A Study of Wideband and Compact Slot Antennas Utilizing Special Dispersive Materials

This paper presents a novel technique for enhancing the slot antenna bandwidth using special dispersive materials for the first time. The dispersive material whose relative permittivity is inversely proportional to the frequency by the power of n is selected and exploited for antenna bandwidth enhancement and size reduction. The concept and theory behind this work are explored. A slot antenna loaded with the new material is proposed and it is shown that the bandwidth of slot antennas using the material with power ${n}{=}2$ can be significantly improved with more than 4 times larger than the traditional case ( ${n}{=}0$ ). The simulated and measured results show excellent properties for wideband improvement and miniaturization which further demonstrates that dispersive materials can open a new path for developing wideband devices and antennas for future wireless communication applications.

SECTION I. Introduction

Modern wireless communication systems have a great demand for wideband and compact antennas for high integration and performance. As multiple antennas for different bands make the system bulky and complicated, a single antenna covering a wider band becomes the best choice. Wideband and miniaturized antennas have been a research topic of huge interest for years. These two requirements often contradict each other, that is, antenna size reduction means a smaller bandwidth. Normally a trade-off has to be made. More and more researchers are trying to reduce the antenna size as well as enhance the bandwidth.

Some techniques of bandwidth enhancement have been proposed. The stacking technique is widely recognized as a well-established method where multiple antennas are vertically or horizontally combined to achieve improved bandwidth, such as the stacked patches in [1]. Besides, fractal technology proves valuable for wideband designs with self-similar patterns at different scales [2]. Impedance matching techniques, exemplified by the L-shaped feeding method [3], and antenna geometry optimization methods, such as adjustments to the structure or shape [4], [5], [6], [7], [8], [9], [10], are extensively employed in the design of wideband antenna. Moreover, combining multiple modes to obtain bandwidth enhancement is also one of the well-known methods [11], [12]. For instance, surface wave propagation has been exploited to generate additional resonances for broadening the impedance-matching bandwidth [13]. In recent years, new types of antennas are also proposed like the concept of magnetoelectric dipoles to develop wideband and unidirectional antennas [14]. Other interesting approaches, such as artificial magnetic conductor (AMC) surfaces, were also introduced to widen the bandwidth as shown in [15] and [16], and metamaterial-based antennas were proposed to obtain wideband characteristics [17], [18], [19]. Although the designs mentioned above exhibit merits of large bandwidth or miniaturization and are desirable for applications with different requirements in terms of bandwidth, radiation pattern, and so on, they all can only either increase the bandwidth or reduce the size, that is, there is a trade-off between the antenna bandwidth and size. To overcome the trade-off between wide bandwidth and compact structure remains a significant challenge. Therefore, this paper is to propose a new approach to address this problem.

In our recent work, we tried to increase the bandwidth of a compact smartphone antenna [20] and a wideband dielectric resonator antenna [21] using a special dispersive material whose relative permittivity is inversely proportional to the frequency square, and the material synthesis, formulation, and fabrication were detailed in [22], [23]. However, that was our initial study, and the general theory of antenna bandwidth enhancement using dispersive materials was not studied, thus in this paper, we will use slot antennas (a basic type of antennas) as an example to study this topic comprehensively. Different techniques have been proposed to enhance the slot antenna bandwidth, such as using rotated slots [24], multiple resonances [25], and parasitic patches [26]. Some slot antennas are loaded with C-shaped rings [27], slit and strip [28], or wire [29] to achieve size reduction. However, these modifications tend to either broaden the bandwidth or reduce the size, but not both. In this paper, the proposed new theory can be applied to various wideband antenna designs, such as new wideband slot antennas, metal rim antennas for smartphone applications, slot-based hybrid antennas, and so on. This concept was realized by a thorough selection process of materials that exhibit dielectric dispersive behaviors within the microwave region where the orientation of electrical dipoles within the material is responsive to alternating electric fields [30]. Our search for the dispersive material used in this work focused on materials possessing high polarity. To the best of the authors’ knowledge, this is the first time to introduce the proposed theory for bandwidth enhancement in slot antennas loaded with a special dispersive material.

