1 Introduction

Nowadays, the field of flexible wearable antennas gains a great interest from many research groups all over the world due to their enormous applications in wireless communications and healthcare systems [1, 2]. According to application, different types of wireless antennas can be used for examples; horn antenna, parabolic antenna, slot antenna, patch antenna, dipole antenna etc. Each type can be constructed using different technologies and designs [3, 4]. In generally microstrip (or patch) antennas are the most widespread type because they are inexpensive, lightweight, small, and simple to manufacture. However, it has a limited bandwidth [5]. Due to this, a number of methods, such as substrate-integrated suspended-line technique [6], slotted patch [7], adding stubs [8], defected ground structures [9], and cutting edges [10] have been proposed to increase the bandwidth of patch antennas. On the other hand, Coplanar Waveguide (CPW) fed printed antennas with a rectangular form provide the wide bandwidths needed for a variety of wireless and wearable applications [11,12,13]. Additionally, utilizing specific concepts such as Artificial Magnetic Conductors (AMCs), meta-material or a horn reflector aims to increase antenna’s gain [14].

The traditional design of wireless antennas was based on using rigid substrates such as FR4. However, developing efficient flexible antennas requires the use of substrates that can accommodate irregularly shaped surfaces such as kapton, Rogers RT/duroid, cotton layer, polyethylene terephthalate (PET) film and paper [15,16,17]. In the present work a CPW fed rectangular patch antenna is designed and implemented. The proposed antenna was investigated as a straight structure and at horizontal and vertical bent. Moreover, the simulation results of the straight structured antenna were settled and validated by performing experimental measurements. For enhancing the proposed antenna parameters, metallic cross line was added to the ground. Additionally, the impedance matching was improved via inset feed mechanism. The presented antenna has resonance frequency about 3.22 GHz making it applicable in WIMAX applications.

2 Methods

2.1 Design Process

The size of proposed CPW fed patch antenna is 0.233λ0 × 0.25λ0 with respect to resonant frequency. High-Frequency Structure Simulator Technology (HFSS), a commercially available simulation package, is used to run the simulations. To attain the desired features, a flexible dielectric substrate is used for the design (Rogers 4003) which has a dielectric constant of 3.5, a thickness of 200 μm and a loss tangent of 0.0027. Rogers 4003 was favored due to its easy availability and its compatibility with ordinary manufacturing procedures making in-house prototype manufacturing possible. The main step in the construction process is to design a rectangular patch antenna. Figure 1 presents the rectangular ring patch antenna embedded with metallic cross-line. Additionally, Table 1 provides a summary of the proposed antenna’s dimensions.

Fig. 1
figure 1

The dimensions and planned antenna design

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Table 1 The anticipated antenna’s dimensions (in mm)
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The semicircular ground and the inserted cross-line inside the rectangular ring added to obtain the desired frequency band. To obtain the 50-Ω excitation for the suggested antenna, a 0.2-mm gap between the CPW feed line and the ground is employed.

Since some specific antennas are primarily intended to be bent or even adhered to particular surfaces while operating, it is important to understand various bending situations. A three studied structures of the presented antenna are illustrated in Fig. 2. The straight antenna is shown in Fig. 2a. The antenna bent as a semi-cylindrical to suit the wearable applications twice, one time along X-axis as shown in Fig. 2b, with radius 15 mm. Also it was bent along Y-axis as shown in Fig. 2c, with radius 14 mm. Antenna manufacturing and the experimental measurements were performed at the National Telecommunication Institute (NTI), Cairo, Egypt. It is worth declaring that, a number of designs were investigated first, but this particular shape was chosen because it can bend without causing a significant shift in the resonance frequency between the straight and bent configurations.

Fig. 2
figure 2

The different studied antenna configurations a straight antenna, b horizontal bent antenna (X-axis), c vertical bent antenna (Y-axis)

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2.2 Design Approach

Firstly, a rectangular ring-shaped patch antenna fed by CPW is constructed. Equations (1) and (2) give a good approximation of the dimensions [18].

$$ W = \frac{c}{{2f_{r} }}\sqrt {\frac{2}{{\varepsilon_{r} + 1}}} $$
(1)
$$ L = \frac{c}{{2f_{r} \sqrt {\varepsilon_{r eff} } }} - 2\Delta L $$
(2)

where W and L are the patch’s width and length, respectively, c represents light speed, fr is the resonant frequency, εr denotes relative permittivity, εreff is the effective permittivity, and ΔL is the effective length. After a number of examinations and adjustments, the design’s proportions are finally determined. The simulation evaluations that were run confirm that adding metal strip makes room for surface currents.

3 Results and Discussion

3.1 Reflection Coefficient

The experimental measurements of the antenna were implemented using vector network analyzer (Rohde & Schwarz ZVB 20, 10 MHz—20 GHz). The performance of the antenna was studied for three cases, straight, horizontal bent (X-axis) and vertical bent (Y-axis). The reflection coefficient of three cases was investigated. Moreover, a comparison between the simulated and experimental measurements was implemented. Because of the soldering process and the SMA connector position and to avoid the antenna damage, we couldn’t measure the antenna at the bent structure, and only the straight antenna was measured. In the simulation results presented in Fig. 3a, the S11 parameter (resonating at 3.25 GHz) was − 52, − 22 and − 28 dB for straight, horizontal bent and vertical bent respectively. This value decreased to − 32 dB for measured straight antenna as shown in Fig. 3b. Such reduction in S11 parameter value may be due to the efficiency of the manufacturing process and soldering accuracy. Moreover, the measured bandwidth is 0.18 GHz for the straight structure antenna.

