2.1. System Operation
Figure 1 shows the block diagram of the proposed WPT system in this work, where four loops and single coil were used at the respective Tx and Rx. The operation frequency
was 13.56 MHz. The loops had different diameters, and thus different mutual inductance with coil. During the operation, one of four loops was connected by the SP4T switch, and the impedance was matched by TMC, to provide the best efficiency with the distance between Tx and Rx. All of these procedures were automatically controlled by the MCUs, which are placed in both Tx and Rx. The MCU in Rx sets up wireless connection between the central and peripheral BLE modules to communicate the information on control voltages of the switches and TMCs. Then, both MCUs connect one of the loops (the same loop in Rx and Tx) and tune the TMC (the same value in Rx and Tx), and the Rx MCU measures the rectified voltage and computes efficiency. Finally, the Rx MCU finds and sets the optimum loop and TMC that generate maximum efficiency.
Figure 2 shows the analog circuit part of the proposed WPT system which consists of a coil and four loops at Tx and Rx, respectively. As shown in this figure, Tx and Rx were symmetric except for the rectifier in Rx. That is, the coils, loops, series loop capacitors (
), SP4T switches, and TMCs (digital capacitor banks) were identical in Tx and Rx. Note that one of the four loops was only connected by an SP4T switch during the operation. TMC was simply designed using a shunt capacitance (digital capacitor bank) by modifying the loop capacitances from the resonant values. It will be explained later in more detail.
Prior to discussing multi-loop technique, a conventional wireless power transfer system using a single loop was analyzed using an equivalent circuit given in
Figure 3. Coils are represented with self-inductance
, self-capacitance
, and resistance
. They were designed to resonate at
and to provide high quality (
Q) factor. A single-turn loop is represented with
and
.
is an external capacitor including a self-capacitance of the loop and determined to resonate with
at
.
and
are the coupling coefficients between coil and loop and between Tx and Rx coils, respectively. Power transfer efficiency (PTE)
η and input impedance (
) of the magnetic resonant WPT at
are given by (1) and (2), respectively [
5]:
where
and
are
Q-factors of loop and coil at
, respectively.
and
are the available power from Tx signal generator with source resistance
(50 Ω), and the power delivered to the matched load (
) in Rx, respectively. Therefore, the PTE
η in (1) is equal to transducer power gain (
) of the 2-port network shown in
Figure 3a with reference impedance
[
13,
14]. In this paper, the term PTE or efficiency is used to evaluate the performance of the wireless power transfer system. Note that
is proportional to 1/
, where
is the distance between the coils in Tx and Rx [
14,
15]. From (1), it can be found that PTE is a strong function of the distance,
, and there exists an optimum
or
given by (3), providing a maximum PTE, at which the input impedance (
) is matched to
(system reference impedance):
Figure 3b shows the simulated PTE using the parameters of the loop and coil fabricated in this work which are given in
Table 1 and
Table 2. The loop 1 was used in this simulation with a capacitance
of 120.7 pF resonating with
= 1.141 μH at
= 13.56 MHz. As shown in this figure, the conventional WPT system with a single loop (loop 1) showed a very high PTE of 87.0% at
= 32.5 cm which was an optimum distance (
) in this case. However, PTE rapidly decreased if
deviated from 32.5 cm.
Figure 4 shows the simulated Re {
} and Im {
} as a function of the distance
of the conventional WPT system (a). It is shown in this figure that
was matched to
at
=
= 32.5 cm, and varied with the distance, as also implied by (1) and (2). Therefore, in order to achieve high PTE, TMC can be designed such that
should be matched to
as
changes. However, the conventional single-loop WPT showed very wide variation in
as
changed from 10 to 100 cm; real part from 4.5 to 760.4 Ω, and the imaginary part from 0.0 to −j85.6 Ω. Therefore, complex TMC is required to transform widely-varying
to
[
9,
10,
11].
In order to solve this problem, the multi-loop WPT can be used based on the fact that
or
is a function of
from (3) [
13]. The coupling factor
between loop and coil can be adjusted by changing the distance
or the size of the loop. In the multi-loop WPT,
was adjusted by connecting a different size loop depending on
, so that there could exist several optimum distances providing impedance matches. In addition, connecting one of four loops depending on the distance greatly reduced
variation as shown in
Figure 4, where Re {
} and Im {
} varied from 4.5 to 67.5 Ω, and from 0.2 to −1.9 Ω, respectively, while
changed from 10 to 100 cm. Therefore, the combination of the multi-loop technique and tunable matching can maintain high PTE over a wide range of the distance.
also varies as the load impedance changes. The simulation shows that this variation due to the load impedance can be mitigated by using multiple loops instead of a single loop.
2.2. Tunable Matching Circuit
As stated earlier, the multi-loop technique can greatly reduce the
variation with respect to
, which simplifies TMC design. In the conventional single-loop WPT system, the loop capacitance
was determined to resonate at
with the loop inductance
. In this work, we used higher loop capacitance (
) (as listed in
Table 3) so that input impedance became inductive, as shown in
Figure 5, and thus impedance match could be simply fulfilled by using a single shunt capacitor only.
Figure 5 shows the input impedance of the WPT system on a Smith chart at distances 40, 45, and 50 cm when the loop 2 is selected. As illustrated, a simple shunt capacitor (173, 120, and 55 pF, respectively) is enough to transform input impedances to
.
