# A Compact Dual-Band Wireless Power Transfer System Based on Circular Edges with DGS Resonators

Mahya Samadbeik, Alireza Siadatan, Maryam Sepehrinour

► To cite this version:

Mahya Samadbeik, Alireza Siadatan, Maryam Sepehrinour. A Compact Dual-Band Wireless Power Transfer System Based on Circular Edges with DGS Resonators. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0150. hal-05106013

HAL Id: hal-05106013

https://utc.hal.science/hal-05106013v1

Submitted on 10 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A Compact Dual-Band Wireless Power Transfer System Based on Circular Edges with DGS Resonators

Mahya Samadbeik,
Department of Electrical
Engineering,
Wes Tehran Branch,
Islamic Azad University,
Tehran, IRAN.

Samadbeik.m@gmail.com

Alireza Siadatan², SMIEEE
Department of Electrical and
Computer Science,
York University,
Toronto, Ontario, Canada.
siadatan@yorku.ca

Maryam Sepehrinour³,
Department of Computer Science
and Technology,
Algoma University,
Brampton Campus, Ontario,
Canada.

maryam.sepehrinour@algomau.ca

## Keywords

«Defected Ground Structure (DGS)», «Wireless Power Transfer (WPT)», «Dual-Band Frequency», «Resonators».

## Abstract

The present study deals with the design of a dual-band wireless power transfer (WPT) system using Defected ground structure (DGS) model resonators. The most important factor will be achieving high conversion efficiency while keeping its structural dimensions small. To improve transmission efficiency and minimize return losses and insensitivity to mismatch between resonators at their resonance frequencies, we introduce a gap in the ground layer. For the proposed system, the transmission power efficiency at frequencies of 330 and 770 MHz is 92.5% and 84.6%, respectively, the simulation results from both CST and ADS software are closely aligned. Also, the figure of merit (FoM) derived from the simulation results is 0.78 and 0.72 at respective resonance frequencies.

## Introduction

Over the past few decades, wireless power transmission technology (WPT) has gained prominence as a means of transmitting electrical energy without conductive wires in a wide range of applications such as radio frequency identification (RFID) [1], and application of implantable biomedical systems in human body [2]. Wireless power transfer (WPT) technology enables the transmission of electric power without the need for physical wires or contacts. This capability has spurred significant research driven by the increasing demand for wireless

portable electronic devices. The optimal design and performance enhancement of electromagnetic systems have always been crucial topics in electrical engineering research. For example, in [3], methods for optimizing the design of a synchronous reluctance machine have been presented, where efforts have been made to enhance the rotor structure and improve the overall system performance. Similarly, in wireless power transfer (WPT) systems, a similar goal is pursued—optimizing the structure of resonators to increase power transfer efficiency. WPT offers the potential for convenient and unrestricted power transmission, simplifying the charging process for everyday electronic devices. One proposed method involves using printed spiral coils in a planar magnetically coupled resonant WPT system, which can achieve an efficiency of 81.68% at a transmission distance of 10 cm, with a size of 100 mm×100 mm. Additionally, wireless sensors have been developed for various applications such as article tracking, location detection, and temperature sensing, operating at 1.6 GHz for power and 2.3 GHz for data transfer [4].

Briefly speaking, the implementation of WPT systems can be broadly classified into three categories. The first category relies on radiative electromagnetic waves based on far-fields [5]. The second and third utilize capacitive [6] and inductive [7] coupling for power transmission, respectively. Due to the potentially harmful effects of the electric field on human body compared to the magnetic field, the inductive coupling method is typically favored. The first application of this technology was the use of large-scale magnetically coupled coils. Later, very strong spiral coupled coils were used to reduce the circuit size of the transmitters and
receivers so that the resonant inductive feeding
for each terminal would lead to impedance
matching between the input and outputs of the
system [8].

