Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Jawad, Nibirh
Master of Applied Science - MASc
University of British Columbia
The use of Wi-Fi networks to access the information on the internet has seen a phenomenal increase in recent times. With the large volume of traffic being transmitted, the amount of confidential information has also increased. Yet access to Wi-Fi networks is only secured through password protection. An improvement in technology used to gain unauthorized access has lead to a concern over information security. One possible way of providing increased security to the Wi-Fi networks is by physically limiting the network to a fixed space. Wi-Fi signals can be contained to a built environment through the use of frequency selective surfaces (FSS) in the form of a Wi-Fi blocking wallpaper. An FSS is a conductive periodic pattern in a 2D array. It is able to selectively block or pass electromagnetic waves. Through careful design it should be possible to produce an FSS which is able to block the two Wi-Fi communication bands. In this thesis we present a analysis of various band stop FSS to reach a design with a high stop band bandwidth. We then modify the design to produce a second stop band at a higher frequency. The two stop bands are designed to be at the same ratio as the Wi-Fi communication bands. Two of the designs are fabricated to verify the performance in experiment. The presence of dielectric substrates and the incident angle of waves are known to modify the performance of FSS. Experiments are carried out to quantify these effects and compensate for them in simulations. A simulation method is developed which can closely predict the performance of the design under real-world conditions. The design with the best performance out of the simulated dual band-stop structures is the interdigitated double hexapole and it shows a -20 dB bandwidth of 24.75% and 10.5% in the first and second stop bands respectively. It is able to cover the entire Wi-Fi spectrum giving a minimum attenuation of -34.1 dB across the 2.4 GHz and -29.24 dB across the 5 GHz Wi-Fi band at normal incidence.
Single-layer dual-wide-band frequency selective surfacesfor Wi-Fi blocking in the built environmentbyNibirh JawadB. Sc. Hons. in Engineering, Bangladesh University of Engineering andTechnology, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)The University of British Columbia(Okanagan)February 2019c© Nibirh Jawad, 2019The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Single-layer dual-wide-band frequency selective surfaces for Wi-Fi block-ing in the built environmentsubmitted by Nibirh Jawad in partial fulfillment of the requirements for the degreeof Master of Applied Science in Electrical Engineering.Examining Committee:Dr. Loı¨c Markley, Electrical EngineeringSupervisorDr. Kenneth Chau, Electrical EngineeringSupervisory Committee MemberDr. Jonathan Holzman, Electrical EngineeringSupervisory Committee MemberDr. Shahria Alam, Civil EngineeringUniversity ExamineriiAbstractThe use of Wi-Fi networks to access the information on the internet has seen aphenomenal increase in recent times. With the large volume of traffic being trans-mitted, the amount of confidential information has also increased. Yet access toWi-Fi networks is only secured through password protection. An improvement intechnology used to gain unauthorized access has lead to a concern over informationsecurity. One possible way of providing increased security to the Wi-Fi networksis by physically limiting the network to a fixed space.Wi-Fi signals can be contained to a built environment through the use of fre-quency selective surfaces (FSS) in the form of a Wi-Fi blocking wallpaper. An FSSis a conductive periodic pattern in a 2D array. It is able to selectively block or passelectromagnetic waves. Through careful design it should be possible to produce anFSS which is able to block the two Wi-Fi communication bands.In this thesis we present a analysis of various band stop FSS to reach a designwith a high stop band bandwidth. We then modify the design to produce a secondstop band at a higher frequency. The two stop bands are designed to be at the sameratio as the Wi-Fi communication bands.Two of the designs are fabricated to verify the performance in experiment. Theiiipresence of dielectric substrates and the incident angle of waves are known to mod-ify the performance of FSS. Experiments are carried out to quantify these effectsand compensate for them in simulations. A simulation method is developed whichcan closely predict the performance of the design under real-world conditions.The design with the best performance out of the simulated dual band-stop struc-tures is the interdigitated double hexapole and it shows a -20 dB bandwidth of24.75% and 10.5% in the first and second stop bands respectively. It is able tocover the entire Wi-Fi spectrum giving a minimum attenuation of -34.1 dB acrossthe 2.4 GHz and -29.24 dB across the 5 GHz Wi-Fi band at normal incidence.ivLay SummaryThis thesis presents the design process of wallpaper capable of blocking Wi-Fifrequencies. This wallpaper can be applied to existing walls to produce roomswhich can contain Wi-Fi signals inside them. The wallpaper is designed using aplanar electromagnetic filter known as a frequency selective surface (FSS). TheFSS is made by printing conducting metallic patterns on a paper backing. Wi-Fi communications occur at two different frequencies. Hence the pattern has tobe designed to block the two specific frequencies simultaneously. In this thesis,we start with a comparison between FSS patterns which block a single frequency,choose the pattern with the best performance, and modify the design to block bothWi-Fi frequencies. We show the experimental verification of the designs throughsome fabricated prototypes. The designs show the ability to block two separatefrequencies in real operating conditions.vPrefaceThis work has been carried out under the supervision of Dr. Loı¨c Markley at theSchool of Engineering in The University of British Columbia. Portions of thisthesis have been presented at the following conference:• ”A Single-Layer Frequency Selective Surface with Dual-Wide-Band Re-sponse,” IEEE AP-S/URSI Conference 2018, Boston, MA, USA, July, 2018viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiDedications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Wi-Fi Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 IEEE 802.11x standards . . . . . . . . . . . . . . . . . . 21.1.2 Wi-Fi security . . . . . . . . . . . . . . . . . . . . . . . 41.2 Wi-Fi blocking and applications . . . . . . . . . . . . . . . . . . 6vii1.2.1 Wi-Fi secure space . . . . . . . . . . . . . . . . . . . . . 71.2.2 Wi-Fi free space . . . . . . . . . . . . . . . . . . . . . . 71.3 Methods of signal blocking . . . . . . . . . . . . . . . . . . . . . 81.3.1 Faraday cages . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Frequency selective surfaces . . . . . . . . . . . . . . . . 101.4 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . 111.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . 122 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Frequency selective surfaces . . . . . . . . . . . . . . . . . . . . 142.2 Classification of frequency selective surfaces . . . . . . . . . . . 162.3 Factors in FSS performance . . . . . . . . . . . . . . . . . . . . . 192.3.1 Angle of incidence and polarization . . . . . . . . . . . . 192.3.2 Substrate properties . . . . . . . . . . . . . . . . . . . . . 212.3.3 Trace conductivity . . . . . . . . . . . . . . . . . . . . . 232.3.4 Periodicity . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Multiband FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.4.1 Multilayer FSS . . . . . . . . . . . . . . . . . . . . . . . 262.4.2 Fractal FSS . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.3 Genetic algorithm based designs . . . . . . . . . . . . . . 282.4.4 Multiresonant FSS . . . . . . . . . . . . . . . . . . . . . 292.5 Single layer FSS designs for Wi-Fi and other communication bands 322.5.1 Square loop design . . . . . . . . . . . . . . . . . . . . . 322.5.2 Metapaper design . . . . . . . . . . . . . . . . . . . . . . 332.5.3 Quarter ring design . . . . . . . . . . . . . . . . . . . . . 35viii3 Analysis of Single Band FSS Designs . . . . . . . . . . . . . . . . . . 373.1 Design requirements . . . . . . . . . . . . . . . . . . . . . . . . 383.1.1 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . 393.1.2 Equivalent Wi-Fi band attenuation . . . . . . . . . . . . . 393.1.3 Fabrication requirements . . . . . . . . . . . . . . . . . . 403.2 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3 Equivalent circuit modeling . . . . . . . . . . . . . . . . . . . . . 423.4 Non-interleaved structures . . . . . . . . . . . . . . . . . . . . . 443.4.1 Non-interleaved tripole design . . . . . . . . . . . . . . . 453.4.2 Non-interleaved quadrupole design . . . . . . . . . . . . 493.4.3 Non-interleaved hexapole design . . . . . . . . . . . . . . 533.4.4 Comparisons of the non-interleaved designs . . . . . . . . 533.5 Interleaved structures . . . . . . . . . . . . . . . . . . . . . . . . 563.5.1 Interleaved tripole design . . . . . . . . . . . . . . . . . . 563.5.2 Interleaved quadrupole design . . . . . . . . . . . . . . . 583.5.3 Interleaved hexapole design . . . . . . . . . . . . . . . . 603.5.4 Comparisons of the interleaved designs . . . . . . . . . . 624 Dual Band Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Dual resonance equivalent circuit model . . . . . . . . . . . . . . 664.2 Interleaved octopole . . . . . . . . . . . . . . . . . . . . . . . . . 694.2.1 Interleaved octopole base design . . . . . . . . . . . . . . 704.2.2 Interleaved octopole with intermediate cross . . . . . . . . 744.2.3 Interleaved octopole with forked cross . . . . . . . . . . . 784.3 Interleaved hexapole . . . . . . . . . . . . . . . . . . . . . . . . 83ix4.3.1 Interleaved double hexapole base design . . . . . . . . . . 834.3.2 Interleaved double hexapole with intermediate tripole . . . 874.3.3 Interleaved double hexapole with forked tripole . . . . . . 914.3.4 Interdigitated double hexapole . . . . . . . . . . . . . . . 954.4 Comparisons of the dual band designs . . . . . . . . . . . . . . . 1005 Experimental Data and Verification . . . . . . . . . . . . . . . . . . 1045.1 First prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.2 Second prototype . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . 1125.4 Anechoic chamber measurements . . . . . . . . . . . . . . . . . 1135.5 Effect of substrates and conductivity . . . . . . . . . . . . . . . . 1185.6 Off-normal measurements . . . . . . . . . . . . . . . . . . . . . 1205.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128xList of TablesTable 2.1 Geometric parameters of the metapaper design . . . . . . . . . 34Table 3.1 A comparison between the performances of the non-interleavedgeometry types . . . . . . . . . . . . . . . . . . . . . . . . . . 55Table 3.2 A comparison between the performances of the interleaved ge-ometry types . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Table 4.1 Geometric parameters of the base octopole design . . . . . . . 70Table 4.2 Geometric parameters of the octopole with intermediate crossdesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Table 4.3 Geometric parameters of the octopole with forked cross design 79Table 4.4 Geometric parameters of the base double hexapole design . . . 84Table 4.5 Geometric parameters of the double hexapole with intermediatetripole design . . . . . . . . . . . . . . . . . . . . . . . . . . 88Table 4.6 Geometric parameters of the double hexapole with forked tripoledesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Table 4.7 Geometric parameters of the interdigitated double hexapole design 95xiTable 4.8 A comparison between the performances of the dual band FSSdesigns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Table 5.1 The geometric parameters of the design printed on to the differ-ent substrates to produce the second prototype. . . . . . . . . . 110Table 5.2 Physical properties of the silver ink used for printing the con-ductive traces on the different substrates. . . . . . . . . . . . . 111Table 5.3 The trace sheet resistance values obtained from the measure-ment using a four point probe machine. . . . . . . . . . . . . . 118Table 5.4 The different property values used in the simulation files tocompensate for the effect of dielectrics and conductivity on thetransmission response. . . . . . . . . . . . . . . . . . . . . . . 119xiiList of FiguresFigure 1.1 A schematic diagram of the overlapping channels in the 2.4GHz Wi-Fi band. 2.4 GHz Wi-Fi channels (802.11b,g WLAN)c©Michael Gauthier, CC BY-SA 3.0 . . . . . . . . . . . . . . 3Figure 1.2 A diagram of the allowed non-overlapping Wi-Fi channels inNorth America according to the different IEEE standards alongwith their corresponding modulation methods. 802.11 non-overlapping channels for 2.4GHz. Covers 802.11b,g,n c©LiebeskindRbeede, CC BY 3.0 . . . . . . . . . . . . . . . . . . . . . . . 5Figure 1.3 A schematic representation of the operating principle of a Fara-day cage showing the difference between conducting and non-conducting walls. . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.1 A schematic showing the application of FSS as (a) a radomeand (b) a dichroic surface sub-reflector. . . . . . . . . . . . . 16Figure 2.2 Classification of different FSS elements according to their shapetype. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17xiiiFigure 2.3 A schematic diagram showing the duality between FSS ge-ometries and their filter responses. . . . . . . . . . . . . . . . 18Figure 2.4 The figures show the effect of (a) incident angle of the waveand (b) polarization of the wave on the effective lengths of theFSS design. (b) is republished with permission of IEEE, from[31] c©2006; permission conveyed through Copyright Clear-ance Center, Inc. . . . . . . . . . . . . . . . . . . . . . . . . 20Figure 2.5 The effect of refraction causes the incident angle of a wave toreduce when it reaches the FSS and reduce its influence on thetransmission response. . . . . . . . . . . . . . . . . . . . . . 23Figure 2.6 A diagram showing the conditions for producing grating lobeson a periodic surface. Diffraction Grating Equation c©Vigneshdm1990,CC BY-SA 4.0 . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.7 An example of (a) a multilayer FSS design and (b) its trans-mission response. Republished with permission of IEEE, from[75] c©2008; permission conveyed through Copyright Clear-ance Center, Inc. . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.8 An example of (a) a fractal FSS design with the lengths p =16.5mm and L = 10mm and (b) its transmission response atdifferent levels of fractal design. Republished with permis-sion of IEEE, from [80] c©2004; permission conveyed throughCopyright Clearance Center, Inc. . . . . . . . . . . . . . . . . 27xivFigure 2.9 An example of (a) a genetic algorithm based FSS design and(b) its transmission response. Republished with permission ofIEEE, from [84] c©2004; permission conveyed through Copy-right Clearance Center, Inc. . . . . . . . . . . . . . . . . . . . 29Figure 2.10 The figure shows (a) the surface design using the ring slot ele-ment, (b) transmission response of the ring-slot FSS design, (c)the meandered line multiresonant element, and (d) the trans-mission response of the meandered line FSS design. (a) and(b) are republished with permission of John Wiley & sons,Inc. , from [89] c©2016; permission conveyed through Copy-right Clearance Center, Inc. (c) and (d) are Republished withpermission of IEEE, from [90] c©2015; permission conveyedthrough Copyright Clearance Center, Inc. . . . . . . . . . . . 30Figure 2.11 The (a) surface design and (b) simulated transmission responseof the square loop FSS design. Republished with permission ofIEEE, from [31] c©2006; permission conveyed through Copy-right Clearance Center, Inc. . . . . . . . . . . . . . . . . . . . 33Figure 2.12 The (a) surface design and (b) transmission response of themetapaper FSS design. Republished with permission of IEEE,from [97] c©2015; permission conveyed through CopyrightClearance Center, Inc. . . . . . . . . . . . . . . . . . . . . . 34Figure 2.13 The (a) surface design with dimensions of d = 39.5mm, r =14.5mm, t = 2.5mm, and g= 0.25mm and (b) simulated trans-mission response of the quarter ring FSS design. Republishedwith permission of IET Journals, from [99] c©2016. . . . . . . 35xvFigure 3.1 A schematic representation of the simulation volume used tofind the transmission response of the different structures. . . . 42Figure 3.2 The equivalent circuit model for a single resonance FSS structure. 43Figure 3.3 The figure shows the (a) lattice arrangement with the param-eters D = 23.64mm and L = 13.36mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the tripole element arranged with thecenters in a rectangular lattice. . . . . . . . . . . . . . . . . . 46Figure 3.4 The figure shows the (a) lattice arrangement with the param-eters D = 49.86mm and L = 15.62mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the tripole element arranged with thepoles facing end-to-end. . . . . . . . . . . . . . . . . . . . . 48Figure 3.5 The figure shows the (a) lattice arrangement with the param-eters D = 23.36mm and L = 11.43mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the quadrupole element arranged withthe poles facing end-to-end. . . . . . . . . . . . . . . . . . . 50xviFigure 3.6 The figure shows the (a) lattice arrangement with the param-eters D = 17.44mm and L = 8.22mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the Jerusalem cross FSS design. . . . . 52Figure 3.7 The figure shows the (a) lattice arrangement with the param-eters D = 25.94mm and L = 12.72mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the hexapole element placed in an end-to-end lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . 54Figure 3.8 The figure shows the (a) lattice arrangement with the param-eters D = 15.43mm and L = 14.43mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the interleaved tripole design. . . . . . 57Figure 3.9 The figure shows the (a) lattice arrangement with the param-eters D = 11.65mm and L = 10.86mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the interleaved quadrupole design. . . . 59xviiFigure 3.10 The figure shows the (a) lattice arrangement with the param-eters D = 13.25mm and L = 11.22mm, (b) transmission re-sponse, (c) electric field intensity (magnitude) at the resonantfrequency, and (d) magnetic field intensity (magnitude) at theresonant frequency for the interleaved hexapole design. . . . . 61Figure 3.11 The (a) surface design with the length D = 12.44mm, w =0.5mm, and g = 0.5mm and (b) simulated transmission re-sponse of the square loop FSS design with modified trace andgap widths. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 4.1 The equivalent circuit representation of a dual band single layerFSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 4.2 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for thebase octopole FSS design. . . . . . . . . . . . . . . . . . . . 71Figure 4.3 Independent tuning of the resonance frequencies of the oc-topole shown through (a) a parametric sweep of the secondaryarm length and (b) a parametric sweep of the primary arm length. 73Figure 4.4 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for theoctopole with intermediate cross FSS design. . . . . . . . . . 75xviiiFigure 4.5 The off-normal transmission response for the octopole with in-termediate cross design at 30 degrees and 60 degrees for bothTE and TM polarization. . . . . . . . . . . . . . . . . . . . . 77Figure 4.6 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for theoctopole with forked cross FSS design. . . . . . . . . . . . . 80Figure 4.7 Independent tuning of the resonance frequencies of the inter-leaved octopole with forked cross shown through (a) a para-metric sweep of the secondary arm length and (b) a parametricsweep of the primary arm length. . . . . . . . . . . . . . . . . 81Figure 4.8 The off-normal transmission response for the octopole withforked cross design at 30 degrees and 60 degrees for both TEand TM polarization. . . . . . . . . . . . . . . . . . . . . . . 82Figure 4.9 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for thebase interleaved double hexapole FSS design. . . . . . . . . . 85Figure 4.10 Independent tuning of the resonance frequencies of the inter-leaved double hexapole shown through (a) a parametric sweepof the secondary arm length and (b) a parametric sweep of theprimary arm length. . . . . . . . . . . . . . . . . . . . . . . . 86xixFigure 4.11 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for thedouble hexapole with intermediate tripole FSS design. . . . . 89Figure 4.12 The off-normal transmission response for the double hexapolewith intermediate tripole design at 30 degrees and 60 degreesfor both TE and TM polarization. . . . . . . . . . . . . . . . 90Figure 4.13 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for thedouble hexapole with forked tripole FSS design. . . . . . . . 93Figure 4.14 The off-normal transmission response for the double hexapolewith forked tripole design at 30 degrees and 60 degrees forboth TE and TM polarization. . . . . . . . . . . . . . . . . . 94Figure 4.15 The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity(magnitude) at ωz1, (e) electric field intensity (magnitude) atωz2, and (f) magnetic field intensity (magnitude) at ωz2 for theinterdigitated double hexapole FSS design. . . . . . . . . . . 96Figure 4.16 Independent tuning of the resonance frequencies of the inter-digitated double hexapole shown through (a) a parametric sweepof the secondary arm length and (b) a parametric sweep of theprimary arm length. . . . . . . . . . . . . . . . . . . . . . . . 98xxFigure 4.17 The off-normal transmission response for the interdigitated dou-ble hexapole design at 30 degrees and 60 degrees for both TEand TM polarization. . . . . . . . . . . . . . . . . . . . . . . 99Figure 4.18 The (a) surface design and (b) simulated transmission responseof the metapaper FSS design with modified trace and gap widths.The values of the dimensions shown in (a) are D = 12mm,L = 11mm, w = 0.5mm, and g = 0.5mm. . . . . . . . . . . . 