![Page 1: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/1.jpg)
Magnetic Induction
and
Magnetic resonance
![Page 2: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/2.jpg)
Magnetic induction and resonance
2
![Page 3: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/3.jpg)
Magnetic Induction
![Page 4: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/4.jpg)
Progress in Magnetic induction transferIn practical use Electric toothbrush, electric shaver, etc.
Electric devices in a wet areaCordless phone, etc.
In progress Enhancement of transfer efficiency
development of efficient coilsreduction in ohmic heating, cooling‐freehigher power: cf. cell phone
Improvement of Safetya metal detectorcertificate ID to avoid charging to wrong devices
Sophistication and functionalitysimultaneous data & power transfer
4
![Page 5: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/5.jpg)
Qi (inductive power standard)
Output voltage is regulated by a digital control loop between the transmitter and receiver.
Communication is unidirectional from the power receiver to transmitter requesting more or less power via backscatter modulation.
In backscatter modulation, the power‐receiver coil is loaded, changing the current draw at the power transmitter.
These current changes are monitored and demodulated into the information required for the two devices to work together.
By Wireless Power Consortium
5
![Page 6: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/6.jpg)
Contact‐less IC(Integrated circuit) card/tag
Inductive power supply using a 13.56 MHz radio wave emitted by a card reader.
Battery‐free: card slimming, no run‐out, less toxic‐substance in disposal
Less driving‐power: FET(Field Effect Transistor)/CPU & reflecting sender. Input voltage modulation by resistance control (not by injection current control.) Nonvolatile memory.
Two‐way telecommunication by modulating the power carrier wave between a Reader/Writer and a card at 100‐400 kbps at a distance of 10 cm.
Card and reader circuits
Felica (sony)
6
![Page 7: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/7.jpg)
High‐speed charging to EVs
IPT hybrid bus(MLIT、Hino motors)
Electric vehicle(Nissan Leaf)
7
![Page 8: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/8.jpg)
IPT: abbreviation for Inductive Power Transmitter.
A plug-less hybrid bus links Haneda Airport‘s terminals covering a distance of about 4.2 km and runs 15 km only by battery charge and 300 km with a dynamo engine.
A coil on the bottom of the bus aligns with a charging coil. A charging coil is embedded in concrete.
150 kW transmission at total charging and discharge efficiency of 80%.
Lithium ion batteries on a roof. Charge voltage 500V, Capacity 80 Ah, 40 kWh. (cf. Toyota Purius 200V, 6.5 Ah, 1.3 kWh) 30 times bigger.
IPT Hybrid Bus
8
![Page 9: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/9.jpg)
Theory: What is Magnetic Induction? What is Magnetic Resonance?
Intel: Intel Developer Forum 2008
9
Electric vehicle(Nissan Leaf)
![Page 10: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/10.jpg)
A set of four independent equations describing the electric and magnetic fields in vacuum :
(1) (Faraday’s law of induction)
(2) (Ampere’s law)
(3) (Gauss’ law)
(4) (Gauss’ law for magnetism)
Maxwell’s equations
0
t
HE
J
t
EH
E
0B
10
![Page 11: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/11.jpg)
Consider a one-turn coil C with an area S and a magnetic flux density Bpassing though C. When B changes in time, integrate the Faraday’s law of induction on S,
(5)
By Stokes’ theorem,
(6)
The induced electromotive force, EMF ε [V] in C is
(7)
Φ[Wb] : magnetic flux in Circuit C.
Electromagnetic induction
0S S
BdS dSt
E
0C S
dr B dSt
E
ddS
B dSt t
11SB dS
![Page 12: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/12.jpg)
If there is no flux leakage from a solenoid coil C1 to C2, EMF ε2 in C2generated by the current I1 in C1 is
(8)
From the reciprocity,(相反定理)
(9)
Mutual inductance is defined as
(10)
Mutual Inductance, M
1 1 1 2 1 12 2 2 21
d dd dd d d d
N SI N N S I IN N Mt t l l t t
1 2 2 21 12
d dd d
N N S I IMl t t
1 221 12
N N SM M Ml
Two solenoid coils C1 and C2 (N1 and N2 turns)
12
![Page 13: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/13.jpg)
EMF ε1 is also induced by I1. In the same way as the previous, self-inductance L1 is expressed as
(11)
Then, general form of induction is written as
(12)
Generally, there is an inequality
(13)or
(14)
where, k (<1) is a “Coupling coefficient.”
Coupling coefficient, k
1 1 1
2 2 2
dd
L M ItM L It
1 2M L L
1 2M k L L
Two solenoid coils
21
1N S
Ll
13
![Page 14: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/14.jpg)
Leakage inductance leakage flux stores energy and thus acts as an inductor in series in each of
the primary and secondary circuits.