The output of WPT systems used in biomedical
implant applications requires low power to
operate. In this regard, we can use DGS-coupled
resonators to design single or dual-band
frequency systems [9]. In high-efficiency power
transfer systems, increasing voltage gain and
optimizing circuit topology are crucial factors.
For instance, in [10], a two-stage asymmetrical Γ-
Z-source inverter is introduced to achieve high
voltage gain, demonstrating the importance of
advanced circuit design in power conversion.
Similarly, in wireless power transfer (WPT)
systems, circuit optimization plays a significant
role in improving power transmission efficiency.
Resonant coupling techniques, whether inductive
or capacitive, are commonly used to enhance
efficiency. These methods leverage resonant
circuits to focus energy within a specific
frequency band. Resonant device solutions, such
as printed spirals with surface-mounted
capacitors, are favored for small electronic
devices and Implantable Medical Devices (IMD)
due to their compact size and high-quality factor
(Q). Open ground structures (DGS) are also
employed in RF and microwave applications to
create low-profile resonators, making them
particularly suitable for WPT systems with
limited space for resonator placement [11].

One of the advantages of the WPT system based
on DGS resonators is their different geometry,
which facilitates manufacturing and reduces the
dimensions of these resonators compared to coil
resonators. In [12], two DGS amplifiers are
cascaded, utilizing different capacitive values to
produce two frequency bands [12]. Although the
geometry used provides good matching for the
dual-band WPT system, it is large in size, and
thus, single-loop DGS overlap is used to reduce
the size by 50%. However, this reduction also
results in a decreased transmission distance [12].
Using H-shaped DGSs for WPT has been
explored in [13]. A study on H-shaped, and semi-
H-shaped resonators for the 300-MHz band was
conducted in [14], achieving efficiency of 68% at
a distance of 13mm for the H-shaped design and
73% at 25mm distance for the semi-H-shaped
design. The microwave band pass filter plays a
crucial role in cellular mobile and satellite
systems, requiring both compactness and high
performance. Key factors for system
improvement include affordability, lightweight

construction, and minimal loss. Utilizing
microstrip lines simplifies design calculations,
while an octagonal closed-loop resonator reduces
curvature effects compared to a square loop
design. The choice of substrate material is
important for achieving minimal loss, lightweight
construction, and cost-effectiveness. It is essential
to keep the loss factor low to reduce
electromagnetic energy dissipation. A high
dielectric constant allows for a smaller filter size.
As new applications and designs emerge,
maintaining high performance is vital for the
filter's effectiveness [15]. The system presented
in [16] combines the main resonator with a
secondary resonator. The size of this design along
with the reduction of the maximum transmission
power in this system facilitates its use in medical
implants. In this article, we improve efficiency
and reduce sensitivity to distance and angular
changes using circular changes in the structure of
the combined resonators and creating a gap on the
ground surface of the resonator.

Section 2 focuses on Semi-H-shape resonators, while Section 3 details the design of the proposed model. Subsequently, and finally, section 4 presents the conclusion.

Modeling Dual-Band DGS Resonators

One of the disadvantages of DGS-coupled
resonators with rectangular sections is misalignment
caused by horizontal shift and orientation angles. As
a case study, the desired two-band structure, as shown
in Figure 1, is obtained by combining the Semi-H-
shape resonators.

<figure><img src="image_2.png" /></figure>
<figure><img src="image_3.png" /><figcaption>Fig. 1. a) WPT structure simulated in HFSS software b) Geometry of the proposed DGS resonator [16].</figcaption></figure>

After simulating the proposed model with HFSS software, the following results were obtained. Figure 2 shows the S parameters for the proposed dual-band power transmission system at 330 MHz frequency and 770 MHz frequency.

<figure><img src="image_4.png" /><figcaption>Fig. 2: Simulation results of S-Parameters of the designed structure [16].</figcaption></figure>

Considering that the maximum transmission power for this structure is achieved at a distance of 17 mm, as displayed in Figure 3, the calculated efficiency is 80 % at 330 MHz and 73% at 770 MHz [16].