101Figure 4.19 The (a) surface design with dimensions of D = 31.6mm, w =0.5mm, and g = 0.5mm and (b) simulated transmission re-sponse of the quarter ring FSS design with modified dimensions.101Figure 5.1 An image of the first handmade FSS prototype consisting of a6x6 grid of elements. . . . . . . . . . . . . . . . . . . . . . . 106Figure 5.2 (a) Side view and (b) front view of the test setup used to mea-sure the transmission through the first prototype board. . . . . 107Figure 5.3 The transmission measurements between the antennas of theopen air test setup with and without the prototype board. . . . 108Figure 5.4 The simulated transmission response of the design chosen forthe second prototype under two different polarizations. . . . . 110Figure 5.5 Open Air transmission measurements for one of the secondprototypes printed on the flexible substrates. . . . . . . . . . . 112Figure 5.6 A front view of the inside of the anechoic chamber built formeasuring the transmission through the prototypes. . . . . . . 114xxiFigure 5.7 A plot comparing the measured data from the four differentsubstrates of the prototypes along with the simulated transmis-sion response of the printed design. . . . . . . . . . . . . . . 115Figure 5.8 A zoomed image of the rough paper prototype. The breaks inthe conducting traces due to imperfect screen printing can beseen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure 5.9 Plots comparing the simulated and measured transmission re-sponses through the (a) PET, (b) vinyl, and (c) paper FSS pro-totypes. The plots also show the simulated reflection from theprototypes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Figure 5.10 A comparison between the simulated and measured transmis-sion responses of the prototype to a 30 degree off-normal TEincident wave. . . . . . . . . . . . . . . . . . . . . . . . . . . 121xxiiAcknowledgmentsA lot of people deserve credit for helping me through my journey to completingthis thesis and hopefully I will not miss out on mentioning any of them.First of all, due credit has to be given to my supervisor, Dr. Loı¨c Markley, fortrusting in me to be a part of this project. Even through some major and minorhiccups along the way, he has been a constant support and mentor. It has beena very rewarding experience working with him and possibly we will be able tocontinue our research collaborations further in the future.I have to acknowledge Andrew from the CLD Western Property Holdings Ltd.,who came forward with this idea of making a wallpaper. The research would nothave been possible without his support and funding endeavours.Next I must acknowledge the team at the applied electromagnetic lab. Startingoff in the lab; Connor, Iman, Masoud, and Vincent, made it very easy for me toacclimatize. Later on being joined by Ali, Cael, Jacques, and Ashtyn, made thetime spent in the lab much more interesting. I should also not forget Madisyn atthis point, who joined in the lab for just one summer as a high school student. Shehelped me out immensely in producing the first foam prototype.I have to give recognition to the Bangladeshi community here in Kelowna. Itxxiiidefinitely won’t be possible to name them all, but all of them were very helpful inmaking me feel at home in a foreign country.It would be amiss if I didn’t mention the people outside of school life. Startingfrom Tawsif, who set up everything so well for me here, that I don’t think anyonehas ever had a smoother transition. Rony bhai, for sharing my love of adventureand the outdoors, I wouldn’t have explored half as much here, if you hadn’t beenaround. TJ, for being one of the most helpful and good-willed persons I have seen.Thanks for carrying so much of my workload and being a wonderful manager.Sanchari, for threatening me with bankruptcy into completing this work on time.Deserae, for helping me not procrastinate and stay on track. And finally Jennifer,Arnab, Niloy, TJ (again), Connor (again), Sanchari (again) and Yushan for beingpart of the group that made everyday that much crazier than it had to have been.I’m much saner to this day thanks to that.Finally I come to family. My mother and father, for being a constant support,even though they had to bear only being able to watch their son on a webcamfrom thousands of miles away. My younger brother Oishik, for carrying on withhis passions and showing me that hope still remains if you follow your dreams.My younger sister Alisa, for tagging me in countless animal videos for no reasonwhatsoever and all the meaningless conversations we had at weird hours. My auntand uncle along with their families, living in Saskatoon and Seattle respectively,who gave me some amazing vacations right when I needed to take a break andrelax. I have been able to finish this work thanks to all of you.xxivDedicationsFirst and foremost this work is dedicated to my Mother and Father; without theirlove, care, and support I would not be here today.But this work is also dedicated to you. Yes, You! You, who has decided mywork is important enough to give a read through. Thank you for taking some timeout of your busy schedule to give an eye over some of the research I did, in betweenfrequent bouts of procrastination, while desperately trying to earn a Masters degree.xxvChapter 1IntroductionIn this thesis we present the design, analysis, and experimental verification ofsingle-layer dual wide-band band-stop frequency selective surfaces (FSS) for useas a Wi-Fi blocking wallpaper. The wallpaper is intended to be manufactured usinglow-cost, easily accessible, bulk printing methods such as screen printing or flex-ography. The signal blocking is enabled through the use of a frequency selectivesurface printed directly on to the wallpaper. In this Chapter, we present a brieftechnical overview of the Wi-Fi network and its security protocols. We then dis-cuss the applications of Wi-Fi blocking in different scenarios. A brief discussion ofthe methods for spatially blocking signals follows. The chapter is concluded withthe objective and motivation for the research carried out in this thesis.1.1 Wi-Fi NetworksIn modern times, Wi-Fi networks have become an inseparable part of our daily life.As more and more of our daily transactions are carried out on the internet, the needto stay connected to it at all times has become a necessity. As a result, we now have1wireless internet connectivity everywhere throughout Wi-Fi networks from hometo the workplace and even city-wide services.The convenience of Wi-Fi networks has led to a widespread proliferation inthe use of the technology to connect to the internet. Roughly 10% of the worldspopulation today uses Wi-Fi connectivity in some form[1]. There are more than20 billion devices in operation using Wi-Fi connectivity. The growth has been sofast, it is estimated that more than 50% of the total internet traffic of the world iscurrently on Wi-Fi networks [2]. With this amount of information passing throughthe Wi-Fi network, it is not surprising that a lot of the data is of a confidentialnature and requires high security measures to stop it from falling in to the wronghands. Yet a Wi-Fi network is discoverable to all users within range who havea Wi-Fi compatible device. Some standard security protocols are put in place tostop information theft from occurring. In the following subsections we discuss thetechnical specifications of Wi-Fi communications and the security protocols used.1.1.1 IEEE 802.11x standards“Wi-Fi” is quite often incorrectly thought to be the abbreviation for “Wireless Fi-delity”. However, “Wi-Fi” is actually a trademark name held by the Wi-Fi allianceused to denote the set of standards known as IEEE 802.11x, which regulate thesetting up and operations of wireless local area networks between interoperabledevices [3]. In order to obtain Wi-Fi certification, devices have to adhere to thesestandards as well as receive interoperability certification from the Wi-Fi alliance.Wi-Fi compatible devices can then connect to the internet through the wirelesslocal area network broadcasted by a wireless access point.Wireless access points are devices which can broadcast a Wi-Fi signal over a2Figure 1.1: A schematic diagram of the overlapping channels in the 2.4 GHzWi-Fi band. 2.4 GHz Wi-Fi channels (802.11b,g WLAN) c©MichaelGauthier, CC BY-SA 3.0fixed distance, within which, any device with Wi-Fi compatibility can discover andtune into the signal and use it to connect to the internet. Wireless access points aremore commonly known as “wireless routers” in daily use and can come in differentshapes, sizes, and specifications. For a commonly available router, the range ofthe Wi-Fi network can be anywhere between 20 meters indoors to a few hundredmeters outdoors. An important factor to note about Wi-Fi networks compared towired internet connections is that anybody within range of the access point witha Wi-Fi compatible device is able to discover the signal and possibly connect toit, while on a wired internet connection only devices physically connected to thenetwork can access the internet.According to the IEEE 802.11x standards, wireless local area network connec-tions can be set up between computers in the 0.9, 2.4, 3.6, 5, and 60 GHz frequencybands. However, the networks that we access regularly through our connected de-vices at home and on public Wi-Fi access points are in the 2.4 and 5 GHz bands.The most common set of standards used in devices today are the 802.11b/g/n/acstandards. The 802.11b/g standards operate at the 2.4 GHz frequency, the 802.11acstandard works at the 5 GHz frequency, while the 802.11n standard works at boththe 2.4 and 5 GHz frequencies. Each of the standards breaks the spectrum down3into multiple channels, the bandwidth of each channel is dependent on the stan-dard and is also the contributing factor to the maximum data rate of the standard.Each standard also has its own modulation scheme to reduce inter-channel inter-ference. The number of allowed channels varies from country to country, howevermost countries have at least 11 overlapping channels in the 2.4 GHz band. In the802.11b standard, the channels are 22 MHz wide each and the center frequencyof each channel is separated from the next one by 5 MHz. Hence, channel 1,6,and 11 are the only channels which can be used simultaneously and not have anyoverlapping operating frequencies between them. The 2.4 GHz band has a totalbandwidth of 100 MHz centered around 2.45 GHz, giving a fractional bandwidthof 4.08%. The 5 GHz band has a total bandwidth of 150 MHz centered at 5.8 GHz,which gives it a fractional bandwidth of 2.59%. A schematic of the Wi-Fi chan-nels and the allowed non-overlapping channels in North America along with theirmodulation schemes is shown in Figure 1.1 and Figure 1.2.1.1.2 Wi-Fi securityWi-Fi networks are mostly secured through password protection protocols. Theearliest of these was called the Wired Equivalent Privacy (WEP), however it wasfound to be inadequate to stop unauthorized access [4]. Current Wi-Fi access pointsuse the Wi-Fi Protected Access (WPA) or Wi-Fi Protected Access II (WPA2) pro-tocols. The WPA2 protocol is considered more safe of the two protocols. TheWi-Fi alliance has very recently announced a WPA3 protocol to come into effectsoon.All of these security protocols employ 64- or 128- bit encryption keys to se-cure the data being sent on the Wi-Fi network. The WPA protocols have the added4Figure 1.2: A diagram of the allowed non-overlapping Wi-Fi channels inNorth America according to the different IEEE standards along withtheir corresponding modulation methods. 802.11 non-overlappingchannels for 2.4GHz. Covers 802.11b,g,n c©Liebeskind Rbeede, CCBY 3.05benefit of producing dynamic keys for each packet rather than the easily decrypt-able static key for the WEP protocol. The WPA2 protocol also employs manda-tory support for the Counter Mode Cipher Block Chaining Message AuthenticationCode Protocol or the CCMP protocol which provides the security services of dataconfidentiality. This ensures that only authorized persons can gain access to infor-mation, authentication, and provides proof of the user being genuine, and accesscontrol in association with layer management [5].In spite of all of these security measures that go in to protecting informationon Wi-Fi networks, the shortcomings of these protocols are also well known andresearched. Technology used to gain unauthorized access always keeps pace withthe security technology and each of them is always looking to stay one step aheadof the other. Recent studies have shown the inadequacies of the password protocolsto advanced attacks and the vulnerability of data on the Wi-Fi network to unwantedeavesdroppers [6, 7]. Due to lack of forward secrecy on the information shared onWi-Fi networks, once the password is decrypted and known to an eavesdropper, itis possible to intercept and save all the data being sent on the Wi-Fi connection.This leads to serious concerns over the security of sending confidential data overWi-Fi networks.1.2 Wi-Fi blocking and applicationsOne particular security measure which could be employed over the encryption pro-tocols is to physically stop the signal from reaching an eavesdropper. ThoughWi-Fi access points broadcast in all directions simultaneously, an engineered envi-ronment can be envisioned which can physically stop the Wi-Fi signals from prop-agating in a particular direction, confining it to a predetermined space and isolating6the signal from unwanted users. This could be defined as a Wi-Fi secure space. Insome situations it might also be desirable to isolate particular individuals from theWi-Fi network. In such cases the environment could be engineered to block Wi-Fisignals from entering the predetermined space. This application can be defined asa Wi-Fi free space. The Wi-Fi secure and Wi-Fi free spaces are elaborated furtherin this section.1.2.1 Wi-Fi secure spaceA Wi-Fi secure space could be a room or set of rooms with Wi-Fi blocking bound-aries on the outermost side with a Wi-Fi access point situated inside the space. Thiswould allow users to access the Wi-Fi network within the space and send data tothe access point which would later send it to the internet along much more securewired connections. Since access to the room can be given to only secure personnel,the data sent along the Wi-Fi channels within this space is also secure from eaves-droppers. Anybody outside the Wi-Fi secure space is unable to discover the Wi-Finetwork, therefore even knowing the password protection key does not give themaccess to the network. This kind of implementation could be attractive to banks,government buildings, large corporations etc. to produce secure meeting rooms orwork spaces where confidential data can easily sent among many people withoutcompromising security.1.2.2 Wi-Fi free spaceA Wi-Fi free space would have the same implementation as a Wi-Fi secure space,however it would lack a Wi-Fi access point within the built environment. Thiswould cause all external Wi-Fi access points to be be undiscoverable within the7Wi-Fi free space. Rather than security, this implementation would isolate a personfrom accessing a Wi-Fi network. If it was necessary to limit the access of a personfrom the data on the internet, this could be a possible solution. Situations likethis could arise mainly in exam rooms and class rooms in schools, where it isconsidered academic misconduct if a student accesses the internet. Apart from that,it could also be used to make low distraction rooms, or in hospitals and laboratoriesin rooms with sensitive equipment that may malfunction or produce spurious datain the presence of the Wi-Fi signal [8, 9].Another added benefit of physically blocking Wi-Fi signals, outside of datasecurity, would be the reduction of interference between networks generated fromdifferent access points. With the numerous home, work, and city access points allaround us working within the same channels, interference is a problem which leadsto lower speeds and failed connections. If the networks are intentionally limited tointended spaces, the cross-network interference can be greatly reduced leading toimproved performance on each separate network [10, 11].1.3 Methods of signal blockingTwo methods which can be used to impede the propagation of waves is discussedin this section. The Faraday cage is a method of blocking signals at all frequen-cies in a fixed space. An FSS can be used to block specific frequencies from thefrequency spectrum. The details of their implementations are discussed in the fol-lowing subsections.81.3.1 Faraday cagesThe Faraday cage is the simplest implementation of using a surface to block Wi-Fisignals. A Faraday cage is basically a space enclosed in all directions by a layerof conducting material. The conducting material can be continuous like a layer ofaluminium foil or discontinuous like a wire mesh as long as the gaps between theconductors are smaller than the wavelength of the signal. A Faraday cage will notlet any electromagnetic waves pass through it, so an internal signal will be keptinside of it, while an external signal will be unable to penetrate inside the cage.It is named after English scientist Micheal Faraday, who first demonstrated theidea in 1863 [12]. A schematic diagram of how a Faraday cage works is shown inFigure 1.3. Non-conducting walls Electric field Conducting walls Figure 1.3: A schematic representation of the operating principle of aFaraday cage showing the difference between conducting and non-conducting walls.The Faraday cage implementation of electromagnetic shielding is fairly com-mon in sensitive laboratory settings, where any outside signal can interfere withdata readings, leading to anomalous results. Most radio astronomy laboratories9will have a Faraday cage room, inside of which, wireless connectivity can be ar-ranged. This ensures that the equipment outside do not pick up spurious land basedsignals used for communications.A complete Faraday cage implementation, where no signal can escape the in-terior of the room (or outside signals coming inside) requires total covering of allsurfaces with conductive material and blocks all frequencies from passing through.For some applications such extreme blocking might not be needed. Only isolatingspecific frequencies might be enough to serve the purpose, security of the Wi-Finetwork being such an example. In fact it might be very important to have accessto some other frequencies in the communication bands like cellular connectivity oremergency wireless communications. In these cases the Faraday cage implementa-tion is unnecessary and excessive. So some other method of signal blocking whichallows selective control over the frequencies to stop is needed.1.3.2 Frequency selective surfacesFSS are spatial electromagnetic filters which can be designed to block specificfrequencies. An FSS is made of a periodic conductive pattern drawn on a di-electric substrate which can produce a filtering effect on an incident wave. Thepattern is generally made of conductive traces of a specified width separated bynon-conducting dielectric gaps. An example of an FSS which we encounter in oureveryday lives is the perforated metal screen on the microwave oven door. Thisis an FSS which is able to block the microwave frequencies yet allow optical fre-quencies to pass through. This keeps us safe from the microwaves, but allows usto keep an eye on the food inside the oven.The filtering effect of the FSS can be determined from its transmission re-10sponse. The transmission response is calculated by having a broadband electro-magnetic wave incident on the FSS surface and measuring the relative magnitudesof the different frequencies that pass through it. FSS can be made to block multiplespecific frequencies while leaving other frequencies unaltered. FSS that can filtermultiple frequencies are known as multiband FSS. To utilize FSS filtering proper-ties to block Wi-Fi communications, a dual band FSS is required which can blocktwo separate frequencies. A dual band FSS which would be able to block the wideband Wi-Fi signals is the main focus of this thesis. Further details of FSS and thebackground behind its use in blocking of electromagnetic waves are given in thenext Chapter.1.4 Motivation and ObjectiveThe objective of this thesis is to find an FSS design for blocking Wi-Fi in a builtenvironment. We envision a Wi-Fi blocking wallpaper, with the Wi-Fi blockingFSS element printed on it with conductive ink. The printing method should below cost and capable of printing in bulk to keep expenses to a minimum. ThisWi-Fi wallpaper could be applied like regular wallpaper as a wall covering. As aconsequence the walls will block Wi-Fi signals from passing through them and canbe used to create Wi-Fi secure and Wi-Fi free spaces. The wall covering industry iscurrently valued at 27.24 billion dollars worldwide and is expected to grow to 35.78billion by 2023 [13]. Adding the Wi-Fi security capabilities to regular wallpaperat low cost and manufacturing an attractive product for the industry provides extramotivation to this research.In order for the FSS to be able to be reproduced in a wallpaper form, the designshould have only one layer of conductive patterning on a single layer of dielectric.11For the wallpaper to block Wi-Fi from the different access points as defined by theIEEE 802.11x standards, it should be able to produce an attenuating effect on boththe 2.4 GHz and 5 GHz bands of the frequency spectrum. The other specified fre-quencies in the IEEE 802.11x standards are not used in private Wi-Fi connectionsand are not considered for blocking. It should also have minimum cost requiredwith design and manufacture, in order to make it an attractive product for the wallcovering industry.1.5 Thesis OrganizationThe rest of this thesis is organized as follows.In Chapter 2, we discuss the history of FSS and its applications, factors that af-fect performance of FSS, and previous work done in using FSS as Wi-Fi shielding.We look at the advantages and disadvantages of the different designs and analyzethe shortcomings of the designs in producing a final marketable product.In Chapter 3, we look at single resonant FSS structures to find a base designwhich we can use to build our final product. We look at the bandwidth of singleresonant structures and try to maximize it to find a suitable starting