Dual-band single-layer frequency selective surfaces for 5G applications

for 5G applications

Dual-band single-layer frequency selective surface

Academic year 2019-2020

Master of Science in de industriële wetenschappen: elektronica-ICT Master's dissertation submitted in order to obtain the academic degree of Vigo)

Supervisors: Prof. dr. ir. Jo Verhaevert, Prof. Inigo Cuinas (Universidade de Student numbers: 01504778, 01501557

for 5G applications

Dual-band single-layer frequency selective surface

Academic year 2019-2020

Master of Science in de industriële wetenschappen: elektronica-ICT Master's dissertation submitted in order to obtain the academic degree of Vigo)

Supervisors: Prof. dr. ir. Jo Verhaevert, Prof. Inigo Cuinas (Universidade de Student numbers: 01504778, 01501557

Global COVID-19 pandemic preamble

At the end of 2019, Coronavirus disease 2019 (COVID-19) broke out in China. It was first identified in December 2019 in Wuhan, the capital of China’s Hubei province, and has since then spread globally, resulting in an ongoing pandemic. It is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Million cases and hundred thousands deaths have been reported across the whole world.

A lockdown was employed and people in several countries were banned from leaving their homes for nonessential matters. All schools, shops, laboratories,... were closed. The outbreak of this virus has had extreme consequences for everyone, including us. This virus prevented us from completing our exchange and we had to return to Belgium earlier than planned. As a result, we weren’t able anymore to go to the university lab and were therefore unable to carry out all planned experiments. Thanks to all the good support and help, we have achieved the best possible results from a distance.

Preface

This Master Thesis has been written as final piece during the education of Master of Science in Electronics and ICT Engineering Technology. This thesis has been developed at the University of Vigo, Spain in the context of an Erasmus+ exchange program.

We would like to thank some people who made it possible to successfully complete this master’s thesis.

First of all, we would like to thank our promoters at the University in Vigo: Professor ´I. Cui ˜nas and Professor M. Garcia. They initially made us feel welcome at the University of Vigo during our Erasmus experience. Moreover, they followed us very well and guided us during our thesis and we could count on them every week if we had some problems or had some questions. Thanks to them, our project was properly managed and adjusted if necessary.

In addition, Professor J. Verhaevert of Ghent University also deserves a special thank you for following up on the entire project from Belgium. We could always contact him for practical or other questions. Then we would like to thank Isabel and the other colleagues in the lab for all their help with the technical problems and for always welcoming us at the lab at the university. Finally, we would like to thank in general both Ghent University and Vigo University for allowing everything to go smoothly despite the less favorable conditions caused by COVID-19. Thanks to the good guidance, we were able to achieve our master’s thesis in a way that each of us is proud of.

Admission to loan

The authors give permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In the case of any other use, the copyright terms have to be respected, in particular with regard to the obligation to state expressly the source when quoting results from this master dissertation.

Abstract

Due to the global rise in the popularity of 5G, the demand for shielding against it grows. This study focuses on radio wave propagation at 5G on sub6GHz bands. This master dissertation aims to provide a suitable dual-band fractal Frequency Selective Surface (FSS) to be used in the lower band 5G frequencies; 750 MHz and 3.5 GHz. Two designs are presented in this master dissertation: The first unit-cell is in the shape of a bowtie, where each of the triangular parts are Sierpi ´nski triangles. One major addition to the unit-cell is a central lumped element to make the manufacturing of the FSS more feasible. As with each different stage of a fractal antenna, behave the different stages of the fractal FSS design differently. For this application, the second stage is sufficient as we are able to cover frequency bands among those included in the FR1 5G spectrum. The second proposed design consists of a combination of basic elements, especially spiral elements, and both designs are tuned around 750 MHz and 3.5 GHz frequency bands. FR-4 dielectric of thickness 1.6 mm is used to model the FSS designs with a respectively dimension of the unit cell of 87x45 mm2_{for the fractal design and 70x70 mm}2_{for the spiral design.}

Simulation demonstrates the performance of the proposed FSS design. Some formulas were derived using linear regression; these formulas have high accuracy and can be used to adapt the design to other frequencies. Some other parameters which are not represented in the aforementioned formulas can also be adjusted for minor tweaking of the design.

invariance against changing incident angles. This design’s resistance is not great and should be taken into account when proposing the installation of a structure based on it. As a last real-world check, a simulation of the inverse of the design is performed. The inverse of the fractal design does not result in perfect bandpass version, but could certainly be implemented as such. The inverse design of the spiral design gives quite good results.

Dual-band single-layer fractal frequency

selective surface for 5G applications

Bram Decoster1_{, ´I˜nigo Cui˜nas}2_{, Manuel Garcia}2_{, Jo Verhaevert}1 Ghent University, Ghent, Belgium1

Universidade de Vigo, Vigo, Spain2

Abstract—Due to the global rise in the popularity of 5G, the demand for shielding against it rises. This research paper aims to provide a suitable dual-band fractal Frequency Se-lective Surface (FSS) for the lower band 5G frequencies; 750 MHz and 3.5 GHz. The unit-cell is in the shape of a bowtie, where each of the triangular parts are Sierpi´nski triangles. One major addition to the unit-cell is a central lumped element to make the manufacturing of the FSS more feasible. As with each different stage of a fractal antenna, behave the different stages of the fractal FSS design differently. For this application, the second stage is sufficient as we are able to cover frequency bands among those included in the FR1 5G spectrum. Some formulas were derived using linear regression; these formulas have high accuracy and can be used to adapt the design to other frequencies. Some other parameters which are not represented in the aforementioned formulas can also be adjusted for minor tweaking of the design. This design does not perform great under large incident angles, and this should be taken into account when proposing the installation of a structure based on it. As a last real-world check, a simulation of the inverse of the design is performed. The inverse does not result in perfect bandpass version, but could indeed be implemented as such.

Index Terms—Frequency Selective Surface (FSS), 5G, Sierpinski dipole, CST microwave studio, fractals, Sierpi´nski triangle

I. INTRODUCTION

5G is all the craze at this moment in time, every country and major telecom network wants to implement it. However, this widespread adaptation of a new technology comes with a lot of new problems. Among the wide collection of frequency bands suitable for implementing 5G, there are also ISM bands, some of them already crowded [1]. To combat this over-saturating issue, many different solutions can be found. For example, if one wants to keep their flat’s wifi signal from interfering with the neighbour’s and vica versa, thick walls with shielding might be possible. This is a simple but blunt method, blunt because it blocks every frequency. This paper aims to provide a suitable, less blunt, approach towards shielding devices from 5G. A Frequency Selective Surface (FSS) is an ideal solution, because it, as the name suggests, selects its frequency for which it shields. It can act as a bandpass or bandstop filter for electromagnetic waves. The design in this paper is meant to be used with the lower 5G frequency bands, within the FR1 spectrum. This FSS will thus provide suppression of the 700 MHz and the 3.5 GHz frequency bands. The bandwidth for both frequencies needs to be at least 400 MHz to be usable in the real world.

An attempt has been made to find a fitting solution using a self-similar design. Earlier research like [2] showed promising results for a single layer FSS dual-band design. A couple of formulas will be derived to apply this design for other frequencies with simple parameter adjustments. The real-world cases with different angles of incidence will be simulated, and the inverse design will be checked. All simulations were done in CST microwave studio [3] following the guidance of Numan and Sharawi [4] and the CST product manual [5].

