Instrumentation & Measurement Magazine 23-4 - 70

Fig. 2. Block diagram of the whole system.

Power Transmission Analysis
Currently, there are two coupling methods which are inductive coupling and resonant system, respectively. For inductive
coupling, the energy transmission may not be high in an airgap in comparison to an iron core of a transformer, and the
efficiency decaying with distance may limit the use of the technology to a small distance [14]. A resonant system effectively
increases the range of transmission distance and demonstrates
high power transmission efficiency in comparison to its inductive counterpart [15]. In addition, the devices need to be
implanted into the human body, and it is necessary to avoid the
radiation heat that causes any damage to human tissues. In order to make the human tissue specific absorption rate (SAR) as
low as possible, the radiated power should be minimized and
energy efficiency should be maximized. The resonant system
is chosen due to the requirements of mid-range energy transfer and high energy efficiency. The resonant system equivalent
circuit is shown in Fig. 3.
In Fig.3, IP and IS are the currents of the transmitting coil
and receiving coil, respectively; RP is the equivalent series resistance of the transmitting coil; RS is the equivalent series
resistance of the receiving coil; RL is the load resistance; LP and
LS are the inductances of the transmitting and receiving coils,
respectively; CP and CS are series resonance capacitors in transmitting and receiving coils, respectively; and M is the mutual
inductance between two coils. The principle of the resonant
system is that the alternating magnetic field is generated by
introducing alternating current at the transmitting coil, and
the induced magnetic flux in the receiving coil is converted
into a current to drive the load. Due to the different distance

between the transmitting coil and the receiving coil, a portion
of the magnetic flux generated by the transmitting coil is coupled to the receiving coil which contributes to power transfer.
The more magnetic flux coupled to the receiver, the higher the
transmission efficiency. The coupling coefficient K is defined
from the mutual inductance M, as shown in (1):
K=

M
LPLS

(1)

Inductive link has an intrinsic resistance which characterizes the coil quality factor Q. In Fig. 2, while the quality
factors of the transmitting and receiving circuits are QP and
QS (QP=ωLP/RP, QS=ωLS/(RL+RS)), by defining the ratio of
the receiving coil resistance to the transmitting coil resistance
(Rr=RL/RP), the transmission efficiency can be simplified to (2):

η=

(

QS2 Rr
QS2 + Rr

)

K 2QSQP (2)

Equation (2) indicates that the transmission efficiency is
related to both quality factors (QP, QS) and the coupling coefficient K. The quality factor of the resonant circuit is equal to 2π
times the energy stored in the resonant circuit and the energy
consumed in each cycle defining from the view of energy [16].
According to the above definition, the high-quality factor indicates that its own loss is small. Therefore, in the resonant WPT
system, high quality factor coil is preferred and how to optimize quality factor will be taken into consideration. In order
to simplify the analysis, here QP=QS=Q. The relationship between transmission efficiency, coupling coefficient and quality
factor are simulated from (2), which is shown in Fig. 4.
As shown in Fig. 4, the coupling coefficient K ranges from
0 to 0.2 and the quality factor Q ranges from 0 to 80. The transmission efficiency generally increases with the increase of Q,
especially when Q approaches to 10 with a steep curve. As Q
increases further, the curve of transmission efficiency becomes
smooth and no longer increases. The maximum transmission
efficiency is close to 0.82, while the quality factor Q is about 20
and coupling coefficient K is 0.2.

Coils Design
Fig. 3. Resonant system equivalent circuit.
70

The coupling coil is one of the most important components
in a WPT system, and it directly determines the transmission

IEEE Instrumentation & Measurement Magazine

June 2020

Instrumentation & Measurement Magazine 23-4

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 23-4