point. We alsolook into the equivalent circuit model which gives us an easy design process aswell as justification of the behaviour of the transmission through the structures inan intuitive manner.In Chapter 4, we look at various double resonant structures and use the equiva-lent circuit model to modify to the elements for better performance, compare theirresponses and note the improvements between different arrangements.In Chapter 5, measurements are carried out on prototypes that were made totest the proof of concept. The printed prototype shows that a product can be man-12ufactured using screen printing which matches the theory and simulations. Thetesting of the prototype is done in house and the factors affecting the transmissionresponse of the FSS are analyzed in actual prototype performance. Finally, Somemodifications are made to simulations to compensate for the effect of the dielectricsubstrate and finite conductivity of the traces. The match between compensatedsimulations and prototype measurements are shown.In Chapter 6, we conclude the work and note some future work that can bedone to produce a final working marketable product.13Chapter 2Background2.1 Frequency selective surfacesA frequency selective surface (FSS) is a 2-D periodic array of conductive ele-ments which can produce a filtering effect on an electromagnetic wave passingthrough it. The conductive elements can be in the form of discontinuous shapeswith non-conducting gaps in between them, or a continuous grid with periodicnon-conducting shapes cut out of it. Any incident electromagnetic wave will gen-erate currents on the conducting elements, while an electric field is set up over thenon-conducting gaps. The conducting elements introduce inductance, while thedielectric gaps between conductors introduce capacitance [14]. These inductancesand capacitances will then have a resonance at a particular frequency of the inci-dent wave. An FSS can have planar elements periodic in a single 2-D plane, it canhave multiple layers of 2-D FSS, or be made up of a 2-D array of 3-D conductiveelements [15–21].The earliest use of periodic structures in electromagnetic devices can be traced14back to a 1919 patent belonging to Marconi and Franklin, in which they constructeda parabolic reflector from wire sections rather than long rods [22]. Research intoperiodic structures and FSS intensified in the 1960s, when their potential for mil-itary applications was recognized. Their application into stealth systems pushedforward the research in this field, leading to diverse applications in antenna design,communication systems, and satellite systems.In stealth technology, the common use of FSS is as antenna radomes or elec-tromagnetic shielding [23–25]. The FSS can reflect unwanted transmissions at onefrequency, while allowing the shielded antenna to transmit at another frequency.The reflected waves can also be scattered in various directions based on the shapeof the radome, thereby reducing the radar cross section of the shielded antenna. Aschematic drawing is shown in Figure 2.1(a).Another common use of FSS is as a dichroic structure in transmitting antennasystems [26, 27]. The term dichroic means that the structure has different trans-mission properties at different frequencies. A sub-reflector made of an FSS can beplaced between two transmitting antennas and a reflector to produce two distinctfocal spots for the reflector. If the FSS is opaque at one frequency and transparentto another, the two transmitting antennas can operate at both frequencies and usethe same reflector for broadcasting their signals. A schematic diagram is shown inFigure 2.1(b).Other fields which have seen the use of FSS include electromagnetic interfer-ence shielding [28, 29] and indoor wireless signal filtering [30, 31]. FSS have alsobeen used in electromagnetic wave absorbers [32–34], antenna array beam steeringelements [35–37], electromagnetic band gap materials [38–40], diplexers [41–43],and polarizers [44–47].15 Antenna Radome f1 f2 (a) Parabolic Reflector Feed 1 f1 f2 Feed 2 Dichroic Surface (b)Figure 2.1: A schematic showing the application of FSS as (a) a radome and(b) a dichroic surface sub-reflector.2.2 Classification of frequency selective surfacesFrequency selective surfaces can broadly be classified into categories based on theirelement geometry type, frequency response, or use of active components. Accord-ing to Munk [22], FSS can be classified into four broad element type families asfollows:1. Center-connected: This includes dipoles, tripoles and other multipolar ele-ments [18, 48, 49].2. Loop types: This could include square loops and rings, as well as any othershape formed by a loop [50–52].3. Solid interior types: These are usually the patch and aperture type structures[53–55].4. Combinations: There are no restrictions on FSS element patterns as long as16they are periodic. Hence combinations of all the above types can be used toproduce a required frequency response [56–58].Some FSS elements grouped according to the classification presented here areshown in Figure 2.2 Centre Connected Loops Patch or Aperture Group 1 Combinations Group 1 Figure 2.2: Classification of different FSS elements according to their shapetype.FSS can also be designed to have a frequency response similar to any of thefour basic filter types, namely low pass, high pass, band pass, or band stop [59–62].Generally FSS filters follow the Babinet dual principle [63, 64], where the com-plimentary responses in the frequency domain will have complimentary structuresin their physical design as well i.e if the conductive and non-conductive elementsof a low pass FSS filter design are inverted it will produce a high pass FSS filter.A schematic representation of the duality between FSS designs is shown in Fig-ure 2.3. As can be seen from the figure, the patch type elements produce a low17pass response, while its physical complimentary structure, the aperture type, pro-duces a high pass response. Again the loop type produces a band-stop response,while the slotted loops produce a band-pass response. Figure 2.3: A schematic diagram showing the duality between FSS geome-tries and their filter responses.Another classification can be made based on the presence of active elementsin the design. A lot of research has been carried out recently into these activeFSS designs [65–68]. These designs utilize the on-off states of switching devicesto produce different frequency responses in different states. Some designs utilizehigh frequency PIN diodes to control the switching between states. When the PINdiode is on, it can create a short between lines producing a continuous mesh typegeometry. When it is off, it will create an open circuit, converting the design to aloop type one. This allows the same design to exhibit the response of a mesh or aloop depending on whether the switch is on or off. Designs without any active orswitching devices on the other hand can be classified as passive FSS designs. Thedesigns considered throughout this thesis are all passive designs.As the objective of this thesis is to produce a single layer, fully printable, pas-sive design which is able to produce two stopbands at the Wi-Fi frequencies, we18exclusively focus on the band stop type geometries. Further analysis of the geome-tries are done in Chapter 3 and Chapter 4 to find the one with best performance interms of -20 dB bandwidth in the stop band(s).2.3 Factors in FSS performanceThere are a few factors which affect the performance of a particular FSS design.The factors include angle of incidence and polarization of the incident wave, di-electric properties of the substrate, conductivity of the traces, and the periodicity ofthe unit cell. These factors have to be considered when designing an FSS, as theycan modify its transmission response. The factors are explained in more detail inthe following sections.2.3.1 Angle of incidence and polarizationIn practice, waves can be incident on the FSS at any angle. The effective lengthsof the surface geometry of the FSS changes for waves incident at an angle. Asshown in Figure 2.4(a), for a wave incident at an angle of α , the length of a stripof L has an effective length of Lcosα . This causes the effective geometry of thesurface to change with the change of incident angle. Since the frequency responseof the FSS is a function of the geometric parameters such as length of traces, thick-ness of traces, and gaps between traces, the change of these parameters causesthe frequency response of the surface to change. Hence a designer must also bevery careful of the off-normal angle response. When designing an FSS for block-ing broadband communication channels it is important to verify that the shift inresonant frequency for off-normal incidence is not so large that the stop bandscompletely move away from the communication bands.19 Lcosα L α Normally incident wave Angularly incident wave (a) (b)Figure 2.4: The figures show the effect of (a) incident angle of the wave and(b) polarization of the wave on the effective lengths of the FSS design.(b) is republished with permission of IEEE, from [31] c©2006; permis-sion conveyed through Copyright Clearance Center, Inc.The polarization of the incident wave can also affect the transmission responseof the FSS. It is well known that conducting strips in parallel with an incidentelectric field behave like inductors, while gaps between conductors act like ca-pacitors [14]. A change of polarization causes the effective lengths of the stripsto change as well providing new gaps to the incident electric field. The effect isshown schematically in Figure 2.4(b). The changing of gaps and conductor widthsalso causes the frequency response of the FSS to change. However this effect canbe reduced by using rotationally symmetric structures which have dimensions thatare less affected by a change of the incident polarization. For example the four polecross element with a 90 degree separation between arms will remain unchanged foreither horizontal or vertical polarization of a normally incident wave. The struc-tures considered in this thesis all have a degree of rotational symmetry, as they areexpected to be robust to changes in polarization of the incident wave at normalincidence. The effect of changing polarization angles at off-normal incidence is20much more complex however, as it incorporates the effects of both factors.The effect of incident angle and polarization on the FSS response cannot becompletely neutralized, however the amount of influence of the incident angle andpolarization will vary between designs. Hence for this thesis we will try to findthe design with the least amount of deviation between the normal and off-normaltransmission response. The effect of a dielectric substrate also reduces the effectof the incident angle of the wave, which is discussed in further detail in the nextsection.2.3.2 Substrate propertiesGenerally an FSS is manufactured by fabricating the conductive pattern on topof a dielectric substrate. The dielectric substrate provides mechanical support tothe whole design. However the dielectric layer also has an effect of changing thefrequency response of the FSS [22]. A dielectric has the effect of reducing thewavelength of an incident wave by a factor of√εr, where εr is the dielectric con-stant. This changes the electrical length of the FSS, thereby changing its frequencyresponse. If the FSS was embedded in an infinite dielectric layer of effective per-mittivity of εr, the resonance frequency, f0, of the transmission response of the FSSwould be shifted down to a frequency, f ′0, with the value,f ′0 =f0√εr.Usually the FSS will be on top of a dielectric, with the layer on only one side.In this case if the dielectric had an infinite extent in one direction, the resonance21frequency would be shifted down to,f ′0 =f0√(εr +1)/2.However in practical situations the dielectric substrate will not be infinite in extentand the resonance frequency will be in the range,f0 < f ′0 <f0√(εr +1)/2.This factor will also be a non-linear function of thickness of the substrate. Hencethe effect of a dielectric substrate is hard to quantify without introducing the ap-propriate layers in the simulation of designs. It can be noted though that the intro-duction of the dielectric layer does not affect the filter type of the FSS design. AnFSS design with dual stop bands will still have the two stop bands after a dielectricis added. Only the total frequency response of the FSS will be non-linearly scaleddown. Therefore it is common practice to design an FSS with the intended filtertype and number of resonances and then apply the appropriate dielectric layers tofind the expected frequency response and bandwidths of the design.A side effect of the dielectric layer however, is to improve stability of thefrequency response to changes in incident angle [22]. According to Snell’s law,obliquely incident waves on a dielectric layer are refracted towards the normal di-rection of incidence. A higher refractive index or higher dielectric permittivityleads to a higher bending of waves towards the normal direction, leading to a re-duction in the effect of the incident wave coming in at an off-normal angle. Theeffect of refraction in a dielectric is shown in Figure 2.5. Hence, the dielectric layer22 Incident wave αi αr ϵr αr < αi Refracted wave Figure 2.5: The effect of refraction causes the incident angle of a wave toreduce when it reaches the FSS and reduce its influence on the trans-mission response.can act not only as a mechanical layer, but also as a layer to improve the off-normalfrequency response of the design.2.3.3 Trace conductivityThe conductivities of the traces in the FSS design also have an important effecton the frequency response. In simulations the traces are designed as perfectlyconducting layers with infinite conductivity. Hence for a band stop FSS, at theresonant frequency they reflect the incident wave perfectly and no energy fromthe wave can pass through the surface due to destructive interference between theincident and reflected waves. However, for traces with real conductivities, thereflected wave cannot be perfectly matched to the incident wave due to losses in theconductive traces. This leads to a reduction in the high reflectivity at the resonantfrequency for the FSS at the resonant frequency. This effect is quantified through areduction in the absolute attenuation in simulations and measurements [22]. Sincethe objective of this thesis is to produce a design which is able to block the Wi-Fibands from being transmitted, the trace conductivity is a very important parameterto be considered. However, it should also be noted that trace conductivity does23not have much influence over the position of the resonances or the bandwidth ofthe stop bands. Hence, while it is an important factor to be considered duringthe fabrication of the FSS, it can be overlooked during the design of the surfacestructure for the required frequency response.2.3.4 PeriodicityThe final factor which needs to be taken into consideration when designing an FSSis the periodicity of the unit cell. The periodicity directly influences the appearanceof grating lobes in the frequency response of the FSS. Grating lobes occur whenthe periodicity of elements becomes comparable to the wavelength of the incom-ing waves. At the grating lobe frequency, the FSS elements produce undesirablesecondary lobes of scattering through higher order constructive interference [69].The phenomenon is shown in a schematic representation in Figure 2.6.The appearance of grating lobes causes an overall reduction in efficiency ofthe FSS in producing the intended frequency response due to energy dispersionthrough higher order modes of propagation. The grating lobes are governed by theequation,D(sinθi + sinθm) = mλ ,where D is the periodicity of the FSS design, θi is the incident angle of the wave,θm is the direction of propagation of the m-th mode, and m is the mode number.For a normally incident wave, the first mode appears when D = λ and propagatesat a grazing angle along the periodic surface [70]. Grating lobes can be avoidedby ensuring the periodicity is well below λ/2. The presence of the dielectric layeris also an advantage in this case, as it shifts down the frequency response of the24Figure 2.6: A diagram showing the conditions for producing grating lobeson a periodic surface. Diffraction Grating Equation c©Vigneshdm1990,CC BY-SA 4.0FSS, but it does not effect the frequency of appearance of grating lobes. Hence byminiaturizing the design and placing it on a dielectric substrate, grating lobes canusually be avoided completely within the range of interest.2.4 Multiband FSSThe basic center-connected, loop, patch, and aperture shapes shown in the classifi-cation of FSS elements produce single band filter responses. FSS which can filtermultiple bands simultaneously are known as multiband FSS. Designing multibandFSS can be done by choosing the appropriate geometry or by stacking multiple lay-ers of single band FSS with different resonant frequencies. Some of the methodsof producing multiband FSS are discussed in this section.252.4.1 Multilayer FSSA popular method for designing an FSS with resonances at multiple different fre-quencies can be by stacking layers of FSS with single resonances [71–75]. In thestudies referenced, the authors first simulate the layers individually and then sim-ulate the entire structure to find the interaction between layers. The interactionsbetween layers appear as a transmission line section between the responses of theindividual resonances. Due to the nature of transmission lines, the interactionsbetween layers are highly dependent on the thickness of the layers. Thus, the gov-erning factors in the response of multilayer designs not only involves the elementdesign of each layer, but also the thickness of the layers in between stacks. Hence,in most cases multiple simulations are needed to match resonance frequencies torequired values.(a) (b)Figure 2.7: An example of (a) a multilayer FSS design and (b) its trans-mission response. Republished with permission of IEEE, from [75]c©2008; permission conveyed through Copyright Clearance Center, Inc.An example of a multilayer design along with its transmission response isshown in Figure 2.7. The design has top layer of loops and a bottom layer of26wires separated by a dielectric substrate. The design shows a dual-band band-passtype response. It has two pass bands centered around 7.8 GHz and 10.4 GHz.2.4.2 Fractal FSSSingle band structures can also be converted to multiband structures with reso-nances at higher frequencies by utilizing fractal geometries [76–81]. By definition,fractals are complex recursive patterns that are infinitely self-similar at all scales[82, 83].(a) (b)Figure 2.8: An example of (a) a fractal FSS design with the lengths p =16.5mm and L = 10mm and (b) its transmission response at differentlevels of fractal design. Republished with permission of IEEE, from[80] c©2004; permission conveyed through Copyright Clearance Cen-ter, Inc.The resonance frequency of an FSS element is mainly defined by its geometricparameters. A fractal structure will have the same repeating pattern with differentdimensions at every scale of the fractal. This will allow it to have resonances whichare harmonics of the original resonance frequency defined by the base structure. Areal fractal pattern for an FSS cannot be made to be infinitely self-recursive. How-ever the total number of levels of recursion can be predetermined. Then the ratio27between dimensions at each level of the fractal can be used to design a required ra-tio between the multiple resonances. For example if dimensions are halved at eachlevel then resonances will occur at double the base frequency. This is an effectiveway of designing a multiband FSS. However, the overall response is highly depen-dent on the frequency response of the base structure. If design requirements suchas bandwidth cannot be met by the base structure then further methods like inter-leaving and composite elements may be required to improve the overall response.A fractal design used in previous studies along with its transmission response isshown in Figure 2.8. The design has a dual-band band-stop type transmission re-sponse. The resonance frequencies of the design change in frequency as more lev-els of the fractal are added to the design. For a level 3 fractal it has two resonancefrequencies of 6.45 GHz and 8 GHz.2.4.3 Genetic algorithm based designsWith the increase in computing power, another method which has grown in popu-larity is the use of computer based algorithms to design the FSS surface. Specifi-cally genetic algorithms have seen use in designing FSSs [84–86]. Genetic algo-rithms are a powerful tool in solving constrained and unconstrained optimizationproblems involving a large number of parameters. Genetic algorithms utilize evo-lutionary techniques and produce solutions by using operators such as selection,cross-over, and mutation [87, 88]. When using these algorithms for FSS design,the unit cell is first discretized and the conductive and non-conductive elementsare assigned values of 1 and 0. Then the algorithm uses the cross-over and muta-tion operators to re-position the conductive elements to find the optimal shape forthe required constraints. However, the design process of these FSS uses extensive28(a) (b)Figure 2.9: An example of (a) a genetic algorithm based FSS design and (b)its transmission response. Republished with permission of IEEE, from[84] c©2004; permission conveyed through Copyright Clearance Center,Inc.computational power and the discretized surface pattern is not always suitable forprinting. The performance of the design is also highly dependent on the resolutionof discretization of the unit cell. A more finely discretized surface will performbetter, however the computational power needed will rise accordingly. An exam-ple of an FSS pattern designed through the use of genetic algorithms along withits transmission response is shown in Figure 2.9. This genetic algorithm based de-sign has a unit cell size of 8 mm and shows a dual-band band-stop transmissionresponse with resonance frequencies at 20 GHz and 28 GHz.2.4.4 Multiresonant FSSCombining multiple resonant paths into one element structure can produce multi-band FSS designs. These are different from the