Figure 1. Different stages for the Sierpi´nski triangle, image from [6]

II. SELF-SIMILAR STRUCTURES AND FRACTAL ANTENNAS

The first time fractals were looked at as something useful to be used to improve real-world applications was by the mathematician Mandelbrot in his book The fractal geometry of nature [7]. Here he explained the occurrence of fractals in nature and the relation to roughness. A couple of years later, Kim and Jaggard published the first paper on fractal antenna theory. Cohen made, a couple of years later, the first real-world fractal antenna [8]. Werner and Gangul bundled Much’s research in fractal antenna design [6]. More general fractal antenna design rules were also bundled in Fractal Apertures in Waveguides, Conducting Screens and Cavities [9].

A. Sierpi´nski triangle

A famous self-similar geometric shape is the Sierpi´nski triangle; the first four different stages of the fractal are

shown in Fig. 1 (the yellow elements are conductive sur-faces). This shape was used in previous antenna and FSS-designs. Romeu and Y. Rahmat-Samii [2] used the triangle to create a bowtie FSS that works for two frequencies. This dual-band design forms the base of the design used in this research.

III. THE UNIT CELL Table I

THE PARAMETERS OF THE UNIT CELL AND THE VALUES OF THEM IN THE FINAL DESIGN.

parameter explanation value (mm) w height of the bowtie 87 t width of the central element 0.5 dx horizontal distance between elements 3 dy vertical distance between elements 2

The objective is to analyse the performance of the surfaces composed by a squared matrix of replicated unit cells; this section describes the unit cell. The designed unit cell with its parameters can be seen in Fig. 2. The unit cell is made up out of a central bowtie complemented with a central lumped element. This bowtie itself is contains three parts, the first two being second stage Sierpi´nski triangles horizontally mirrored into each other. The third and special element is the central lumped element connecting the two triangles. In Table I, all the design parameters and their respective final sizes are summed up and explained.

Figure 2. Unit cell design.

A. Extra central element

The main difference between the bowtie from [2] and the one from this paper is visible on the drawing: the added central lumped element with a width of t. This element

is an excellent granular tuning parameter; the simulation results of the tuning can be found in section IV-B. Another benefit of adding this lumped element is the effect it has on the production of the physical FSS. The point of the two triangles touching is essential and the contact area is very small. If the two are not connected as expected, the resonance could be completely different. More on the complete structure resonance can be read in section VII. B. Number of iterations

Fractal objects have multiple stages. This section investigates the effects of the different stages of the unit cell design. On Fig. 3, the different stages can be seen. When the design does not iterate on itself and is thus in stage one, there is only one notch at the lower frequency band in the attenuation frequency response, around 900 MHz. This can be seen in Fig. 4. When the second stage design is implemented, a second notch at the higher frequency band of 3.5 GHz also appears. This means that, at least, a stage two unit cell is needed to get the dual-band characteristic. When the design iterates more upon itself to stage three and four, no further improvements can be noted. These higher iterations increase complexity and thus make it more challenging to produce. This is why the final design sticks with the second stage. Another

Figure 3. The different stages

notable effect of increasing the number of iterations is the shift of the two peaks. The fourth iteration has a complete shift to the left but also brings the two peaks closer towards each other. This can be a reason to pick the higher number of iterations over the lower amount, even though it increases the production difficulty.

Figure 4. The different stages

IV. DESIGN PARAMETERS

This section provides a guide to adjust this unit cell so it can be used with other frequencies. All the adjustable parameters and their explanation are listed in Table I. The four parameters in order of importance are w, t, dy and dx. Designing a unit cell, like the one purposed in this paper, starts with the general size of the element [10], [11]. The size is directly tied to the resonance wavelength. Even more specific, in this design, the unit cell will determine the placement of the first resonance frequency. This can be concluded from the iteration results discussed in section III-B. On Fig. 3 the first stage only resonates at the lower of the two frequencies (it only has a valley around 800 MHz and not around 3.5 GHz, considering the design dimensions).

The dx and dy parameters depict the distance between the individual bowties and will be fixed to 3 and 2 mm respectively for the next section. When these values are too low, the different bowties will touch, and the known response of the FSS will be lost. This also eases the way the simulations can be done in CST microwave studio. A. Simulating in CST microwave studio

The simulations were done using the FSS unit cell template, and this ensured a correct basic setting of key simulation setting such as the boundaries and background. All simulations were done using unit cell boundaries, which ensured a three by three unit cell surface to be simulated. The unit cell boundary settings enabled the Floquent boundary simulation mode, Zmin was selected as the Floquent port [5]. The frequency solver was set up so that frequencies from 0 up to 6 GHz were taken into account. The frequency plots in this paper, are always S21 plots (in CST the Smin(1), Zmax(1) result [4]). To obtain the later explained formulae 1, 2, 3 and 4, parameter sweeps were performed with varying values for t, w, dx and dy. Where, with each sweep, only one of the prementioned parameters varies in an interval.

B. Unit cell size w and central element width t

As explained in the first part of this section, the two parameters that allow the most consistent flexibility in

adjusting for frequency and bandwidth are w and to a lesser extent t. w stands for the size of the element and is measured from the top of the bowtie to the bottom. t is defined as the width of the central lumped element and has a limited range. The size parameter w is investigated from 70 to 100 millimetres. In this interval, the frequency shifts follow a linear relationship. The range is fixed from 0.5 to 2.8 millimetres. Its lower limit is due to the physical design limitations of a copper trace width. The lower limit is so that the different bowties will not end up touching each other.

The two intervals that are described in the previous paragraph were used to do a parameter sweep in CST microwave studio. The results from these simulations were then analyzed to derive formulas for the frequency and bandwidths of the two valleys. Using Python, the results were plotted on four different graphs as point clouds, and these can be seen in Fig. 5.

From the previously mentioned plots in Fig. 5, it is clear that there is some linear relationship for the centre frequencies as well as the bandwidths. These linear relationships lead to the following four formulas (Form. 1, 2, 3 and 4) that were derived using linear regression. The precision for these formulas is also noted right beside the equation. These numbers are only valid in the intervals from the simulations. The formulas could be valid for a little while longer, but the curves will begin to diverge from the planes with increasing and decreasing w values.

f = 0.0434t− 0.0134w + 1.9238 p = 98.939% (1)

Formula 1 is a good starting equation to decide where the first peak needs to be. It is valid from 750 MHz up to 1150 MHz. Again it is to be noted that the increase in overall size w has a large effect on the resonance.

f = 0.0249t− 0.0443w + 7.3136 p = 98.626% (2)

The second formula has a wider useful interval, from 3.4 GHz to 4.3 GHz. This means that the same change in w yields a more drastic frequency shift in the second resonance band than in the first lower one. t in comparison seems to have less of an effect when the formulas are looked at more closely; t has about 50% less of an effect on the low band centre frequency position than the high-frequency centre band position. The precision of both formulas 1 and 2 is both high and similar. This means that both can be a good starting point for designing a similar design around 800 MHz or 3.5 GHz.