Fig. 3
figure 3

a S11 for the proposed antenna, b Simulated versus measured S11 for the straight antenna

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3.2 Radiation Patterns

The suggested antenna’s radiation pattern’s E-plane in the three cases, straight, horizontal bent and vertical bent (\({\mathrm{E}}_{\uptheta }\) at φ = 00 and the H = plane radiation pattern (\({\mathrm{E}}_{\uptheta }\) at φ = 900) is presented in Fig. 4a. E- plane radiation pattern shows that the antenna radiate bi-directional in the three cases, while H-plane pattern indicates that antenna radiate bi-directional in case of straight, quasi omnidirectional in case of vertical bent and approximately omnidirectional in horizontal bent curve. The radiation pattern for the straight antenna in both simulation and experimental implementations is shown in Fig. 4b. The E-plane far-field patterns from the two models are significantly matched. However, the Ensemble-based H-plane far-field pattern has a maximum at θ = 0 and a null near θ = 90°. The model’s failure to account for the probe’s placement and its assumption that the substrate’s dielectric material is truncated and does not extend past the patch’s boundaries to cover the ground plane are the causes of the differences between the two patterns. From the E-plane radiation pattern presented in Fig. 4b for the suggested antenna; it can be explained that the antenna’s emission in the E-plane and H-Plane radiation patterns is bi-directional.

Fig. 4
figure 4

The Radiation pattern E-plane at φ = 0 and H-plane at φ = 900 a the three simulated cases (straight, horizontal bent, vertical bent b the straight antenna in both simulated and measured cases

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Figure 5a, b, and c respectively show the 3-D radiation patterns for the proposed antenna at 3.22 GHz for the three configurations: straight, horizontal, and vertical twisted. The color red denotes the strongest radiated E-field, while the color green denotes the weakest.

Fig. 5
figure 5

The 3-D radiation pattern for the proposed antenna: a straight b Horizontal bent c Vertical bent

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3.3 Current distributions

To show the mechanism of operation, the variation in the current distribution between the straight, vertical and horizontal bent antennas is demonstrated in Fig. 6a, b and c respectively. The resonance frequency is always indicated by a drop in the current distribution at the antenna surface. The intensive current is represented in red, while blue areas have a zero current. The effective area that causes the suggested antenna to resonate at a specific frequency is also shown in the figure. It also proves that the l dip at 3.22 GHz is produced by the antenna’s construction. In addition, the illustration provides a concise summary of the fact that the current density is horizontally oriented. Moreover, the maximum current concentration is seen in the upper and bottom regions of the rectangular ring.

Fig. 6
figure 6

The current distribution of the proposed antenna, a straight, b vertical bent, c horizontal bent

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3.4 Gain, VSWR and Total Efficiency

Figure 7a displays the proposed antenna’s attained gain. The maximum obtained gain was 11.5 dB at frequency 2.6 GHz, while at 3.22 GHz the gain was 13 dB. Given the small size of the antenna and the degenerative impact of the SMA connector, the measuring process had restrictions that contributed to the zero gain at 2.4 GHz. The diameter of the SMA connector drops to around one-fourth of the guided wavelength at 2.4 GHz, \({\uplambda }_{\mathrm{g}}= \frac{{\uplambda }_{0}}{\sqrt{{\upvarepsilon }_{\mathrm{eff}}}}\) where \({\upvarepsilon }_{\mathrm{eff}}\) and \({\uplambda }_{0}\) represent the effective dielectric constant and the free space wavelength respectively [19]. Around 2.4 GHz squinting radiation pattern causing decline in the proposed antenna’s radiation performance [20,21,22]. Furthermore, the total efficiency of the proposed antenna was calculated. The Straight shaped antenna shows an efficiency = − 3.8 dB, while the vertical and horizontal bent antennas has − 3.2 and − 4.8 dB efficiency respectively.

Fig. 7
figure 7

a Antenna gain b SWR for the simulated straight antenna

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The measured and simulated antenna’s voltage standing wave ratio (VSWR) is almost identical as illustrated in Fig. 7b. The VSWR was \(\le \) 2 for a functional band from 1.5 to 6 GHz which is appropriate for L-band, S-band and C-band. The fabrication and measurement conditions can be responsible for the tiny discrepancy between the two results.. In Fig. 8, an actual photo of the manufactured antenna is displayed.

Fig. 8
figure 8

A real photograph of the fabricated antenna

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In order to verify the results, the proposed antenna characteristics were compared with some pertinent research that has been published in literature, as shown in Table 2.

Table 2 A comparison of the suggested antenna and some published studies
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4 Conclusion

In conclusion, CPW- fed antenna is studied and presented. The proposed design is suitable for S-band applications. To achieve impedance matching, an inset feed mechanism is used, and then a stepped feed structure. The simulation is run using various bending analyses. In the case of a straight antenna, there is a logical correlation between the results of simulation and measurement. Performance metrics for the proposed antenna are evaluated, including return loss, VSWR, gain, efficiency, and radiation patterns. With the suitable gain, stable radiation characteristics are reported. The suggested work is therefore intended for the suggested wireless applications. Additionally, the derived antenna parameters show small variations across the three scenarios (straight, horizontal and vertical bent) that place this antenna in the wearable applications category.