1. Introduction
A near-field communication based on a coil antenna (CA) running at around 13.56 MHz frequency band is commonly used nowadays due to its easy integration, low cost and even operating without a network [
1]. According to the inductive coupling, it can provide users with WPT mode to charge power and NFC mode to exchange information. Conventional handheld wireless devices based on a CA are bulky and multi-turn because of the limitation at the desired operational frequency band of 13.56 MHz [
2]. However, the best reason for selecting the coil structure to be applied in a near-field situation is that power can be transmitted at high efficiency, regardless of alignment, by adjusting the magnitude and phase due to the eddy current generated along the multi-turn metallic coils. The issues of the body effect size reduction and bandwidth increases based on the CA; therefore, this has become a hot topic [
3]. Simultaneously, with the demand for high-speed information exchange and limited by the crowding of handheld wireless devices, utilizing near-field interaction is more advantageous than using a SIM card [
4,
5,
6,
7]. Before some electronic components are integrated into a near-field wireless system, several related investigations into the dimension and turns of plane CA should be conducted to prevent the performance from degradation [
8]. In most applied cases, CAs are integrated on the bottom of a battery pack, the thickness of which therefore must be taken good care of in design. However, the main aim of this paper is to miniaturize a CA based on a designed matching circuit. A 1-mm FR4 substrate is therefore taken to replace a battery pack in the following design. Meanwhile, a simple multi-turn CA is highly sensitive to alignment because of the narrow impedance bandwidth. If the dimension of the CA becomes smaller, it will be harder to maintain an original state of reflection coefficient at the desired frequency of 13.56 MHz, making it even more difficult to transmit power. Therefore, an approach to widening the impedance bandwidth also must be under consideration when miniaturizing a CA. Afterwards, the Q-factor determining the efficiency of transmitted energy is an important index for the whole RF system to be paid attention to, as fabricating a CA as small as possible with a high Q-factor is also necessary for wide impedance bandwidth [
9]. The traditional approach to making the CA resonate at 13.56 MHz by simply cascading a resistance of 50 Ohm and a certain capacitance due to the standard impedance matching of 50 Ohm at the source port (as shown in
Figure 1) was abandoned. However, it still has some reference values for following investigations and comparison due to its success in transmitting and receiving power at a certain frequency [
10].
From its performance on the Smith chart in
Figure 1d, the red dotted line and green solid line represent the S-parameter of a three-turn CA with and without a matching circuit, respectively. Simultaneously, the blue arrow line denotes the matching process of the desired frequency from the red dotted line to the green solid line at 13.56 MHz. The original three-turn CA denoted by the green line resonates at around 290 MHz, far away from the desired frequency of 13.56 MHz. However, this three-turn CA can finally operate at 13.56 MHz after cascading several electronic elements consisting of a resistance of 50 Ohm and a capacitance of 26.7 pF as shown in
Figure 1b,c. Indeed, the conventional CA can operate at all frequencies desired by simply cascading a capacitor of a certain value and a 50 Ohm resistance because, according to the design specification of an RF system, there is a standard resistance of 50 Ohm matched at the feed port. Meanwhile, the CA itself has a particularly parasitic resistance whose value is rather small compared to the value of the feed port. Therefore, cascading a 50 Ohm resistor and a capacitor can easily make the CA resonate at around 13.56 MHz, ignoring the requirement of conjugate in the RF system. However this will definitely result in a considerable waste of source because most power will be consumed on heat by the resistor. The introduction of Q-factor can deal with this conventional problem with the best optimized performance achieved. For the above-discussed reasons, deigning a matching circuit with a suitable value of resistance is essential. To deal with this problem, a matching circuit based on electronic elements aimed at making a miniaturized CA scientifically operate at 13.56 MHz is designed [
11]. Therefore, equivalent circuit parameter extraction and analysis of the CA is a necessary precondition before miniaturizing it.