This paper is organized as follows. In Section II, the theory of bandwidth enhancement is introduced first. As the proof of concept, the simulated results of a simple slot antenna loaded with special dispersive materials are given. The material and antenna fabrication, measurement results, and discussions are detailed in Section III, followed by the conclusions in Section IV.

SECTION II. Theory and Design

Since the dielectric constant of traditional materials is usually frequency invariant in the desired band, the electrical length of the antenna is frequency variant, resulting in narrow band-width. However, it is considered this would offer stable performance. As we will show, from the material point of view, dispersive materials are worthwhile to be investigated for performance enhancement. The proposed material can be defined by the frequency dependency of the relative permittivity as illustrated below:\begin{equation*} \varepsilon _{r}(f) = \frac {k}{f^{n}} \gt 1 \tag {1}\end{equation*} where k is the material coefficient and f is the frequency. The relative permittivity is inversely proportional to the frequency by the power of n. Fig. 1 (a) shows the relative permittivity of several materials with different power n. Their relative permittivity are 62.5 at 0.8 GHz, and it shows that the higher the power n, the larger the slope of the permittivity.

FIGURE 1.

Concept and theory illustration for bandwidth enhancement and size reduction. (a) The relative permittivity of the special dispersive material with different values of power n; slot antennas with (b) a smaller slot and (c) a larger slot; (d) a dielectric block loaded for size reduction; (e) a larger block/slot and (f) a smaller block/slot loaded for covering different narrow bands; (g) the proposed wideband miniaturized antenna using the special dispersive material.

A. Theory of Bandwidth Enhancement and Miniaturization

To illustrate the usefulness of the new material, a slot antenna is employed as an example. As shown in Fig. 1 (b) and (c), the antenna has a slot with a length of l and a width of w in the middle of a big conducting ground plane. It is well-known that the bandwidth of the slot antenna is narrow, and the electrical length of the slot perimeter is around one wavelength at the corresponding frequency. Normally, slot antennas with smaller or larger slots are used for covering the higher or lower bands, respectively, as shown in Fig. 1 (b) and (c). To reduce the slot size or cover a further lower band, a dielectric block can be loaded on one side of the slot, as shown in Fig. 1 (d). However, due to their limited bandwidth, multiple antennas with dielectric blocks and slots of various sizes are needed simultaneously to cover different bands, as shown in Fig. 1 (e) and (f). Different from that, by exploiting the dispersive material, a compact wideband system with only one single antenna can be achieved, as shown in Fig. 1 (g). To simplify the analysis, suppose the whole half-space at one side of the slot is filled with one material with relative permittivity $\varepsilon _{r }$ (f). In the first case, when the loading material is the vacuum ($\varepsilon _{r }$ (f) ${=}\varepsilon _{r } {=}1$ ), the wavelength ${\lambda }_{0}$ (f) is well-known as: ${\lambda }_{0}$ (f) ${=}{c}$ /f, where c is the speed of light and f is the frequency. The free space wavelength versus frequency curve is shown in Fig. 2. It can be seen that the wavelength changes significantly with the frequency. For the case when the loading material is the traditional dielectric material with a constant relative permittivity $\varepsilon _{r}$ , the effective wavelength ${\lambda }_{eff }$ (f) can be obtained as [31]:\begin{equation*} \lambda _{eff}(f) = \frac {\lambda _{0}}{\sqrt {\varepsilon _{reff}}} = \frac {\lambda _{0}}{\sqrt {\left ({{1 + \varepsilon _{r}}}\right)/2}} = \frac {c}{f\sqrt {\left ({{1 + \varepsilon _{r}}}\right)/2}} \tag {2}\end{equation*} where ${\lambda }_{0}$ is the free space wavelength, and $\varepsilon _{reff }$ is the effective permittivity. The case with $\varepsilon _{r }$ (f) ${=}\varepsilon _{r}{=}62.5$ (${n}{=}0$ ) is also shown in Fig. 2. Compared with the case of free space, with the dielectric loading effect, the slot length can be reduced, thus device miniaturization can be achieved. However, the wavelength also changes significantly with the frequency, and a narrow bandwidth is expected. Therefore, the third case with dispersive materials is investigated here for exploiting new approaches to widen the bandwidth. In this case, the new effective wavelength $\lambda ^{\prime }_{eff}$ (f) can be deduced based on (1) as:\begin{equation*} {\lambda ^{\prime }}_{eff}(f) = \frac {\lambda _{0}}{\sqrt {\varepsilon _{reff}}} = \frac {\lambda _{0}}{\sqrt {\left [{{ 1 + \varepsilon _{r}(f) }}\right ]/2}} = \frac {\lambda _{0}}{\sqrt {\left ({{1 + k/f^{n}}}\right)/2}} \tag {3}\end{equation*} when the relative permittivity is greatly larger than unity, it can be simplified as:\begin{equation*} {\lambda ^{\prime }}_{eff}(f) = \frac {\lambda _{0}}{\sqrt {k/\left ({{2f^{n}}}\right)}} = \frac {\sqrt {2}c}{\sqrt {k}f^{1 - n/2}} \tag {4}\end{equation*}