1 1 1
2 2 2
21 2 21 11
22 222 1 1
0d0d
dd
V L M IV M L It
k L L V Ik L MItM k Lk L L V
2leak1,leak2 1,2 1,21 0L k L L k
Leakage inductance Equivalent circuit with leakage inductance (2)
V1 L1 L2
M
V2
I1 I2
Lleak1 Lleak2
V1 V2
I1 I2
ε1 ε2
Original circuit (1)
14
211 2 21 1
22 22 1 1 2
21 2 2 1 11 1 leak1 1
22 2 leak2 22 1 1 2 2
1 0 0d0d0 1
1
1
k Lk L L VV IV Itk L L V k L
k L L V k L dI tV L dI tV L dI tk L L V k L dI t
(15)
(16)
(17)
![Page 15: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/15.jpg)
Power factor (力率) in AC power system
Power factor: P(real power)/S(apparent power) =cosφ
No delay (φ=0, cosφ=1)
Zero power factor(φ=90, cosφ=0)
15
![Page 16: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/16.jpg)
Power factor correction (力率改善)
Cancellation by compensation capacitorsIn both primary and secondary sides
1,2 20 leak1,leak2
1CL
C1 C2
Lleak1 Lleak2
C1 C2Lleak2
Series/Series type
Parallel/Parallel type
16
(18) Lleak1
![Page 17: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/17.jpg)
Equivalent circuit with power factor correction
Power factor correction condition for k≈0 is ω=ω1=ω2
AC frequency: ωCircuit resonant frequency:
Source(src)
Load (ld)
Primary Secondary
Incident wave Transmission wave
1,2 1,2 1,2 1,2 1,2( 1 / ) Z R i L C R
Z0Z0
C1 C2
R1 R2
L1 L2
Double resonating circuit
1,2 1,2 1,21 / L C
17
(19)
(20)
![Page 18: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/18.jpg)
Analysis of equivalent circuit
Kirchhoff 2nd law
Input power from source Pin and output power at load Pwork
transfer efficiency
1 1 1src 0 2src
20 2 2 2 1 0 2
0 ( )
Z i M I IV Z ZVi M Z Z I I i MZ Z Z M
in src 1P V I
2 2work 0
2in 1 2 1 0 2 21 0 2 0 2
2 21 2 2 0
1( ) 1 1
P Z MP R R Z Z Z RZ Z Z M Z Z
M R R R Z
2work 0 2P Z I
Z0Z0
C1 C2
R1 R2
L1 L2
18
(21)
(22)
(23)
![Page 19: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/19.jpg)
Analysis of equivalent circuit, ctd.
Figure‐of‐Merit (性能指標, fom)
coupling coefficient: Q factor:
transmission efficiency η
Optimum impedance ratio (Load resistance/internal resistance)
2 21 2k M L L
1,2 1,2 1,2Q L R2 2
2 21 2
1 2
M k Q Q fomR R
2 20 2 1 2opt
1 1Z R k Q Q fom
0 22
2 0
11 1 1 1Z R
fom R Z
2
max 22
22 2
1
1 1 1 11 1 1 11
fom
fomfomfom fom
19
(24)
(25)
(26)
(27)
![Page 20: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/20.jpg)
Theoretical transmission efficiency
Transmission efficiency at optimum impedance ratio.
To achieve high efficiency← higher Q factor
← higher frequency, ω(>10kHz)
2
max 221 1
fom
fom
2 20 2 1 2opt
1 1Z R k Q Q fom at
Q L R
20
(28)
(29)
![Page 21: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/21.jpg)
Summary of Magnetic Induction Power Transfer
21
Leakage inductance due to air gap results in lowpower factor.
Power factor is compensated by adding capacitors.
Perfect compensation condition is equal to aresonant condition.
transfer efficiency is a function of the figure-of-merit kQ.
![Page 22: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/22.jpg)
Magnetic Resonance Power Transfer
![Page 23: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/23.jpg)
Demonstration of WPT by Magnetic Resonance
MIT demonstrationPower: 60 WDistance: 1.8 m Coil diameter: 0.6 m. Efficiency: 45%RF: 10 MHz
With a pair of high Q coils23
![Page 24: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/24.jpg)
Quality factor of resonating circuits
Γ: band width
0 0 1
2R L
Q
01 LQ
R C R L
RLC circuit
Ohm R2 2R L R R L
Definition:
ω0ωL ωR
C
R
L
Resonance curve
2Energy Stored
QEnergy Dissipated per cycle
Low Q case; energy is rapidly dissipated through Joule heating and radiationHigh Q case; energy is stored for long period. (high quality coil or circuit) but resonance band width becomes narrow.
24
Video
Task
(1)
(2)
![Page 25: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/25.jpg)
Magnetic Induction ? or Resonance?
Coupling coefficient k >0.5. → Magne c induc on with
‐ Compensation capacitor (power factor correction)‐High AC frequency >10KHz (high Q)
Coupling coefficient k =0.1~0.001. → Magne c Resonance coupling with
‐ very high Q of the order of 1000‐ Higher AC frequency ~10MHz ‐ low resistance and radiation‐ narrow resonance frequency band
transfer distance and efficiency
2opt 1 21r r k Q Q
25
![Page 26: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/26.jpg)
High Q coils (1)
Resonance frequency Designed:10.56±0.3MHz Measured:9.90MHz
Q factor Designed:2500(σ=5.9×107m/Ω
assumed) Measured:950±50(Due to
surface oxidization?)
