1 Introduction

In 1988, Dr. Nathon Conen manufactured the first fractal antenna that fulfilled all of his user requirements in terms of compact size, wider bandwidths, lower price, and ease of fabrication [1]. The term fractal was first coined by B. Mandelbrot, fractal from the Latin word fractus which means irregular or broken. This word used to describe a new set of objects more complex than squares, circles or triangles which were well defined using Euclidean geometry. However, other everyday objects, such as clouds, blood vessels, and irregular shapes such as the coast could not be described by Euclidean geometry. Other great mathematicians such as W. Sierpinsky, N Von Koch, D. Hilbert, and H. Minkowski also contributed to the field of fractal geometries. Their fractals inspired the antenna engineering community to investigate whether these geometries could be used as antennas [2].

Over the past few decades, the use of fractal geometries had a significant impact on many areas of science and engineering; one of which is antennas [1,2,3,4,5,6]. Antennas using some of these geometries for various telecommunications applications are already commercially available. The use of fractal geometries has been shown to improve several antenna characteristics to varying degrees.

Modern telecommunication systems require antennas with wider bandwidths and smaller dimensions than conventionally possible [4,5,6]. This has initiated antenna research in various directions, one of which is the use of fractal shaped antenna elements. In recent decades, several fractal geometries have been introduced into antenna design with varying degrees of success in improving their characteristics. Some of these geometries have been particularly useful in reducing the size of the antenna, while other designs are aimed at incorporating multiband, broadband or ultra-wideband characteristics. The research presented here is intended to analyze the geometric characteristics of fractals that influence the performance of antennas that use them. Several antenna configurations based on fractal geometries have been reported in the literature [4,5,6,7,8]. The majority of the structures have a low profile with moderate gain and can be made to operate in several frequency bands and are therefore multifunctional. In this work, the multiband aspect in antenna design is further explored, with a particular focus on identifying fractal properties that impact the multiband characteristics of the antennas.

The use of electrochemical sensors and biosensors has grown considerably due to their simplicity, reliability, speed, and selectivity [7,8,9,10,11,12,13,14,15,16,17,18]. They were the most attractive alternative tools for conventional analytical methods in various fields, medicine and clinical biology or environmental monitoring. In this work, fractal shapes and their properties are discussed. The proposed antennas are fed by a microstrip line and their structure is based on a fractal geometry where the resonant frequency of the antenna is lowered by applying iteration techniques. The bandwidth has been optimized by combining different geometries resulting in a hybrid fractal antenna. The analysis and design of the fractal antennas was performed using the CST Microwave Studio simulation software. The proposed antenna, has a low profile, lightweight and easy to fabricate. For the detection of fructose concentration in water, a container is placed on top of the antenna on the front of the radiating element, the container is each time filled with water mixed with glucose with different concentrations. The sample placed on the antenna modifies the radio electrical properties of the antenna (reflection coefficient). After analysis of the results obtained by simulation and measurement, the curve relating the reflection coefficient of the fractal antenna with the concentration of fructose in the water is deduced. The obtained results are presented and discussed.

2 Design and fabrication of fractal antennas

The three proposed forms of fractal antennas are optimized by using commercial software CST Microwave Studio, which is based on the finite-integration time-domain (FITD). The three different fractal antennas are presented in Fig. 1, which are designed from two basic antennas, one of circular shape, and the other square, as shown in Fig. 1. The three antennas are fed, by a 50 Ω microstrip line.

Fig. 1
figure 1

Schematic of the different fractal antennas: a 0th iteration (square patch). b 2th iteration (hybrid fractal patch) [8]. c 3th iteration (hybrid plus fractal patch) our proposed antenna. e 0th iteration (circular patch). f hexagonal fractal patch. g Miludas fractal patch

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As shown in Fig. 2; the hybrid plusfractal patch antenna is designed by adding Minkowski curves at the boundaries of the base structure, cutting circles from the base shape, and inserting squares in such a way [9] that the corners of the inserted squares touch the boundaries of the circular slots.

Fig. 2
figure 2

Two-dimensional drawing of prototypes: a hexagonal fractal patch, b Miludas fractal patch. c Hybrid plus fractal patch antenna (b1 = 4 mm, b2 = 2.5 mm, b3 = 5 mm, b4 = 1.61 mm, a1 = 3.625 mm, a2 = 1.2 mm)

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The antennas are fabricated on 1.56 mm-thick dielectric substrate FR4 with the relative permittivity of 4.3 and loss tangent of 0.02. The metal pattern used 0.035 mm-thick copper with the conductivity of σ = 5.96 × 107 S/m. The base structure is a conventional square. The dimensions of the square patch [8] are calculated from the basic transmission line equations. The patch is associated with a microstrip line feed of length ‘Lf’ and width ‘Wf’. A defected ground plane of length ‘Lg’ and width ‘Wg’ is used which is united with a rectangle of length ‘Lg’ and width ‘Wg”. The various optimal geometrical dimensions shown in Fig. 2 are quantified in Table 1, 2 and 3.

Table 1 Summary of the design parameters for the hybrid plus fractal patch antenna
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Table 2 Summary of the design parameters for hexagonal fractal patch antenna
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Table 3 Summary of the design parameters for our Miludas fractal patch antenna
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The first antenna consists of making an antenna having a square conductive plate, this copper plate is fed by a rectangular feed line, which ensures the excitation of this chosen square antenna. Is called "iteration 0", with a thickness of 0.035 mm and denials of 29 * 29 mm, implanted once on an FR4 substrate, with a thickness of 1.56 mm and length 38 * 38 mm2, placed on a metal pattern (ground plane) square of copper, with a thickness of used 0.035 mm-thick copper with a conductivity of σ = 5.96 × 107 S/m, which has 38 * 38 mm2. Where the electrical size has λ0/8.

Figure 3 shows the front view of fabricated three structures. Four prototypes have been tested and measured at the center for development of advanced technologies (CDTA) as shown in Figs. 4 and 5. In the first phase the S-parameters of the three developed antennas were measured and then the results of the measurements were compared with the simulation results as illustrated in Figs. 6, 7, 8, 9. In the second phase the S-parameters of the antennas were measured by adding water samples mixed with fructose to the upper side of the antenna. The objective is to study the behavior of the antenna according to the added fructose concentration.

Fig. 3
figure 3

Photography of fabricated various forms of antennas: a hybrid fractal antenna [8]; b hybrid plus fractal antenna; c Miludas fractal antenna; d hexagonal fractal antenna

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Fig. 4
figure 4

Analyzer calibrator

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Fig. 5
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Antenna connected with the analyzer port

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Fig. 6
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Comparison between S11 (dB) simulated with CST and measured of the hybrid fractal antenna of the article

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Fig. 7
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Comparison between S11 (dB) simulated with CST and measured of the hybrid plus fractal antenna Fr4 substrate

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Fig. 8
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Comparison between S11 (dB) simulated with CST and measured of the hexagonal fractal antenna

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Fig. 9
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Comparison between S11 (dB) simulated with CST and measured of the Miludas fractal antenna with Fr4 substrate

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The following table illustrates quantitatively our comparisons between the frequency resonance values calculated by simulation under the microwave studio CST and measured by the network analyzer in the CDTA (Table 4).

Table 4 The resonance frequencies values calculated and measured practically
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3 Biosensor analysis with a different concentrations of fructose

Figure 10 shows the RF measurement system (vector network analyzer) for the proposed design with deferent concentrations of fructose. Figure 11 shows the measured reflection scattering parameter S11 of different concentrations of water-fructose. As seen, the resonance frequency is shifted down from 3.5 to 4.5 GHz for the concentrations of fructose change from 0.2 to 0.6 (g/ml), and deionized water at 25 °C (see Table 5).

Fig. 10
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Functional tests with a different concentrations of fructose

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Fig. 11
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The measured reflection response of the water–fructose test samples for calibration of the biosensor

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Table 5 The reflection response (S11) and frequency vs. water–fructose test samples
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The series of measurements was oriented on the ability of the sensor to detect sugar in a liquid of low concentration. Table 5 and Fig. 11 show an increase in resonant frequency for each increase in the amount of sugar in the liquid. We observe a decrease in the frequency shift at the frequency without sugar with 310.2, 300.2 and 262.7 MHz for concentrations of 0.2, 0.4 and 0.6 g/ml of sugar and a decrease in the shift of parameter S11 compared to parameter S11 without sugar with 9.861, 8.73 dB, and for concentrations of 0.2, 0.4 and 0.6 g/ml of sugar. So we deduce a proportional relationship between the quantity of sugar and the resonance frequency and the parameter S11.

