Instrumentation & Measurement Magazine 23-4 - 71

Fig. 4. Relationship between transmission efficiency, quality factor and
coupling coefficient.

efficiency and maximal transmission distance of the system.
The inductance of the coil is determined by the structure and
material. Here, copper hollow spiral coils with wire radius of
0.3 mm are employed. The free running frequency f can be attained by (3):
f=

1
2π LC

(3)

where L is the coil inductance and C is the series capacitance.
According to (3), when the resonance frequency is set to 13.56
MHz and the coil inductance is given, the matched capacitor
can be obtained. The coupling coefficient K of two coupling
coils is shown in (4):
K=

μπ N2 r 4

(

2 d2 + r 2

)

(4)
LP LS

where d is the distance between two coils, r is inner radius
of the coil, μ is permeability of the vacuum, and N is the
number of turns in the coil. It can be seen from (4) that the
coupling coefficient K can be determined by the inductance
of two coils and the distance. Parameters of coils are shown
in Table. 1.
The theoretical capacitance is calculated from (3) to approximate the resonance frequency of 13.56 MHz, but the match
capacitance actually deviates from the theoretical value. The
measured match capacitance is also given in Table 1, which has
an inaccuracy less than 5%. Recall Fig. 4, where the maximum
transmission efficiency is 0.82, corresponding to a coupling
coefficient K of 0.2. Combined with (4), the distance can approximately reach 20 mm with a 5.5 pF capacitor, while the
resonance happens.

Table 1 - Coils parameters
Inner diameter

20 mm

40 mm

50 mm

Self-inductance

11.05 uH

18.86 uH

23.5 uH

Theoretical Capacitance

12.48 pF

7.3 pF

5.8 pF

Match capacitance

12.5 pF

7.5 pF

5.5 pF

9.7

16.9

19.4

Quality factor
June 2020

Fig. 5. Diagram of the LDO dynamic load circuit.

Rectification and Voltage Regulation
A full-wave bridge rectifier consisting of four 1N5819 Schottky
diodes is used to achieve high frequency ac-dc conversion. The
forward voltage drop of each diode is only 0.2 V and the loss of
the rectifier can be reduced, since the frequency of the ripple is
doubled after rectifying. A low-pass filter is used to filter out
the ripple, but the filtered voltage may still be noisy. Applying
this voltage to a biomedical device that requires precise power
supply may interfere with the operation of internal sensitive
circuits. Therefore, it is necessary to reduce the noise and stabilize the output voltage by the voltage regulator. LDO is one of
the voltage regulators and is a good choice for most biomedical
systems, according to its stablity and low power consumption.
Here, TPS7a69-q1 LDO is adopted with the input voltage ranging from 4 V to 40 V. The output voltage is 3.3 V with maximum
load current up to 150 mA.

Dynamic Load Circuit
Most digital circuits such as MCU and DSP are driven by clock
signals, where the corresponding load current acts similar to
clock signal. As a result, the total current will vary irregularly.
The response ability of LDO to dynamic load circuit is one of
the most important specifications, namely load regulation. To
test the load regulation of the WPT system, here, a load regulation measurement circuit is setup for emulating the dynamic
load current. The schematic is shown in Fig. 5.
In Fig. 5, OUT node is directly from LDO output, VSource is
the reference voltage from signal generator, and Vfb is the feedback voltage sampling from resistor Rref. The TI OPA 842 with
400 MHz GBW is used to ensure fast transition. The programmable signal generator is utilized to generate the square wave
to the positive input of the Operational Amplifier (OPA). The
negative input of OPA is kept the same to the square voltage.
Then, the square load current can be set by VSource/Rref .

Measurement and Analysis
The physical implementation of the entire prototype is shown
in Fig. 6. The sinusoidal signal source is connected to the
transmitting coil through two input nodes A and B. The coil
transmission distance can be adjusted during the experiment.
Terminals C, D, E are intermediate test nodes, which are rectifier output, LDO output, and output of power transistor,

IEEE Instrumentation & Measurement Magazine 71

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