BW = 0.1312t− 0.0175w + 2.7797 p = 98.267% (3)

When the design requirements are taken into account, then the design needs to have at least a bandwidth of 400 MHz around the centre frequencies at the -10 dB level. The centre frequency for the lower band varies around 800 MHz and not the predetermined 700 MHz, but this does not have to be a problem. The bandwidth is a lot larger than 400 MHz. This means that at 700 MHz, the suppression or reflectivity is still -10 dB and that the total

(a) Frequency shift around 800 MHz (b) Frequency shift around 3.5 GHz

(c) Bandwidth shift around 800 MHz (d) Bandwidth shift around 3.5 GHz Figure 5. The effects of w and t

width around 700 MHz is more than sufficiently damped. In Fig. 5-c the bandwidth variation interval is visible on the z-axis; it ranges from 1.3 GHz to 2 GHz. This is wide enough and can be effectively tweaked with formula 3. The influence of t on the bandwidth is this time higher than the influence of w. This can be interesting for some applications. One can, for example, achieve a high-bandwidth and low first frequency band by using a high w value and high t value. The precision of this formula is again relatively high, with more than 98% accuracy.

BW =−0.0708t+0.0022w+1.2205 p = 61.558% (4)

The last of the formulas is an interesting one. The first and maybe most important of the differences with the other formulas is clearly visible in Fig. 5-d. The fitted plane decreases in bandwidth with higher t values. This is the opposite of the lower band response. This means that trying to achieve a wider bandwidth at the lower centre frequency yields a smaller bandwidth around the higher centre frequency. It must be said that the precision of this formula is a lot lower than the precision of the other for-mulae. The noise with this one is high. Using this formula for the bandwidth might result in a good approximation of the real-world response, but it is advisable to first look to the other formulae before the fourth one.

C. Distance between bowties dx and dy

The distance between the bowties is represented by the parameters dx and dy. The exact depiction of dx and dy is visible in Fig. 2. When this FSS-design adjusted for another frequency using this paper, it is best to start with fixed values for dx and dy; all previous formulae were derived for dx and dy values of respectively 3 and 2 mm. Afterwards, when w and t are fixed, minor adjustments of dx and dy towards the centre frequency can be performed. The results for parameter sweeps of dx and dy can be seen in Fig. 6. The other two parameters w and t were fixed at 87 mm and 0.5 mm respectively. Both dx and dy were again limited so that the neighbouring unit cells would not touch each other. This would, as mentioned in previous sections, result in unexpected behaviour. In Fig. 6-a the low band centre frequency shift does differ a lot from dx to dy. The dx curve follows a logarithmic path but the dy variation is more akin to a quadratic function. This means that one needs to be careful when adjusting one of the parameters; the results could be surprising, do not expect a linear behaviour. Fig. 6-b shows that the response for dx and dy is more similar to each other, both follow a logarithmic function1_{. One could even expect}

1_{The equations for the trendlines and the trendlines themselves are not}

depicted here because they will change together with changes in w and t, see these graphs as guidelines

(a) Around 800 MHz

(b) Around 3.5 GHz Figure 6. The effects of dx and dy variation

linear behaviour near the previously achieved frequency (using the formulae from section IV-B).

If all the previously mentioned formulae and little dx and dy adjustments were correctly implemented, then one should now have the design they were aiming for.

Figure 7. Resistance against different incident angles

V. ANGLE OF INCIDENCE

As with everything that is simulated and designed on the computer, it is important that it is tested for as many different use cases as possible. The simulation results

from all previous sections use incident waves that are perpendicular to the FSS-surface. This section will check the design robustness under different angles of incidence. Fig. 7 shows the simulation results for different angles, where φ and θ are angles in the dy and dx directions. The bowtie has a decent invariance against changes in the θ direction. This means that the resistance against changing angles in this direction is strong. Some extra noise above 4.5 GHz is introduced, but the behaviour around 700 MHz and 3.5 GHz stays more or less the same as long as the size of θ does not exceed 45°. The story for φ is entirely different, the slightest change (more than 10°) in angle and the lower frequency behaviour will begin to disappear, which means that the design is not strong against polarisation of the incident wave. The FSS might still be usable because the notch is still wide at -10 dB. However, this is questionable and should be tested on a real-world fabrication of the complete FSS. If a wave is tilted in both directions, a similar result is visible as with only φ changes. This is likely since the unit cell is not uniformly symmetric.

VI. THE INVERSE OF THE DESIGN

The design in Fig. 2 has band-reject characteristics. If an FSS gets inverted, a bandpass FSS should be the result. The direct and inverse unit cells are shown in Fig. 8. The result of the simulation is not a perfect bandpass variant, the inverse FSS struggles around the 800 MHz dip, this is visible in Fig. 9. This is not a big issue but makes it more difficult to use this form as a good bandpass FSS.

(a) normal (b) inverse Figure 8. The inverse design

VII. FULL50BY50CENTIMETRES SIMULATION AND FURTHER RESEARCH

The final step of the work is to manufacture a FSS prototype of an approximate size of 50 by 50 centimetres, designed by placing copies of the unit cell in a matrix deployment. This is done to check the behaviour in real-world experiments, including the possible mutual coupling among adjacent unit cells. Due to the COVID-19 pandemic, the full 50 by 50 centimetres FSS could not be manufactured. This is only a minor confirmation step of the CST microwave studio design results and would only take about a day to complete. Further research at the university can be done to verify the acquired results,

Figure 9. The direct vs the inverse design

to get an idea of the full surface response, a full FSS structure simulation has been done CST. The simulation is a plane wave simulation where only the electric field results will be analysed in the following section. The full structure is visible in Fig. 10.

Figure 10. The complete FSS-surface

In Fig. 11(a) and (b) the different excitations are clearly visible. The lower frequency resonates with the bigger overall bowtie structure and the higher frequency resonates with the smaller triangle cutouts of the second iteration.

VIII. CONCLUSION

This paper proposed bowtie FSS-design to block the lower band 5G frequencies. Multiple simulation results proved that this is a decent attempt, with wide and deep peeks around the desired centre frequencies of 700 MHZ and 3.5 GHz. Through the formulas derived here in this publication (see section IV-B), other researchers could adapt the design to be used for their purposes. The other important parameters were shown to be less reliable in adjusting, but they can be used for minor tweaking of the

(a) E-field at 800 MHz (b) E-field at 3.5 GHz Figure 11. E-field comparison

centre frequencies. Different angles of incidence show that the design is limited in real-world application uses due to its poor performance in φ changes. It does not mean that it will not be usable, just that this fact needs to be considered before going through with implementing it. The inverse design results in a bandpass FSS that is certainly not perfect, but could be good enough depending on the application. Due to the global pandemic, the final 50 by 50 centimetres testing was done with a computer simulation in CST microwave studio, delaying the experimental test with a prototype. Here could be concluded that the larger outer parameter of the bowtie resonated with the lower band centre-frequency and that the inner cutout triangles resonate most with the higher band frequency. As an overall conclusion, one could say that this design is versatile and has its good and bad sides; but that real-world usage is a certain possibility.

REFERENCES

[1] D. Ferreira, I. Cui˜nas, R. F. Caldeirinha, and T. R. Fernandes, “Dual-band single-layer quarter ring frequency selective surface for Wi-Fi applications,” IET Microwaves, Antennas and Propagation, vol. 10, no. 4, pp. 435–441, 2016.

[2] J. Romeu and Y. Rahmat-Samii, “Fractal FSS: A novel dual-band frequency selective surface Photoconductive Antenna Optimization for Wireless Sensor Application in THz band View project Develop-ment of mmW-Photonic Antenna Systems integrated with InGaAs Photodiodes View project Fractal FS,” IEEE Trans. on Antennas and Prop., vol. 48, no. 7, 2000.

[3] Dassault Syst`eme, “CST microwave studio,” 2020.

[4] A. B. Numan and M. S. Sharawi, “Extraction of material parameters for metamaterials using a full-wave simulator [education column],” IEEE Antennas and Propagation Magazine, vol. 55, no. 5, pp. 202– 211, 2013.