FIGURE 2.

The relationship between the wavelength and the operating frequency for different cases with different materials.

Especially, when the power ${n}{=}2$ , the effective wavelength is:\begin{equation*} {\lambda ^{\prime }}_{eff}(f) = \frac {\sqrt {2}c}{\sqrt {k}} = {\mathrm { constant}} \tag {5}\end{equation*}

Fig. 2 also shows the cases with different power n and an inverse relationship can be observed that the wavelength slope decreases with the power n (${n} \leq 2$ ), in other words, the wavelength gets smoother when using a larger power compared with a smaller one, which means that the wavelength becomes less sensitive to the frequency for a larger power. Therefore, using the new material with a larger power has the potential to obtain bandwidth enhancement. Especially, when the power ${n}{=}2$ , the wavelength becomes frequency-independent which could be the optimum case for bandwidth enhancement. Fig. 3 illustrates the relationship between the antenna bandwidth and the power n. Here the bandwidth is defined based on the requirement of a ± 5% variation of the wavelength at 0.8 GHz (0.067 m), spanning from 0.07 m to 0.06 m. The antenna bandwidth increases from 13.5% (0.76 – 0.87 GHz) to 18.1% (0.73 – 0.875 GHz), 42.4% (0.6 – 1 GHz), then decreases to 21.5% (0.725 – 0.9 GHz), respectively when the power ${n}{=}0$ , 1, 2, 3. Based on the concept and theory illustrated above, a new slot antenna design will be detailed in the following section.

FIGURE 3.

The relationship between the antenna bandwidth and the power n.

B. Slot Antenna Design

For the proof of concept, a slot antenna loaded with dispersive materials is used for simulation. A slot with a length of ${l}{=}$ 79 mm and a width of ${w}{=}$ 5 mm is cut in the middle of a ground plane with a dimension of 150 mm $\times $ 150 mm, as shown in Fig. 1 (g). The dispersive materials with a thickness ${d}{=}$ 2 mm have the same length and width as the slot and are placed just above the slot. The used relative permittivity for different power n is shown in Fig. 1 (a) with the same relative permittivity of 62.5 at 0.8 GHz, and the loss tangent is selected as 0.001. In this paper, CST Microwave Studio [32] is utilized for antenna simulation and optimization following the import of material property data into the software. The feeding port is placed near the slot edge at a distance of 7.5 mm. The material whose relative permittivity is inversely proportional to the frequency square (${n}{=}2$ ) is first studied for bandwidth comparison between traditional and new designs. Fig. 4 shows the reflection coefficient, radiation efficiency, and gain for the new slot antenna loaded with the new material with power ${n}{=}2$ . The simulation results for the slot antenna loaded with traditional materials with a constant relative permittivity of 62.5 are also included for comparison. It can be seen that the traditional case with ${n}{=}0$ has a narrow band (0.773 – 0.806 GHz, 4.17%), while the new slot antenna with ${n}{=}2$ shows a significantly wider bandwidth (0.669 – 0.824 GHz, 20.86%) which is more than 5 times larger than the traditional one. Besides, the gain values are similar for both cases. Compared with the traditional case, the total efficiency for the new antenna remains above -1 dB over a greatly wider band.

FIGURE 4.

(a) The simulated reflection coefficient, (b) radiation efficiency, and gain for the slot antenna loaded with dispersive materials (${n}{=}2$ ). The traditional case (${n}{=}0$ ) is also included for comparison. The efficiency below -4 dB is not shown.