fractal structures in that they do notutilize the same shape in a recursive pattern. Rather multiple different structuresare combined to resonate at different frequencies [89–96]. These designs require anelaborate design procedure, as the multiple resonant paths can interact with each29(a) (b)(c) (d)Figure 2.10: The figure shows (a) the surface design using the ring slot el-ement, (b) transmission response of the ring-slot FSS design, (c) themeandered line multiresonant element, and (d) the transmission re-sponse of the meandered line FSS design. (a) and (b) are republishedwith permission of John Wiley & sons, Inc. , from [89] c©2016; per-mission conveyed through Copyright Clearance Center, Inc. (c) and(d) are Republished with permission of IEEE, from [90] c©2015; per-mission conveyed through Copyright Clearance Center, Inc.30other and produce unwanted frequency response effects. Also the multiple reso-nance mechanisms may be coupled to each other, resulting in a design which doesnot have independent control over the resonant frequencies through individual ge-ometric parameters. Usually for these designs changing one geometric parameterof the elements results in all resonance frequencies and bandwidths being changed.Hence designing the exact geometry for a required response can require multipledesign steps to achieve. Some examples of multiresonant FSS elements along withtheir transmission responses are shown in Figure 2.10. In Figure 2.10(a), half of theunit cell is shaped as a ring type conductive element, while the other half is a slotring element. The responses from the two halves interact to produce a transmissionresponse which is different from either a ring element or a slot element. The finaldesign has a dual-band band-stop characteristic with two stop bands centered at2.36 GHz and 3.36 GHz. In Figure 2.10(c), the meandered arms of the FSS ele-ment have different lengths causing them to resonate at different frequencies. Theoverlap between the edges of the arms will also cause the resonances to interactand reshape their overall transmission response. The meandered arm FSS elementproduces a dual-band band stop frequency response with -15 dB bandwidths of12.4% at 2.54 GHz and 5.04% at 3.54 GHz.The final structure considered in this thesis is a multiresonant element, howeveras will be further discussed in the following chapters, it has independent resonancemechanisms which allows the resonance frequencies to be tuned individually bymodifying a single geometric parameter.312.5 Single layer FSS designs for Wi-Fi and othercommunication bandsIn this thesis we intend to produce a fully printed, independently tunable, dualband, band stop Wi-Fi blocking wallpaper using single layer FSS design. Somegroups have previously tried to design FSS for blocking communication bandsin the built environment, however until now there has not been a commerciallyavailable design on the market. We discuss some of the previously reported designsin this section.2.5.1 Square loop designIn a study conducted by Sung, Sowerby, Neve, and Williamson [31], the authorslook at the square loop FSS as a base design to produce a single band FSS forthe 2.4 GHz Wi-Fi band. The square loop is chosen as the base design based ona comparison between different element geometries done in [69]. A prototypeis produced by using aluminium tape on different substrates and the results arecompared to simulations operating at 5.6 GHz. While the study shows the squareloop to be a good candidate for blocking the 2.4 GHz band, it does not look into thescope of design for simultaneously blocking the 5.8 GHz band. The surface designwith dimensions as well as simulation results are shown in Figure 2.11. From thesimulation results, it can be seen that the design has a -20 dB fractional bandwidthof 19.23% at a resonant frequency of 5.6 GHz.32(a) (b)Figure 2.11: The (a) surface design and (b) simulated transmission responseof the square loop FSS design. Republished with permission of IEEE,from [31] c©2006; permission conveyed through Copyright ClearanceCenter, Inc.2.5.2 Metapaper designA study was done by Niembro-Martin, Barros, Eymin-Petot-Tourtollet, and Lemaitre-Auger in France trying to produce a design for blocking dual band Wi-Fi signals[97]. The base design used is the tripole structure, which has a large -20 dB band-width. The secondary resonance path is created by adding secondary branchesalong the primary arms of the tripoles. These secondary arms interact with thearms from neighbouring elements and produce the secondary resonance. The fi-nal element design ends up being tightly coupled, made to resonate exactly at theWi-Fi frequencies. The interaction between the primary and secondary arms leadsto a dependence between the resonant frequencies. Changing the length of onlythe primary arm causes the positions of the secondary arms to move. Hence, boththe resonance frequencies end up changing simultaneously. The design has manyindependent geometric variables, each of which influences the frequency response.33(a) (b)Figure 2.12: The (a) surface design and (b) transmission response of themetapaper FSS design. Republished with permission of IEEE, from[97] c©2015; permission conveyed through Copyright Clearance Cen-ter, Inc.The transmission response has bandwidths of 14% and 8.9% at the resonant fre-quencies of 2.5 GHz and 5.6 GHz respectively. The surface design with some ofthe major dimensions labelled and simulated transmission response are shown inFigure 2.12. The value of the dimensions corresponding to the labels are given inTable 2.1. The trace widths for this design were set to 250µm. The authors ofthis study chose flexography as the method of printing conductive traces on papersubstrates. However, they reported imperfections in printing of the narrow tracewidths using their chosen method [98].Table 2.1: Geometric parameters of the metapaper designA B C D F G H11 mm 4.2 mm 0.5 mm 3.6 mm 2.4 mm 3.6 mm 2.1 mm342.5.3 Quarter ring designFerreira, Cuin˜as, Caldeirinha, and Fernandes use a circular ring as the base elementin a dual band FSS design in [99]. The ring is subdivided in four leaf shapes bydrawing arcs with radius equal to the radius of the main loop. This structure thenproduces two resonances, one corresponding to the circumference length of themain ring and the other corresponding to the perimeter lengths of the subdividedleaf structures.(a) (b)Figure 2.13: The (a) surface design with dimensions of d = 39.5mm, r =14.5mm, t = 2.5mm, and g = 0.25mm and (b) simulated transmissionresponse of the quarter ring FSS design. Republished with permissionof IET Journals, from [99] c©2016.This structure also has its resonances tightly coupled, as the radius of the sub-dividing arcs are equal to the radius of the main loop. Hence the ratio betweenthe primary and secondary resonances will also maintain a specific value. The de-sign has only 3 independent geometric variables and correspondingly the designpresents very little flexibility for tuning of the resonance frequencies separatelyfrom each other. In this study the authors use PCB printing technology, which isable to reproduce the smaller dimensions quite accurately. The design produces35stop bands of 20% and 2.8% bandwidth at resonance frequencies of 2.5 GHz and5.2 GHz respectively. The surface design with the dimensions labelled and thesimulation results are shown in Figure 2.13.These designs have all been previously studied to try and produce an FSSblocker for communication bands. In the following chapters we will look intothe effectiveness of different geometries in producing wide stop bands and choosethe geometry well suited for blocking broadband communications. We will presenta comparison between the designed structures against these previous works as wellat the end of Chapter 3 and Chapter 4.36Chapter 3Analysis of Single Band FSSDesignsThe start of our study into designing a dual band, single layer, band stop FSS beginswith a comparison between single band FSS elements to find the pattern with thelargest bandwidth. The elements are set up without a dielectric substrate in airand the transmission through them is simulated. The dimensions of the elementsare chosen to obtain the same resonance frequency in the transmission response.The -20 dB bandwidth of the response is chosen as the main metric of comparisonbetween the designs. The design with the largest -20 dB bandwidth is considered asthe best candidate for modification to produce a dual band, band stop FSS. Addingin the second resonance can cause the primary bandwidth to be reduced. Followingthis method to find the base design ensures that the primary band still retains a largeattenuation bandwidth after modification.In general, the center-connected and loop type geometries produce band stop37filter characteristics. Many of these structures have previously been simulatedand documented, however each study chooses trace widths, gap widths, lengthsof arms, and resonance frequencies differently. In this chapter, we set up simu-lations for each of the designs with equal trace and gap widths to compare themunder the constraints of a particular fabrication method. This thesis intends to de-velop a design which is possible to be printed on traditional wallpaper substrateswith low cost, bulk printing methods such as screen printing or flexography. Thiswill allow the final product to be affordable from an economic perspective.The focus in this chapter is kept on the center-connected elements. All thestructures are designed to be resonant at the same frequency and their bandwidthsare compared. The only variables which have been changed between these struc-tures are the length of the conducting arms or the lattice arrangements. Before wego in to the discussion of the geometries and the performances, we discuss the de-sign requirements considered for the designs and briefly explain the setup used tosimulate all the structures.3.1 Design requirementsIn designing the surfaces for Wi-Fi blocking applications, a few requirements haveto be brought into consideration. The main constraints which have been chosenin the design process of this thesis are the -20 dB bandwidths of the transmissionresponse, the minimum attenuation level over equivalent Wi-Fi bands, and the di-mensions required for low-cost, bulk manufacture of the design. The specificationfor each of these requirements is discussed in detail in this section.383.1.1 BandwidthThe major design requirement considered in this thesis is to achieve a minimumof -20 dB attenuation in the stop bands. The 2.4 and 5 GHz Wi-Fi bands havefractional bandwidths of 4.08% and 2.59% respectively. These values are the min-imum amount of stop band bandwidth considered necessary for a design to be acandidate for fabrication as a Wi-Fi blocking wallpaper.As discussed in Section 2.3, the transmission response of an FSS deviates fromthe normal incidence, free-standing case due to differences in incident angle, polar-ization, and the presence of dielectric substrates. Hence the design with the widest-20 dB bandwidth is desired in order to ensure robust performance.The -20 dB bandwidth is also the figure of merit used to compare between thedesigns. As will be shown in the simulation results, the designs with the largerbandwidths provide higher attenuation over the Wi-Fi bands. So, the bandwidthcan be used as a good quantitative measure for selecting the best performance outof the different designs.3.1.2 Equivalent Wi-Fi band attenuationA supplemental figure of merit for designs is the minimum attenuation over equiv-alent Wi-Fi bands. This is the minimum attenuation provided by the designs if theWi-Fi bands were placed at its resonance frequency. It is calculated by finding theattenuation over a band of 4.08% at the first resonance frequency and 2.59% at thesecond resonance frequency of the design. A higher value for the minimum at-tenuation is desired, as it will mean a lower transmission of Wi-Fi signals througha fabricated prototype. This figure of merit is only calculated for the dual bandstructures discussed in Chapter 4.393.1.3 Fabrication requirementsThe final design requirement which is considered is the ability to reproduce thedesign using low-cost, bulk printing methods. For this thesis, the requirements areset considering screen printing of the designs using conductive ink on flexible sub-strates. The manufacturer selected for prototype printing, NovaCentrix, requiredwidths of traces and gaps to be above a minimum threshold for accurate printing.Very fine traces may not transfer properly from the screen to the substrate. Alsonarrower lines of ink are prone to being absorbed into the substrate. The trace andgap widths were required to be set equal as well, as the conductive ink can bleedinto the surrounding region during curing of the ink. As a result the dimensions forthe trace and gap widths was set to 500µm for all the simulated designs.3.2 Simulation setupThe COMSOL Multiphysics full wave frequency domain solver is used to simu-late all the structures described in this thesis. To obtain the simulated transmissionthrough a particular design, the FSS is built using perfect electric conductors inthe simulator in the xy-plane, suspended in free space. Though practical structureswill have a dielectric support, as previously discussed the dielectric will influencethe frequency response by introducing a scaling of the resonance frequencies atnormal incidence. As off-normal operation is not considered for the single banddesigns, the free standing FSS structure can be used to compare the bandwidths ofthe different patterns. A single unit cell of the FSS is bounded along the x and yfaces by periodic boundary conditions to emulate the periodicity of the FSS. Inputplane wave ports are placed equidistant from the FSS plane along the z directionfaces of the volume and backed by perfectly matched layer boundaries to absorb40any scattering. The input waves are linearly polarized along the y-axis for simula-tions, unless otherwise noted. The frequency is swept from 1 GHz to 10 GHz witha resolution of 50 MHz steps. The total distance between the input port and FSSplane is 120 mm to ensure that near field evanescent modes (i.e high-order modes)do not influence the measurement of transmission. The formula for the factor ofexponential decay, A, of evanescent modes is given by,A = e−β z,where β is the propagation constant and z is the length of propagation. The propa-gation constant β is given by the relation,β =√(2piD)2−(ωc)2.Here D is the unit cell size and ω is the frequency of the mode [100].From the formulas we can see that the least decaying mode will occur for thelargest value of D or the largest value of ω . All of the unit cells for the structuressimulated in this thesis have a maximum dimension lesser than or equal to 26mm.1 Using the formula for exponential decay, the evanescent modes at the highestfrequency of 10 GHz in the sweep range are decayed by a factor of -126 dB over thedistance of 120 mm. Hence it can be assumed safely that the simulation volumeis large enough to exclude the effects of evanescent modes in the transmissioncalculations. The very large simulation volume ensures that even with a larger unit1The one exception to this is the end-to-end arrangement of the tripole structure presented inSection 3.4.1. This structure has a rectangular unit cell with a dimension of 49.86 mm in the y-direction and 28.05 mm in the x-direction. That being said, grating lobes do not appear over thefrequency of interest since the reduced unit cell has a maximum dimension of 28.05 mm.41cell size, the attenuation of the evanescent fields will be large enough. A schematicdiagram of the simulation volume is shown in Figure 3.1. … … x y z Perfectly matched layer Input Port Perfectly matched layer Perfectly matched layer Perfectly matched layer FSS Plane Perfectly matched layer Perfectly matched layer Perfectly matched layer Periodic Boundary Conditions Perfectly matched layer Perfectly matched layer Perfectly matched layer Output Port Perfectly matched layer Perfectly matched layer Perfectly matched layer Perf l atched layer . . . . . . . . . . Figure 3.1: A schematic representation of the simulation volume used to findthe transmission response of the different structures.3.3 Equivalent circuit modelingThough all the structures in this chapter are simulated using a full wave simulatorto find their frequency response, their transmission properties can also be modelledby a simple equivalent circuit. As was mentioned previously, conductive stripsparallel to the electric field of an incident wave shows inductive behaviour anddielectric gaps between conductors behave like capacitors [14]. Thus, the idealFSS surface can be modeled as an equivalent circuit consisting of inductive andcapacitive components in series as a shunt branch to the input excitation. In thesimulations, the conductors are considered to be ideal with infinite conductivity and42 C1 L1 Input Port (Z0 = η0) Output Port (Z0 = η0) Figure 3.2: The equivalent circuit model for a single resonance FSS structure.the dielectric medium is considered lossless, so the equivalent circuit is composedpurely of reactive elements. The shunt LC branch can be analyzed using generalcircuit analysis and shown to be resonant at a single frequency given by,ω =1L1C1.The fractional bandwidth (FBW) of the equivalent circuit can be related to theinductance and capacitance of the branch through the relation,FBW ∝ η0√C1L1,where η0 is the characteristic impedance of free space, as the simulations are car-ried out in air. The relationship shows that to obtain a large fractional bandwidth,the capacitance must be large or the inductance small.Using this simple model, well informed guesses can be made about the be-haviour of any particular geometry before it is simulated. For example, singleconductors in an electric field will have a lower equivalent capacitance than a twowire system in the same field. Thus the model can be used to predict the perfor-mance of a design by looking at the arrangement of conducting strips and compar-ing the expected relative magnitudes of inductance and capacitance. Conversely,43the equivalent circuit model can be used to justify relative properties of differentstructures by comparing their inductive and capacitive components. The compo-nents can be calculated by using the equations for resonance frequency and band-width and matching them to the values found from simulations. These values canthen be used as a supplemental quantitative value next to the bandwidth for com-paring different structures. We will use the equivalent circuit model throughoutthe analysis of the structures to calculate their equivalent inductive and capacitivecomponents and compare the values. The equivalent circuit model is expanded todual resonant cases in the next chapter and is a strong tool in the design of dualband structures for introducing predictable modifications to the surface to improvethe performances and match requirements.3.4 Non-interleaved structuresThe single resonant structures visited here are the center-connected pole types.Adjacent elements are isolated from each other by dielectric gaps. Each geometrywill have a different transmission response corresponding to their geometric pa-rameters. The lattice arrangement of the elements will also cause same elementsto produce different transmission responses. Two types of lattice arrangements areinvestigated for these types of structures. In one arrangement, they are placed inlattices such that there is no overlap between the poles of individual elements i.e.no element falls within the same area as an adjacent one. These arrangements arediscussed here as non-interleaved structures. They can also be placed in a latticewhere space between individual elements is reduced as far as possible and thereis an overlapping region between the poles of individual elements. The effect ofthese lattice arrangements are discussed in the next section.443.4.1 Non-interleaved tripole designOut of the center-connected multiple pole structures, the tripole has the minimumnumber of arms that can be arranged by rotating the arms with an angle less than180 degrees between them. The three arms are separated from each other by 120degrees. This basic tripole structure can be placed into a non overlapping end-to-end lattice in multiple different ways. Two different arrangements are described inthe following subsections.Rectangular lattice arrangementIn the rectangular lattice arrangement, the tripole elements are placed in a latticewith a lattice constant of 23.64 mm in the horizontal direction and 14.35 mm in thevertical direction. These particular values are chosen as they produce the standardgap widths chosen for this study. In the vertical direction the tip of one elementis 500µm away from the center of the next element. In the horizontal direction,the tripole arms at an angle have a gap of 500µm between them. This set up hasthe elements so that their poles are aligned along the edges of a chevron shape.The lattice setup is shown in Figure 3.3(a). All the trace and gap widths are set avalue of 500µm for the simulations. The pole lengths were set so that the reso-nant frequency is at 5450MHz. As mentioned previously standardizing the tracewidth, gap width, and resonant frequency allows for a comparison between thedifferent lattice arrangements and element geometries under the given fabricationconstraints.The transmission response of the arrangement is shown in Figure 3.3(b). Thestop band has a -20 dB attenuation from 5.35GHz to 5.57GHz, which gives afractional bandwidth of 4.08%. The magnitudes of electric field and magnetic45DwgL(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m0.40.81.21.6(c)A/m50100150200250(d)Figure 3.3: The figure shows the (a) lattice arrangement with the parametersD= 23.64mm and L= 13.36mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the tripole ele-ment arranged with the centers in a rectangular lattice.field intensities at the resonance frequency in the FSS plane are also shown inFigure 3.3(c),(d). It can be noted that the electric field is concentrated in the gaps atthe tip of poles between adjacent elements, while the magnetic field is concentratedalong the pole in the electric field direction at the resonant frequency. This impliesthat the inductance in the equivalent circuit