[5] Dassault Syst`emes, CST Studio Suite Help. 2019.

[6] D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antennas and Propagation Magazine, vol. 45, no. 1, pp. 38–57, 2003.

[7] B. B. Mandelbrot, The fractal geometry of nature. San Francisco: W.H.Freeman & Co Ltd, 1982.

[8] P. Felber, “Fractal Antennas,” tech. rep., 2000.

[9] B. Ghosh, S. N. Sinha, and M. V. Kartikeyan, Fractal Apertures in Waveguides, Conducting Screens and Cavities, vol. 187 of Springer Series in Optical Sciences. Cham: Springer International Publishing, 2014.

[10] B. A. Munk, Frequency Selective Surfaces Theory and Design. New York (N.Y.) : Wiley, 2000., 2000.

[11] B. A. Munk, Finite Antenna Arrays and FSS. Hoboken, NJ, USA: John Wiley & Sons, Inc., jul 2003.

Dual-band single-layer spiral frequency selective

surface for 5G applications

STEPHANIE MAES1,*, ÍÑIGO CUIÑAS2, MANUEL GARCIA2,AND JOVERHAEVERT1

1_{Ghent University, Ghent, Belgium} 2_{Universidade de Vigo, Vigo, Spain}

*_{E-mail Stephanie Maes: stephanie.maes@ugent.be}

This study proposes a frequency selective surface (FSS) design to be used in 5G FR1 bands. A dual-band single layer unit cell of FSS for dual band response is presented. The proposed design consists of a combination of basic elements, especially spiral elements, and is tuned at both 750 MHz and 3.5 GHz frequency bands. FR-4 dielectric of thickness 1.6 mm is used to model the FSS design with a dimension of the unit cell of 70x70mm2_{. Simulation and model validation through measurements demonstrate the}

performance of the proposed FSS design. The performance of variants are also demonstrated by the CST simulation. This study focuses on radio wave propagation at 5G on sub6 GHz bands.

1. INTRODUCTION

There is many research and engineering work related to indoor and outdoor wideband radio wave propagation[1], but the interest of 5G bands is growing and will probably reach very interesting results. 5G is becoming the new standard for mobility in general, and for mobile Internet in particular. The new technology is much faster than the current 4G and many more people are able to use it at the same time. Frequency selective surface (FSS) may be applied in order to block only specific frequency bands, while allowing other wireless bands to pass through, or vice-versa[2]. Such FSS may be integrated into existing structures as a wall paper, with the unit cell pattern printed in some conducting material, or within the wall itself, through combination with the isolation material layers[3]. In this paper we try to find a design, consisting of spirals, which is a band reject exactly on the frequencies 750 MHz and 3.5 GHz. In addition to finding the right design, formulas are also drawn up that make it possible to tune the design in such a way that the frequencies can be adjusted more precisely.

In Section 2 the proposed FSS design is presented and de-tailed. Section 3 depicts the inverse of the design. In Section 4 the simulation results can be observed, whereas in Section 5 the formulas for tuning the parameters are distracted and discussed. In Section 6 the effect of varying the incidence angle is examined. Finally, in Section 7 the main conclusions from this work are summarised. And Section 8 explains what can be done in the future.

Fig. 1.Unit Cell Design.

2. FSS UNIT CELL DESIGN

The proposed design is based on two spiral elements[4], where the dimensions were optimized to yield a frequency response appropriate for the 750 MHz and 3.5 GHz 5G FR1 bands. FR1 is the portion of the spectrum assigned to sub-6 GHz for 5G bands. In Figure1the proposed FSS design is shown. In this figure, the black elements are the conductive surfaces. The double arrow lines delimit the unit cell dimensions. The extreme dimension of one unit cell contains 70x70 mm and the structure itself is comprised of two elements. The first element is a rectangular

loop along the outside of the figure, with a gap of length 0 mm and with only 1 turn. Because of the gap of length 0, it actually amounts to a surrounding square with a width of 1.6 mm. The second element is a 4 arms spiral. These arms are obtained from two circles, the outer circle with a radius of 14 mm and the inner circle with a radius of 17 mm. To obtain this design, the left moon is shifted a bit from the centre of the ground plane. The lowest point of the ‘moon’ is shifted 3.9 mm to the right of the center and 5.4 mm downwards, as is shown in Figure1. This moon was copied 4 times with a 90◦_{rotation seen from}

the center. Another way to obtain the design is to start again from the left moon and draw the two circles on the basis of the radius of both the outside and inside of the moon. To obtain the outside of the moon, draw a circle with centre (-7.5, -2.5) and a radius of 14 mm. To obtain the inner of the moon, draw a circle with centre (1, 10) and a radius of 17 mm. The coordinates of the centres are viewed from the centre of the ground plane, where the coordinates are (0, 0). Copy this moon 4 times over 90◦_from

the centre (0, 0). Now, the 4 spiral arms are obtained. Table1 shows the values of the dimensions.

Table 1.dimensions unit cell design

abbreviation parameter value d dimension 70mm w width surrounding square 1.6mm g gap between square and cell 2.45mm in_r radius of inner circle 17mm out_r radius of outer circle 14mm l length inside the square 53.5mm shift_r shift to the right of first moon 3.9mm shift_d shift downwards of first moon 5.4mm

3. FSS DESIGNS

A. Band reject variant

The proposed design, depicted in Figure1is a band reject FSS variant, where the conducting portions are represented by black color. This FSS provides a band reject frequency response for

Fig. 2.Band reject and band pass FSS simulation results both 750 MHz and 3.5 GHz 5G frequency bands, visualised in Figure2.

B. Band pass variant

The band pass variant of the proposed FSS is basically the ‘nega-tive’ of the band reject FSS as is depicted in Figure3. It is also called the inverse design of the previous one and it yields a band pass response at both desired 5G frequency bands, also shown in Figure2[5].

Fig. 3.Inverse of the unit cell design

4. SIMULATION RESULTS

The design consists of several parameters, as showed in Table1. This design is optimized to have 2 notches at certain frequencies, namely 750 MHz and 3.5 GHz. The values for the parameters shown in table 1give the best possible result for this. It is also possible to obtain similar results by slightly modifying the parameters. And by changing parameters, other desired frequencies can also be obtained. To achieve these results, many simulations were performed with the program CST Studio Suite 2019[6]. These simulations are discussed in this section. For each situation there is a formula derived. These formulas are obtained by applying linear regression and will be discussed and compared in the next section. Furthermore, decisions are made about which formulas are needed in each situation to obtain the desired frequencies or parameters.

The FSS unit cell template was used to perform the correct simulations. This template ensured the correct basic settings. The frequency range settings were chosen from 0 to 6 GHz. The frequency plots shown in this paper are the S21 (Zmin) plots [6]. To derive formulas, multiple simulations were performed on the same design, where 1 parameter was changed each time. In CST these are called parameter sweeps.

Formulas are derived for 4 situations. Each formula has two parameters in function of the frequency or the bandwidth. All formulas are found through linear regression. For each of them, the accuracy will also be given. This provides a good idea of how useful and accurate the formula is and whether or not it can be used to tune the design.

The four cases investigated are the following:

A Tuning the surrounding square with parameters ’w’ and the scale of the square.

B Tuning the whole design with parameters ’w’ and the scale of 4 spiral arms.

C Tuning the 4 arms spiral design with parameters in_r and out_r.

D Tuning the whole design with parameters the scale of the square and the gap of the space in between the moons.

