# Resonant inductive coupling

(Redirected from Resonant transformer)

Resonant inductive coupling, Synchronized Magnetic-flux Phase Coupling or electrodynamic induction is the near field wireless transmission of electrical energy between two coils that are tuned to resonate at the same frequency. The equipment to do this is sometimes called a resonant or resonance transformer. While many transformers employ resonance, this type has a high Q and is often air cored to avoid 'iron' losses. The two coils may exist as a single piece of equipment or comprise two separate pieces of equipment.

Resonant transfer works by making a coil ring with an oscillating current. This generates an oscillating magnetic field. Because the coil is highly resonant, any energy placed in the coil dies away relatively slowly over very many cycles; but if a second coil is brought near it, the coil can pick up most of the energy before it is lost, even if it is some distance away. The fields used are predominately non-radiative, near field (sometimes called evanescent waves), as all hardware is kept well within the 1/4 wavelength distance they radiate little energy from the transmitter to infinity.

One of the applications of the resonant transformer is for the CCFL inverter. Another application of the resonant transformer is to couple between stages of a superheterodyne receiver, where the selectivity of the receiver is provided by tuned transformers in the intermediate-frequency amplifiers.[1] Resonant transformers such as the Tesla coil can generate very high voltages with or without arcing, and are able to provide much higher current than electrostatic high-voltage generation machines such as the Van de Graaff generator.[2] Resonant energy transfer is the operating principle behind proposed short range (up to 2 metre)[3] wireless electricity systems such as WiTricity or Rezence and systems that have already been deployed, such as Qi power transfer, passive RFID tags and contactless smart cards.

## Resonant coupling

Basic transmitter and receiver circuits, Rs and Rr are the resistances and losses in the associated capacitors and inductors. Ls and Lr are coupled by small coupling coefficient, k, usually below 0.2

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 through 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.[4]

### Coupling coefficient

k is the coupling coefficient, Le1 and Le2 is the Leakage inductance

The coupling coefficient is the fraction of the flux of the primary that cuts the secondary coil, and is a function of the geometry of the system. The coupling coefficient, k, is between 0 and 1.

Systems are said to be tightly coupled, loosely coupled, critically coupled or overcoupled. Tight coupling is when the coupling coefficient is around 1 as with conventional iron-core transformers. Overcoupling is when the secondary coil is so close that it tends to collapse the primary's field, and critical coupling is when the transfer in the passband is optimal. Loose coupling is when the coils are distant from each other, so that most of the flux misses the secondary, in Tesla coils around 0.2 is used, and at greater distances, for example for inductive wireless power transmission, it may be lower than 0.01.

### Energy transfer and efficiency

The general principle is that if a given oscillating amount of energy (for example a pulse or a series of pulses) is placed into a primary coil which is capacitively loaded, the coil will 'ring', and form an oscillating magnetic field. The energy will transfer back and forth between the magnetic field in the inductor and the electric field across the capacitor at the resonant frequency. This oscillation will die away at a rate determined by the gain-bandwidth (Q factor), mainly due to resistive and radiative losses. However, provided the secondary coil cuts enough of the field that it absorbs more energy than is lost in each cycle of the primary, then most of the energy can still be transferred.

The primary coil forms a series RLC circuit, and the Q factor for such a coil is:

$Q = \frac{1}{R} \sqrt{\frac{L}{C}} \,$,

For R=10 ohm,C=1 micro farad and L=10 mH, Q is given as 10.

Because the Q factor can be very high, (experimentally around a thousand has been demonstrated[5] with air cored coils) only a small percentage of the field has to be coupled from one coil to the other to achieve high efficiency, even though the field dies quickly with distance from a coil, the primary and secondary can be several diameters apart.

It can be shown that a figure of merit for the efficiency is:[6]

$U = k \sqrt{Q_1 Q_2}$

Where Q1 and Q2 is the Q factor of the source and receiver coils.

And the maximum achievable efficiency is:[6]

$\eta_{opt} = \frac {U^2} {(1 + \sqrt{1 + U^2}) ^ 2}$

### Power transfer

Because the Q can be very high, even when low power is fed into the transmitter coil, a relatively intense field builds up over multiple cycles, which increases the power that can be received—at resonance far more power is in the oscillating field than is being fed into the coil, and the receiver coil receives a percentage of that.

### Voltage gain

The voltage gain of resonantly coupled coils is directly proportional to the square root of the ratio of secondary and primary inductances.

### Transmitter coils and circuitry

Unlike the multiple-layer secondary of a non-resonant transformer, coils for this purpose are often single layer solenoids (to minimise skin effect and give improved Q) in parallel with a suitable capacitor, or they may be other shapes such as wave-wound litz wire. Insulation is either absent, with spacers, or low permittivity, low loss materials such as silk to minimise dielectric losses.