representation arises from the length ofthe conducting poles while the capacitance arises from the coupling between theadjacent elements over the gap between them. The equivalent circuit model canbe used to find the equivalent inductance and capacitance values for the design.46These values can be found by using the equation for the resonance frequency andtuning the inductance value until the bandwidth of the equivalent circuit matchesthe value from the simulation. For this structure the equivalent L and C valuesare 12.7nH and 65.7fF respectively. The equivalent circuit parameters and thegeometric parameters are tabulated and compared later in Section 3.4.4.This lattice arrangement of the elements is not symmetric in the vertical andhorizontal directions, hence it is expected to not be polarization independent. Ifthe electric field were to be aligned along the x-axis, it would encounter differ-ent lengths of conductor than it does when oriented along the y-axis. This wouldchange the equivalent inductance values in the equivalent circuit model leading toa different transmission response than the one shown in Figure 3.3(b).End-to-end lattice arrangementThe rectangular lattice arrangement of the tripoles has a lack of symmetry as it hasdifferent element spacings in the horizontal and vertical directions. The elementscan be packed in a more symmetric lattice by placing them with their poles facingend to end. In this lattice the tip of the pole of one element is placed with a smallgap away from the tip of 5 other elements. To facilitate this arrangement, everyother tripole needs to be flipped along the vertical direction with respect to its ad-jacent element. This ends up having the tripoles with the same vertical orientationbeing placed at 3 non-consecutive vertices of a regular hexagon, while the polesof two adjacent tripoles lie along the sides of a regular rhombus. The center-to-center distance between two tripoles along their poles is equal to 31.74 mm, whilethe center-to-center distance of the nearest neighbors of any tripole is 16.62 mm.These values are selected to keep the gap between arms equal to the standard value.47LDwg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m1.534.56(c)A/m20406080100(d)Figure 3.4: The figure shows the (a) lattice arrangement with the parametersD= 49.86mm and L= 15.62mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the tripole ele-ment arranged with the poles facing end-to-end.The lattice arrangement is shown in Figure 3.4(a). The geometric parameters areagain selected with the standardized values for the trace and gap widths of 500µm,as well as choosing pole length to set the resonant frequency to 5450MHz.The transmission through this lattice arrangement is shown in Figure 3.4(b).The bandwidth of this design is from 5.3GHz to 5.61GHz, which gives a frac-48tional bandwidth of 5.68%. This is an improved value than the rectangular latticearrangement. The reason for the improvement in bandwidth can be inferred fromthe electric and magnetic field intensity plots shown in Figure 3.4(c) and (d) andvalidated through the equivalent circuit model parameters. The magnetic field isstill concentrated along the tripole arms, while the electric field is concentrated inthe gaps between the poles at the resonance frequency. The magnitude of the fieldsremains similar to the end to end lattice case, however now the capacitance is in-creased as there is increased confinement of the fields due to the multiple closelyspaced pole ends. The calculated equivalent circuit parameters give L and C valuesof 8.7nH and 96.3fF respectively.3.4.2 Non-interleaved quadrupole designThe quadrupole is a center-connected multipolar element with four equal lengtharms. The quadrupole has a 90 degree symmetry of rotation, which allows it to havea higher polarization stability compared to the tripole elements. The quadrupolecan however only be placed in the single lattice arrangement where the elementsare placed with the poles end-to-end with the centers of the elements at the verticesof a square. The lattice constant of the arrangement is equal to 23.36 mm, whichis twice the pole length plus the width of the gap equal to 500µm. The surfacearrangement is shown in Figure 3.5(a). The dimensions of the elements are set toobtain a resonant frequency of 5450MHz.The transmission response of the structure is shown in Figure 3.5(b). Thequadrupole design has a stop band with -20 dB attenuation from 5.39GHz to5.54GHz. This corresponds to a fractional bandwidth of 2.74%. Compared to thetripole arrangements this design has a poorer bandwidth performance. This is re-49L D wg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m0.511.52(c)A/m2060100140180(d)Figure 3.5: The figure shows the (a) lattice arrangement with the parametersD= 23.36mm and L= 11.43mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the quadrupoleelement arranged with the poles facing end-to-end.flected in the equivalent circuit parameters, which are calculated to be 20.3nH and42.5fF. The equivalent circuit parameters show that the quadrupole has a higherinductive component compared to the tripole arrangements. When analyzing thestructure the source of this extra inductance is evident though as the quadrupolepresents two pole lengths in the direction of the electric field along the y-axis.This increases the inductive component to almost double the value of the tripole50arrangements. For the rectangular lattice tripole arrangement, we see that there isonly pole length in the y-direction. Again the end-to-end tripole lattice arrange-ment has multiple poles branching out from the end-to-end gap in the y-direction.This produces multiple inductances in parallel to the input excitation causing thetotal equivalent inductance to have a smaller value.Jerusalem cross structureWhile the tripole can be placed in the end-to-end arrangement to confine the elec-tric fields and increase the capacitive component of the equivalent circuit, this isnot possible for the quadrupole structure. In order to increase the bandwidth of thestop band in the quadrupole transmission response, the capacitance of the structurecan be increased by adding hats to the end of the poles of the quadrupole. This cre-ates a structure referred to as the Jerusalem cross in previous works [22]. To give acomparison of the performance of the Jerusalem cross with respect to other struc-tures described here, it was simulated with the standardized trace and gap widthsused for this thesis. The hat was given a length of 4.1 mm. The surface arrange-ment is given in Figure 3.6(a) and the simulated transmission response is given inFigure 3.6(b).The electric and magnetic field intensities in the FSS plane at the resonancefrequency are shown in Figure 3.6(c) and (d). From the electric field intensity,we can see the field is now more confined between the hats on the end of thepoles compared to the end-to-end quadrupole arrangement. We can predict thatthis will increase the capacitive component of the equivalent circuit and the designwill have a higher bandwidth. From the transmission response, we can see that thedesign attenuates an incident wave at the -20 dB level from 5.33GHz to 5.60GHz,51L D wgh(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m1234(c)A/m2060100140180(d)Figure 3.6: The figure shows the (a) lattice arrangement with the parametersD = 17.44mm and L = 8.22mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the Jerusalemcross FSS design.giving a fractional bandwidth of 4.94%. Using the equivalent circuit model, wefind the equivalent inductance and capacitance of the design to be 11.2nH and77.1fF, which is a greater equivalent capacitance than the regular quadrupole caseas expected.523.4.3 Non-interleaved hexapole designThe final non-interleaved element investigated is the hexapole structure with sixpoles. Having six arms gives the element a 60 degree rotational symmetry, whichis a smaller angle of symmetry than the tripole or the quadrupole. This elementcan only be placed in an end to end lattice when not interleaved similar to thequadrupole. In this non-interleaved arrangement the center-to-center distance be-tween elements is 25.94 mm, which is the length of two poles from the elementsand the gap between them. The corresponding surface geometry is shown in Fig-ure 3.7(a). The transmission through a unit cell of the surface is shown in Fig-ure 3.7(b).This structure has a fractional bandwidth of 4.53% at the resonance frequencyof 5450MHz. The -20 dB band starts at 5.33GHz and goes until 5.82GHz. Theequivalent circuit parameters obtained from the equivalent circuit model for thisstructure are 12.1nH and 70.32fF. As can be seen from the electric field and mag-netic field intensity plots shown in Figure 3.7(c),(d), the electric field is localizedbetween the ends of the arms, hence this structure has a similar bandwidth to allthe other structures with this end-to-end coupling mechanism.3.4.4 Comparisons of the non-interleaved designsWe summarize the non-interleaved designs in a tabular form in Table 3.1. The tableincludes the arm lengths and periodicity of each design along with the fractionalbandwidths and equivalent circuit parameters. The trace and gap widths for eachdesign were set to 500µm and the resonant frequency for each design was set to5450 MHz.As can be seen from the data, the end-to-end tripole arrangement has the high-53LDwg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m1.546.59(c)A/m2060100140180(d)Figure 3.7: The figure shows the (a) lattice arrangement with the parametersD= 25.94mm and L= 12.72mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the hexapoleelement placed in an end-to-end lattice.est bandwidth of all the designs. However it has the highest periodicity as well,which means it will be more susceptible to grating lobes appearing at higher fre-quencies of the incident wave. For the end-to-end tripole arrangement, the onsetof grating lobes is theoretically at approximately 6 GHz, while for the other ar-rangements the onset frequency is above 11 GHz. The inductance is in generalproportional to the length of the poles, as can be noticed in the progression fromthe Jerusalem cross to the hexapole and finally the rectangular tripole arrangement.54Table 3.1: A comparison between the performances of the non-interleavedgeometry typesDesignnamePeriodicityDArm lengthLFBW EquivalentinductanceL1EquivalentcapacitanceC1Tripole(rectangular)23.64 mm 13.36mm 4.08% 12.7nH 65.7fFTripole(end-to-end)49.86 mm 15.62 mm 5.68% 8.7nH 96.3fFQuadrupole 23.36 mm 11.43 mm 2.74% 20.3nH 42.5fFJerusalemcross17.44 mm 8.22 mm 4.94% 11.2nH 77.1fFHexapole 25.94 mm 12.72 mm 4.53% 12.1nH 70.32fFThe exceptions are the end-to-end arrangement of the tripoles which has an equiv-alent inductance much less than would be expected for the length of the poles aswell as the quadrupole arrangement which has a much higher inductance. For theend-to-end arrangement, the lower inductance compared to the arm length can beattributed to the presence of the multiple poles close to each other which increasesthe coupling between elements. This also changes the inductive properties of thearm giving rise to the lower equivalent inductance value. The rectangular tripolearrangement as well as the Jerusalem cross have the increased length for couplingthrough the end-to-center and hat-to-hat coupling. However, for the quadrupolethe only coupling mechanism is through the end-to-end coupling between poles,where much of the field can also be lost to fringing effects. Hence it has the lowercapacitance value (and higher inductance value). It can be noted from this analysis,that the presence of larger area for coupling the electric field leads to a higher ca-pacitance and a lower inductance from a smaller periodic structure. The reflection55of larger coupling area corresponding to larger capacitances will also be seen in theinterleaved structures.3.5 Interleaved structuresWe note from the non-interleaved structures, that arrangements of the lattice thatare able to reduce inductance and increase the capacitance perform better in termsof bandwidth. One way in which inductance can be further decreased while in-creasing capacitance at the same time is by interleaving the elements. Interleavingthe elements causes the overlapping edges of the elements to create a parallel twowires system, which has a lower equivalent inductance and higher capacitance thana single wire in an electric field. To demonstrate this effect, in this chapter we inter-leave the tripole, quadrupole, and hexapole elements visited in the previous sectionand compare their transmission responses. The tripole is interleaved by bringingadjacent elements closer to each other leading to a end-to-center arrangement ofpoles, while the quadrupole and hexapole are interleaved by creating an overlapregion between the poles of adjacent elements. Each surface is shown in figuresto illustrate the design and the geometric parameters of the designs along with theperformance metrics are compared at the end of this section.3.5.1 Interleaved tripole designThe tripole is interleaved by bringing adjacent elements closer together so that theirpoles are arranged in a end-to-center configuration. Starting from a center tripole,the center of 3 other identical tripoles are placed after a gap at the end of the armsof the tripole. The center-to-center distance between tripole elements is 15.43 mm.This arrangement continued infinitely leads to the interleaved tripole arrangement.56LDwg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m1.534.56(c)A/m4080120160200(d)Figure 3.8: The figure shows the (a) lattice arrangement with the parametersD= 15.43mm and L= 14.43mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the interleavedtripole design.This greatly increases the packing of elements in the unit cell compared to the non-interleaved structures. This close packing also reduces the length of conductivetrace presented to the incident electric field compared to the non-interleaved de-signs. This should allow the design to have a lower equivalent inductance. The gapbetween the tip of the poles of one element and the centers of the adjacent elementis set to the standard 500µm, as is the width of the conductive traces. The lengthof the tripole arms are chosen to produce a resonance frequency of 5450MHz. The57final surface design is shown in Figure 3.8(a).The simulated design has a much improved bandwidth in the stopband overthe non-interleaved lattice arrangements as expected. The transmission responseof the design is shown in Figure 3.8(b). The electric and magnetic field intensitiesare also shown in Figure 3.8(c) and (d). As with the other cases, the magneticfield is localized along the conductive arms while the electric field is localized tothe gap between the tip of the poles and the center of the adjacent element in thesame direction as the incident electric field. This once again corroborates with ourequivalent circuit modelling of equivalent inductive and capacitive elements. Thefractional bandwidth of this structure is 9.78%, with the -20 dB attenuation bandextending from 5.19GHz to 5.73GHz. The equivalent circuit modelling gives theequivalent inductance and capacitance of the design as 5.4nH and 157.4fF.3.5.2 Interleaved quadrupole designThe interleaved quadrupole can be formed by starting with one element and ap-plying a small horizontal and vertical shift to the adjacent element. The verticalshift is 1 mm, which is just the combined length of a gap and the conducting tracewidth. The horizontal shift is 11.61 mm, which is the width of a gap and halfthe trace width added to the length of one pole of the quadrupole. This has theelements ending up with a center-to-center distance of 11.65 mm. The elementshave then been moved in close together to have a spacing between the centers justslightly larger than one arm length. The spacing between the tip of the pole ofone element and the center of the adjacent element is equal to the standard gapwidth, while also the gap between overlap region of the poles from two adjacentelements is also equal to the standard value. A whole row can be constructed by58LD wg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m0.250.500.751(c)A/m306090120150(d)Figure 3.9: The figure shows the (a) lattice arrangement with the parametersD= 11.65mm and L= 10.86mm, (b) transmission response, (c) electricfield intensity (magnitude) at the resonant frequency, and (d) magneticfield intensity (magnitude) at the resonant frequency for the interleavedquadrupole design.applying the same shifts to adjacent elements. Once a row is completed the imme-diate next vertical row can be constructed by applying a vertical shift of 11.61 mmand a horizontal shift of 1 mm. This finally gives a unit cell shaped like a rhombus,with the centers of elements on the vertices of the rhombus and the arms parallelto the sides. The surface of the interleaved quadrupole surface geometry is givenin Figure 3.9(a).The transmission spectrum for the interleaved quadrupole design is given in59Figure 3.9(b). The fractional bandwidth of the stopband is 12.71% at 5450MHz.This is an approximately 9% increase compared to the non-interleaved quadrupolestructure. The electric and magnetic field intensities are shown in Figure 3.9(c)and (d), these show that the electric field at resonance is now localized in the gapbetween two adjacent arms of elements. This longer coupling length should giveit a higher capacitance than the end-to-end coupling case of the non-interleavedstructures. The equivalent circuit inductance and capacitance parameters as calcu-lated from the equivalent circuit model are 4.3nH and 198.8fF. The capacitanceand inductance have changed by a factor of almost 5 from the non-interleaved case.3.5.3 Interleaved hexapole designThe interleaved hexapole structure can be formed in the same manner as the inter-leaved quadrupole geometry in a single row. A shift which leaves a gap betweeninterleaving arms equal to 500µm is chosen, while the tip of the pole of one el-ement has the same amount of gap with the center of the adjacent element. Thevalue of the horizontal shift in the x-direction between adjacent elements on thesame row thus is equal to 13.22 mm, while the vertical y-direction shift is 1 mm.To create a second row above the first one, a shift which places the center of theadjacent element halfway between the two elements immediately below it has tobe chosen. Using the standard trace and gap widths, the shift between two rowsis 5.74 mm in the horizontal x-direction and 11.94 mm in the vertical y-direction.This leaves the centers of three adjacent hexapoles on the vertices of a equilateraltriangle while three interleaving arms of each nearest neighbor hexapole lies alongthe sides of the equilateral triangle. The center-to-center distance between adja-cent elements is 13.25 mm. The minimum unit cell however is still a rhombus as60LD wg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m0.523.55(c)A/m20457095120(d)Figure 3.10: The figure shows the (a) lattice arrangement with the parame-ters D = 13.25mm and L = 11.22mm, (b) transmission response, (c)electric field intensity (magnitude) at the resonant frequency, and (d)magnetic field intensity (magnitude) at the resonant frequency for theinterleaved hexapole design.in the case of the interleaved quadrupole. The surface geometry for the interleavedhexapole is shown in Figure 3.10(a).The transmission response of the structure is shown in Figure 3.10(b). Thetransmission response has a -20 dB attenuation level starting from 4.91GHz to5.96GHz, giving it a fractional bandwidth of 19.32% at the resonance frequencyof 5450MHz. This is an almost five fold increase in bandwidth over the non-interleaved case. Again to find the source of this increase in bandwidth we can look61at the electric and magnetic field intensities shown in Figure 3.10(c) and (d). Ascan be seen, the electric field is now localized in the gap between the interleavedarms giving it a higher capacitive coupling than the end-to-end coupling of thenon-interleaved structures. The equivalent circuit modelling gives the structure anequivalent inductance and capacitance of 3.0nH and 286.7fF respectively.3.5.4 Comparisons of the interleaved designsA table summarizing the geometric dimensions of the interleaving geometry struc-tures along with their bandwidths and equivalent circuit parameters are given herein Table 3.2. The trace and gap widths of all the structures were set to 500µm forcomparison, while the resonant frequencies of the interleaved structures were setto 5450MHz.The square loop design previously reviewed in Section 2.5.1 is also scaled tothe dimensions used in this thesis and included in the comparison. The design di-mensions are scaled to provide a comparison under the same fabrication constraintsconsidered for the other designs. The surface design and transmission response ofthe square loop FSS is shown in Figure 3.11. The scaled square loop FSS has aunit cell size of 12.44 mm and shows a 11.1% fractional bandwidth in the stopband centered at 5450 MHz. The equivalent circuit parameters corresponding tothe simulated frequency response are 4.90nH and 175.4fF.The data shows that the interleaved arrangements have much higher band-widths than the non-interleaved structures and correspondingly a much higher equiv-alent capacitance. Though the pole lengths are still of similar length, the equivalentinductance of the designs are much less compared to the non-interleaved cases. Asinferred previously, the large coupling area between the side-to-side overlap of the62xyw gD(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)Figure 3.11: The (a) surface design with the length D = 12.44mm, w =0.5mm, and g = 0.5mm and (b) simulated transmission response ofthe square loop FSS design with modified trace and gap widths.arms increases the capacitance as well as decreases the equivalent inductance of aparticular length of conductive trace. The square loop design studied previouslyalso shows this behaviour as there is large edge-to-edge coupling between adjacentelements. The interleaved hexapole is interesting however, as it has a longer armlength, yet shows lesser inductance than expected. Again this can be attributed tothe close presence of the other arms of the hexapole, as they are separated by only60 degrees, compared to 90 degrees