A. Tuning the surrounding square with parameters ’w’ and the scale of the square ’s’

Parameter ’w’ stands for the width of the surrounding square. The scale of the surrounding square is based on the original design (scale 1). All surrounding squares that are larger, have a scale greater than 1. The smaller squares have a scale smaller than 1. The limits in which the parameters should be are the following: scale of the square: [0.80; 0.99] and w: [0.2;2].

Fig. 4.w changes, while the scale of the square is constant.

Fig. 5.w = constant, the scale of the square changes.

In Figure4, the scale varies and ’w’ is constant. Figure5 is reversed. As we can see when ‘w’ changes, there happens almost nothing. Only the yellow and the green curve change, but that is because they are on the verge of a limit. When the scale changes, the frequencies are shifted a little.

B. Tuning the whole design with parameters ’w’ and the scale of 4 spiral arms ’sc’

Parameter ’w’ stands again for the width of the surrounding square. The scale of the four spiral arms is considered as the scale of the 4 arms together. This piece of the design, described in Section 2 has a scale of 1. When the scale is smaller than 1, the arms will shrink. The limits in which the parameters should be are the following: w: [0.2;2] and scale of spiral arms: [0.5;1.5].

Fig. 6.w changes, the scale of the spiral arms is constant.

Fig. 7.w = constant, the scale of the spiral arms changes.

The first graphs in Figure6all have the same scale, with a different ‘w’. We already know that ‘w’ has no big impact. When we take a look at the second graph in Figure7, there we see graphs where ‘w’ is constant and the scale changes. It is clear that the scale of the moons has a big impact on the 3.5 GHz frequency. We can see in Section 5 that we can derive pretty good formulas to tune the frequencies by adapting w and the scale.

C. Tuning the 4 arms spiral design with parameters in_r and out_r

The parameters in_r and out_r are shown in Figure1. The lim-its in which the parameters should be are the following: in_r: [11;15] and out_r: [14;19].

Fig. 9.in_r = constant, out_r changes.

When in_r changes, we see that the higher frequency shifts. Out_r has no big impact on the frequencies. The formula in Section 5 will give a very good result for the higher frequencies.

D. Tuning the whole design with parameters the scale of the square ’s’ and the gap in between the moons

The scale of the square has already been described above. The gap in between the moons is created by adapting the parameters shift_r and shift_d. When these parameters increase, the gap will become bigger. With some help of these parameters, the surface in between the arms is calculated and this one stands for the size of the gap. The limits in which the parameters should be are the following: scale of the square: [0.80; 0.99] and gap: [0;162].

Fig. 10.gap = constant, the scale changes.

Figure10is the simulation of some different values for the scale on one value for the gap. When changing the gap, this will result in almost the same graphs. So changing the gap and the scale of the square has no big impact on the 3.5 GHz, the low frequencies shift only a little. Anyway, as we will see in Section 5 the formulas give really good results for both frequencies, so they are useful.

5. FORMULAS FOR TUNING PARAMETERS

Depending on what you want to adjust, it can be useful to use different formulas. This section discusses which formula (and which parameter) to use best in each situation. An overview of all formulas with their accuracy, respectively for the frequency at 750 MHz, the bandwidth at 750 MHz, the frequency at 3.5 GHz and the bandwidth at 3.5 GHz, are shown in Table2, Table 3, Table4and Table5.

Table 2.Formulas for the frequency shift around 750 MHz for each situation.

situation formula accuracy A f = 0.04332 w - 4.3775 s + 4.8701 98.47% B f = 0.0367 w - 0.0118 sc + 0.7078 92.61% C f = -0.0026 in_r + 0.0009 out_r + 0.7903 68.35% D f = -1.5195·10−5_{s−4.3180gap+4.7757 95.45%}

Table 3.Formulas for the bandwidth shift around 750 MHz for each situation.

situation formula accuracy A BW = 0.0715 w + 0.1448 s + 0.0612 97.01% B BW = 0.0489 w - 0.0613 sc + 0.2292 92.14% C BW = -0.0064 in_r + 0.0019 out_r + 0.3128 83.02% D BW = 5.76·10−5_s+2.23·10−1_{gap+0.0426 66.20%}

Table 4.Formulas for the frequency shift around 3.5 GHz for each situation.

situation formula accuracy A f = 0.1545 w -2.3784 s + 5.7782 33.89% B f = 0.1230 w - 1.8316 sc + 5.3374 99.45% C f = -0.2780 in_r + 0.0284 out_r + 6.9321 97.86% D f = 0.0043 s - 1.8474 gap + 4.9024 96.72%

Table 5.Formulas for the bandwidth shift around 3.5 GHz for each situation.

situation formula accuracy A BW = 0.0514 w - 0.0612 s + 0.8283 19.83% B BW = 0.0512 w + 0.2212 sc + 0.0521 72.01% C BW = -0.0121 in_r - 0.0216 out_r + 0.9128 35.25% D BW = 0.0019 s + 0.1369 gap + 0.1418 86.16%

It is clear that the surrounding square determines the frequencies at 750 MHz, and the spiral arms determine the frequency at 3.5 GHz. If we want to change the frequency and bandwidth to the lowest frequency, it is best to look at situation A and D, described in the previous section. Situation C only changes parameters that affect the spiral arms. Thus the 3.5 GHz frequency changes as seen in Figure8and Figure9. The frequencies at 750 MHz almost remain the same. Situation B changes the scale of the arms and the width of the square. But in Figure4it already became clear that a change in the width does not have much impact. It is therefore best to use formulas from situation A and D when tuning the lower frequencies. If the

accuracy is studied, it is clear that they have a high percentage accuracy for the frequencies. This means they are both useful. For the bandwidth there is a better relationship in situation A than in situation D and that is why it is advisable to use the formula from situation A.

Finally, to tune the frequency and bandwidth to 3.5 GHz, situation A can already be excluded. Because situation A only changes the parameters of the surrounding square and this will not affect the higher frequencies. This can also be seen in the accuracy in Tables4and5. The results to find the 3.5 GHz frequency give very high percentages for situation B, C and D. All three are useful. Depending on the range in which a notch has to be obtained, it is recommended to look at the graphs of these situations in Section 4 and conclude from this which situation will give the best results for what is desired. Situation D shows the best percentage to determine the bandwidth. But taking a look at the graphs in Figure10, it is clear that there is only a little shift when adjusting the parameters and the notches remain about the same. This explains the high percentage, but it is not relevant to apply it. Situation B also shows a high percentage. A clear shift in situation B can be observed in Figure7. This formula is therefore recommended to tune the bandwidth around 3.5 GHz.

Of course all formulas can be used to achieve a solid result. So if one is looking to calculate one specific parameter, it is best to choose a formula that contains that parameter. Based on that formula, one can start with the desired notches. By subsequently combining other formulas the entire design can be tuned. It is important to take into account between which boundaries the formulas can be applied. The specific boundaries for each situation are given in Section 4.

Fig. 11.Step-by-step plan for finding the desired frequency. In Figure11is a block scheme of the step-by-step plan for finding the desired frequencies with this basic design shown. The correct situation is searched in the first step, depending on the desired frequency, situation A, B, C or D is found. The next step is to apply the right formula. With some help of the Tables above, the right formula can be found. The third and last step is to correct or tune the frequency by changing the other parameter. If in reality, the frequency is not quite correct yet, the other parameter of the formula can be changed slightly. The accuracy rates are already pretty high, but they are not perfect. So there is some margin of error.