A tunable capacitor can be implemented by varactor or digital capacitor bank. The varactor exhibits a relatively small capacitance variation ratio (< 1:3.25) considering power handling capability and breakdown and requires an analog control voltage, which is generated by low-pass filtering the PWM output of the MCU [
13]. The low-pass filter should be designed to have enough settling time to reduce the ripples in the control voltages, which leads to a long time required to tune the capacitance.
On the contrary, the digital capacitor bank can be easily tuned at very high speed by the MCU. In this work, five of 10-bit digital capacitors (NCD2100TTR by IXYS) were used in parallel as tunable capacitors to provide the capacitance from 33.0–187.8 pF (1:5.69), depending on the digital control voltages, as illustrated in
Figure 2. The capacitance was adjusted to a very high speed of 220 μsec by applying a serial digital data (
) and clock signal (
) from MCU.
2.3. Coil and Loops
The number of turns and diameter of the coil were determined to provide a high
Q-factor at the resonance frequency
of 13.56 MHz. There were four loops with different sizes, as shown in
Figure 2. The diameter of each loop was determined such that the coupling coefficient (
) between the coil and the loop allowed impedance match at certain distances. For example, the largest loop 1 (diameter = 34 cm) allowed an impedance match at around
= 35 cm, and the smallest loop 4 around
= 100 cm. Therefore, one of the four loops will be connected by the SP4T switch to provide an impedance match depending on the distance
. The coils and loops were fabricated using a copper wire of a diameter of 0.3 cm and their dimensions are presented in
Table 1. This includes the extracted inductance,
Q-factor, and resistance from the measured data using vector network analyzer and LCR meter.
The coil and loops were separated by 1.5 cm (
). Coupling coefficients
between the coil and each loop were computed using INCA calculator and listed in
Table 1 [
16]. The same tool was also used to find coupling coefficients
between Tx and Rx coils as a function of distance
as listed in
Table 2. The values in
Table 1 and
Table 2 were used to design and simulate the conventional single-loop and proposed multi-loop WPT systems.
2.4. SP4T Switch
In the proposed WPT, one of four loops was connected depending on the distance, which was carried out by the SP4T switch. Relays (ARE10A06 by Panasonic) are widely used as switches, since they have high power capability, very low loss (~0 dB), and high isolation at a few tens of MHz frequencies [
13]. However, they consume a lot of direct current (DC) power (200 mW per relay) with low switching speed (~10 ms). In addition, the driver circuit was required, because MCU output current is too small to directly drive the relays. In order to solve these problems, the relays can be replaced with semiconductor switches, which have almost no DC power consumption, high switching speed, and simple driver circuit. However, the semiconductor switch exhibits a non-negligible loss even at a few tens of MHz frequencies. For example, the GaAs SPDT switch (HMC544A by Analog Devices) shows 0.25 dB loss at
(13.56 MHz), so that total loss of the SP4T switch is 0.5 dB. It corresponds to an on-resistance of 5.3 Ω. This may drastically reduce PTE of the WPT system, when the input impedance of the WPT system (
in
Figure 3a) is lower than 50 Ω. In the WPT system in [
13], Re {
} ranges from 5 to 50 Ω and is matched to 50 Ω by TMC.
Figure 6 shows the simulated loss of the switch with on-resistance of 5.3 Ω when the switch is terminated with the impedance
at both ports. The loss is 0.5 dB (efficiency = 89.1%) at
= 50 Ω. It greatly increases to 3.7 dB (efficiency = 42.6%) at
= 5 Ω. Note that the switch is used at both Tx and Rx, so that the total PTE will be dramatically reduced by the loss of the switch. Therefore, the semiconductor switches are not well-suited for high PTE WPT systems.
In order to minimize the PTE degradation due to the switch, we adopted a very low-loss SP4T MEMS switch (ADGM1304EBZ by Analog Devices). It exhibits about 0.12 dB loss at 13.56 MHz (on-resistance of 1.6 Ω) which allows only 1.3 dB loss even at = 5 Ω. It also allowed high switching speed (~30 μs) and low power dissipation of 9.9 mW, which was consumed by a companion driver integrated circuit (IC) to generate the high drive voltage of the MEMS switch. In addition, it operated as reflective open at off ports and has very high isolation about 70 dB, which were essential to minimizing the energy coupling to the unselected loops. The digital outputs of the MCU directly controlled the MEMS switch and selected one of four ports to be connected.
2.5. Rectifier
As shown in
Figure 2, the Rx was terminated with a matched load
of 50
. The power transferred to the matched load was converted to DC voltage (
) by the rectifier, which was connected in parallel with a load
. The rectifier exhibited a very high input impedance at 13.56 MHz, so that it did not change the Rx termination impedance. The designed rectifier consisted of Schottky diode (SMS7621 by Skyworks) and RC filter (
and
in
Table 3) minimizing the ripples in
. DC output voltage (
) is proportional to input power (
) or the received power. Therefore, the measured
was used to estimate the received power and find the optimum loop and capacitance for best efficiency. It was read by the MCU with 10-bit analog-to-digital converter (ADC), which allowed the voltage resolution of 3.22 mV, which corresponds to PTE uncertainty less than 1%.
Figure 7 shows the measured relation between
and
with a fitted-curve, where
is an input power to a load
with the rectifier in parallel as shown in
Figure 2. The Rx MCU utilizes the fitted polynomial equation (4) to calculate the received power
from the read
and compute PTE: