2. Impediments of dual-band near-field wireless energy transfer resonator designs

For a single-band near-field WET resonator design, designers delve into achieving maximum power transfer efficiency (PTE) between a pair of coupled resonators by designing the highest possible quality factor (Q-factor). However, there is an apparent complexity for designing resonators operating in more than one frequency band. PTE for either one of the frequency bands tends to surpass its counterpart. As such, concurrent capitalization on PTE for both frequency bands, f1 and f2, remains as one of the ultimate challenges.

Another concern is the inversely proportionate relation between Q-factor and bandwidth. Increasing PTE of the affected frequency band is feasible by developing resonators with enhanced Q-factor. This comes at the expense of higher bandwidth which is pivotal especially for resonators aiming for concomitant power and data transfer functionalities as portrayed in Figure 1. PTE for f1 is higher with improved Q-factor than f2 but falls behind in terms of bandwidth since it is constrained by Q-factor. On the other hand, redesigning higher Q-factor resonator in contemplation of attaining improved PTE at f2 unfortunately leads to bandwidth degradation. As such, there is always a dilemma between achieving PTE equilibrium for f1 and f2 and maximum PTE and bandwidth for each frequency bands.

Imperfect positioning of loop resonator is yet another impairment of WET system which impacts its performance metrics specifically coupling coefficient, k, and PTE [7–9]. Strict adherence toward perfect alignment between a pair of loop resonator in assuring maximum transfer efficiency is seemingly impossible in practical sense because of misalignment be it planar, lateral, or angular frequently supervened [10]. Referring to Figure 2, planar displacement refers to the angle of rotation ar when both centers are axially aligned. Separated at a fixed axial distance, z, the center of receiving loop resonators is shifted by a distance, ax, known as

horizontal lateral displacement, while ay is referred as vertical lateral displacement. The occurrence of simultaneous planar and the respective lateral displacements are visualized by ar with either ax or ay offsets. Angular displacement occurs when the plane of receiving loop resonator is being tilted by an angle θ [11]. Similarly, the consequences of displacement should be taken into consideration in the design of

Types of displacements between near-field coupled resonators: (i) planar; (ii) concurrent planar and lateral (x-axis); (iii) concurrent planar and lateral (y-axis); (iv) lateral (x-axis), (v) lateral (y-axis);

dual-band coupled resonators.

Figure 1.

Figure 2.

51

(vi) angular.

Transfer efficiency equilibrium for dual-band near-field coupled resonators.

Dual-Band Resonator Designs for Near-Field Wireless Energy Transfer Applications

DOI: http://dx.doi.org/10.5772/intechopen.89218

Dual-Band Resonator Designs for Near-Field Wireless Energy Transfer Applications DOI: http://dx.doi.org/10.5772/intechopen.89218

#### Figure 1. Transfer efficiency equilibrium for dual-band near-field coupled resonators.

#### Figure 2.

Provision of more than one frequency band is enabled by resonator which is intended for several functions either concurrent power and data transfer or concurrent wireless charging at multiple standards. At present, there are two principal standards for wireless charging of consumer electronics specifically smartphones. The Wireless Power Consortium, otherwise known as Qi, is one of the leading wireless charging standards operating in low-frequency (LF) band, 110–205 kHz [2]. AirFuel Alliance is the merger between Power Matters Alliance (PMA) and the Alliance for Wireless Power (A4WP, also known as Rezence) [3]. A4WP employs magnetic resonance coupling technique operating at 6.78 MHz 15 kHz [4], while both Qi and PMA engage in inductive charging technique. The range of PMA's operating frequency is from 277 to 357 kHz [5]. Nonetheless, unlicensed industrial, scientific and medical (ISM) radio bands of up to 13.56 MHz are commonly selected to be the operating frequency for both inductive and magnetic resonant techniques

This chapter commences with challenges in relation to dual-band near-field WET design and the corresponding key performance metrics followed by design approaches and rectification techniques currently employed to alleviate the adverse

effects on performance metrics with the intention of providing insights for designers in deciding and further enhancing current rectification options available in the design of dual-band near-field resonators. This framework, however, solely pertains to front-end resonator designs excluding end-to-end scope of near-field

2. Impediments of dual-band near-field wireless energy transfer

For a single-band near-field WET resonator design, designers delve into achieving maximum power transfer efficiency (PTE) between a pair of coupled resonators by designing the highest possible quality factor (Q-factor). However, there is an apparent complexity for designing resonators operating in more than one frequency band. PTE for either one of the frequency bands tends to surpass its counterpart. As such, concurrent capitalization on PTE for both frequency bands, f1 and f2, remains

Another concern is the inversely proportionate relation between Q-factor and bandwidth. Increasing PTE of the affected frequency band is feasible by developing resonators with enhanced Q-factor. This comes at the expense of higher bandwidth which is pivotal especially for resonators aiming for concomitant power and data transfer functionalities as portrayed in Figure 1. PTE for f1 is higher with improved Q-factor than f2 but falls behind in terms of bandwidth since it is constrained by Q-factor. On the other hand, redesigning higher Q-factor resonator in contemplation of attaining improved PTE at f2 unfortunately leads to bandwidth degradation. As such, there is always a dilemma between achieving PTE equilibrium for f1 and f2 and

Imperfect positioning of loop resonator is yet another impairment of WET system which impacts its performance metrics specifically coupling coefficient, k, and PTE [7–9]. Strict adherence toward perfect alignment between a pair of loop resonator in assuring maximum transfer efficiency is seemingly impossible in practical sense because of misalignment be it planar, lateral, or angular frequently supervened [10]. Referring to Figure 2, planar displacement refers to the angle of rotation ar when both centers are axially aligned. Separated at a fixed axial distance, z, the center of receiving loop resonators is shifted by a distance, ax, known as

in the current research community [6].

Recent Wireless Power Transfer Technologies

WET systems.

50

resonator designs

as one of the ultimate challenges.

maximum PTE and bandwidth for each frequency bands.

Types of displacements between near-field coupled resonators: (i) planar; (ii) concurrent planar and lateral (x-axis); (iii) concurrent planar and lateral (y-axis); (iv) lateral (x-axis), (v) lateral (y-axis); (vi) angular.

horizontal lateral displacement, while ay is referred as vertical lateral displacement. The occurrence of simultaneous planar and the respective lateral displacements are visualized by ar with either ax or ay offsets. Angular displacement occurs when the plane of receiving loop resonator is being tilted by an angle θ [11]. Similarly, the consequences of displacement should be taken into consideration in the design of dual-band coupled resonators.

### 3. Performance metrics

Figure-of-merit (FOM) consideration yields a comparative insight for a diverse WET system design [12]. Derivation of FOM originates from analytical expression of link transfer efficiency (PTE) based on circuit theory (CT) [13] and reflected load theory (RLT) [14] as shown in Eq. (1) and Eq. (2). FOM is reliant on coupling coefficient, k, and Q-factor parameters which are derived from Eq. (3) and Eq. (4). Proportional relationship is shared between coupling coefficient, k, and mutual inductance, M, with an inverse correlation shared between the latter and product of square root of transmitting and receiving self-inductances, L1,2. Q-factor, Q1,2, is proportional to angular frequency, ω, and self-inductances but inversely proportional to transmitting and receiving resistances, R1,2:

$$PTE = FOM\left[\left\{\mathbf{1} + \left(\mathbf{1} + FOM\right)^{0.5}\right\}\right]^{-1} \tag{1}$$

$$FOM = k^2 Q\_1 Q\_2 \tag{2}$$

between each two turns on a pair of loops with turn radii, ri and rj. μ and n1,2 represent conductor permeability and number of loops' turns, while ρ is the factor which is dependent on loop profile. K and E refer to complete elliptic integrals of

Dual-Band Resonator Designs for Near-Field Wireless Energy Transfer Applications

ri þ rj � �<sup>2</sup> <sup>þ</sup> <sup>z</sup><sup>2</sup> h i�0:<sup>5</sup>

Xn2 j¼1

Other FOMs used as performance quantification are summarized in Table 1.

There are accompanying implications with the choice of operating frequency on WET links. With higher frequency, the manifestation of eddy currents results in a nonuniformly distributed current density in conductive trace. The probability of current flowing toward the surface of a conductor known as skin effect amplifies alternate current resistance followed by power and heat dissipations [25]. Proximity effect is yet another dilemma of nonuniform current distribution due to current crowding on the inner loop edge caused by nearby conductive traces or layers [26]. On the contrary, current density is uniformly distributed at lower frequency in which eddy current effects are negligible. As such, feasibility of achieving higher power transfer efficiency is established with lower operating frequency at kHz than higher operating frequency at MHz at the expense of transfer range extension and

For dual-band WET links, the ratio between frequencies selected is equally important since it is proportional to the transfer efficiency variance between f1 and f2 [28]. Additionally, selecting a larger ratio between frequencies with both power and data being transmitted at significantly lower and higher operating frequency bands turns out to be one of the isolation options available in curbing interference [23]. Table 2 summarizes frequency selections opted for dual-band resonator designs. For example, variance of PTE between kHz and MHz frequencies is larger

References f1 f2 Ratio, f2=f1 Variance, ΔPTEf1\_f2 (%)

[30] 100 kHz 13.56 MHz 136 <10 [29] 100 kHz 6.78 MHz 68 3 [31, 32] 200 kHz 6.78 MHz 34 7.4, <8 [33] 300 MHz 900 MHz 3 8 [24] 300 MHz 675 MHz 2 7 [34–36] 6.78 MHz 13.56 MHz 2 15, 11.93, 1.68 [37] 90.3 MHz 138.8 MHz 2 1 [23] 300 MHz 700 MHz 2 1 [38] 470 MHz 730 MHz 2 11.4

Summary of frequency selections for dual-band near-field WET resonator.

<sup>ρ</sup>�<sup>1</sup> <sup>1</sup> � <sup>0</sup>:5ρ<sup>2</sup> � �Kð Þ� <sup>ρ</sup> <sup>E</sup>ð Þ<sup>ρ</sup> � � (5)

Mij ri, rj, z � � (7)

(6)

the first and second kind:

4. Frequency selection

reduced displacement sensitivity [27].

Table 2.

53

Mij ¼ 2μ rirj

DOI: http://dx.doi.org/10.5772/intechopen.89218

� �0:<sup>5</sup>

M ¼ ρ

Xn1 i¼1

ρ ¼ 2 rirj � �0:<sup>5</sup>

$$k = M(L\_1 L\_2)^{-0.5} \tag{3}$$

$$Q\_{\mathbf{1},2} = aL\_{\mathbf{1},2} \left(R\_{\mathbf{1},2}\right)^{-1} \tag{4}$$

Performance metrics that are commonly used are power transfer efficiency, Qfactor, and coupling coefficient. As discussed in Section 2, PTE and Q-factor share a positive correlation which is further validated from Eq. (1) and Eq. (2). Nevertheless, optimum coupling coefficient is often desirable in maximizing PTE. Since k is dependent on M and M is negatively correlated to transfer distance, z, a cautionary reminder is to ensure optimum transfer distance between transmitting and receiving resonators. This is validated with subsequent Equations [15] that reveal the correlation between M, z, and k [16]. Mij indicates partial mutual inductance


Table 1. Figure-of-merits (FOM). Dual-Band Resonator Designs for Near-Field Wireless Energy Transfer Applications DOI: http://dx.doi.org/10.5772/intechopen.89218

between each two turns on a pair of loops with turn radii, ri and rj. μ and n1,2 represent conductor permeability and number of loops' turns, while ρ is the factor which is dependent on loop profile. K and E refer to complete elliptic integrals of the first and second kind:

$$M\_{\vec{\eta}} = 2\mu \left( r\_i r\_j \right)^{0.5} \rho^{-1} \left[ (\mathbf{1} - \mathbf{0}.5\rho^2) \mathbf{K}(\rho) - E(\rho) \right] \tag{5}$$

$$\rho = 2\left(r\_i r\_j\right)^{0.5} \left[\left(r\_i + r\_j\right)^2 + z^2\right]^{-0.5} \tag{6}$$

$$\mathcal{M} = \rho \sum\_{i=1}^{n\_1} \sum\_{j=1}^{n\_2} \mathcal{M}\_{ij}(r\_i, r\_j, z) \tag{7}$$

Other FOMs used as performance quantification are summarized in Table 1.

