1 Introduction

In recent years, the repaid development of wearable applications and biomedical systems requires bendable and flexible devices. These devices can be used in smartphones, laptops, RFID tags, sensors, sports, fire fighters, IoT applications, and biomedical devices [1, 2]. Flexible and curved antennas are considered the main part of wireless wearable systems [3]. Flexible antennas can take any shape curved, or folded without affecting the antenna parameters such as matching and radiation characteristics.

Wideband and ultra-wideband (UWB) systems can support applications with low power, fading reduction, security, lower penetration loss, and high data rates [4]. Federal Communications Commission (FCC) states that the spectrum of the UWB systems is from 3.1 GHz up to 10.6 GHz [5]. Thanks to UWB system features, researchers developed new techniques to combine flexible antennas to work in wideband operation. The antenna used in the UWB system should have an omnidirectional pattern, wideband impedance matching with high efficiency, small size easy fabrication, and easily combine with other circuits [6,7,8]. Flexible wideband antennas plays important role in wearable systems because it allows wearable systems used in curved structures. Researchers designed several flexible antennas to operate in a wide band range [9,10,11]. Monopole antenna can be used in a wideband application for their features such as wideband impedance matching, omnidirectional radiation pattern, compact size, and ease to combine with other circuits. Flexible antennas are realized using flexible substrate materials and operate under curved behavior [12,13,14,15,16,17,18,19,20,21,22,23,24].

Studying time domain response in wideband antenna operation is considered a vital part of antenna design. The pulse used in the wide band system is very short which produces a wide band frequency range. So, this short pulse can be distorted in transmitting and receiving modes [25, 26]. Time-domain behavior is studied to ensure that our antenna has low distortion features.

In this paper, flexible, wideband, and thin antenna for wireless application is designed and investigated. We studied two configurations (flat and bent). Both configurations operated at a frequency band from 2.4 GHz to 10 GHz. The simulated results using CST Microwave Studio software are validated by measuring the results for both configurations. All antenna parameters such as antenna gain, radiation patterns, efficiency, and S-parameters are studied. Time-domain responses for both configurations are investigated and studied which confirmed that the proposed antenna achieved good time response results. The proposed antenna has several advantages such as small size, flexibility, wideband operation, and reasonable peak gain. Finally, the measured results track well with the simulated ones. Our paper is organized as follows: Sect. 2 is investigated the detailed design of the flat antenna and the effect of bending on the antenna performance. The time-domain features using Gaussian pulse as an input signal are studied for the two configurations in Sect. 3. Finally, Sect. 4 is the conclusion.

2 Antenna Design

2.1 Flat monopole Antenna Structure

First of all, the flexible substrate material RO3003 with good performance is chosen in the design. The substrate has a thickness, dielectric constant, and loss tangent equal to 0.254 mm, 3, 0.0013, respectively. The antenna configuration and the fabricated photo of the antenna are illustrated in Fig. 1. The antenna consists of a monopole antenna with a rectangular patch attached to a microstrip line with a width of 0.6 mm to obtain 50 Ω impedance. The rectangular patch has tapered edges and the ground plane has partial ground to achieve the wideband operation we need. The tapered edges angle and the partial ground length are optimized to obtain the desired frequency band. The proposed antenna has an overall size of 4.1 × 3.8 cm2. The substrate has the advantages of flexibility and robustness. The antenna is etched using chemical etching and the SMA connector is soldered using welding tin. The antenna is simulated using CST microwave studio and measured using VNA Agilent N9918A. Figure 2 shows the simulated and measured S11 which confirms that first; the antenna is operated from 2.4 GHz up to 10 GHz with S11 lower than − 10 dB. Secondly, the simulated results have the same trend as the measured results. However, a very small shift is seen between the two results this is due to the fabrication and the measured process.

Fig. 1.
figure 1

2D structure of flat configuration monopole antenna a front view b back view c Fabricated photo front view d Fabricated photo back view

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Fig. 2
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The simulated and measured S11of the flat monopole antenna

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Figure 3 illustrates the flat antenna radiation patterns measurement inside an anechoic chamber. The measurements are obtained by using the antenna measurement system Starlab 18 [27] with a dynamic range of 60 dB in the frequency range from 1 to 18 GHz.The normalized simulated and measured radiation patterns at 3 GHz, 5 GHz, and 8 GHz are illustrated in Fig. 4. The antenna is measured at three planes x–z plane, y–z plane, and x–y planes. The patterns have low distortion at higher frequency bands because of the impact of the higher-order mode. The simulated results have good agreement with the measured results with small variations between them. The simulated and measured gain of the flat antenna is shown in Fig. 5. The measured average gain of the antenna equals around 3.5 dBi.