for the quadrupole. As the amount of couplingdecreases between the structures and the equivalent capacitance becomes lower,the arm length and periodicity need to increase to keep the resonant frequency at5450 MHz. This however leads to the designs becoming more susceptible to theonset of grating lobes at higher frequencies.63Table 3.2: A comparison between the performances of the interleaved geom-etry typesDesignnamePeriodicityDArm lengthLFBW EquivalentinductanceL1EquivalentcapacitanceC1Interleavedtripole15.43 mm 14.43 mm 9.78% 5.4nH 157.4fFInterleavedquadrupole11.65 mm 10.86 mm 12.71% 4.3nH 198.8fFInterleavedhexapole13.25 mm 11.22 mm 19.32% 3.0nH 286.7fFSquareloop12.44 mm 11.44 mm 11.1% 4.9nH 175.4fFFrom the table it can quite clearly be seen that in terms of fractional bandwidth,the interleaved quadrupole and interleaved hexapole perform far better than otherelements or lattice arrangements. Hence these two designs will be taken as the basefor further modification to produce a second resonant band with a view to produc-ing a design with dual wide stop bands at the Wi-Fi frequencies in the followingchapter.64Chapter 4Dual Band StructuresIn the previous chapter, we investigated the different FSS geometries that producea single resonance and have compared their bandwidths to find the best perform-ing designs. In this chapter, we modify those geometries to produce a dual bandFSS structure. As the interleaved multipolar geometries showed the widest -20dB bandwidths, we will only be investigating methods to produce dual resonancesfrom these base structures. As seen from the field plots at the resonance frequen-cies, the primary resonances occur from currents and voltages through a path alongthe interleaved arms. In producing a second resonance, emphasis will be kept onkeeping the primary resonance as unaltered as possible. Hence, the secondary res-onance path will be built into the empty spaces between the base single resonantgeometries. Having separate paths for the two resonances will ensure that the res-onant frequencies can be tuned independently. This allows the design to be easilymodified to change the ratio between the two resonance frequencies if necessary.The primary resonant element was designed to have rotational symmetry to makeit robust to the incident polarization. The secondary resonance path is similarly65added in such a way that maintains this rotational symmetry of the element. Theequivalent circuit model for the dual resonant structures is also presented in thissection. The analysis of the equivalent circuit gives us a better insight into the op-eration of the two resonances and allows us to make well informed modificationsto the geometry to improve the performance.4.1 Dual resonance equivalent circuit modelIn the single resonant designs, the resonance was modelled by a single shunt LCbranch. To model the second resonance in the dual resonant equivalent circuit an-other shunt LC branch is added. The two resonances occur in the same layer andhence the two shunt branches are connected to the same node. As was discussedpreviously, in the case of multilayer designs, a transmission line section has tobe added between the two branches to model the propagation of waves betweenthe separate layers. However, as the designs considered here all have resonancesgenerated from the same layer, there is no transmission line section between thetwo shunt branches in the equivalent circuit. Also, since the simulations were per-formed using perfect conducting layers in free space, the circuits can be modelledby purely reactive elements. The equivalent circuit model for the dual resonantstructures is shown in Figure 4.1.The shunt branches can be reduced to a single equivalent impedance given byZ(ω) =1Y (ω)=jω2p (ω2−ω2z1)(ω2−ω2z2)ωω2z1ω2z2(C1 +C2)(ω2−ω2p ).Fosters reactance theorem states that the phase of the impedance of purely pas-sive reactive elements increases monotonically with frequency [101]. A conse-66 C1 C2 L1 L2 Input Port (Z0 = η0) Output Port (Z0 = η0) Figure 4.1: The equivalent circuit representation of a dual band single layerFSS.quence of this theorem is that any passive reactive network will have a reactancewith alternating poles and zeros. Since our equivalent circuit model only has purelyreactive elements, its frequency response will have alternating poles and zeros. Thepole and zero frequencies are given byω2z1 =1L1C1ω2z2 =1L2C2,and,ω2p =C1 +C2C1C2(L1 +L2).The pole frequency can also be expressed in terms of the zero frequencies asω2p =ω2z1ω2z2(C1 +C2)ω2z1C1 +ω2z2C2,The position of the zero in the impedance can be further reduced by taking theapproximation, ω2z2 >> ω2z1. Under this approximation it can be shown thatω2p ≈ ω2z1 +1L1C2.In other words the frequency of the pole is mainly dependent on the inductance67in the primary resonance and the capacitance in the secondary resonance for widelyspaced resonances. Since the primary resonance has already been designed to givemaximum bandwidth, we do not want to change the inductance in the primaryresonance. The only way that remains to move the frequency of the pole is bychanging the capacitance in the secondary resonance. This idea will be used forimproving the performance of the secondary resonance in the following sections.Again, as is the case for the single resonant equivalent circuit, the fractionalbandwidth of the stop bands (FBW) is a function of the inductance and capacitancein the branch which can be expressed asFBWn ∝ η0√CnLn.The relation between FBW and the ratio of reactances implies that the band-width of either resonance can be increased by decreasing the inductance or increas-ing the capacitance in the resonant paths. As we are already looking to change thecapacitance in order to move the frequency of the pole, it will have the added effectof changing the bandwidth of the secondary resonance at the same time. Since thefrequency of the pole, second zero, and the bandwidth of the second resonance areall related to the capacitance in the secondary resonance path, these are not inde-pendent quantities. The increase in bandwidth can also be interpreted as the polemoving down in frequency providing further range for attenuation in the stop bandin the second resonance.In the following sections, we present the different dual resonant structuresbased on the interleaved quadrupole and interleaved hexapole base structures. Inthe design of the geometry, the independent dimensions are selected to produce68resonance bands at comparable frequencies. Since the traces will be screen printedon flexible paper type substrates with liquid conductive ink, there is are some lim-itations to the printing process. The traces can bleed into the surrounding regionsand cause shorts between elements. Hence the gap widths need to be kept on thesame order as the trace widths. Again, during screen printing, if the trace widthsare too narrow there is a possibility that there will be breaks in lines due to im-proper screen transfer or due to absorption of ink into the porous paper substrate.The width of conductive traces and gaps are set to 500µm each, keeping thesefabrication requirements in mind.4.2 Interleaved octopoleIn this section we take the interleaved quadrupole single resonant structure andintroduce a second resonance. In order to maintain the rotational symmetry, weadd a second quadrupole with shorter arms on top of the base structure. The secondquadrupole is set at an offset angle with respect to the base structure to have itsarms in the empty spaces between adjacent quadrupole elements. This producesan eight-poled element, which is referred to as the octopole. The periodicity ofthe base structure also has to be increased slightly to accommodate the secondquadrupole without overlapping with the primary arms of the base structure. Thelattice constant was previously 0.75 mm larger than one arm length, however nowit is 3.5 mm larger. This reduces the bandwidth of the primary resonance by asmall amount. Increasing the periodicity while keeping the primary arm lengthsunchanged causes a reduction in overlap. This reduction of overlap in turn causesthe equivalent capacitance of the primary resonance to decrease leading to decreasein the primary bandwidth. Also as will be shown in the following sections, the69octopole by itself does not have the required transmission response needed to blockWi-Fi. Hence some further modifications will be made in to design structures withan improved bandwidth. The base octopole geometry and the modified structuresare discussed in the following subsections.4.2.1 Interleaved octopole base designThe element in the base octopole design has eight arms of alternating length. Itis built from the base interleaved quadrupole from Section 3.5.2 by adding thesecond quadrupole on top of it with an offset of 45 degrees. The element stillmaintains rotational symmetry. The geometric parameters of the design are givenin Table 4.1 corresponding to the dimensions shown in Figure 4.2(a). The trans-mission response of the design is shown in Figure 4.2(b).Table 4.1: Geometric parameters of the base octopole designP1 P2 w g D12 mm 9 mm 0.5 mm 0.5 mm 15.5 mmAs can be seen from the transmission response, the position of the pole fre-quency is closer to the secondary resonance. Also the bandwidth of the secondresonance is also very narrow, barely covering the extent of the second Wi-Fi band.Ideally the pole frequency would be closer to midway between the resonances, thiswould allow the second resonance band to have a higher bandwidth as well. Thisdesign has a primary bandwidth of 10.1% at 4.55 GHz and a secondary bandwidthof 2.75% at 9.1 GHz. We can calculate the attenuation on the Wi-Fi bands byconsidering a band of equivalent bandwidth within the stop bands. For equivalentWi-Fi bands, the base interleaved octopole design shows a minimum attenuation70(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m0.30.60.91.2(c)A/m10306090120(d)x104 V/m1.534.56(e)A/m60120180240300(f)Figure 4.2: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the base octopole FSSdesign.71of -27.7 dB across the 1st Wi-Fi band and -20.68 dB across the second Wi-Fi bandat normal incidence.The bandwidths can also be explained in terms of the equivalent circuit con-cepts. The capacitance in the primary resonance band arises from the edge-to-edgeoverlap of the major arms. This produces a strong field coupling and contributesto the large bandwidth. However for the second resonance band, the capacitanceis generated from the in plane end-to-end coupling of the minor arms. The electricfield at the two resonance frequencies is shown in Figure 4.2(c)-(f). At the primaryresonance the in plane electric field is strongest in the edge-to-edge overlap regionbetween the major arms. At the secondary resonance, the field is strongest betweenthe ends of the minor arms. While the primary resonance field is highly localized,the secondary resonance fields are not and there is likely to be a lot of fringingfields which do not directly contribute to the equivalent capacitance. This is theprobable cause for the lower capacitance in the secondary resonance circuit. Theequivalent circuit parameters can be calculated by using the resonance frequen-cies and bandwidths in the equations obtained for the equivalent circuit model.Since the equivalent circuit for the dual resonant designs have 4 components, weneed 4 equations to solve them. Three equations can be found from the two reso-nance frequencies and pole frequency. The value of the primary inductance is thentuned to match the equivalent circuit bandwidth to that of the simulated design.Using this method, the base interleaved octopole design has calculated equivalentcapacitances and inductances of L1 = 6.5nH, L2 = 11.12nH, C1 = 188.5fF, andC2 = 27.66fF.One important property of the dual resonant structures studied in this thesis isthe independent tunability of the resonances. This can be shown by doing a para-72Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P2 = 10 mmP2 = 9.5 mmP2 = 9 mm(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P1 = 11 mmP1 = 11.5 mmP1 = 12 mm(b)Figure 4.3: Independent tuning of the resonance frequencies of the octopoleshown through (a) a parametric sweep of the secondary arm length and(b) a parametric sweep of the primary arm length.metric sweep of the primary and secondary arm lengths as shown in Figure 4.3for the base octopole structure. In Figure 4.3(a), the transmission response is un-changed in the primary resonance, however the secondary resonance shifts as afunction of the secondary arm length with longer arm lengths resonating at a lowerfrequency and shorter arm lengths resonating at a higher frequency. Independenttuning can also be shown for the primary resonance by modifying the length of theprimary arm while keeping the secondary arm length constant, as in Figure 4.3(b).We can define a sensitivity parameter to quantify the independence of tuning be-tween the two resonance frequencies. We define the sensitivity parameter σmn asthe ratio between the percentage change in resonance m to the percentage changein resonance n, when resonance n is being tuned. As an equation we can write thisout asσmn =∆ fm/ fm∆ fn/ fn∣∣∣∆Ln.For the base interleaved octopole design, we obtain values of σ12 = 0.041%/%73and σ21 = 0.038%/%. This shows that the non-tuning resonance shifts by less than1% in frequency when the tuning resonance is shifted by 20% in frequency.4.2.2 Interleaved octopole with intermediate crossA higher capacitance is needed in the secondary resonance path in order to pro-duce a larger bandwidth in the second resonance band and move the pole frequencydown to a lower frequency. To convert the end-to-end coupling of the minor armsto an edge-to-edge coupling, we introduce a quadrupole to the space between theminor arms. This leads to a larger overlap region between the minor arms and theinner quadrupole, causing a higher intensity in the electric field and tighter cou-pling. This in turn produces a higher capacitance in the secondary resonance andsimultaneously increases the bandwidth in the second resonance band and push theposition of the pole down in frequency. The values of the geometric dimensionscorresponding to the design of Figure 4.4(a) are given in Table 4.2. The transmis-sion response of this structure is shown in Figure 4.4(b) along with the electric fieldintensities at both the resonant frequencies.Table 4.2: Geometric parameters of the octopole with intermediate cross de-signP1 P2 w g t D12.48 mm 7.2 mm 0.5 mm 0.5 mm 6.24 mm 16.01 mmWe note from the transmission response that the bandwidth in the second res-onance has doubled when compared to the base design. The primary band hasa change in bandwidth of -0.4%. The bandwidths of the primary and secondarybands are now 9.7% at 4.25 GHz and 5.5% at 9.4 GHz respectively. These band-74P1DtwgP2(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m2468(c)A/m104580115150(d)x104 V/m0.523.55(e)A/m2060100140180(f)Figure 4.4: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the octopole with inter-mediate cross FSS design.75widths are sufficient to block the Wi-Fi bands up to a minimum attenuation level of-27.13 dB in the 1st band and -25.65 dB in the 2nd band for normal incident waves.The pole position has moved down in frequency by 760 MHz, as expected from anincrease in capacitance. The electric field plot also shows the increased localiza-tion in intensity between overlap of the minor arms and the inner quadrupole arms.Whereas for the base octopole design, the electric field is localized at the tip of thearms, here it has a distribution similar to a parallel plate capacitor. The end-to-endcoupling can possibly have a lot of fringing fields, which makes it difficult to pre-dict the equivalent capacitance in the design. The edge-to-edge coupling makesthe capacitive behaviour of the design much more predictable. The interleaved oc-topole with intermediate cross has equivalent circuit parameters of L1 = 7.4nH,L2 = 5.63nH, C1 = 189.2fF, and C2 = 50.76fF.The off-normal behaviour of the FSS also has to be investigated to judge itsefficiency in operating in practical conditions as a Wi-Fi blocking wallpaper. Theoff-normal transmission response is shown in Figure 4.5.The transmission response of the design is simulated at 30 degree and 60 de-gree incident angles for both TE and TM polarizations. At the off-normal incidentconditions, there is considerable shift in the resonance frequencies of the FSS. Thechange in response is different for the TE and TM off-normal cases as well. Theprimary band has a comparatively lesser change, with a 50 MHz shift in resonancefrequency at the 60 degree incident angle for TE polarization and 250 MHz shiftfor 60 degree incidence at TM polarization. The secondary resonance undergoesa more visible change at TM incidence though, with the stop band breaking intothree separate resonances, the deepest of which occurs at a frequency 650 MHzbelow the normal incidence resonance frequency.76Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50TEM (0 degree)TE (30 degree)TE (60 degree)TM (30 degree)TM (60 degree)Figure 4.5: The off-normal transmission response for the octopole with inter-mediate cross design at 30 degrees and 60 degrees for both TE and TMpolarization.This change in resonance frequencies can be attributed to the change in electri-cal dimensions of the traces for off-normal incidence. For TE off-normal incidence,the electric field is normal to the trace directions and there is no major change to theelectrical dimensions. Hence the resonance frequency and bandwidths are almostunchanged. However for the TM incidence, there is an electric field componentin the direction of the traces. This causes the electrical dimensions apparent tothe electric field to change with the incidence angle. The magnitude of the elec-tric field in the direction of the traces also changes with the change in incidentangle, which causes the off-normal TM polarization response of the design to de-viate further from the normal incidence response. We can calculate the minimum77attenuation levels for the equivalent Wi-Fi bands from the off-normal simulations.For the TE polarization, the interleaved octopole with intermediate cross providesa minimum attenuation of -26.75 dB and -23.74 dB across the two bands at 30degree incidence. At 60 degree incidence the minimum attenuation levels are -28dB and -31.17 dB. For TM incidence the performance is much degraded though.At 30 degree incidence the design provides a minimum attenuation of -20.42 dBin the first band but a maximum of -9.03 dB in the second band. For 60 degreeincidence the performance deteriorates further providing a minimum attenuationof -11.08 dB in the first band and a maximum of -0.53 dB in the second band. Thisshows that the second Wi-Fi band will be allowed to pass through this design withminimal attenuation for the TM large angle off-normal incidence.4.2.3 Interleaved octopole with forked crossWhile the intermediate cross with the octopole produces a large enough bandwidthto cover both Wi-Fi bands at normal incidence, the drift in resonant frequencyduring off-normal incidence shows the necessity for a larger bandwidth. The in-termediate cross increased the capacitance over the base octopole design, howeverto get a larger bandwidth a higher capacitance is needed. One way of increasingcapacitance in planar elements such as waveguides is by producing interdigitatedcapacitors. To use this technique in the secondary resonance, we can use forkedcross intermediate structures instead of the basic cross of same conductor width.The forked cross will have a base thickness greater than the thickness of the oc-topole traces. However the end of the cross is forked to accommodate the overlapwith the minor arm of the octopole. This produces an interdigitated structure forthe capacitance in the secondary resonance path, increasing the equivalent capaci-78tance value and increasing the bandwidth of the secondary resonance. The valuesof the geometric parameters are given in Table 4.3. The simulated transmissionresponse is shown in Figure 4.6(b).Table 4.3: Geometric parameters of the octopole with forked cross designP1 P2 w g t wt D12 mm 6.24 mm 0.5 mm 0.5 mm 7.2 mm 2.5 mm 16.01 mmThe response shows an increase of 500 MHz bandwidth in the secondary stopband over the non interdigitated structure of the previous subsection, to produce afractional bandwidth of 10.75% at 9.3 GHz in the secondary resonance band. Thebandwidth in the primary band changes from 9.7% at 4.25 GHz for the non-forkedcross to 8.1% at 4.5 GHz for the forked cross, while the pole frequency also shiftsdown by 990 MHz. There is a gradual loss of bandwidth in the primary bandas the pole is shifted down in frequency and the secondary bandwidth becomeslarger, however this is an acceptable trade-off, as the primary band has already beenoptimized to have a bandwidth much higher than that of the primary Wi-Fi band.As a result the minimum attenuation levels do not change much from the previousdesign in the primary stop band. This design produces minimum attenuation levelsof -25.13 dB and -31.23 dB across two equivalent Wi-Fi bands at normal incidence.The equivalent circuit parameters for this design are calculated to be L1 = 8.6nH,L2 = 2.64nH, C1 = 145.3fF, and C2 = 111.3fF.We can also show the independent tunability for the interleaved octopole withforked cross intermediate structure by performing parametric sweeps of the armlengths. The corresponding transmission responses are shown in Figure 4.7. The79P1Dt wgP2wt(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x105 V/m0.30.60.91.2(c)A/m4080120160200(d)x104 V/m1234(e)A/m10356085110(f)Figure 4.6: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the octopole with forkedcross FSS design.80Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P2 = 7.2 mmP2 = 6.72 mmP2 = 6.24 mm(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P1 = 11.04 mmP1 = 11.52 mmP1 = 12 mm(b)Figure 4.7: Independent tuning of the resonance frequencies of the inter-leaved octopole with forked cross shown through (a) a parametric sweepof the secondary arm length and (b) a parametric sweep of the primaryarm length.calculated sensitivity parameters for this design are σ12 = 0.062%/% and σ21 =0.051%/%, showing that the level of independence of tuning the resonance fre-quencies does not change much from the base interleaved octopole design. Theproperty of independent tuning is retained through out the designs even after theaddition of the intermediate cross.The off-normal response of the structure is also simulated and it is shown inFigure 4.8. We can see that both the primary and secondary resonance frequenciesshift by 50 MHz at the 60 degree TE incidence. The bandwidth also increasesfor this polarization and incident angle. The minimum attenuation levels do notchange much from the normal incidence case either. At the 30 degree incidence theattenuation is a minimum of -25.4 dB and -33.51 dB across the two Wi-Fi bands.For the 60 degree incidence the levels are at -25.15 dB and -37.02 dB. For theTM polarization, the primary band shifts by 200 MHz, which is an improvementover the intermediate cross design. However, the secondary band still undergoes81Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50TEM (0 degree)TE (30 degree)TE (60 degree)TM (30 degree)TM (60 degree)Figure 4.8: The off-normal transmission response for the octopole withforked cross design at 30 degrees and 60 degrees for both TE and TMpolarization.splitting into three distinct bands, with the band closest to the resonance shifting by100 MHz from the resonance frequency at the normal incidence. The equivalentWi-Fi band minimum attenuation levels are -19.23 dB and -16.29 dB for the twobands at 30 degree incidence. At 60 degree incidence are a minimum of -10.63 dBand -4.12 dB over the first and second band respectively, while the maximum valuesare -18.34 dB and -26.03 dB. It can be noted that while the performance for theTM incidence has still degraded, it has a better performance in terms of minimumand maximum attenuation levels than the interleaved octopole with intermediatetripole.In practical applications of a design, the waves can be incident at any angle. In82order to efficiently block the waves of the targeted frequency, the stop bands shouldnot shift so much that there is a large decrease in attenuation. From the data forthe off-normal response of this design at TE polarization, it can be noted that theattenuation is still at a comparable level to the normal incident case for the Wi-Fibands. However, the attenuation at TM incidence can be seen to be quite smallerthan the other cases of polarization and incident angle. If the low attenuation of theTM off-normal incidence or the shift in resonance frequency can be solved, thisdesign shows promise to be a candidate for a final prototype of a Wi-Fi blockingwallpaper.4.3 Interleaved hexapoleThe quadrupole is a good base for the dual resonant structures as it has a largerempty space between the base structure to introduce the second resonant path. Interms of performance however the hexapole produces a better primary resonancebandwidth. So using the same technique of superimposing a second hexapole ontop of the base design with an offset rotation, we can create a double hexapolesurface geometry capable of producing a double resonance. The space between theelements is much less compared to the quadrupole geometry though. However, thereduced space for incorporating a secondary resonance path is a small drawbackfor the improved performance. The double hexapole based dual resonant structuresare described in the following subsections.4.3.1 Interleaved double hexapole base designThe base double hexapole design has a second hexapole with shorter arms imposedon top of the primary interleaved hexapole design shown in Section 3.5.3. The pe-83Table 4.4: Geometric parameters of the base double hexapole designP1 P2 w g D13.2 mm 9.35 mm 0.5 mm 0.5 mm 16.73 mmriodicity of the unit cell has to be increased by a small amount over the primaryinterleaved hexapole design as increased space is needed to fit the second hexapoleand ensure it does not produce a short to the primary arm of the adjacent ele-ment. For the interleaved hexapole the periodicity was 2 mm larger than the polelength, to accommodate the second hexapole the periodicity is now 3.5 mm largerthan one pole length. Increasing the periodicity while keeping the arm lengths un-changed causes the overlap between the two adjacent arms to decrease. This leadsto some reduction in bandwidth in the primary band for the double hexapole de-sign, as the decrease in overlap between the arms reduces the capacitance in the pri-mary resonance equivalent circuit. The secondary resonance is produced throughthe end-to-end coupling of the minor arms, which produces a weaker capacitancecompared to the edge-to-edge coupling. As a result the secondary bandwidth islower than the primary bandwidth. Also the position of the pole is closer to thesecondary resonance frequency, showing the lower capacitance in the secondaryequivalent circuit. The equivalent circuit parameters for the base interleaved dou-ble hexapole design are calculated to be L1 = 3.4nH, L2 = 14.26nH, C1 = 391.4fF,and C2 = 19.72fF.The surface design is shown in Figure 4.9(a) and the corresponding geometricparameters are summarized in Table 4.4. The transmission response of the geome-try is plotted in Figure 4.9(b). The weak end to end coupling capacitance can alsobe seen in the field plots shown in Figure 4.9(c)-(f). The bandwidths are 19.4% at84xyP1DP2wg(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m1234(c)A/m20406080100(d)x104 V/m2.557.510(e)A/m60130200270340(f)Figure 4.9: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (magni-tude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f) mag-netic field intensity (magnitude) at ωz2 for the base interleaved doublehexapole FSS design.854.35 GHz and 1.7% at 9.49 GHz in the primary and secondary band respectively.The pole between the zeros is located at 8.74 GHz. The design provides minimumattenuation levels of -32.82 dB and -17.18 dB to the equivalent Wi-Fi bands.When compared to the base octopole design, this is a higher bandwidth by9.3% in the primary stop band, but a lower bandwidth by 1.05% in the secondarystop band. However, the bandwidth in the secondary stop band can be increasedthrough techniques previously used to increase the second resonance bandwidthfor the interleaved octopole structures. As was notable in that case, increasing thebandwidth in the secondary bandwidth caused the primary bandwidth to decreaseby a small amount. In this case, a similar trend is expected. Yet as the primarybandwidth is much larger than the interleaved octopole, an overall improvement inperformance should occur.Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P2 = 9.35 mmP2 = 9.075 mmP2 = 8.8 mm(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P1 = 13.2 mmP1 = 12.65 mmP1 = 12.1 mm(b)Figure 4.10: Independent tuning of the resonance frequencies of the inter-leaved double hexapole shown through (a) a parametric sweep of thesecondary arm length and (b) a parametric sweep of the primary armlength.As was the case with the base octopole structure, we also show the indepen-dent tunability of the resonance frequencies here by doing a parametric sweep of86the length of the primary and secondary arms. The transmission response of theparametric sweeps are shown in Figure 4.10. As can be seen the secondary reso-nant frequency varies as a function of the length of the secondary arm, while theprimary resonance remains relatively stable in position and vice-versa. The sensi-tivity parameters as calculated for the double hexapole design are σ12 = 0.041%/%and σ21 = 0.024%/%. Again we can see that the tuning is fairly independent, witha 20% change in the tuning frequency causing a less than 1% change in the non-tuning frequency.4.3.2 Interleaved double hexapole with intermediate tripoleA comparison with the bandwidths of the Wi-Fi bands shows that the base doublehexapole design would be unsuitable for blocking the secondary Wi-Fi band, sincethe bandwidth of the second resonance band is insufficient to cover the 5.8 GHzband at normal incidence to the minimum -20 dB level we have defined for thisthesis. Hence, similar to the improvements to the base octopole design, we add anintermediate tripole to the double hexapole design. The tripole is added to the spacebetween the base elements to increase edge-to-edge coupling of the electric field inthe secondary resonance path. The surface design is shown in Figure 4.11(a) andthe geometric parameters labelled are summarized in Table 4.5. As in the case withthe octopole with intermediate cross, the double hexapole with intermediate tripolealso shows a much wider bandwidth in the second resonant band. The simulatedtransmission response for the surface geometry is shown in Figure 4.11(b). Thesecondary resonance bandwidth is now at 4.1% at 9.35 GHz which is an increaseof 2.4% over the base design. The primary resonance has a bandwidth of 18.7%at 4.45 GHz, which is a decrease of 0.7% from the base design. When compared87Table 4.5: Geometric parameters of the double hexapole with intermediatetripole designP1 P2 w g t D12.9 mm 7.525 mm 0.5 mm 0.5 mm 4.8 mm 16.43 mmto the octopole with the intermediate cross, this design has a 9% higher bandwidthin the primary resonance band, but has a 1.1% lesser bandwidth in the secondaryresonance band. the position of the zero is also shifted down by 790 MHz from thebase design. The interleaved hexapole with intermediate tripole design providesa minimum attenuation of -34.16 dB and -23.36 dB across two equivalent Wi-Fibands at normal incidence.The simulated field plots are shown in Figure 4.11(c)-(f). The increased lo-calization of coupling between the minor arms and the intermediate tripole can beseen in the electric field plot at the second resonance frequency. This overlappingarrangement of double hexapole secondary arms and the intermediate tripoles pro-duces a capacitance which is similar in nature to a parallel plate capacitor, whichin turn increases the equivalent capacitance from the fringing field capacitance asobserved in the base double hexapole design. The equivalent circuit parameters forthis design are L1 = 3.6nH, L2 = 6.46nH, C1 = 355.8fF, and C2 = 44.88fF.When compared to the percent bandwidths of the Wi-Fi spectrum, we can seethat at normal incidence this design attenuates both Wi-Fi bands at a minimum -20 dB level. The design was fabricated and tested to verify the bandwidths andanalyze the operation of the design with the presence of the substrate. The detailsof the fabrication process and experimental analysis is described in Chapter 5.The off-normal characterization is important if the design is to be consideredas a possible candidate for a working prototype. The off-normal performance of88P1DtwgP2(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m0.523.55(c)A/m104070100130(d)x104 V/m2.557.510(e)A/m3065100135170(f)Figure 4.11: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the double hexapolewith intermediate tripole FSS design.89Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50TEM (0 degree)TE (30 degree)TE (60 degree)TM (30 degree)TM (60 degree)Figure 4.12: The off-normal transmission response for the double hexapolewith intermediate tripole design at 30 degrees and 60 degrees for bothTE and TM polarization.this structure is shown in Figure 4.12.For both the TE and TM polarizations, the primary resonance is quite stable upto 60 degrees incidence with a 50 MHz shift in the resonance frequency. The band-width increases for the TE polarization at 60 degrees incident angle. Though thereis a slight splitting of the band at higher frequencies, it occurs below the -20 dBattenuation level. The second resonance is fairly stable at 60 degrees TE incidence,with a shift of 100 MHz and an increase in bandwidth. However, the 60 degreeTM incidence shows a large deviation in operation, with no stop band up to the-20 dB attenuation magnitude. For 30 degree TM incidence, the secondary reso-nance shifts by 350 MHz and sees a splitting of the band into 2 distinct stop bands,90similar to the case of the Interleaved octopole with intermediate crosses. In termsof attenuation across equivalent Wi-Fi bands, the interleaved double hexapole withintermediate tripoles performs well for the TE polarization. The minimum atten-uation levels across the two bands are -36.02 dB and -22.28 dB for a 30 degreeincident angle, while it is -33.78 dB and -22.04 dB for a 60 degree incident angle.For the TM polarization, the performance is maintained at the 30 degree incidentangle, providing a minimum attenuation level of -30.95 dB in the first band and amaximum attenuation of -15.65 in the second band. However the performance isdegraded significantly for the 60 degree incident angle with a minimum attenuationof -22.46 dB in the first band and a maximum attenuation of -1.68 dB in the secondband. The small attenuation in the second band shows that the design will allowWi-Fi signals with TM polarization to pass through at the high incidence angle.4.3.3 Interleaved double hexapole with forked tripoleThough the double hexapole with intermediate tripoles has a sufficient rejectionbandwidth to suppress both the Wi-Fi bands to a minimum -20 dB level, furtherimprovements can be made by including the interdigitated overlap in the interme-diate structure. The interdigitation is achieved by increasing the trace widths of theintermediate tripole and creating notches at the end to accommodate the overlapwith the minor hexapole arms. The width of the trace of the tripole is selected sothat the gaps and trace widths in the overlap is equal to the standard throughoutthe rest of the design. The geometric parameters are given in Table 4.6 and thecorresponding lengths are labelled in the surface design shown in Figure 4.13(a).91Table 4.6: Geometric parameters of the double hexapole with forked tripoledesignP1 P2 w g t wt D13.2 mm 7.7 mm 0.5 mm 0.5 mm 4.675 mm 2.5 mm 16.73 mmThe transmission response of the structure as well as the field plots in planeare shown in Figure 4.13(b)-(f). We can see the bandwidths in the stop bandshave changed to 18.5% at 4.32 GHz and 4.9% at 9.23 GHz in the primary andsecondary stop bands respectively. The field is now strongly concentrated in theoverlap between the minor arm and interdigitated tripole structure at the second res-onance frequency. The zero position is also further pushed down in frequency from7.95 GHz in the previous structure to 7.45 GHz in this structure. The interleaveddouble hexapole with forked tripole intermediate structure provides a minimumattenuation level of -33.06 dB and -24.85 dB to equivalent Wi-Fi bands at nor-mal incidence. The design has equivalent circuit parameters equal to L1 = 3.7nH,L2 = 4.62nH, C1 = 367.7fF, and C2 = 64.5fF.The off-normal response is simulated and plotted in Figure 4.14. The simula-tion is done for TE and TM polarization at 30 and 60 degree incidence angles. Theprimary resonance is robust for this design, with the resonance frequency shiftingless than 25 MHz for both polarizations at the 60 degree incidence. The secondresonance is fairly stable for the TE incidence, with a shift of 100 MHz in the res-onance frequency. For the TM resonance a splitting of the stop band occurs at thehigh incidence angles, however the stop band is still evident at the 30 degree inci-dence with a shift of 400 MHz in the resonance frequency. In terms of attenuationlevels of the Wi-Fi bands, the TE polarized waves undergo a minimum attenuation92P1DtwgP2 wt(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m0.51.52.53.5(c)A/m1030507090(d)x104 V/m0.523.55(e)A/m104070100130(f)Figure 4.13: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the double hexapolewith forked tripole FSS design.93Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50TEM (0 degree)TE (30 degree)TE (60 degree)TM (30 degree)TM (60 degree)Figure 4.14: The off-normal transmission response for the double hexapolewith forked tripole design at 30 degrees and 60 degrees for both TEand TM polarization.of -35.04 dB and -23.22 dB in the two stop bands for 30 degree incidence. Atthe 60 degree incident angle the minimum attenuation is -36.19 dB and -25.5 dBacross the two bands. For TM polarized waves at 30 degree incidence, there is aminimum attenuation of -30.14 dB over the first band, however the second bandhas a maximum attenuation of -9.53 dB. The performance suffers further at the 60degree wave incidence, with a minimum attenuation of -20.26 in the first band anda maximum attenuation of -1.7 dB in the second band. Clearly the design doesnot provide high attenuation for incident waves at higher incident angles with TMpolarization.When compared to the analogous octopole structure, we can see that the double94hexapole based structure has the larger bandwidth in the primary resonance. Thedouble hexapole with forked tripole has and increase in bandwidth of 10% overthe octopole with forked cross. For the secondary resonance, the double hexapolebased structures have a slightly smaller bandwidth, however improvement tech-niques such as adding the tripole and interdigitating the tripole allows the band toencompass the bandwidth required to attenuate both the Wi-Fi bands to a level of-20 dB.4.3.4 Interdigitated double hexapoleWhile the interdigitated intermediate tripole increases the bandwidth significantlyenough to cover both Wi-Fi bands, this idea can be extended to the base struc-tures to increase the stop band bandwidth even further. By interdigitating the basehexapole structure, the packing of the structure can be brought much closer. Thesecond hexapole can also be rotated symmetrically at an angle of 30 degrees, re-sulting in a double hexapole with a 30 degree angle between each pair of arms.The corresponding surface geometry is shown in Figure 4.15(a) and the labelledgeometric parameters are listed in Table 4.7.Table 4.7: Geometric parameters of the interdigitated double hexapole designP1 P2 w g t wt D15.6 mm 9.75 mm 0.5 mm 0.5 mm 6.63 mm 2.5 mm 22.75 mmIf we look into this geometry, we note that the capacitance should be much in-creased along the primary arms compared to the offset interleaved double hexapoleof the previous subsections. Also as the arms are thicker in the non-overlappingregions, they will have lesser inductance. Both of these factors together will lead95P1 DtwgP2 wt(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)x104 V/m0.751.502.253(c)A/m1020304050(d)x104 V/m0.51.52.53.5(e)A/m1020304050(f)Figure 4.15: The (a) surface design, (b) transmission response, (c) electricfield intensity (magnitude) at ωz1, (d) magnetic field intensity (mag-nitude) at ωz1, (e) electric field intensity (magnitude) at ωz2, and (f)magnetic field intensity (magnitude) at ωz2 for the interdigitated dou-ble hexapole FSS design.96to a much increased bandwidth in the first resonant band.For the second resonant path the arms of the second hexapole are made widerthan the regular width, with the overlapping regions having gaps and trace widthsequal to the standard measurements. The inner tripole has the same increased widthas well, leading to further symmetry in the design. These factors also increase thecapacitance and decrease the inductance in the secondary resonance.If we look at the transmission response shown in Table 4.7(a), we can see thatthe increase in the bandwidths is quite large compared to the increase between theother iterations of the interleaved double hexapole design. The primary resonancenow has a bandwidth of 24.75% at 4.25 GHz, which is an increase of 6.25% in frac-tional bandwidth over the interleaved double hexapole structure with forked inter-mediate tripole. The secondary resonance has a bandwidth of 10.5% at 9.08 GHz,an increase of 5.6% in fractional bandwidth over the previous structure. The de-sign shows a minimum attenuation level of -34.1 dB and -29.24 dB over equivalentWi-Fi bands. A similar interdigitation was not shown in the octopole structureshowever, since each double hexapole structure has a better performance comparedto its octopole counterpart in the primary resonance, it can be assumed that thisstructure will have a better bandwidth as well.The increased localization of the electric fields can be seen from the field plotsshow in Figure 4.15(c)-(f). The electric and magnetic fields are localized in theoverlapping regions for both the primary and secondary resonant paths at theircorresponding resonant frequencies. The design has equivalent circuit parametersof L1 = 2.9nH, L2 = 2.59nH, C1 = 487.9fF, and C2 = 118.9fF.We can show the independent tunability of the interdigitated double hexapoledesign by carrying out parametric sweeps of the primary and secondary arm lengths.97Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P2 = 11.05 mmP2 = 10.4 mmP2 = 9.75 mm(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Tranmission (dB)-45-40-35-30-25-20-15-10-50P1 = 14.3 mmP1 = 14.95 mmP1 = 15.6 mm(b)Figure 4.16: Independent tuning of the resonance frequencies of the inter-digitated double hexapole shown through (a) a parametric sweep ofthe secondary arm length and (b) a parametric sweep of the primaryarm length.Changing the primary arm length while keeping all other parameters equal causesthe primary resonance frequency to change correspondingly. While the same canbe shown for tuning the secondary resonance frequency through the secondaryarm length. The parametric sweep results are shown in Figure 4.16. The calculatedsensitivity values for the interdigitated double hexapole design are σ12 = 0.41%/%and σ21 = 0.09%/%. The values show that the primary resonance is slightly moreindependent to tuning than the secondary. The primary resonant frequency canbe tuned up to 10%, while the secondary resonant frequency undergoes less than1% of change. In case of tuning the secondary resonance frequency however, theprimary resonance frequency shifts by about 1% for every 3% change in the sec-ondary.Figure 4.17 shows the off-normal incidence performance of the designed struc-ture at TE and TM polarization at 30 degree and 60 degree angles of incidence.The interdigitated double hexapole has a fairly robust response in the primary98Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50TEM (0 degree)TE (30 degree)TE (60 degree)TM (30 degree)TM (60 degree)Figure 4.17: The off-normal transmission response for the interdigitated dou-ble hexapole design at 30 degrees and 60 degrees for both TE and TMpolarization.stop band. For the TE 60 degree off-normal incidence, the primary resonant fre-quency shifts by 50 MHz. For