#### 4. Frequency selection

3. Performance metrics

Recent Wireless Power Transfer Technologies

tional to transmitting and receiving resistances, R1,2:

FOM Concerned parameters Dual-

PL(Vs)�<sup>2</sup> Transfer efficiency, load power, and voltage source [17]

(ARX)�1.5 Transfer efficiency, transfer distance, and area of receiver [18, 19]

and outermost side length [20]

Transfer efficiency, transfer distance, and outermost side lengths of transmitter and receiver [22]

PTEz(do)�<sup>1</sup> Transfer efficiency, transfer distance,

PTEz(A)�0.5 Transfer efficiency, transfer distance, and area [21]

PTEz(A)�0.5 Transfer efficiency, transfer distance, and area [23, 24]

transmitting, receiving resonator [12]

Q1 Q2 Coupling coefficient, Q-factor

k2

PTE<sup>2</sup>

PTEz<sup>3</sup>

PTEz/ (do\_tx � do\_rx)0.5

Table 1.

52

Figure-of-merits (FOM).

Figure-of-merit (FOM) consideration yields a comparative insight for a diverse WET system design [12]. Derivation of FOM originates from analytical expression of link transfer efficiency (PTE) based on circuit theory (CT) [13] and reflected load theory (RLT) [14] as shown in Eq. (1) and Eq. (2). FOM is reliant on coupling coefficient, k, and Q-factor parameters which are derived from Eq. (3) and Eq. (4). Proportional relationship is shared between coupling coefficient, k, and mutual inductance, M, with an inverse correlation shared between the latter and product of square root of transmitting and receiving self-inductances, L1,2. Q-factor, Q1,2, is proportional to angular frequency, ω, and self-inductances but inversely propor-

PTE <sup>¼</sup> FOM <sup>1</sup> <sup>þ</sup> ð Þ <sup>1</sup> <sup>þ</sup> FOM <sup>0</sup>:<sup>5</sup> h i n o �<sup>1</sup>

FOM <sup>¼</sup> <sup>k</sup><sup>2</sup>

Q1, <sup>2</sup> ¼ ωL1, <sup>2</sup> R1, <sup>2</sup>

Performance metrics that are commonly used are power transfer efficiency, Qfactor, and coupling coefficient. As discussed in Section 2, PTE and Q-factor share a positive correlation which is further validated from Eq. (1) and Eq. (2). Nevertheless, optimum coupling coefficient is often desirable in maximizing PTE. Since k is dependent on M and M is negatively correlated to transfer distance, z, a cautionary reminder is to ensure optimum transfer distance between transmitting and receiving resonators. This is validated with subsequent Equations [15] that reveal the correlation between M, z, and k [16]. Mij indicates partial mutual inductance

band

(1)

Q1Q<sup>2</sup> (2)

� ��<sup>1</sup> (4)

<sup>k</sup> <sup>¼</sup> M Lð Þ <sup>1</sup>L<sup>2</sup> �0:<sup>5</sup> (3)

Significance

Q parameters

load

No Independent optimization of k and

efficiency and power delivered to

distance and outermost side lengths

No Take into account of transfer

No Equitable assessment between various transfer distance and

No Take into account of transfer

No Equitable assessment between various transfer distance and

No Equitable assessment between various transfer distance and asymmetrical pair of resonators

Yes Equitable assessment between various transfer distance and

geometry designs

geometry designs

geometry designs

There are accompanying implications with the choice of operating frequency on WET links. With higher frequency, the manifestation of eddy currents results in a nonuniformly distributed current density in conductive trace. The probability of current flowing toward the surface of a conductor known as skin effect amplifies alternate current resistance followed by power and heat dissipations [25]. Proximity effect is yet another dilemma of nonuniform current distribution due to current crowding on the inner loop edge caused by nearby conductive traces or layers [26]. On the contrary, current density is uniformly distributed at lower frequency in which eddy current effects are negligible. As such, feasibility of achieving higher power transfer efficiency is established with lower operating frequency at kHz than higher operating frequency at MHz at the expense of transfer range extension and reduced displacement sensitivity [27].