The remainder of this paper is organized as follows:
Section 2 introduces and interpret two approaches to miniaturizing the CA in theory. Two important RF modules to improve the performance of the CA are literally designed. Furthermore, two systematic design flows based on series and parallel equivalent circuits are presented in three steps. After designing the three-step flow for miniaturizing the CA in principle, this paper then provides two ways to check the results, namely, an electronic circuit and ANSYS, in
Section 3. Finally, according to the concluded results, some further perspectives are presented in the last section.
2. Design of Miniaturization in Theory
This section presents a complete design flow of miniaturizing a CA by way of an equivalent circuit in theory. An extracted equivalent circuit module can efficiently replace the antenna for calculation in an RF system due to the mature high-frequency electronic theory. Two approaches proposed in this paper to miniaturize the CA and widen the impedance bandwidth are based on this. Before designing a matching circuit for the CA, some rules and parameters influencing performance of an RF system should be introduced first. As shown in
Figure 2, most antennas can be regarded as a radio-frequency circuit consisting of a capacitor, resistor and inductor, whose values can be extracted and calculated by HFSS software in simulation or by multimeter in measurement. Furthermore, these equivalent circuits can be divided into series equivalent circuits and parallel equivalent circuits according to their connections among electronic elements, as shown in
Figure 2 for the following calculations [
12].
The conventional CA’s inductance is about 1 to 2 uH, as it has 3-turn metallic loops and a 50 × 80-mm
2 dimension, which can be regarded as a constraint condition to find an appropriate design specification in order to determine the miniaturized CA’s amount of turns. This is because either too large or too small inductance will deteriorate the performance of transfer. Therefore, if excellent performance in transferring power and information is required from the miniaturized CA, its inductance will be approximately equal to 1 to 2 uH, which is also key to miniaturizing a CA. In fact, the relationship among the inductance value and variable parameters of the CA can be formulated by the following equation, Equation (1) [
13]:
In this equation, dependent variable
L whose unit is
nH is an estimated value of the CA that can be approximately achieved by extracting parameters from the CA. The variables
ly and
Dx, corresponding to
Figure 1a, represent the average perimeter and line width of a CA, respectively. Their unit is centimeter, and
K is a constant with the value of 1.47 when the coil antenna is rectangle. If the CA is annular, the constant
K is equal to 1.07. These are both obtained by empirical conclusion, which can be deemed suitable for designing coil antennas. The variable
N denotes the turns of the CA. Therefore, if a size reduction is required for constant inductance, this equation should be made full use of. According to Equation (1), the inductance decreases due to the CA’s dimension reduction. Complying with the guide of inductance (Equation (1)), miniaturizing the CA will therefore reduce the value of
Ly and
Dx, causing a decrease in gross inductance. For the same performance as a conventional CA, some methods such as
K reduction or
N increase to maintain the inductance between 1 and 2 uH should be adopted. By analyzing the dynamic equation, Equation (1), increasing the variable
N will play a more important role in maintaining its inductance than reducing the variable
Dx or constant
K. For an obviously effective result, this paper decides to keep the inductance constant by adding the turns of the CA. The inductances of a three-turn and five-turn CA are calculated and tabulated based on the dynamic equation, Equation (1), as shown in
Table 1 (unit: nH).
According to
Table 1, a conventional three-turn CA itself has an inductance of 1.68 uH, exactly located in the range of 1 to 2 uH. However, both inductances of four-turn and five-turn miniaturized CAs are within the desired range; the latter has the closer inductance to the conventional three-turn CA highlighted by bold font. The turns of the coil antenna are therefore determined to be five for its inductance named L
ant being about 1.706 uH, meeting the requirement of design specification. Corresponding to
Figure 2, CA’s equivalent resistance in the series mode named
Rs_ant can be achieved by multimeter in measurement and by a software simulator in simulation. Furthermore, CA’s equivalent resistance in the parallel mode named
Rp_ant can be achieved by the following equation, Equation (2) [
14]:
In this equation,
Rp_ant is the resistance in the parallel equivalent circuit at 13.56 MHz.