This plan can be applied in any situation using the above information and the formulas given in the tables.

6. ANGLE OF INCIDENCE

In this section the effects of variation in the angle of incidence are examined and the robustness of the design will be checked

under different angles of incidence.

Fig. 12.Far field of 3.5 GHz.

Here φ corresponds to the azimuth. This is the angle between the projected vector and a reference vector on the reference plane. The angle that changes in height along the frontal or median plane is called the elevation angle and here corresponds to θ. Figure12is the far field around 3.5 GHz. The far field is defined as the ratio between radiated power and delivered power. So, if efficiency is equal to 1, all delivered power is radiated. The figure also shows a unit cell of the FSS, the axis system, and the angles. Both angles can vary from 0◦_{to 90}◦_.

A. φ= 0◦andθranges from 0◦to 90◦

If φ remains constant at 0◦_{and the angle θ changes, we observe}

that the notch stays constant at 750 MHz and the bandwidth grows with the angle of θ. At the 3.5 GHz frequency there is a lot of disturbance while increasing θ. This is also clear in Figure 12where we see the color is changing into red while θ increases.

Fig. 13.Simulation results of changing theta.

B. θ= 0◦_{andφranges from 0}◦_{to 90}◦

Changing φ, while θ has kept constant has almost no impact on the design. Only when we turn 70◦_{, we have a small shift to the}

left on the higher frequency. We can see this clearly in Figure14 and in Figure12.

Fig. 14.Simulation results of changing phi.

C. Bothθandφvary from 0◦_{to 90}◦

Fig. 15.Simulation results of changing theta and phi.

When we take a look at some random simulations of θ and φ in Figure15, we see that there are a lot of notches in between 2 GHz and 6 GHz. There is no relation between θ and φ for the higher frequency. Therefore it is not really useful to draw up a formula for the notch of 3.5 GHz. However, the formulas can be derived and applied for the notches of 750 MHz. In the same way as done in Section 5, formulas from the simulations are derived for the frequency and bandwidth in function of the angles θ and

φ. Formula1gives the equation for the frequencies around 750

MHz with an accuracy of 79.8%.

f=5.1294·10−4_{θ−8.8195·10}−6_{φ+0.7671 (1)}

Formula2gives the equation to calculate the bandwidth around 750 MHz in function of θ and φ with an accuracy of 69.2%.

BW=5.9564·10−3_{θ−1.10276·10}−5_{φ+0.1525 (2)}

Fig. 16.The effects of θ and phi: frequency and bandwidth shift around 750 MHz.

To make a conclusion regarding the perspectives we can say that the design has a relatively stable frequency response in the aforementioned 5G bands.

This means that the design is very consistent with the polar-ization of the incident wave, but is not so strong against differ-ent angles of incidence. Anyway, the notches at 750 MHz and around 3.5 GHz are maintained with all tested incidence angles.

7. CONCLUSION

This paper proposes a dual-band single-layer FSS design based on a combination of two spiral elements, a surrounding square and a four-arms element, to be used in 5G applications. This design was presented in both band reject and band pass variants. Specific dimensions were proposed, in order for the structure to be effective at both 750 MHz and 3.5 GHz 5G bands, simul-taneously. A negative variant of the proposed design is also briefly investigated. From the simulation results, formulas were derived from the frequencies to tune, so that a desired frequency could be obtained. Or the formulas could be used to find a value for a particular parameter. Also a relatively good angular stabil-ity was observed for incident angles up to 20◦_{of incidence angle.}

The design can be used to obtain similar frequencies, as the 750 MHz and the 3.5 GHz frequencies by adjusting parameters using the obtained formulas. In a more generic case, this FSS design could also be useful for other applications where the target frequency bands have a relative offset similar to the 5G bands.

8. FUTURE WORK

Due to the COVID-19 pandemic, we were not allowed to go to the lab. As a result of this, not all planned experiments could be performed. This is a situation caused by force majeure that we could not ignore. As soon as this situation is over, the next step is to fabricate the prototype of the FSS and do some measurements. The FSS will contain 7 columns of 7 rows, which means that the unit cell will be repeated 49 times. This gives us an FSS of 50x50 cm.

It was not possible to simulate the 50x50 cm board with the equipment available during the confinement at home. We pro-vide some insight on the behaviour of a board with multiple unit cells. To get an idea of the full surface response, a part of the full FSS structure simulation has been done in CST. The simulation is a plane wave simulation where only the electric field results will be analyzed. The E-fields of the FSS are shown in Figure18 and in Figure19. It clearly seems that the E-field concentrates on the arm-spirals at 3.5 GHz and on the squared frame at 750

Fig. 17.Frequency selective surface 50x50 cm.

MHz, so these simulations reinforce the previous appreciation. What we cannot assure is whether there is a frequency shift around these canonical frequencies or not when considering seven unit cells instead of only one. But the electromagnetic behaviour considering mutual coupling seems to maintain the main conclusions of the unit cell analysis.

Fig. 18.E-field at 750 MHz. Fig. 19.E-field at 3.5 GHz. All measurements done in the laboratory on this FSS can be compared with the obtained results done with the simulations in CST[7]. In general, CST is a good program so it is expected to give quite good results.

REFERENCES

1. Rajiv, “What are 5G frequency bands,” 2018.

2. B. A. Munk, Frequency Selective Surfaces Theory and Design. New York (N.Y.) : Wiley, 2000., 2000.

3. Y. V. Mohan Jayawardene, “3-D EM Simulation of Infinite Periodic Arrays and Finite Frequency Selective Horns,”

4. P. E. Mayes, “Frequency-Independent Antennas and Broad-Band Derivatives Thereof,” Proceedings of the IEEE, vol. 80, pp. 103–112, 1992.

5. D. Ferreira, I. Cuiñas, R. F. Caldeirinha, and T. R. Fernandes, “Dual-band single-layer quarter ring frequency selective surface for Wi-Fi applications,” IET Microwaves, Antennas and Propagation, vol. 10, no. 4, pp. 435–441, 2016.

6. Dassault Systèmes, CST Studio Suite Help. 2019. 7. Dassault Système, “CST microwave studio,” 2020.

Contents

Global COVID-19 pandemic preamble v

Preface vii

Admission to loan ix

Abstract xi

Extended abstracts xiii

Table of contents xxvii

List of Figures xxxi

List of Abbreviations xxxiii

1 Introduction 1

2 General information 3

2.1 5G . . . 3 2.1.1 Sub-6 GHz spectrum . . . 4 2.2 Frequency Selective Surfaces . . . 4

3 Fractal FSS 7

3.1 Fractals . . . 7 3.1.1 Fractal antennas . . . 7 3.1.2 Sierpi ´nski triangle . . . 8 3.2 The unit cell . . . 8 3.2.1 Extra central element . . . 10 3.2.2 Number of iterations . . . 10

3.3 Design parameters . . . 10 3.3.1 Simulating in CST microwave studio . . . 12 3.3.2 Unit cell size w and central element width t . . . 13 3.3.3 Distance between bowties dx and dy . . . 16 3.4 Angle of incidence . . . 16 3.5 The inverse of the design . . . 17 3.6 Full 50 by 50 centimetres simulation and further research . . . 19

4 Spiral FSS 21

4.1 Spiral antennas . . . 21 4.2 FSS unit cell design . . . 22 4.3 FSS designs . . . 23 4.3.1 Band reject variant . . . 23 4.3.2 Band pass variant . . . 24 4.4 Simulation results . . . 25