For dual-band WET links, the ratio between frequencies selected is equally important since it is proportional to the transfer efficiency variance between f1 and f2 [28]. Additionally, selecting a larger ratio between frequencies with both power and data being transmitted at significantly lower and higher operating frequency bands turns out to be one of the isolation options available in curbing interference [23]. Table 2 summarizes frequency selections opted for dual-band resonator designs. For example, variance of PTE between kHz and MHz frequencies is larger


Table 2.

Summary of frequency selections for dual-band near-field WET resonator.

than MHz frequencies with reduced ratio of f2 to f1. However, research work demonstrated in [29] reports on reduced PTE variance with higher frequency ratio by implementing other rectification techniques which will be discussed in subsequent sections. In general, it is observed that there is higher probability of concurrently capitalizing PTE for both frequencies by designing resonators with lowest possible ratio of f2 to f1.

design approach comes with their respective strengths and weaknesses which deserved appropriate assessment as tabulated in Table 3. Single-coil approach is preferred owing to minimum cross-coupling as compared to multi-coil [34]. Even though designing two separate coils in multi-coil approach necessitate more geometrical area, there is a greater potential in exploiting on highest possible transfer efficiency at two different frequencies in a single transmitter as it allows indepen-

Dual-Band Resonator Designs for Near-Field Wireless Energy Transfer Applications

Apart from deciding on the type of design approach to engage with, dual-band support configuration ought to be determined as well. Applicable configurations [28] involve designing either identical support mode as in dual-band transmitter (TX) and dual-band receiver (RX) or nonidentical support mode as in dual-band transmitter and single-band receivers. Bearing in mind that there is no superior design approach, rectification techniques employed address the respective shortcomings. Referring to Figure 3, rectification techniques for dual-band resonator designs which will be discussed in the following subsections encompass aspects relating to resonator design, resonator configuration, and impedance transforma-

There is a penchant in designing printed spiral coils which encompassed conductive trace etched on dielectric substrates over conventional solenoid coils owing to lightweight and compactness features apart from having privilege of freedom in geometrical optimization [45] and conformity capability on malleable substrates [46] as compared to its predecessor. Equivalent series resistance (ESR) and substrate's dielectric losses are commonly contemplated to boost Q-factor of loop resonator designed [47] since the performance metric indicator, kQ, product can be

where ESR = [(R11R22) � (R12R21)]0.5 for two-port system. Despite the fact that higher inductance could be acquired by increasing number of turns, ESR is not exempted. Direct current (DC) and alternate current (AC) resistances are components of ESR for a loop resonator. Hence, it is obligatory to exercise caution in geometrical layout alteration specifically number of turns, n, conductor width, wc, and spacing between conductor trace, sc. Figure 4 illustrates comparison between a conventional layout of spiral resonator with uniform distribution of wc and sc and

By designing inconstant conductor width distributions and spatial distributions, Q-factor enhancement is attained in double-layer printed spiral resonator [49], printed circular resonator [50], and stacked multilayer printed spiral resonator [51]. This is made possible as losses induced by eddy current are hindered with designs that involve gradual decrement of conductive trace widths from the outermost loop to the innermost loop [52] unlike conventional constant width for all loops. It is worth keeping in mind that designing larger constant conductor width for all turns and smaller constant spacing between adjacent conductor trace will only reinforce the total resistance [53]. However, ensuring ratio between conductor width and spacing to be relatively small aids in the reduction of proximity effects [54].

kQ <sup>¼</sup> j j <sup>Z</sup><sup>21</sup> ESR�<sup>1</sup> (8)

derived from impedance matrix components given by [48]:

nonuniform layout refinement between each loop turns.

dent selection of inductance and quality factor [31].

DOI: http://dx.doi.org/10.5772/intechopen.89218

tion network.

55

6. Rectification techniques

6.1 Resonator design
