IEEE Power Electronics Magazine - March 2016 - 16

from the power source to the output of
the seconding circuit is minimized

hallmark of the subsequent radio and
television signal transmission.
For magnetically coupled circuits,
resonance refers to the energy oscillations between the magnetic field and
the electric field. In electrical engineering terminology, it means energy oscillations between an inductive element
(energy stored in the magnetic field)
and a capacitive element (energy stored
in the electric field). For loosely coupled windings, the leakage inductance
is considerable. A capacitor can be
added in series with the leakage inductance to reduce or cancel the effect of
the leakage inductance. Consider two
magnetically coupled winding systems,
as shown in Figure 1(a). For a loosely
coupled system, the leakage inductance
could be larger than the mutual inductance. Thus, the leakage reactance
^ ~L lk h could limit the current flow to
the output, particularly when the operating frequency ^ f = ~/2r h is large. If
a series capacitor is added and tuned
at the resonance frequency ^ fo h of the
LC resonator for both the primary and
secondary windings, as shown in Figure 1(b), the leakage reactance can be
effectively canceled out, and the resulting impedance in the power flow path
R1

1
j a ~L lk - ~C k = 0,

(1)

where fo = 1/ ^2r L lk /C h and L lk is
the leakage inductance of the winding
and C is the resonance capacitor. The
approach of using the negative reactance of a capacitor to cancel the positive reactance of the leakage inductance is a type of impedance matching
aiming at reducing the reactance of
the power-flow path in ac circuits.
Impedance matching can be used for
other purposes and is a topic that will
be discussed later in this article.

Some of Tesla's Early Work on
Magnetic Resonance
In 1893, Tesla described his high-frequency and resonance investigations in
[6]. Inspired by the work of Heinrich
Hertz and Oliver Lodge, Tesla reported
several experimental setups of his WPT
study using a high-frequency oscillator
for medical/therapeutic applications [1].
Three of these setups are shown in Figure 2. Figure 2(a) shows two magnetically coupled windings (primary winding P
and secondary winding S ). The primary

j~Llk1

j~Llk2

R2

M12

winding is connected in parallel with a
condenser C (capacitor) and is fed by a
high-frequency generator G. The frequency was set in the range of 5-10 kHz.
In the secondary winding, the two output terminals are labeled as T. In the
description of this setup, Tesla added,
"Two plates of large surfaces, forming an
adjustable condenser, may be used for
the purpose of synchronizing the secondary with the primary circuit."
Tesla further discussed the use
of resonant circuits in Figure 2(b), in
which two parallel-connected condensers C are connected in series with
the primary winding P. The two ends
of the secondary winding are connected to two sets of parallel plates tt and
t't' of considerable surface (i.e., a form
of variable capacitor). The voltage and
current obtained from the two output
terminals T T can be regulated by simply varying the distance between the
two pairs of plates tt and t't', respectively. In modern terminology, this
WPT system consists of a series-resonant primary winding and a seriesresonant secondary winding.
As Tesla continued to explain the
operation of the system in [1, Figure  2(c)], he emphasized the use of
high frequency, winding resistance
as low as possible, and the importance of establishing synchronism
between the oscillations in the primary and secondary circuits. The Q
factor for an inductor is
~L
Q= R ,

(a)
R1

j(~Llk2 -1/~C2)

j(~Llk1 -1/~C1)

R2

M12

(b)
fig 1 An equivalent circuit of (a) two magnetically coupled windings and (b) two magnetically coupled windings with series capacitor compensation.

16

IEEE PowEr ElEctronIcs MagazInE

z	March 2016

(2)

where ~ is the angular frequency, L is
the inductance, and R is the winding
resistance.
These features are the factors essential to high-quality (Q) factor (i.e.,
high Q factor) and magnetic resonance of the coupled windings. One of
the short-range WPT applications demonstrated by Tesla was to wirelessly
power a lamp, as shown in Figure 3.
The contributions of Tesla to the
concept of using magnetic resonance
were recognized in another memorial
article published in August 1943 by
L.P. Wheeler [the president of the Institute of Radio Engineers in 1943]. In [8],



Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - March 2016

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