4.4.1 Tuning the surrounding square with parameters ’w’ and the scale of the square ’s’ . . . 26 4.4.2 Tuning the whole design with parameters ’w’ and the scale of 4 spiral arms

’sc’ . . . 27 4.4.3 Tuning the 4 arms spiral design with parameters in r and out r . . . 28 4.4.4 Tuning the whole design with parameters the scale of the square ’s’ and the

gap in between the moons . . . 29 4.5 Formulas for tuning parameters . . . 29 4.6 Angle of incidence . . . 32 4.6.1 φ = 0◦_{andθ ranges from 0}◦_{to 90}◦ _{. . . . 33}

4.6.2 θ = 0◦ _{andφ ranges from 0}◦_{to 90}◦ _{. . . . 34}

4.6.3 Bothθ and φ vary from 0◦_{to 90}◦ _{. . . . 35}

5 Comparison between the FSS 37

5.1 Low band frequency response . . . 37 5.2 High band frequency response . . . 38 5.3 The inverse design . . . 38 5.4 Angle of incidence . . . 38 5.5 Final thoughts . . . 39

6 Conclusion 41

A Fractal FSS additional figures 45

List of Figures

3.1 Different stages for the Sierpi´nski triangle, image from [1] . . . 8 3.2 Unit cell design. . . 9 3.3 The different stages . . . 11 3.4 The different stages . . . 12 3.5 The effects of w and t . . . 13 3.6 The effects of dx and dy variation . . . 15 3.7 Resistance against different incident angles . . . 17 3.8 The inverse design . . . 18 3.9 The direct vs the inverse design . . . 18 4.1 Unit Cell Design. . . 22 4.2 Band reject and band pass FSS simulation results . . . 24 4.3 Inverse of the unit cell design . . . 24 4.4 w changes, while the scale of the square is constant. . . 26 4.5 w= constant, the scale of the square changes. . . 26 4.6 w changes, the scale of spiral arms is constant. . . 27 4.7 w= constant, the scale of the spiral arms changes. . . 27 4.8 out r= constant, in r changes. . . 28 4.9 in r= constant, out r changes. . . 28 4.10 gap= constant, the scale changes. . . 29 4.11 Step-by-step plan for finding the desired frequency. . . 32 4.12 Far field of 3.5 GHz. . . 33 4.13 Simulation results of changing theta. . . 34 4.14 Simulation results of changing phi. . . 34 4.15 Simulation results of changing theta and phi. . . 35 4.16 The effects of θ and phi: frequency and bandwidth shift around 750 MHz. . . 36 5.1 Both FSS designs’ frequency responses side by side . . . 37

5.2 Both FSS designs’ invariance against different angles of incidence . . . 39 A.1 The complete FSS-surface . . . 45 A.2 E-field comparison . . . 46 B.1 The complete FSS-surface . . . 47 B.2 E-field comparison . . . 48

List of Abbreviations

4G Fourth-generation wireless communication 5G Fifth-generation wireless communication

BSs base stations

COVID-19 Coronavirus disease 2019

CST Computer Simulation Technology FSS Frequency Selective Surface

SARS-CoV-2 severe acute respiratory syndrome coronavirus 2

Chapter 1

Introduction

5G is all the craze at this moment in time, every country and major telecom network wants to implement it. However, this widespread adaptation of a new technology comes with a lot of new problems. Among the wide collection of frequency bands suitable for implementing 5G, there are also ISM bands, some of them already crowded [2]. To combat this over-saturating issue, many different solutions can be found. For example, if one wants to keep their flat’s WiFi signal from interfering with the neighbour’s and vice versa, thick walls with shielding might be possible. This is a simple but blunt method, blunt because it blocks every frequency.

This master dissertation aims to provide a suitable, less blunt, approach towards shielding devices from 5G. A Frequency Selective Surface (FSS) is an ideal solution, because it, as the name suggests, selects its frequency for which it shields. It can act as a bandpass or bandstop filter for electromagnetic waves. The designs in this master dissertation are meant to be used with the lower 5G frequency bands, within the FR1 spectrum. This FSS will thus provide suppression around the 750 MHz and the 3.5 GHz frequency bands. The bandwidth for both frequencies needs to be at least 400 MHz to be usable in the real world.

An attempt has been made to find a fitting solution using self-similar designs. Earlier research like [3] showed promising results for a single layer FSS dual-band design. A couple of formulas will be derived to apply these designs for other frequencies with simple parameter adjustments. The real-world cases with different angles of incidence will be simulated, and the inverse designs will be checked. All simulations were done in CST microwave studio [4] following the guidance of Numan and Sharawi [5] and the CST product manual [6].

Chapter 2 is about the general information. Here 5G and FSS are discussed in detail. In Chapter 3, Fractal FSS is explained. The design of the unit cell is discussed, the design parameters are examined, the influence of the angle of incidence is discussed, the inverse design is shown and a full 50 by 50 centimeter simulation is discussed. Chapter 4 depicts Spiral FSS and the same sections as in Chapter 3 are discussed here, but applied to the Spiral FSS design. Subsequently, in Chapter 5 a comparison is made between the different FSSs. Finally Chapter 6 contains the conclusion of this master thesis.

Chapter 2

General information

2.1 5G

The Fifth-generation wireless communication (5G) is a telecommunications standard. This is characterized by greater data throughput and less latency compared to the Fourth-generation wireless communication (4G). Today, this communication technique has not yet been fully launched. 5G can achieve extremely high speeds, in addition, one of the biggest differences with its predecessor is that it can also send more data [7]. It is more reliable, it has more connections and it consumes less energy from the device, which will make the battery last longer. The 5G mobile wireless communication standard brings a host of new technologies. The number of active antenna elements supported by base stations (BSs) will be assumed to allow three-dimensional beamforming with a high degree of spatial multiplexing for multiple users. BSs will include extensively spatially distributed active antenna systems to increase the macro diversity of connections, protect users’ access distance, and improve network coverage. In addition, centralized processing of receivers and signals on servers in the cloud will yield significant gains in network capacity and energy efficiency.

5G takes us to a ”smart” world, where everything is in wireless contact with everyone via the wireless worldwide web. 5G forms the basis for virtual reality, unmanned cars, the internet of things, the use of artificial intelligence and it enables remote operations. Users are also expected to be able to download movies in seconds. What at first sight seems like a great prospect, can also turn into a threatening nightmare with unprecedented consequences. Like any wireless transmission system, 5G also requires to use frequency spectrum to transmit data.

But 5G uses a frequency range that has never been used before. In order to support higher bandwidth, 5G requires the high frequency range of sub 6 GHz and millimeter waves.

Technologies such as 5G must support higher data rate requirements that the traditional GSM or LTE-network is unable to. Bandwidth of a transmission signal is the distance between the lower and upper cutoff frequency. If a higher frequency is used, a larger bandwidth can be used for data transfer [8].

2.1.1 Sub-6 GHz spectrum

This master thesis focuses on the sub-6 GHz spectrum. This spectrum is the candidate for early implementation of 5G networks around the world. It will use unused spectrum under the 6 GHz range, it can support higher bandwidth than LTE frequency bands. Compared to the millimeter wave spectrum, the frequency below 6 GHz is less complex in infrastructure development, implementation and future network improvements.

