WOLFRAM|DEMONSTRATIONS PROJECT

Electromagnetic Fields in Wireless Power Transmission

Wireless power transmission makes use of a pair of magnetically coupled coils, each in series with a capacitor. The characteristic frequency is discussed in the companion Demonstration "Wireless Power Transmission." The present Demonstration is concerned with the electromagnetic fields associated with a wireless transmission system. The parameters are the following (as defined in the companion Demonstration):
V
i
=100
V
rms
(frequency=f)
,
r
i
=10Ω
,
r
o
=1kΩ
,
C
1
=
C
2
=200pF
L
1
=
L
2
=16.54mH
,
L
12
=0.709mH
(corresponding to
a=b=0.5m
,
R=5mm
,
N
1
=
N
2
=100
,
d=1m
)
Maximum power is transmitted at the resonance frequency
f
res
=87.5kHz
.
The instantaneous input voltage
v
i
(t)
and currents
i
1
(t)
,
i
2
(t)
can be defined from the corresponding phaser solution of the circuit equation. The field of the coaxial coil system can be readily analyzed using the vector potential
A
, which is a linear function of
i
1
(t)
and
i
2
(t)
. Assuming a near field, the electric and magnetic fields can be obtained by
E=-∂A/∂t
and
H=curlA/
μ
0
, respectively. The power flow through space is given by the Poynting vector
S=EH
.
The field in the
x
-
z
plane is shown for a selected frequency and phase (i.e., time). The electric field perpendicular to the
x
-
z
plane is not shown. The magnetic field and Poynting vectors are shown by blue and orange arrows, respectively. The color indicates the magnitude of the energy density
w=
ϵ
0
2
E
/2+
μ
0
2
H
/2
. All of these are plotted on a logarithmic scale.