The polynomial curve fitting can be used to extract the concentration of water–fructose test samples. A common polynomial model is generally used based on the second order polynomial as indicated in the expression under:

$$C = 0.09341 \times \left( {S_{11} } \right)^{2} + 2.211 \times S_{11} + 13.29$$
(1)

To find out the fructose concentration C (g/ml) of the tested sample, an empirical equation can be modeled based on the relationship between the coefficient S11 (dB) and the fructose concentration C (g/ml) using the curve fitting method (Fig. 13), which is the linear curve fitting as expressed below:

$$C = { - 0}{\text{.1862 }} \times S_{11} { - 2}{\text{.0251}}$$
(2)

The sensitivity S of the sensor can be found from [10]:

$$S = \frac{{\Delta S_{11} }}{\Delta C}$$
(3)

S = 0.1862 dB/(g/ml).

The polynomial curve fitting can be used to extract the concentration of water–fructose test samples. A common polynomial model is generally used based on the second order polynomial, as indicated in the expression under:

$$C = - 308.8 \times \left( {f_{R} } \right)^{2} + 2406 \times f_{R} - 4687$$
(4)

To decide the fructose concentration C (g/ml) of the tested sample, an empirical equation can be modeled based on the relationship between the frequency (GHz) and the fructose concentration C (g/ml) using the curve fitting method (Fig. 15), which is the linear curve fitting as expressed below:

$$C = {7}{\text{.5748 }} \times f_{R} { - 28}{\text{.9746}}$$
(5)

The sensitivity S of the biosensor can be found from:

$$S = \frac{{\Delta f_{R} }}{\Delta C}$$
(6)
$$S = \frac{1}{7.5748} = 0.132\,\, {\text{GHz/(g/ml)}}.$$

Figures 12, 13, 14, and 15 show a positive relationship between the fructose concentration and the reflection coefficient and resonance frequency, given us the sensitivity of the biosensor, in that point, we consider that our hybrid plus fractal antenna is working perfectly in the biomedical domain.

Fig. 12
figure 12

Polynomial curve fitting of fructose concentration vs. reflection coefficient (S11)

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Fig. 13
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Linear curve fitting of fructose concentration vs. reflection coefficient (S11)

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Fig. 14
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Polynomial curve fitting of water–fructose test samples (g/ml) vs. frequency (GHz)

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Fig. 15
figure 15

Linear curve fitting of fructose concentration vs. frequency (GHz)

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The sensitivities are normalized to the permittivity of the liquid sample, Here, the fructose is used for standard comparison LUT case. According to the results shown in Table 6, the proposed sensor offers good sensitivity and the highest dB magnitude variation.

Table 6 Comparison between the resonator type for complex permittivity measurement of this work and some existing works
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The major performance characteristics for our biosensor are confirmed by comparison with analogues (see Table 6). We have made a comparison of the most important characteristics of our biosensor to prove its effectiveness and importance in relation to what is currently available and modern, which is proven by this study.

4 Conclusion

This novel high sensitivity biosensor for the detection of low concentrations (water-fructose) with two methods: frequency method and S11 parameter method presented in this paper. The resonance frequency and the peak attenuation (S11 dB) are sensitive to the sample concentrations variation, the good performance is obtained.

In this article, a study of a liquid sensor based on a new fractal antenna was carried out. The optimization of a sensor based on a fractal antenna for the characterization and analysis of liquid and aqueous solutions of low concentration or volume has been carried out leading to a sensor formed of a fractal resonator coupled to a linear microstrip line. The sensor was made whose measurement results on liquids in the presence of chemical species of very low concentrations showed a high sensitivity comparable or even superior to the performance recently published. These structures also feature miniaturized dimensions and low manufacturing cost.