The current distributions of the new antenna at 0.7 GHz and 0.8 GHz are shown in Fig. 5, respectively. It can be seen that the current distributions remain almost the same at different frequencies, indicating the mode purity over the band, thanks to which, the radiation patterns are similar, as shown in Fig. 6, showing the merit of stable radiation over a wide band and good cross-polarization performances with a level lower than -50 dB at boresight.

FIGURE 5.

The current distributions of the new slot antenna (${n}{=}2$ ) at (a) 0.7 GHz, and (b) 0.8 GHz.

FIGURE 6.

The normalized radiation patterns of the new slot antenna (${n}{=}2$ ). (a) Co-polarization and (b) cross-polarization at phi = 0 deg; (c) co-polarization and (d) cross-polarization at phi = 90 deg.

Besides the material with power ${n}{=}2$ mentioned above, other materials with different power n are considered. Without changing the structure, the antennas loaded with different materials are used for simulation. The relationship between the bandwidth of the slot antenna and the power n is shown in Fig. 7. The antenna bandwidth can be exponentially increased to 5.30% (0.765 – 0.805 GHz), 7.36% (0.751 – 0.809 GHz), 10.02% (0.735 – 0.812 GHz), 20.86% (0.669 – 0.824 GHz) and 28.72% (0.641 – 0.856 GHz), for the cases with ${n}{=}0.5$ , 1, 1.5, 2, 2.5, respectively. The higher the power n, the larger the bandwidth. When the power n is larger than 2.5, the bandwidth starts to decrease. It is also evident that the maximum bandwidth occurs when the power n is around 2.5, deviating from the expected case of ${n}{=}2$ as demonstrated in (5). This discrepancy can be attributed to the previous assumption, wherein it was assumed that the entire half-space area is filled with the new material and the relative permittivity is significantly larger than unity. However, this assumption does not align with practical structures, where a small dielectric with limited relative permittivity is normally used. Additionally, the observed bandwidth also depends on specific antenna structures, feeding methods, and optimizations.

FIGURE 7.

The relationship between the bandwidth of the new slot antenna and the power n. Two cases, including the fully and partially filled slot antennas, are considered. Averaged values are incorporated to depict the trend as a function of the power n.

The new slot antenna mentioned above features a fully filled material surrounding the slot, with the same length and width. It is worthwhile to investigate the antenna performance of bandwidth enhancement when using a partially filled material. In this case, based on the previous structure, the length of the loading material is decreased to 60 mm and other parameters remain unchanged. The reflection coefficients of the new partially filled slot antenna are shown in Fig. 8. It can be seen that the resonant frequencies shift upward compared to the fully filled slot antenna with the same power ${n}{=}2$ . This shift is attributed to the reduced effective permittivity, resulting from the decreased volume of the loading material. It can also be observed that the bandwidth of the partially filled slot antenna using a larger power (${n}{=}2$ ) is wider than the case with a smaller power (${n}{=}1$ ). The explicit relationship be-tween the bandwidth and the power n for the partially filled slot antenna is also depicted in Fig. 7. The antenna bandwidth is slightly lower than the fully filled antenna (except ${n}{=}3$ ), with a similar trend of power dependency. More importantly, it is demonstrated that the partially filled configuration can also be used for bandwidth enhancement, which could be beneficial for applications with limited size or space.

FIGURE 8.

The reflection coefficients of the new slot antenna partially filled with dispersive materials with different values of power n.

In conclusion, the simulation results and discussion presented above demonstrate the concept and theory of bandwidth enhancement for slot antennas.

SECTION III. Fabrication, Measurement, and Discussion

To validate this new concept, a prototype antenna is fabricated using the material prepared at the University of Liverpool [22], [23]. The development of the desired material has been a complex and challenging task, with no precedent known. Ideally, we would like to use a material with the power index ${n}{=}2$ to verify the antenna design. However, we have not yet managed to develop such an ideal material, and we are still working on it. Instead, a solid composite material with power ${n}{=}0.5$ , comprised of plasticized poly (vinylidene fluoride) containing nano-sized silica particles, is developed in order to prove the theoretical concept and used to test the performance of the slot antenna. Fig. 9 (a) shows the photographs of the material samples. The measured real and imaginary parts of the relative complex permittivity of the material are shown in Fig. 9 (b). The fitting line of the relative permittivity is also given. The fitting function is:\begin{equation*} \varepsilon _{r}(f) = \frac {22.83 \times 10^{4.5}}{f^{0.5}} \tag {6}\end{equation*}

FIGURE 9.