<figure><img src="image_5.png" /><figcaption>Fig. 3: Simulation results of the efficiency of the designed structure [16].</figcaption></figure>

In the circular DGS-coupled resonator, sensitivity to angular rotation is significantly improved. The structure of the resonators is completely symmetrical, achieving resonance state through two resonance loops and the corresponding capacitors. Given that the placement of the transmitter and receiver may vary in certain medical devices and other applications, we examine, in details, the sensitivity of this structure to the angular rotation between the receiver and transmitter in Figure 4.

<figure><img src="image_6.png" /><figcaption>Fig. 4: Sensitivity to angular rotation a) Angular rotation of receiver and transmitter relative to each other b) Frequency response changes for different angular rotation angles between receiver and transmitter relative to each other</figcaption></figure>

As illustrated, the transmission response of this structure exhibits significant variations with angular rotation, leading to increased transmission loss as the locations of the resonators shift in relation to each other. As a result, to design an
ideal model that enhances system performance at resonance frequencies, increases efficiency, and reduces sensitivity to angular changes, we propose a model that creates a gap on the ground surface of the resonator, minimizes transmission losses and increases efficiency. Additionally, to further reduce the sensitivity to the rotation of the two resonators, the symmetry of the circuit is increased taking into account that the simplest and most practical way to increase the symmetry is to change the structure of the resonators to a circular shape. Figure 5 depicts the designed model of WPT system with a circular cross-section.

<figure><img src="image_7.png" /><figcaption>Fig. 5: Proposed resonator structure with adaptive gap and circular edges</figcaption></figure>

The main resonator creates a lower frequency band (To produce f1, the loop includes self-inductance L1 and capacitor C1). At f1, the surface current distribution around the main resonator contains only C1 capacitor (outer circle). The second resonator generates a higher frequency band, (to produce f2, the loop includes self-inductance L2 and is equivalent to capacitor series C1, C2). At f2, the surface current distribution exists around the second resonator (smaller loop), which includes the capacitor C1 and C2. To determine the self-inductance of coils, we analyze the impedance curve at the desired frequencies. The initial inductance values, corresponding to each frequency of dual-band DGS are obtained using (1) [17], where Z11 and Z22 represent the impedance seen at the corresponding DGS input. The values of Z11 and Z22 are obtained through simulation, where f is the resonant frequency and it is calculated from (2) [17].

$$L_1 = \frac{Im(Z_{11})}{2\pi f_1} \qquad L_2 = \frac{Im(Z_{22})}{2\pi f_2} \qquad (1)$$

$$f_1 = \frac{1}{2\pi\sqrt{L_1 C_1}} \qquad f_2 = \frac{1}{2\pi\sqrt{L_2 \frac{C_1 C_2}{C_1+C_2}}} \qquad (2)$$

For this design, using equations (1), (2) and software simulation, the values of inductances and capacitances are shown in Table 1.

<table><caption>Table I. The caption must be followed by the table</caption><thead><tr><td>Parameters</td><td>Values</td></tr></thead><tbody><tr><td>C<sub>1</sub></td><td>0.68 pF</td></tr><tr><td>C<sub>2</sub></td><td>2.7 pF</td></tr><tr><td>C<sub>3</sub></td><td>1.5 pF</td></tr><tr><td>L<sub>1</sub></td><td>330 nH</td></tr><tr><td>L<sub>2</sub></td><td>75 nH</td></tr></tbody></table>

The Stub capacitor is obtained by equation (3) [7]. So β is the phase shift constant and Z0=50 Ω.

$$C_{\text{stub}} = \frac{\tan(\beta l_{\text{stub}})}{\omega Z_0} \qquad (3)$$

At resonance, electromagnetic fields fall within resonators, exchanging electric and magnetic energy periodically. Outside the resonators, the fields decay evanescently, unless they are coupled with another resonator. Negative index metamaterial (NIM) can enhance evanescent waves, effectively reducing the distance between resonators. Designing NIM involves reconstructing structural properties such as effective permeability and permittivity to exhibit left-handed characteristics. Evanescent wave amplification is crucial for magnetic resonant coupling, requiring negative effective permeability. This study presents an equivalent circuit model that can provide a deeper understanding compared to existing theoretical models [19].