26
Helical type (MIT) Spiral type (Ryukoku univ.)
Resonance frequency 21MHz (diameter 5.5cm)
Q factor Measured:1000 with pitch 5mm
![Page 27: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/27.jpg)
High Q coils (2)
Resonance frequency Designed:13.54MHz Measured:13.43MHz
Q factor Designed:308 Measured:341
Mica Condenser
Cupper wire
27
Loop type (UT)
![Page 28: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/28.jpg)
Energy losses in a coil
28
1. Ohmic loss: 1/Qohm
2. Dielectric material loss: 1/Qd
3. Radiation loss: 1/Qr
1/Q=1/Qohm+1/Qd+1/Qr = (Rohm+Rd +Rr)/ωL
![Page 29: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/29.jpg)
1. Ohmic loss: 1/Qohm
ohmic 2l lRa a
Skin depth (resistivity: ρ)
Skin effect (表⽪効果)High frequency AC is distributed within a conductor such that the current density is largest near its surface and this “skin” becomes thinner with frequency.
29
2
Resistance (cable diam.: a, cable length: l)
![Page 30: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/30.jpg)
2. Dielectric material loss: 1/Qd
Equivalent series resistance in capacitor (寄⽣抵抗) Rp
rP
c d
1tan I CRI Q
30
Dissipation factor, tanδ
tanδ= 0.02-0.002 (@1GHz) for good capacitors.
Need care for covers, coatings and surface oxidization for solenoid coil wires.
(3)
![Page 31: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/31.jpg)
3. Radiation loss: 1/Qr
Radiation loss of a one-turn loop coil (coil diam. D, wavelength λ)
31
Then,
470
rad8
3c DR
Inductance L is also a function of D as,
0 2ln 2.2022
l DLa
3 3
rr
3 2ln 2.202 1.338
L D D DQR a
(for D/a=50)
(4)
(5)
(6)
![Page 32: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/32.jpg)
How to measure Q factorExcitation
coil
Rogowskicoil
resonator
TG outputSA input
3dB3dB
f1 f0 f2
32
12
0
fff
QL
Resonance curve
![Page 33: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/33.jpg)
Transmission efficiency analysis (1)
2 2
0 2 0 21
,1 1
k Q rZ Z r Z Rix ix
1,2 01,2 1,2 1,2 1,2 1,2
1,2 1,2 1,2 0
1 11 1L
Z R i L R i R ixC C R
Assume, power source freq. ω is slightly different from circuit resonance freq. ω0Then,
Where
1,2 0 0
1,2 1,2 0 0
1Lx Q
C R
Impedance Ratio
33
(7)
(8)
(9)
![Page 34: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/34.jpg)
Double resonating circuit
1 01 1 1src 0 2src2
2 02 2 2 1 01 2 020 ( )( ) ( )
Z Z i M I IV Z ZVi M Z Z I I i MZ Z Z Z M
Kirchhoff's voltage law
Efficiency2 2 2
2 01 02 1 2 1 221 21 2 22 2
1 01 2 02 1 2 1 2
4 4
( )( ) ( ) (1 )(1 )
M Z Z k Q Q r rs
Z Z Z Z M ix r ix r k Q Q
R1
Vsrc
Z01
C1
L1
R2
Z02
C2
L2
Transmission efficiency analysis (2)
34
(10)
(11)
![Page 35: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/35.jpg)
Efficiency Map at high kQ(>1)
35
![Page 36: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/36.jpg)
0
0.2
0.4
0.6
0.8
1
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
(ω-ω0)/ω0
0
0.2
0.4
0.6
0.8
1
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
(ω-ω0)/ω0
Frequency Matching & Impedance Matching
r=5
p
0 2
k
kQ=10k=0.01Q=1000
kQ=10k=0.01Q=1000
r=13
Frequency Matching Impedance Matching
36
![Page 37: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/37.jpg)
Summary of Magnetic Resonance Power Transfer
37
High transfer efficiency, ie. High kQ, is achievableby high Q even at low k.
High Q is available in high frequency range ofseveral MHz.
Bandwidth in which two high Q coils can resonateis very small.
Input & output impedance matching is importantfor efficient power transfer.
![Page 38: Magnetic Induction and Magnetic resonanceInduction_Resonance).pdf · Electromagnetic induction 0 SS B ... Magnetic Induction ? or Resonance? ... Kirchhoff's voltage law Efficiency](https://reader031.vdocument.in/reader031/viewer/2022021818/5aa9285b7f8b9a90188c749f/html5/thumbnails/38.jpg)
QuestionWe want to design a high quality coil of Q=1000 with 1 m cupper wire. Available minimum resistance R=0.1 Ω and maximum inductance L=10 μH.
How much angular frequency of AC is required?
38
Back