Rp_self can be regarded as pure resistance when the initial CA only resonates at current frequency. On the right of the equation,
ƒ(ant) and
ƒ(self) are the frequencies of the desired and current state, respectively. Additionally, the capacitance of the miniaturized CA named C
ant can be calculated by the LC equation, Equation (3)
In this equation, ƒ is the currently operational frequency and L is the inductance of the miniaturized CA. In this equivalent circuit, L = Lant. All their real values are given in the following section for calculation in simulation. Here, step one, parameter extraction of equivalent circuit, is complete.
Additionally, an equivalent circuit of the CA can not solely resonate at the desired frequency of 13.56 MHz until a matching circuit is connected with it. Therefore, the characteristics of RF electronic elements should be investigated and calculated before they are adopted in a matching system. A Smith chart can visually present the influence of every electronic element on the equivalent circuits of the CA, as shown in
Figure 3.
In the above Smith chart, a shunt and series capacitor and inductor can be found. Every electronic element has its own property on the electronic system when connected to it. Shunt inductance can make the currently operational point extracted from the CA move along the red circle anticlockwise, and the shunt capacitance can make the currently operational point move along the red circle clockwise. Similarly, series inductance denoted by the blue arrow line can make the currently operational point move along the green point clockwise, and the series capacitor can make the current operational point move along the green point anticlockwise. According to RF electronic circuit theory, every operational state of an extracted equivalent circuit can be mapped on the corresponding Smith chart. An excellently designed matching circuit should move the current operational point to the center of the circle, making the whole RF system resonate at a frequency of 13.56 MHz. Before deigning the matching circuit, an index, the Q-factor, should be selected carefully in different equivalent models, as it will have a great influence on the performance of the near-field wireless system. Here, suppose the Q-factor is equal to 10, meeting the requirement of industry specification ISO14443. Therefore, the gross resistance of matching and equivalent circuits in the series situation named
Rs_tol can be calculated by Equation (4). Similarly, the gross resistance in the parallel situation named
Rp_tol can be obtained by Equation (5).
where the
Rs_m1 and
Rp_m1 are the resistances needed to be deployed in the matching circuit. The ω is the angular frequency at the best operational state. Here,
ω is equal to 2π × 13.56 MHz.
L is the value of inductance of the miniaturized CA at the same frequency. Furthermore, the respective values of
Cs_m1 and
Cs_m2 can be easily obtained based on Equation (6) due to the conjugate relation after normalization in the Smith chart [
15].
According to the Smith chart, every value of matching electronic elements can be calculated easily, and the detailed process is presented in the following section. Similarly, the parallel matching circuit can be designed with the same process. Finally, the second step of the RF electronic system named the interim circuit is complete, and the matching circuits for the series and parallel equivalent circuits can be obtained, as shown in
Figure 4.
However, according to existing literature, small antenna cannot obtain broad bandwidth unless some additional technologies are adopted. After integrating a matching circuit, an LC resonator must be introduced to the RF electronic system for a broader bandwidth as a third step. According to Equation (3), an LC resonator designed to exactly resonate at 13.56 MHz can efficiently widen the bandwidth according to RF electronic rules as seen in
Figure 5. Moreover, small values of inductance and large values of capacitance have good performance in widening the impedance bandwidth at low frequency.
Several pairs of specific parameters of the LC resonator meeting the restriction of Equation (3) are listed in
Table 2. After fine adjustment, the final data are determined by plotting the performance of the electronic elements on a Smith chart.
In summary, after miniaturizing the dimension of the CA, establishing an equivalent circuit according to extracted parameters from the miniaturized coil antenna is the first key step. Then, the second step is to design a specially matching circuit for the circuit achieved in the first step. Furthermore, an LC resonator operating at around 13.56 MHz is introduced for higher performance [
16].