The equivalent circuit in the structure of resonators with circular edges, based on the arrangement of simulated inductors and capacitors is shown in Figure 6. In the simplified equivalent circuit, the first loop which contains C1 and L1, generates the f1, while the second loop which contains Cp (C1, C2), and L2 generates the f2.
<figure><img src="image_8.png" /><figcaption>Fig. 6: Equivalent circuit model of the circular edges DGS</figcaption></figure>

The TX and RX resonators are identical, resulting in similar LC circuits facing each other. In this design, C3 represents the gap created on the resonator and functions as a capacitor. M1 and M2 denote the mutual inductances, and k1 and k2 are the magnetic coupling coefficients. These values are directly influenced by the distance between the resonators and are derived from equations (4) and (5), which consider the Z-parameters of the proposed system [20].

$$M_1 = \frac{lm(Z_{12})}{2\pi f_1} \qquad M_2 = \frac{lm(Z_{21})}{2\pi f_2} \qquad (4)$$

$$K_1 = \frac{M_1}{L_1} \qquad K_2 = \frac{M_2}{L_2} \qquad (5)$$

The analysis and design of metamaterials are typically grounded in effective medium theory, which simplifies the electromagnetic response of the unit cell in the near-field by replacing the metamaterial with a homogeneous continuous medium described by effective parameters. This theory uses periodicity to extract the properties of the metamaterial for design and analysis. However, practical applications may be affected by truncation effects, and when incorporated into wireless power transfer systems, the interaction between coils can impact the metamaterial's response.

To analyze the system's electromagnetic response, the metamaterial can be represented as a simple RLC resonant circuit using an equivalent circuit model, simplifying the theoretical analysis of WPT systems that utilize metamaterials [21]. Table 2 shows the design values of the proposed model.

<table><caption>Table II. The caption must be followed by the table</caption><thead><tr><td>Parameters</td><td>Values (mm)</td></tr></thead><tbody><tr><td>W<sub>sub</sub></td><td>20</td></tr><tr><td>L<sub>sub</sub></td><td>20</td></tr><tr><td>W<sub>f</sub></td><td>1.9</td></tr><tr><td>L<sub>f</sub></td><td>10</td></tr><tr><td>L<sub>stub</sub></td><td>5</td></tr><tr><td>W<sub>0</sub></td><td>16</td></tr><tr><td>L<sub>0</sub></td><td>14</td></tr><tr><td>W<sub>1</sub></td><td>2</td></tr><tr><td>L<sub>1</sub></td><td>7</td></tr><tr><td>W<sub>S1</sub></td><td>0.3</td></tr><tr><td>L<sub>S1</sub></td><td>3</td></tr><tr><td>W<sub>S2</sub></td><td>0.2</td></tr><tr><td>L<sub>S2</sub></td><td>5</td></tr><tr><td>W<sub>S3</sub></td><td>0.5</td></tr><tr><td>L<sub>S3</sub></td><td>5</td></tr><tr><td>g</td><td>1</td></tr></tbody></table>

The design process involves placing the main and second resonators in the same spatial region, which reduces the dimensions of the system. To achieve maximum efficiency, the U factor is defined as shown in equation (6) [22].

$$U = k\sqrt{Q_1 Q_2} \qquad (6)$$

where Q1 and Q2 are the unloaded quality factors of the TX and RX respectively. Due to the similarity of the resonators on both sides, as a result, Q1 and Q2 are called Q factors. If we consider Figure 7 for wireless power transfer calculations, the Q values are obtained as (7) [22].