Fig. 3
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The measured radiation patterns setup of the flat monopole antenna

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Fig. 4
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The normalized simulated and measured radiation patterns of flat monopole antenna a at 3 GHz b at 5 GHz c at 8 GHz

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Fig. 5
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The simulated and measured peak average gain of the flat monopole antenna with frequency

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2.2 Effect of Bending on the Antenna Performance

In this section, we compare the results from the bent antenna with the previous flat antenna to show the effect of bending on the antenna performance and validate the flexibility of the proposed antenna. The effect of the bending on the antenna performance at different antenna radii of curvature R is illustrated in Fig. 6a. It is clear that the antenna still achieved wideband operation from 2 GHz up to 10 GHz with S11 lower than − 10 dB which confirms the antenna stability with bending. The previous antenna is curved using a cylindrical structure with a radius R of 62 mm and a dielectric constant of 1.03 as shown in Fig. 6b. The S11 of the bending antenna is shown in Fig. 7. It is noticed that the antenna still has a wide band feature with bandwidth extended from 2.4 GHz up to 10 GHz with S11 lower than -10 dB. Also, the bent antenna shows the same S11 performance as the previous flat antenna which confirms the stability of the proposed antenna.

Fig. 6
figure 6

Bended monopole antenna. a The effect of the bending at different radii (R) (simulated results) b the fabricated photo at R = 62 mm c Measured radiation pattern setup

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Fig. 7
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Comparison between the measured S11 of the bent and flat configurations

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The bent antenna radiation patterns are measured inside an anechoic chamber as shown in Fig. 6c. The radiation patterns are compared with the radiation patterns of the flat antenna at 3 GHz, 5 GHz, and 8 GHz and at x–z, y–z and x–y planes as shown in Fig. 8. It is illustrated that the antenna has the same results as the previous flat antenna with slight deformation at the higher frequency bands. The antenna peak gain is compared with the previous antenna gain as shown in Fig. 9. The average peak gain of the curved antenna equals 3.5 dBi approximately.

Fig. 8
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Measured normalized radiation patterns between the bent and flat configurations a at 3 GHz b at 5 GHz c at 8 GHz

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Fig. 9
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Measured average peak gain between the bent and flat configurations

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3 Time Domain Study

Studying time-domain response is considered a vital part of wideband antenna design. The time-domain response claims that the designed antenna can transmit a narrow pulse in the time domain which translated to a broad band in the frequency domain to support wideband applications. This study can be done by fabricating two identical antennas (transmitting and receiving). Instead of putting the two antennas inside an anechoic chamber one is fixed and the other is rotated with different φ angles as [28, 29], three different layouts face to face, face to the side, and side to side are used. Studying time-domain response is done for both flat and bent antennas. Firstly, the two identical flat antennas are separated by 110 cm as shown in Fig. 10 and two ports VNA are used to measure the insertion loss S21 between them. The S21 magnitudes of the three antennas orientations are shown in Fig. 11. It is seen that the S21 magnitudes from 2.4 GHz up to 5.5 GHz have the same levels of around − 35 dB and the levels are reduced from − 35 dB to around − 55 dB at the upper-frequency band from 6 to 10 GHz. This is due to the radiation pattern features at the lower and upper-frequency bands. The measured S21 phases in rad for the three configurations are illustrated in Fig. 12. By studying the phase between the two antennas is important to show the linearity behavior of the system. The nonlinear features can be distorted in the transmitted signal. The unwrapped rad phase as shown in Fig. 12b is calculated to enhance the visualization and to detect easily the nonlinearity regions of the phase. From Fig. 12, we can notice that the phase responses for all orientations are the same with a linear feature. However, the face-to-side orientation has deviated slightly from 8.5 GHz to the end of the band. So, after this study, we can claim that the proposed antenna behaves well in time domain response.

Fig. 10
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Time-domain response setup of the measured straight monopole antenna a Face to Face b Face to side c Side to Side

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Fig. 11
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The measured insertion loss (S21)for different flat antenna layouts

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Fig. 12
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The measured insertion loss phase (S21)for different flat antenna layouts a normal rad phase and c unwrapped rad phase