(a) Photographs of the material samples; (b) the measured real and imaginary part of the relative complex permittivity of the new material sample with power ${n}{=}0.5$ .

It can be seen that the power n of the new material sample is 0.5 from 0.4 GHz to 2 GHz, and the material coefficient k is $22.83\times 10{^{{4.5}}}$ . The material with power ${n}{=}2$ is also shown here for comparison. To make a fair comparison, the loss tangent at each frequency for each case is set as the same as the measured loss tangent of the developed samples. The configurations of the slot antenna for fabrication and measurement are shown in the inset of Fig. 10 with detailed parameters. FR-4 substrate is used here for ease of fabrication and measurement. There is a slot area with a length of l and a width of w in the middle of the substrate, forming the loading area of the new material. The loading material, with a height of 2 mm, has the same length and width as the slot area.

FIGURE 10.

The measured and simulated reflection coefficients of the new slot antenna. (a) The top view, and (b) the bottom view of the slot antenna for fabrication and measurement. ${L}{=}$ 150 mm, ${W}{=}$ 150 mm, l = 118 mm, ${w}{=}$ 2 mm, ${g}{=}36$ .5 mm; (c) the antenna prototype with the cable line.

The measured and simulated reflection coefficients are shown in Fig. 10. The antenna prototype is shown in the inset.

The measured bandwidth is around 30.5%, covering from 0.638 GHz to 0.868 GHz, which is very close to the simulated bandwidth of 29.8% (0.652 – 0.879 GHz). There is a good agreement between the simulated and measured results for the samples with power ${n}{=}0.5$ , which demonstrates the feasibility of the concept and theory illustrated in this paper. As a traditional material (${n}{=}0$ ) with the same loss tangent as that of the fabricated samples is not available in our lab or commercial market, the simulated results for the traditional material can only be given here for comparison. Even so, from the simulated results of the slot antenna based on low loss tangent in previous sections and the measured results, the bandwidth enhancement can be expected when using the new material and the bandwidth can be further improved with a larger power n, as can be seen from Fig. 11. The bandwidth of the traditional case with power ${n}{=}0$ is around 25.9%, while it is 29.8% for the case with ${n}{=}0.5$ , which has been increased by about 4%. With ${n}{=}2$ , the bandwidth can be more than 4 times greater than the traditional case. Fig. 12 shows the measured and simulated normalized radiation patterns at phi = 0 deg. The antenna demonstrates excellent cross-polarization performance, achieving levels lower than -50 dB at boresight. The measured results agree well with the simulation. Table 1 gives a comparison between the proposed antenna and the related designs. Note that the bandwidth of slot antennas normally increases with the slot width. It can be seen that the proposed antenna features a small size, wide bandwidth, and stable radiation patterns. The future work involves conducting additional measurements using different materials.

TABLE 1 Comparison of the Proposed Antenna With Prior Art

FIGURE 11.

The relationship between the bandwidth of the slot antenna and the power n.

FIGURE 12.

The measured and simulated normalized radiation patterns at phi = 0 deg. (a) Co-polarization and (b) cross-polarization at 0.7 GHz; (c)co-polarization and (d) cross-polarization at 0.8 GHz.

SECTION IV. Conclusion

This paper has introduced a study of broadening the slot antenna bandwidth while keeping it small by employing a new material whose relative permittivity is inversely proportional to the frequency by the power of n. The concept and theory are discussed and illustrated in detail using a slot antenna loaded with the new material. It shows the merits of bandwidth enhancement, compact structure, and simple feeding method without matching networks which are promising for modern wireless communication. The proposed concept, theory, and design method can be applied to various novel designs such as wideband fractal slot antennas, slot-based hybrid wideband antennas, back-cavity slot antennas, and so on. We believe that this approach will open up a new direction in the development of wideband and miniaturized microwave devices and antennas for broadband radar and communication applications in the future.