<figure><img src="image_9.png" /><figcaption>Fig. 7. WPT equivalent circuit</figcaption></figure>

In this system, kQ is calculated based on equation (7) and the value of kQ is 26 for the 330 MHz frequency band and 12 for the 770 MHz frequency band.
frequency band. The maximum efficiency value will be calculated as (8) [23].

$$kQ = \frac{\omega_0 L_M}{\sqrt{R_1 R_2}} \qquad (7)$$

$$\eta_{max} = \left( \frac{U}{1+\sqrt{1+U^2}} \right)^2 \qquad (8)$$

## Results And Discussion

The magnetic field in the proposed DGS is distributed at 330 MHz and 770 MHz frequencies based on Figure 9. These results are obtained based on software simulation.

<figure><img src="image_10.png" /><figcaption>Fig. 9: Magnetic field distribution in the proposed DGS</figcaption></figure>

At relevant frequencies, based on the calculations and the distance of 17mm between transmitter and receiver, the maximum efficiency values obtained are 92.5% and 84.6%, respectively. After simulating the proposed model with HFSS software, the following results were obtained. Figure 8(a) shows the S parameters for the proposed dual-band power transmission system at 330 MHz frequency and 770 MHz frequency. Based on the distance between the resonators (17 mm), the maximum efficiency value indicated in Figure 8(b), compares the efficiency of the initial system design with that of the improved design at relevant frequencies. As shown in Figure 8(b) the efficiency in the green graph has increased from 80% to 92.5% at a frequency of 300MHz and from 73% to 84.6% at a frequency of 770MHz. Clearly, the new system demonstrates enhanced efficiency. Additionally, a figure-of-merit (FoM) is used to compare the performance of WPT systems (9) [23].

$$FoM = \frac{\eta_{WPT} d_{WPT}}{\sqrt{X_{WPT} Y_{WPT}}} \qquad (9)$$

<figure><img src="image_11.png" /><figcaption>Fig. 8: Simulation results for the designed system a) S-parameters b) Comparison of basic and improved system efficiency WPT equivalent circuit</figcaption></figure>

By comparing the transient response changes of the simple WPT structure with those of the WPT structure featuring an adaptive gap and circular edges, it is evident that the latter is less sensitive to angular changes. Figure 10 illustrates the comparison of the sensitivity of the frequency response for these two structures is shown.

<figure><img src="image_12.png" /><figcaption>Fig. 10: DGS Sensitive to angular changes for Improved WPT and Simple WPT</figcaption></figure>

Finally, we use Table 3 to compare the values from this work with those of other WPT systems. By examining different articles over the years, it becomes evident that, based on acceptable figures-of-merit (FoM) values, the presented model occupies a favorable position in terms of
dimensions, distance between transmitter-receiver and efficiency. A review of Table 3 indicates that all critical aspects of design have been considered in this study. For example, in [24], larger dimensions were used in the design, while the article presented in [25] reported low efficiency. Conversely, in [23], the increased efficiency led to a reduction in the distance between the receiver and transmitter. In our design, however, we have prioritized the influential factors, resulting in improvements in both efficiency and FoM.

<table><caption>Table III. Comparison of results between the proposed model and other WPT systems</caption><thead><tr><th>WPT system</th><th>f<sub>0</sub> (mm)</th><th>d</th><th>SIZE (mm<sup>2</sup>)</th><th>η (%)</th><th>FOM</th></tr></thead><tbody><tr><td rowspan="3">[24] (2021)</td><td>300</td><td rowspan="3">23</td><td rowspan="3">43x38</td><td>70.1</td><td>0.4</td></tr><tr><td>433</td><td>66</td><td>0.38</td></tr><tr><td>700</td><td>65</td><td>0.37</td></tr><tr><td rowspan="2">[12] (2017)</td><td>300</td><td rowspan="2">16</td><td rowspan="2">15x30</td><td>71</td><td>0.76</td></tr><tr><td>700</td><td>72</td><td>0.77</td></tr><tr><td rowspan="2">[16] (2019)</td><td>300</td><td rowspan="2">17</td><td rowspan="2">20x20</td><td>80</td><td>0.68</td></tr><tr><td>675</td><td>73</td><td>0.6</td></tr><tr><td rowspan="2">[23] (2023)</td><td>190</td><td rowspan="2">10</td><td rowspan="2">20x20</td><td>97</td><td>0.47</td></tr><tr><td>1400</td><td>95</td><td>0.46</td></tr><tr><td rowspan="2">[25] (2021)</td><td>381</td><td rowspan="2">11</td><td rowspan="2">18x18</td><td>60</td><td>0.4</td></tr><tr><td>750</td><td>54</td><td>0.36</td></tr><tr><td rowspan="2">This Work</td><td>330</td><td rowspan="2">17</td><td rowspan="2">20x20</td><td>92.5</td><td>0.78</td></tr><tr><td>770</td><td>84.6</td><td>0.72</td></tr></tbody></table>