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At this point, to show the behavior of the received signal, the input signal is converted to the frequency domain by applying fast Fourier transfer (FFT) in Matlab and multiplied with the transfer function of the system S21 as shown in Eq. (1). The Gaussian Pulse is chosen as the input pulse to apply to the system as shown in Fig. 13a, also the pulse parameters are chosen to cover all operated frequency bands as shown in Fig. 13b. The response of the system is calculated by converting the frequency domain to the time domain by inverse fast Fourier transform (IFFT) as illustrated in Eq. (2). The normalized received pulse at different three orientations is illustrated in Fig. 14. First, the three pulses have the same shape as the input pulse with the pulses centered at 2.2 ns with 1.7 ns delayed from the input signal. Second, the three pulses have small fluctuations around the pulse this is due to the nonlinear behavior of the phase response. Finally, we can conclude that the received signals are correlated with the input signal which means a good time-domain response.

$$R_{s} \left( \omega \right) = FFT\left( {T_{s} \left( t \right)} \right)H\left( \omega \right)$$
(1)
$$R_{s} \left( t \right) = IFFT\left( {R_{s} \left( \omega \right)} \right)$$
(2)
Fig. 13
figure 13

The normalized input signal Gaussian Pulse a Time-domain b Frequency doamin

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Fig. 14
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The normalized received Gaussian Pulse at different flat antenna configurations

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Another important factor that should be studied to evaluate the time response and the quality of the received signal of the wideband systems is the system fidelity factor (SFF) [28]. The SFF is a factor ranging from 0 to 1 also this factor should be more than 0.5 to achieve an undistorted signal. The SFF can be calculated using Eq. (3).

$$SFF = \mathop {\max }\limits_{n} \left( {\frac{{\int\limits_{ - \infty }^{\infty } {T_{s} \left( t \right)R_{s} \left( {t + \tau } \right)d\tau } }}{{\begin{array}{*{20}c} {\left( {\sqrt {\int\limits_{ - \infty }^{\infty } {\left| {T_{s} \left( t \right)} \right|}^{2} dt} } \right)} & {\left( {\sqrt {\int\limits_{ - \infty }^{\infty } {\left| {R_{s} \left( t \right)} \right|}^{2} dt} } \right)} \\ \end{array} }}} \right)$$
(3)

The input signal in the time domain is convoluted with the received signal in the time domain with variable shift τ then the output is divided on both input and received signals, then we took the maximum of the output and normalize it to achieve the calculated SSF. All of this process can be calculated using Matlab. The measured SSF equals 0.842, 0.853, and 0.913in the side-to-side, face-side, and face-to-face orientations. From SFF results, we can claim that the transmitted pulse can be received without distortion which means the proposed antenna can be used in wideband systems.

Secondly, The measured setup of the bending antenna is achieved with the same steps as the previous flat antenna as shown in Fig. 15. There are three different layouts of the antenna to measure the insertion loss S21 between them. The S21 magnitudes and phase are measured and plotted in Figs. 16 and 17, respectively. The S21 magnitudes have the same levels of -30 dB up to 6 GHz and are reduced to around − 55 dB at the end of the band. The phase shows linear operation up to 8.5 GHz for the three configurations but the face-to-face configuration and side-by-side configuration are deviated from 8.5 GHz up to 10 dB.

Fig. 15
figure 15

Time-domain response setup of the measured bending monopole antenna a Face to Face b Face to side c Side to Side

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Fig. 16
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The measured insertion loss (S21)for different bending antenna layouts

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Fig. 17
figure 17

The measured insertion loss phase (S21)for different bending antenna layouts a normal rad phase b unwrapped rad phase

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The normalized Gaussian pulse is used as the input pulse and the normalized received pulses calculated from Eq. (2) are shown in Fig. 18. The received pulses show a good correlation compared to the input signal instead of little fluctuations around the pulses. The SFF is calculated for three configurations using Eq. (3). The measured SFF for the curved antenna equals 0.853, 0.912, 0.901 for side-to-side, face-to-side, and face-to-face orientations. From the previous results, we can claim that the proposed antenna gives stable performance even if the antenna is bent. Finally Table 1 shows our work compared with other research. From Table 1, we can conclude that our work has good performance which makes it a good choice for wideband and wireless systems.

Fig. 18
figure 18

The normalized received Gaussian Pulse at different curved antenna configurations

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Table 1 Proposed flexible antenna versus selected reported works
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4 Conclusion

A wide-band flexible monopole antenna printed on a thin substrate has been designed and fabricated. The proposed antenna has been worked at 2.4 GHz up to 10 GHz with well-matched behavior. Two flat and bending configurations are studied to show the flexibility behavior of the proposed antenna. The antenna average gain equals 3.8 dB with omnidirectional and bidirectional radiation patterns. The time-domain performance has been carried out with a cross-correlation higher than 90% between the Gaussian input pulse and the received pulse for both configurations. The measured and simulated results conclude that the proposed antenna can be used in wireless systems.