Colpitts oscillator. In resonant energy transfer the inductor would be the transmitter coil and capacitors are used to tune the circuit to a suitable frequency.

To progressively feed energy/power into the primary coil with each cycle, different circuits can be used. One circuit employs a Colpitts oscillator.[5]

In Tesla coils an intermittent switching system, a "circuit controller" or "break," is used to inject an impulsive signal into the primary coil; the secondary coil then rings and decays.

The receiver of a smart card has a coil connected to a chip which provides capacitance to give resonance as well as regulators to provide a suitable voltage

The secondary receiver coils are similar designs to the primary sending coils. Running the secondary at the same resonant frequency as the primary ensures that the secondary has a low impedance at the transmitter's frequency and that the energy is optimally absorbed.

Example receiver coil. The coil is loaded with a capacitor and two LEDs. The coil and the capacitor form a series LC circuit which is tuned to a resonant frequency that matches the transmission coil located inside of the brown matt. Power is transmitted over a distance of thirteen inches.

To remove energy from the secondary coil, different methods can be used, the AC can be used directly or rectified and a regulator circuit can be used to generate DC voltage.

## History

This advanced Tesla coil was designed to implement wireless power by means of the disturbed charge of ground and air method.

In 1894 Nikola Tesla used resonant inductive coupling, also known as "electro-dynamic induction" to wirelessly light up phosphorescent and incandescent lamps at the 35 South Fifth Avenue laboratory, and later at the 46 E. Houston Street laboratory in New York City.[7][8][9] In 1897 he patented a device[10] called the high-voltage, resonance transformer or "Tesla coil." Transferring electrical energy from the primary coil to the secondary coil by resonant induction, a Tesla coil is capable of producing very high voltages at high frequency. The improved design allowed for the safe production and utilization of high-potential electrical currents, "without serious liability of the destruction of the apparatus itself and danger to persons approaching or handling it."

In the early 1960s resonant inductive wireless energy transfer was used successfully in implantable medical devices[11] including such devices as pacemakers and artificial hearts. While the early systems used a resonant receiver coil, later systems[12] implemented resonant transmitter coils as well. These medical devices are designed for high efficiency using low power electronics while efficiently accommodating some misalignment and dynamic twisting of the coils. The separation between the coils in implantable applications is commonly less than 20 cm. Today resonant inductive energy transfer is regularly used for providing electric power in many commercially available medical implantable devices.[13]

Wireless electric energy transfer for experimentally powering electric automobiles and buses is a higher power application (>10 kW) of resonant inductive energy transfer. High power levels are required for rapid recharging and high energy transfer efficiency is required both for operational economy and to avoid negative environmental impact of the system. An experimental electrified roadway test track built circa 1990 achieved 80% energy efficiency while recharging the battery of a prototype bus at a specially equipped bus stop.[14][15] The bus could be outfitted with a retractable receiving coil for greater coil clearance when moving. The gap between the transmit and receive coils was designed to be less than 10 cm when powered. In addition to buses the use of wireless transfer has been investigated for recharging electric automobiles in parking spots and garages as well.

Some of these wireless resonant inductive devices operate at low milliwatt power levels and are battery powered. Others operate at higher kilowatt power levels. Current implantable medical and road electrification device designs achieve more than 75% transfer efficiency at an operating distance between the transmit and receive coils of less than 10 cm.

In 1995, Professor John Boys and Prof Grant Covic, of The University of Auckland in New Zealand, developed systems to transfer large amounts of energy across small air gaps.[citation needed]

In 1998, RFID tags were patented that were powered in this way.[16]

In November 2006, Marin Soljačić and other researchers at the Massachusetts Institute of Technology applied this near field behavior, well known in electromagnetic theory, the wireless power transmission concept based on strongly-coupled resonators.[17][18][19] In a theoretical analysis,[20] they demonstrate that, by designing electromagnetic resonators that suffer minimal loss due to radiation and absorption and have a near field with mid-range extent (namely a few times the resonator size), mid-range efficient wireless energy-transfer is possible. The reason is that, if two such resonant circuits tuned to the same frequency are within a fraction of a wavelength, their near fields (consisting of 'evanescent waves') couple by means of evanescent wave coupling. Oscillating waves develop between the inductors, which can allow the energy to transfer from one object to the other within times much shorter than all loss times, which were designed to be long, and thus with the maximum possible energy-transfer efficiency. Since the resonant wavelength is much larger than the resonators, the field can circumvent extraneous objects in the vicinity and thus this mid-range energy-transfer scheme does not require line-of-sight. By utilizing in particular the magnetic field to achieve the coupling, this method can be safe, since magnetic fields interact weakly with living organisms.