This frequency range has never been independently tested for safety before. As a result of the advantages over the predecessor, it is likely that some frequency bands will soon become highly saturated. There are also situations where the frequencies of the 5G network can cause interference. With the arrival of 5G, there will be many more radio waves running through the atmosphere, which is detrimental to the weather satellites that will see the weather more difficult. Television productions are also at risk when 5G comes on the market. Wireless microphones and transmitters can disturb and even fail, with all the consequences that will follow. In certain situations, it may be useful to limit the coverage of existing and emerging 5G networks to pre-defined areas. Reinforced walls or even metallic shielding are some simple examples which can significantly diminish wireless coverage. These examples, however, do not discriminate specific frequency bands, which is where frequency selective surfaces (FSS) can be useful. FSS may be employed in order to block only specific frequency bands, while allowing other wireless bands to pass through, or vice versa.

2.2 Frequency Selective Surfaces

A frequency Frequency Selective Surface (FSS) is a thin, repetitive surface that is designed to reflect through, or absorb, electromagnetic fields based on the frequency of the field. A simple example of an FSS is the screen of a microwave oven. An FSS can be seen as an optical filter,

through which a regular, periodic pattern on the surface of the FSS can be filtered. The way in which an FSS is constructed, as well as the angle of approach and the polarization, have an influence on its properties [9].

Chapter 3

Fractal FSS

3.1 Fractals

Fractals are self-similar structures, made famous by mathematicians as Mandelbrot. He was maybe the first who saw their potential to be used to improve real-world applications in his book The fractal geometry of nature [10]. Here he explained the occurrence of fractals in nature and the relation to roughness. Fractals have a couple of major features [11]:

• Self-similarity

• A simple recursive definition

• Irregularities that cannot be described with Euclidean geometry • A detailed form

• An infinite circumference

The pure fractal theory is beyond the scope of this research, more information about fractals can be found in books like [10] or [11].

3.1.1 Fractal antennas

The first to apply Mandelbrot’s ideas were Kim and Jaggard, who published the first paper [12] on fractal antenna theory a couple of years after Mandelbrot’s famous book. Cohen made, a couple of years later, the first real-world fractal antenna [13]. Werner and Gangul bundled Much’s research in fractal antenna design [1]. More general fractal antenna design rules were also bundled in

Fractal Apertures in Waveguides, Conducting Screens and Cavities [14]. Fractal antennas have some significant advantages to standard antennas. Firstly, they can be made smaller due to the interesting characteristic of the infinite circumference of fractals. Cohen discovered that using the Cohen snowflake, the size of a radio antenna could be four times smaller. Later research also showed that with each iteration, more frequency bands could be received or transmitted using one antenna.

3.1.2 Sierpi ´nski triangle

Figure 3.1: Different stages for the Sierpi´nski triangle, image from [1]

A famous self-similar geometric shape is the Sierpi ´nski triangle; the first four different stages of the fractal are shown in Fig. 3.1. This shape was used in previous antenna and FSS-designs. Romeu and Y. Rahmat-Samii [3] used the triangle to create a bowtie FSS that works for two frequencies. This dual-band design forms the base of the design used in this research.

3.2 The unit cell

The objective is to analyse the performance of the surfaces composed by a squared matrix of replicated unit cells; this section describes the unit cell. The designed unit cell with its parameters can be seen in Fig. 3.2. The unit cell is made up out of a central bowtie complemented with a central lumped element. This bowtie itself is contains three parts, the first two being second stage

Table 3.1: The parameters of the unit cell and the values of them in the final design.

parameter explanation value (mm)

w height of the bowtie 87

t width of the central element 0.5

dx horizontal distance between elements 3

dy vertical distance between elements 2

Sierpi ´nski triangles horizontally mirrored into each other. The third and special element is the central lumped element connecting the two triangles. In Table 3.1, all the design parameters and their respective final sizes are summed up and explained.

3.2.1 Extra central element

The main difference between the bowtie from [3] and the one from this paper is visible on the drawing: the added central lumped element with a width of t. This element is an excellent granular tuning parameter; the simulation results of the tuning can be found in section 3.3.2. Another benefit of adding this lumped element is the effect it has on the production of the physical FSS. The point of the two triangles touching is essential and the contact area is very small. If the two are not connected as expected, the resonance could be completely different. More on the complete structure resonance can be read in section 3.6.

3.2.2 Number of iterations

Fractal objects have multiple stages. This section investigates the effects of the different stages of the unit cell design. On Fig. 3.3, the different stages can be seen. When the design does not iterate on itself and is thus in stage one, there is only one notch at the lower frequency band in the attenuation frequency response, around 900 MHz. This can be seen in Fig. 3.4. When the second stage design is implemented, a second notch at the higher frequency band of 3.5 GHz also appears. This means that, at least, a stage two unit cell is needed to get the dual-band characteristic. When the design iterates more upon itself to stage three and four, no further improvements can be noted. These higher iterations increase complexity and thus make it more challenging to produce. This is why the final design sticks with the second stage.. Another notable effect of increasing the number of iterations is the shift of the two peaks. The fourth iteration has a complete shift to the left but also brings the two peaks closer towards each other. This can be a reason to pick the higher number of iterations over the lower amount, even though it increases the production difficulty.

3.3 Design parameters

This section provides a guide to adjust this unit cell so it can be used with other frequencies. All the adjustable parameters and their explanation are listed in Table 3.1. The four parameters in order of importance are w, t, dy and dx. Designing a unit cell, like the one purposed in this paper, starts with the general size of the element [9, 15]. The size is directly tied to the resonance wavelength. Even more specific, in this design, the unit cell will determine the placement of

Figure 3.3: The different stages

the first resonance frequency. This can be concluded from the iteration results discussed in section 3.2.2. On Fig. 3.3 the first stage only resonates at the lower of the two frequencies (it only has a valley around 800 MHz and not around 3.5 GHz, considering the design dimensions).

Figure 3.4: The different stages

The dx and dy parameters depict the distance between the individual bowties and will be fixed to 3 and 2 mm respectively for the next section. When these values are too low, the different bowties will touch, and the known response of the FSS will be lost. This also eases the way the simulations can be done in CST microwave studio.

3.3.1 Simulating in CST microwave studio

The simulations were done using the FSS unit cell template, and this ensured a correct basic setting of key simulation setting such as the boundaries and background. All simulations were done using unit cell boundaries, which ensured a three by three unit cell surface to be simulated. The unit cell boundary settings enabled the Floquent boundary simulation mode, Zmin was selected as the Floquent port [6]. The frequency solver was set up so that frequencies from 0 up to 6 GHz were taken into account. The frequency plots in this paper, are always S21 plots (in CST the Smin(1), Zmax(1) result [5]). To obtain the later explained formulae 4.1, ??, 4.2 and ??, parameter sweeps were performed with varying values for t, w, dx and dy. Where, with each sweep, only one of the prementioned parameters varies in an interval.

3.3.2 Unit cell size w and central element width t

(a) Frequency shift around 800 MHz (b) Frequency shift around 3.5 GHz

(c) Bandwidth shift around 800 MHz (d) Bandwidth shift around 3.5 GHz

Figure 3.5: The effects of w and t

As explained in the first part of this section, the two parameters that allow the most consistent flexibility in adjusting for frequency and bandwidth are w and to a lesser extent t. w stands for the size of the element and is measured from the top of the bowtie to the bottom. t is defined as the width of the central lumped element and has a limited range. The size parameter w is investigated from 70 to 100 millimetres. In this interval, the frequency shifts follow a linear relationship. The range is fixed from 0.5 to 2.8 millimetres. Its lower limit is due to the physical design limitations of a copper trace width. The lower limit is so that the different bowties will not end up touching each other.