## Conclusion

The proposed structure consists of interrelated resonators, yielding acceptable results between the simulated and constructed models. In this study, the optimal distance between the transmitter and receiver is determined to be 17 mm. This system achieves a maximum efficiency of 92.5% at 330 MHz and 84.6% at 770 MHz. The FoM coefficients measured for the two mentioned frequency bands are 0.78 and 0.72. Additionally, the incorporation of circular edges has contributed to the system's reduced sensitivity to the rotation of the receiver and transmitter, while also increasing efficiency and reduces losses and noise. By using a gap on the resonator, a capacitor is placed in the equivalent circuit of the designed system without changing the size of the system, which according to the simulation results, we

observe high efficiency and by increasing the efficiency in the system, we transmit more voltage wirelessly. This voltage is used to charge the batteries of medical equipment implanted in the human body. Additionally, the incorporation of circular edges has contributed to the system's reduced sensitivity to the rotation of the receiver and transmitter, while also increasing efficiency.

## References

[1]. Lin DB, Wang TH and Chen FJ.: Wireless power transfer via RFID technology for wearable device applications, 2015 IEEE MTT-S 2015 International Microwave Workshop Series on RF and Wireless Technologies for Biomedical and Healthcare Applications (IMWS-BIO), Taipei, Taiwan IEEE: 210-211, 2015.

[2]. Ahire DB and Gond VJ.: Wireless power transfer system for biomedical application, International Conference on Trends in Electronics and Informatics (ICEI), Tirunelveli IEEE: 135-140, 2017.

[3]. Aghazadeh H, Afjei E and Siadatan A.: Sizing and detailed design procedure of external rotor synchronous reluctance machine, IET Electric Power Applications: 13(8), 1105-1113, 2019.

[4]. Atallah HA, Ahmed RH and Abdel-Rahman AB.: Novel design of a compact tunable dual band wireless power transfer (TDB-WPT) system for multiple WPT applications, Frontiers of Information Technology & Electronic Engineering, 25(4), 616-628, 2024.

[5]. Yedavalli PS, Riihonen T, Wang X and Rabaey JM.: Far-Field RF Wireless Power Transfer with Blind Adaptive Beamforming for Internet of Things Devices, IEEE Access, 5: 1743-1752, 2017.

[6]. Lao K, Deng W, Sheng J and Dai N.: PQ-Coupling Strategy for Droop Control in Grid-Connected Capacitive-Coupled Inverter, IEEE Access, 7: 31663-31671, 2019.

[7]. Maulana E, Abidin Z and Djuriatno W.: Wireless Power Transfer Characterization Based on Inductive Coupling Method, Electrical Power, Electronics, Communications, Controls and Informatics Seminar (EECCIS), Batu, East Java, Indonesia:164-168, 2018.

[8]. Jolani F, Yu Y and Chen Z.: A Planar Magnetically Coupled Resonant Wireless Power Transfer System Using Printed Spiral Coils, IEEE Antennas and Wireless Propagation Letters, 13: 1648-1651, 2014.

[9]. Verma S, Rano D and Hashmi M.: A Novel Dual-Band Defected Ground Structure for Short Range Wireless Power Transfer Applications, IEEE Wireless Power Transfer
Conference (WPTC), London, United Kingdom: 188-191, 2019.