Apple Inc. applied for a patent on the technology in 2010, after WiPower did so in 2008.[21]

## Comparison with other technologies

Compared to inductive transfer in conventional transformers, except when the coils are well within a diameter of each other, the efficiency is somewhat lower (around 80% at short range) whereas tightly coupled conventional transformers may achieve greater efficiency (around 90-95%) and for this reason it cannot be used where high energy transfer is required at greater distances.

However, compared to the costs associated with batteries, particularly non-rechargeable batteries, the costs of the batteries are hundreds of times higher. In situations where a source of power is available nearby, it can be a cheaper solution.[22] In addition, whereas batteries need periodic maintenance and replacement, resonant energy transfer can be used instead. Batteries additionally generate pollution during their construction and their disposal which is largely avoided.

## Regulations and safety

Unlike mains-wired equipment, no direct electrical connection is needed and hence equipment can be sealed to minimize the possibility of electric shock.

Because the coupling is achieved using predominantly magnetic fields; the technology may be relatively safe. Safety standards and guidelines do exist in most countries for electromagnetic field exposures (e.g.[23][24]) Whether the system can meet the guidelines or the less stringent legal requirements depends on the delivered power and range from the transmitter.

Deployed systems already generate magnetic fields, for example induction cookers and contactless smart card readers.

## References

1. ^ Carr, Joseph. Secrets of RF Circuit Design. pp. 193–195. ISBN 0-07-137067-6.
2. ^ Abdel-Salam, M. et al. High-Voltage Engineering: Theory and Practice. pp. 523–524. ISBN 0-8247-4152-8.
3. ^ "Power Your Entire Home Without Wires!". Revision3 on msn.com with Dnews announcer Trace Dominguez @tracedominguez. 2014-03-23. Retrieved 2014-03-23.
4. ^ Steinmetz, Dr. Charles Proteus (1914). Elementary Lectures on Electric Discharges, Waves, and Impulses, and Other Transients (2nd ed.). McGraw-Hill.
5. ^ a b Wireless Power Transfer via Strongly Coupled Magnetic Resonances André Kurs, Aristeidis Karalis, Robert Moffatt, J. D. Joannopoulos, Peter Fisher, Marin Soljacic
6. ^ a b WiTricity White Paper- Highly Resonant Wireless Power Transfer: Safe, Efficient, and Over Distance- Highly Resonant Wireless Power Transfer: Safe, Efficient, and Over Distance 2013 Morris Kesler
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10. ^ U.S. Patent 593,138 Electrical Transformer
11. ^ J. C. Schuder, “Powering an artificial heart: Birth of the inductively coupled-radio frequency system in 1960,” Artificial Organs, vol. 26, no. 11, pp. 909–915, 2002.
12. ^ SCHWAN M. A. and P.R. Troyk, "High efficiency driver for transcutaneously coupled coils" IEEE Engineering in Medicine & Biology Society 11th Annual International Conference, November 1989, pp. 1403-1404.
13. ^ "What is a cochlear implant?". Cochlearamericas.com. 2009-01-30. Retrieved 2009-06-04.
14. ^ Systems Control Technology, Inc, "Roadway Powered Electric Vehicle Project, Track Construction and Testing Program". UC Berkeley Path Program Technical Report: UCB-ITS-PRR-94-07, http://www.path.berkeley.edu/PATH/Publications/PDF/PRR/94/PRR-94-07.pdf
15. ^ Shladover, S.E., “PATH at 20: History and Major Milestones”, Intelligent Transportation Systems Conference, 2006. ITSC '06. IEEE 2006, pages 1_22-1_29.
16. ^ RFID Coil Design
17. ^ "Wireless electricity could power consumer, industrial electronics". MIT News. 2006-11-14.
18. ^ "Gadget recharging goes wireless". Physics World. 2006-11-14.
19. ^ "'Evanescent coupling' could power gadgets wirelessly". NewScientist.com news service. 2006-11-15.
20. ^ Aristeidis Karalis; J.D. Joannopoulos, Marin Soljačić (2008). "Efficient wireless non-radiative mid-range energy transfer". Annals of Physics 323: 34–48. arXiv:physics/0611063. Bibcode:2008AnPhy.323...34K. doi:10.1016/j.aop.2007.04.017. "Published online: April 2007"
21. ^ "Ready for ANOTHER patent war? Apple 'invents' wireless charging."
22. ^ "Eric Giler demos wireless electricity". TED. July 2009. Retrieved 2009-09-13.
23. ^ http://www.icnirp.de/documents/emfgdl.pdf ICNIRP Guidelines Guidelines for Limiting Exposure to Time-Varying ...
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26. ^ Ubeam