

Simulation Performance: By the basic parameters, calculated results and performance given with and Without the External object in between the coils.

Comparison of ResultsComparison of Results::

Two loops D/r Qrad Q=ω/2Γ ω/2κ κ/ Γ

R=30cm,a=2mm,ε=10,d=4mm,Qabs=4886.

3 30729 4216 63.7 68.7

5 29577 4194 248 17.8

Results without Extraneous objects:

Results with Extraneous objects:

Two loops D/r Qrad Q=ω/2Γ ω/2κ κ/ Γ

R=30cm,a=2mm,ε=49+16i,d=4mm,Qabs=4886.

3 30729 4136 62.6 67.4

5 29577 4106 235 17.6

Advantages:

☼ Unaffected by the day night cycle, weather or seasons.

☼ This is an eco friendly system..

☼ It is boon for the devices which uses midrange power.

Limitations:

☼ The resonance condition should be satisfied and if any error exists, there is no possibility of power transfer.

☼ If there is any possibility of very strong ferromagnetic material presence causes low power transfer due to radiation.

Wireless Electricity concept is a boon for devices which uses midrange energy. The Power transfer is explained with the help of Magnetic resonance and Coupled mode theory. By the above paper, we can conclude the below points. i) The optimal regime of efficient power transfer is Strongly coupled regime.ii) High κ/Γ ratio gives high power output. For no changes in κ/Γ ratio, there is no change in power transfer. iii) After designed the parameters with FEFD method and simulating for the κ/Γ ratio changes with and without the external objects, we can conclude that there is no large variation in κ/Γ ratio.

1. An article published in the Science Magazine as “Wireless Power Transfer via Strongly Coupled Magnetic Resonances” by Andre kurs, Science 317, 83(2007); Dol:10.1126/ science.1143254.

2. H. Haus , “Waves and Fields in Optoelectronics”, Prentice hall Publishers, Englewood

3. http://electron9.phys.utk.edu/optics507/modules/m6/coupled_resonators.htm

4. “Efficient Non-Radiative Midrange Energy Transfer” by Aristeidies karalis, Marlin Soljacic.

5. Website: www.comsol.com6. Tutorials of COMSOL Software-Acoustics and RF Module

Tool.