IEEE Power Electronics Magazine - March 2016 - 26

l = ^~/2 h k; C 1 = ^~/2Q 1h and C 2 =
^ ~/2Q 2 h are the intrinsic loss rates of

Thus, l/ C 1 C 2 & 1 simply means
k Q 1 Q 2 & 1, which has been a wellknown concept in electrical engineering for several decades [16].
For a midrange application, the
transmission distance is relatively
large, and, therefore, the mutual coupling coefficient k is relatively small.
For a small k, using a high Q factor
for each resonator would increase
the energy efficiency as described in
(3b) This point has been well known
in electrical engineering for a century

the first resonator and the second resonator, respectively.
According to [29], this condition of
(4) is a regime of operation that has
not been studied extensively. However, the term l/ C 1 C 2 of the coupled
mode theory is equal to k Q 1 Q 2 in
the electric circuit theory, where k
is the mutual coefficient between the
two coupled coils; Q 1 and Q 2 are the
Q factors of the two coil-resonators.

N

N-1
3

2

1
Y
X

ro

2rw

a

+V

(a)
C
ln- 1

f

L
ln

M

ln+ 1

M

f

(b)
fig 12 (a) The magnetoinductive waveguide based on coil-resonators (using magnetic
resonance) and (b) its equivalent circuit (redrawn from [26]).
KPS

KSR

Sending

Receiving KRD
Load

Power

KPR

Z0

KSD

Z0

VS +

+ V4
KPD
KPR, KSD, KPD, Weak Coupling
(a)

I1
IS

Z0

CP

CR

LP
+
MPS
+
MPS
+
M
SR

Zin

I3

I2

LS

CS

-

V4
LR
LD
+
+
MSR
MRD
+
MRD
-

I4
CD

Z4

(b)
fig 13 (a) The schematic of the four-coil WPT system proposed in [29] (using magnetic
resonance) and (b) its equivalent circuit.

26

IEEE PowEr ElEctronIcs MagazInE

z	March 2016

[1]. Regarding the suggestion of using
resonance for efficient energy transfer
[29], [30], David Schneider commented
in IEEE Spectrum [31] that "It's not a
new idea: Tesla's eponymous coils use
that very same principle."
The four-coil system in [29] and [30]
has been analyzed by several research
groups using the standard electric circuit theory [32]-[34]. Cheon et al. [32]
provides a detailed analysis and an
equivalent circuit of this system (Figure
13). Basically, it shows that the operating principle of the four-coil setup in
[29] and [30] can be described by the
standard-coupled circuit equations.
The equivalent circuit is shown in Figure 13(b). With an operating frequency
at about 10 MHz, the stray capacitance
of the resonator coil can be used as the
resonance capacitor. The essence of this
four-coil WPT system lies in the provision of the two extra mutual inductance
terms of the coupled loops (i.e., k 12 and
k 34 ). The authors of [32] point out that
the four-coil system of [29] and [30]
transmits power based on the impedance matching of the source impedance
and the input impedance of the entire
four-coil WPT system. To achieve such
impedance matching for maximum
power transfer [i.e., Z o = Z in in Figure
13(b)], the following condition has to
be met:
k 12 k 34
k 23 = 1.

(5)

The availability of k 12 and k 34 provides
the flexibility in meeting this condition.
For example, for a midrange transmission distance between the two coupled
resonators, their mutual coupling coefficient k 23 is small (e.g., 0.01), by
adjusting k 12 and k 34 to be 0.1, the condition of (5) can be met. The flexibility
of tuning the coupling coefficients for
satisfying (5) is a contribution of this
four-coil system, although such a system involves no new scientific principles. However, this is done at the
expense of system energy efficiency.
Its system energy efficiency is 15%,
meaning that an input power of 400 W
is needed to power a 60-W light bulb.
Therefore, the four-coil WPT system
proposed in [29] and [30] is unsuitable



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