[10]. Esmaeili S, Karimi S, Tarassodi P and Siadatan A.: Two-stage asymmetrical Γ-Z-source inverter with high voltage gain and reduced shoot-through duty ratio, 2016 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), 956-961, 2016.

[11]. Ferreira F, Feldman M, Bulla G, Brusamarello V and Müller I.: Compact near field wireless energy transfer systems using defected ground structures, IEEE Journal of Microwaves, 3(3), 951-961, 2023.

[12]. Tahar F, Barakat A, Saad R, Yoshitomi K and Pokharel RK.: Dual-Band Defected Ground Structures Wireless Power Transfer System with Independent External and Inter-Resonator Coupling, IEEE Transactions on Circuits and Systems II: Express Briefs, 64(12): 1372-1376, 2017.

[13]. Hekal Sh and Abdel Rahman AB.: New compact design for short-range wireless power transmission at 1GHz using H-slot resonators, 9th European Conference on Antennas and Propagation (EuCAP) Proc. Lisbon, Portugal: 12-17, 2015.

[14]. Hekal Sh, Abdel-Rahman AB, Jia H, Allam A, Barakat A and Pokharel RK.: A Novel Technique for Compact Size Wireless Power Transfer Applications Using Defected Ground Structures, IEEE Transactions on Microwave Theory and Techniques, 65(2): 591-599, 2017.

[15]. Krishna N and Padmasine KG.: A review on microwave band pass filters: Materials and design optimization techniques for wireless communication systems, Materials Science in Semiconductor Processing, 154, 107181, 2023.

[16]. Sharaf R, Abdel Rahman AB, Abdel Hameed AS, Barakat A, Hekal S and Allam A.: A New Compact Dual-Band Wireless Power Transfer System Using Interlaced Resonators, IEEE Microwave and Wireless Components Letters, 29(7): 498-500, 2019.

[17]. Abdel Rahman A, Verma AK, Boutejdar A and Omar AS.: Compact stub type microstrip bandpass filter using a defected ground plane, IEEE Microwave and Wireless Components Letters, 14(4): 136-138, 2004.

[18]. Kupreyev D, Dautov K, Hashmi M and Verma Sh.: Design of a Compact DGS based Dual-band RF WPT System for Low-Power Applications, IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), Incheon, Korea: 1-2, 2019.

[19]. Adepoju W, Bhattacharya I, Sanyaolu M and Esfahani EN.: Equivalent circuit modeling and experimental analysis of low frequency metamaterial for efficient wireless power

transfer, IEEE Access, 10, 87962-87973, 2022.

[20]. Dautov K, Kudaibergenova ZH, Hashmi M, Nauryzbayev G and Chaudhary MA.: Analysis and Experimental Validation of Circularly Slotted Near-Field WPT Systems, IEEE Int. Midwest Symp. Circ. Syst. (MWSCAS), Lansing, MI, USA: 263-266, 2021.

[21]. Rong C, Yan L, Li L, Li Y and M. Liu.: A review of metamaterials in wireless power transfer, Materials, 16(17), 6008, 2023.

[22]. Takashi O.: The kQ Product as Viewed by an Analog Circuit Engineer, IEEE circuits and systems magazine, IEEE 17(1): 27-32, 2017.

[23]. Atallah HA, Hussein R and Abdel Rahman AB.: Tunable Dual Band Wireless Power Transfer (TDB-WPT) System for Short Range Applications, IEEE Transaction on Circuits and Systems—II: Express Briefs, 70(2): 476-480, 2023.

[24]. Verma Sh, Rano D, Malhotra S and Hashmi MS.: Measurements and Characterization of a Newly Developed Novel Miniature WIPT System, IEEE Transactions on Instrumentation and Measurement, 70, 2021.

[25]. Jiang X, Tahar F, Miyamoto T, Barakat A, Yoshitomi K and Pokharel RK.: Efficient and compact dual-band wireless power transfer system through biological tissues using dual-reference DGS resonators, IEEE MTT-S International Microwave Symposium (IMS), Atlanta, GA, USA IEEE: 54-57, 2021.