the TM 60 degree incidence, the resonance fre-quency shifts by 200 MHz. The secondary resonance is again less robust than theprimary resonance. However, for the interdigitated double hexapole design, thesplitting of the band is less prominent than the other designs. At the 30 degree TEincidence, the resonant frequency shifts by less than 50 MHz. At the 60 degreeTE incidence, a splitting of the band is noticeable, however the -20 dB bandwidthremains over the same frequency range. For the TM incidences, the higher incidentangle causes the performance to deteriorate quite significantly. However at the 30degree incidence, there is a shift of 200 MHz. We can also calculate the attenuation99over equivalent Wi-Fi bands for the off-normal incidence. For TE polarization at30 degrees, the interdigitated double hexapole design provides a minimum attenu-ation of -35.94 dB and -30.95 dB over the two Wi-Fi bands. At a 60 degree obliqueincidence, the corresponding attenuation levels are -39.88 dB and -20.84 dB. ForTM polarization, the minimum attenuation levels are -27.55 dB and -17.62 dB for30 degree incident angle. For the 60 degree incident angle, the interdigitated dou-ble hexapole design provides a maximum of -26.34 dB and -7.52 dB attenuationover the two Wi-Fi bands.4.4 Comparisons of the dual band designsA table comparing the performance of the different dual band FSS designs is pre-sented in Table 4.8. The table shows the fractional bandwidths of the designsin their two stop bands along with the resonance frequency, the equivalent cir-cuit components of the designs, and the minimum attenuation levels achievable inequivalent Wi-Fi bands at normal, TE 60 degree, and TM 60 degree incidence.The metapaper design studied in Section 2.5.2 and the quarter ring design stud-ied in Section 2.5.3 are also scaled in dimensions and added to the comparison here.These dual-band designs are simulated using the scaled dimensions to provide acomparison under the fabrication constraints specified in this thesis. The scaledmetapaper design is shown in Figure 4.18 along with its transmission response.After scaling the structure to have equal trace and gap widths to match the standardvalues, the metapaper design was seen to have bandwidths of 15.4% and 7.54% atthe resonant frequencies of 3.85 GHz and 9.7 GHz respectively. The quarter ringdesign is given in Figure 4.19. The design produces stop bands of 10.99%, 0.5%and 0.6% bandwidth at resonance frequencies of 3.8 GHz, 7.4 GHz and 8.85 GHz100xywgDL(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)Figure 4.18: The (a) surface design and (b) simulated transmission responseof the metapaper FSS design with modified trace and gap widths. Thevalues of the dimensions shown in (a) are D = 12mm, L = 11mm,w = 0.5mm, and g = 0.5mm.respectively.xywgD(a)Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50Simulated transmission(b)Figure 4.19: The (a) surface design with dimensions of D = 31.6mm, w =0.5mm, and g = 0.5mm and (b) simulated transmission response ofthe quarter ring FSS design with modified dimensions.For a few designs, e.g. the base interleaved octopole design, the base inter-leaved double hexapole design, metapaper, and quarter ring, the off-normal datawas not generated, hence not included in the table. Also, some of the designs, e.g.the interleaved octopole with intermediate cross, have a maximum level of atten-101Table4.8:AcomparisonbetweentheperformancesofthedualbandFSSdesignsDesignFBWEq.circuitcomponentsMin.Wi-Fiattenuationlevelsname1stband2ndbandL1C1L2C2NormalTE60◦TM60◦Interleavedoctopole(base)10.1%@4.55GHz2.75%@9.1GHz6.5nH188.5fF11.12nH27.66fF-27.7dB,-20.68dBN/AN/AInterleavedoctopole(intermediatecross)9.7%@4.25GHz5.5%@9.4GHz7.4nH189.2fF5.63nH50.76fF-27.13dB,-25.65dB-28dB,-31.17dB-20.42dB,-9.03dB(max)Interleavedoctopole(forkedcross)8.1%@4.5GHz10.75%@9.3GHz8.6nH145.3fF2.64nH111.3fF-25.13dB,-31.23dB-25.15dB,-37.02dB-10.63dB,-20.63dB(max)Interleaveddoublehexapole(base)19.4%@4.35GHz1.7%@9.49GHz3.4nH391.4fF14.26nH19.72fF-32.82dB,-17.18dBN/AN/AInterleaveddoublehexapole(intermediatetripole)18.7%@4.45GHz4.1%@9.35GHz3.6nH355.8fF6.46nH44.88fF-34.16dB,-23.36dB-36.02dB,-22.28dB-22.46dB,-1.68dB(max)Interleaveddoublehexapole(forkedtripole)18.5%@4.32GHz4.9%@9.23GHz3.7nH367.7fF4.62nH64.5fF-33.06dB,-24.85dB-36.19dB,25.5dB-20.26dB,-1.7dB(max)Interleaveddoublehexapole(interdigitated)24.75%@4.25GHz10.5%@9.08GHz2.9nH487.9fF2.59nH118.9fF-34.1dB,-29.24dB-39.88dB,-20.84dB-17.63dB,-7.52dB(max)Metapaper15.4%@3.85GHz7.54%@9.7GHz4.9nH348.8fF2.69nH100.2fF-29.52dB,-28.18dBN/AN/AQuarterring10.99%@3.8GHz0.5%@7.4GHz7.7nH227.8fF98.62nH4.69fF-26.49dB,-3.12dBN/AN/A102uation in the second Wi-Fi equivalent band. This is due to the fact that the stopbands have shifted in frequency and no longer encompass the normal incidenceequivalent Wi-Fi band frequencies.Due to the large bandwidths of the interdigitated double hexapole design, theshifts in the resonant bands due to off-normal incidence can be accommodated forin the design. The design has primary and secondary bandwidths which are 6 timesand 4 times larger than the 2.4 GHz and 5.8 GHz Wi-Fi bands respectively at nor-mal incidence. It is able to provide a larger attenuation than other designs overboth Wi-Fi bands for off-normal incidence. The addition of dielectric substratesalso improves the robustness of the off-normal behaviour of the transmission re-sponse. Considering these factors, the interdigitated double hexapole design is aprobable candidate for producing a viable Wi-Fi blocking wallpaper.103Chapter 5Experimental Data andVerificationIn the last two chapters, we have investigated the different FSS designs that are ableto produce wide stopbands over two separate resonant frequencies. While the sim-ulations show that designs which encompass both Wi-Fi bands are indeed possible,there are many factors which influence the performance of the FSS in a practicalcase. Some of these factors have been described in Chapter 2. In order to comparethe performance of fabricated designs to the simulations and distinguish the differ-ences between ideal and practical performance of the FSS designs, prototypes weremade and analyzed. Detailed descriptions of the fabrication and analysis processis presented in this Chapter along with the major insights into the practicality ofproducing a working Wi-Fi blocking wallpaper.1045.1 First prototypeFabricating a prototype using printing technology has a lot of associated coststhrough material costs, screen design, and manufacturer costs. Hence, before goingto a specialized manufacturer, a low cost, easy to build prototype was manufacturedby hand using simple materials. This first prototype was used as a proof of practi-cal performance of the FSS designs outside of simulations. The design chosen forthis prototype was the base interleaved octopole described in Section 4.2.1. Thisdesign was chosen as it is the least complicated of the dual resonant structures,which makes it easier to reproduce by hand. This design does not have the bestperformance of the dual band designs, however the objective of this prototype wasonly to show the presence of two stop bands in practical testing conditions.The prototype was made by transcribing the lattice points by hand on to apolystyrene board. The polystyrene board used was the Owens Corning FOA-MULAR polystyrene rigid insulation with a thickness of 2.54cm. The particularmaterial was chosen as it is mostly composed of air, giving it a dielectric constantclose to that of free space. This ensures that the effect of the dielectric on the de-sign does not become a major factor in performance. The polystyrene board is alsoeasy to shape and cut into the required size, while it is rigid enough to hold the FSSdesign in place and stand between the testing apparatus.The conductive traces were made out of commercially available conductivecopper tape. The specific copper tape used for this prototype was the 3M 1181A-ND with a width of 6.35 mm and a thickness of 0.07 mm. According to its datasheet it has a sheet resistance of 5mΩ/sq. The prototype was made out of an arrayof 6 by 6 unit cells comprising a total area of 60cm by 60cm. The FSS design was105Figure 5.1: An image of the first handmade FSS prototype consisting of a6x6 grid of elements.surrounded by 30 cm of aluminium foil on all sides to reduce stray transmissionsthrough the prototype. An image of the prototype is shown in Figure 5.1.To test the transmission through the built prototype, it was balanced betweentwo wide-band Vivaldi antennas connected to a vector network analyzer (VNA).The Vivaldi antennas were the RFSPACE TSA900-12000 branded PCB based an-tennas, with a VSWR below 2 for the range 1.4 - 12 GHz. The VNA used in thelab is the Rohde and Schwartz ZVA67 capable of measuring a range of frequen-cies from 10 MHz to 67 GHz. The antennas were connected to the separate twoports available on the VNA with 6 ft long GORE Phaseflex R© 0KR01R010720 2.92mm cables. The ports were calibrated for the transmission measurement by usinga Rohde and Schwartz automatic calibration unit. The measurement setup wasplaced on a table in an open air space in the lab. The setup is shown in Figure 5.2.The transmission measurement from the setup is shown in Figure 5.3, where the106measurements with and without the first prototype are shown simultaneously.(a)(b)Figure 5.2: (a) Side view and (b) front view of the test setup used to measurethe transmission through the first prototype board.107Frequency (GHz)1 1.5 2 2.5 3 3.5 4 4.5 5Attenuation (dB)-70-65-60-55-50-45-40-35-30-25-20-15TransmissionWithout prototypewith prototypeFigure 5.3: The transmission measurements between the antennas of the openair test setup with and without the prototype board.As can be seen from the transmission response, the prototype produces twovisible notches in the transmission when placed between the two antennas. Thewhole measurement has a lot of high frequency ripples though, as the readingswere made in open air, due to the unavailability of anechoic facilities at the time.As such, it is quite difficult to exactly measure the resonant frequencies of theprototype along with the absolute attenuation at the resonant frequency. The ripplesare particularly large at the resonance frequency where the transmissions throughthe prototype are already reduced. Also the transmission is seen to be enhancedat some frequencies with the prototype in place, which can only be attributed tospurious measurements from scattering and diffraction. Due to this inaccuracy inmeasurement due to unwanted sources of errors, the transmission results cannot becompared to the simulation results. However the dual notches in the transmission108through the prototype provides a justification of the FSS design used in producing adual band response. It also gives grounds for manufacturing an advanced prototypeat a higher cost and accuracy using technologies able to print conductive traces onflexible substrates.5.2 Second prototypeThe second prototype was printed using commercial screen printing techniques onwidely available flexible dielectric substrates. The design chosen was the doublehexapole with intermediate tripoles from Section 4.3.2. This structure provides ahigher bandwidth over both bands than the design chosen for the first prototype.It has a pole frequency shifted further towards the primary resonance, which is aproperty that is important to justify from the simulations. It has a tuneable sec-ond resonance frequency, which is a property that gives more flexibility to thefrequency response of the design. It also has thinner trace and gaps and a higherfill factor, which can be a test of the accuracy of the printing process. The higherbandwidth and zero frequency provide comparable points between the simulationsand measurements.The prototypes were printed from NovaCentrix, a company specializing inprinted electronics based in Austin, Texas. The geometric parameters of the designsent out for printing is given in Table 5.1 and the corresponding simulated trans-mission response for two different normal polarizations is shown in Figure 5.4.109Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-45-40-35-30-25-20-15-10-50x- polarizationy- polarizationFigure 5.4: The simulated transmission response of the design chosen for thesecond prototype under two different polarizations.Design variable Description ValueL1 Major arm length 20.16mmL2 Minor arm length 9.66mmL3 Tripole arm length 7.56mmw trace width 0.5mmg1 gap between traces 0.5mmg2 gap between elements 5.4mmD periodicity 25.66mmTable 5.1: The geometric parameters of the design printed on to the differentsubstrates to produce the second prototype.Four different types of substrates were chosen for printing the prototypes namely,110Property ValueParticle size 1.5µmSheet resistance 10-23mΩ/sqBulk resistivity 11-27µΩ · cmCuring temperature 250-120 ◦CTable 5.2: Physical properties of the silver ink used for printing the conduc-tive traces on the different substrates.clear PET plastic sheet, vinyl paper, smooth cellulose paper and rough cellulose pa-per. The conductive traces were printed using screen printing techniques using a325 mesh screen (325 square openings per 1 square inch) as specified by the man-ufacturer. The conductive ink used was the HPS-FG57B, a silver flake based inkdissolved in butyl carbitol. The properties of the ink as specified by its data sheetis given in Table 5.2. As specified by the manufacturer, the particular screen andink used for printing was expected to give a trace thickness of 20µm and a surfaceresistance below 50mΩ/sq.A 4ft× 4ft polystyrene foam wall was constructed as a physical support forthe prototype. The material used was the same as the physical backing used forthe first prototype. The outermost border of the wall with a thickness of 1 ft wascovered with aluminium foil to reduce stray transmissions through it. This left agap of 2ft×2ft open in the center of the wall to attach the printed prototypes. Thefoam wall was mounted on triangular foam legs to provide further stability. Thewideband Vivaldi antennas previously used for testing were fitted with polystyrenefoam stands to align them with the center of the foam wall. The antenna standswere placed 70 cm away from both sides of the wall. Open air measurements weretaken for all of the prototypes, the readings for just one sample is shown in Fig-ure 5.5.111Frequency (GHz)1 2 3 4 5 6 7 8 9 10Transmission (dB)-40-35-30-25-20-15-10-505Measured transmissionFigure 5.5: Open Air transmission measurements for one of the second pro-totypes printed on the flexible substrates.Similar to the open air measurements for the first prototype, we can see thetwo distinct stop bands in the transmission response. However, a ripple is presenton the signal due to reflections and scattering, making it difficult to carry out anexact comparison between simulated and measured results. Also it can be seenthat the transmission between the antennas goes higher than 0 dB at some frequen-cies. In order to find a solution to this measurement problem, a small anechoicchamber was built in the lab for testing. The anechoic experiment chamber setupis described in the next section.5.3 Experimental setupTo reduce the effect of noise from the transmission measurements though the pro-totypes, an anechoic chamber was built in a corner of the lab. The frame of the112chamber was built of 2 in× 4in wood planks and plywood boards. The chamberhad outer dimensions of 4ft× 4ft× 6ft. The side walls were braced on verti-cal stilts and placed on plywood floorboards. One front facing wall was placedon caster balls for easy insertion and removal. This made it possible to close offthe whole chamber once the prototype was placed on the wall. The ceiling of thechamber was suspended on the side walls, with bracing horizontal planks to preventsagging. The inner sides of the chamber were lined with electromagnetic reflectionabsorbing foam sourced from ETS-Lindgren. Three different types of foam wasused for the inner lining. Flat 3 in thickness foam was used for the ceiling andfloor boards, pyramidal 3 in foam was used for the side walls, while pyramidal 5 infoam was used for the walls directly behind the antennas for better absorption ofthe scattered waves. Some pyramidal foam was also used on the ceiling and sidewalls to increase the efficiency of scattering absorption. An image of the anechoicchamber is shown in Figure 5.6.The foam wall for supporting the prototype was placed midway between thetwo ends of the chamber. The antennas were placed 70 cm away from the foamwall on both sides and 15 cm inside from the walls of the chamber. The antennaswere connected by 10 ft long Carlisle WHU18-1836-144 Workhorse R© cables tothe VNA for measurements. The VNA was calibrated using the automatic calibra-tion setup. The setup is calibrated only for transmission measurements, as we arelooking only at the transmission through the prototype.5.4 Anechoic chamber measurementsThe transmission measurements through the prototypes were taken in two steps.First, a measurement through the foam wall was taken. This sets a base line for the113Figure 5.6: A front view of the inside of the anechoic chamber built for mea-suring the transmission through the prototypes.transmission from one antenna to the other. Then a second reading was taken aftermounting the prototype under test on the foam wall. The ratio of these readingscan then be taken in post-processing to find the transmission through the prototypeitself and reduce the effect of other effects that may influence the measurement.The measurements were taken in the 1-8 GHz range with 2000 intermediate datapoints. An intermediate frequency (IF) of 1 KHz was used on the VNA to producea smoother output and reduce the effect of noise on the readings. A large IF band-width produces quicker measurements, however it is more susceptible to inaccuratemeasurements. A small IF bandwidth will give accurate measurements, however itwill take a longer time to sweep through all the data points. Hence, the choice of IFbandwidth is a trade-off between measurement speed and accuracy. The recordeddata was post-processed using MATLAB software and the measured data from the114Frequency (GHz)1 2 3 4 5 6 7 8Transmission (dB)-50-45-40-35-30-25-20-15-10-50Vinyl sheetPET sheetRough paperSmooth paperSimulatedFigure 5.7: A plot comparing the measured data from the four different sub-strates of the prototypes along with the simulated transmission responseof the printed design.four different types of prototypes along with the simulated transmission for thedesign is shown in Figure 5.7.There are a few notable points in the comparison between the simulated trans-mission response and the measured responses of the prototypes.Firstly, all the prototypes have resonances which are slightly shifted in fre-quency from the simulated response. This is due to the effect of the substrate onthe transmission response. This effect was not considered in the simulated design,as the substrate parameters were not known before manufacturing the prototypes.The shift in frequency can be modelled through appropriate layers of dielectrics inthe simulation, however a detailed explanation of the process is given in followingsections.Secondly, the rough cellulose paper has an almost flat transmission response.115Figure 5.8: A zoomed image of the rough paper prototype. The breaks in theconducting traces due to imperfect screen printing can be seen.This shows that it does not attenuate any of the frequencies to any significant de-gree. Visual inspection of the prototype shows that the traces on the substrate areimperfect and broken in many places. A zoomed image where the printing defectsare visible is shown in Figure 5.8. These defects lead to a breakdown of the period-icity of the design and causes the measured transmission response to deviate fromthe simulated response.Finally, the clear PET plastic sheet produces the deepest notch among theprinted prototypes. The conductivity of the traces are the main determining fac-tor in the depth of the notches in the stop bands. A higher conductivity or lower116resistivity should give a deeper notch. This implies that the PET plastic proto-type should have traces with the lowest surface resistance among the all the other.This is corroborated by values stated by the manufacturer as well as measurementscarried out in the lab.The manufacturer used two different curing processes for the plastic based sub-strates versus the cellulose substrates. According to the fabrication report, the cur-ing process for the PET plastic sheet and vinyl sheets gave a higher conductivitythan the one used for the smooth and rough cellulose papers. Out of the plasticsheets, the PET sheet had trace conductivities slightly higher than the vinyl sheetaccording to their measurements. Again, the traces on the smooth and rough cel-lulose papers had a conductivity about 3 times lower than the ones on the plasticsubstrates.A measurement was also made using a Signatone S-302 four point probe ma-chine in the lab. The recorded values are given in Table 5.3. However, the thicknessfor the traces are not known and generally in a four point probe measurement thetraces are considered to have semi-infinite extent in the lateral dimension, which isnot the case here. As such, the values cannot be taken to be the absolute values ofsurface resistivity for the traces. But it can be noted that, the trends in the valuesobtained closely match the trend of values stated by the manufacturer. The traceson PET substrates do have a lower value than those on the vinyl sheets, while thenatural paper has a resistivity 3 times larger than the ones on the plastic substrates.The rough paper has a significantly larger surface resistivity than the other threesamples. These relative values between the conductivities of the traces on differ-ent substrates has to be taken into account when compensating in the simulations,which is done in the next section.117Substrate type Sheet resistance of tracePET sheet 200mΩ/sqVinyl sheet 250mΩ/sqSmooth paper 750mΩ/sqRough paper 1250mΩ/sqTable 5.3: The trace sheet resistance values obtained from the measurementusing a four point probe machine.5.5 Effect of substrates and conductivityTo compensate for the effect of substrate dielectric constant and trace conductiv-ities, a few modifications were made to the simulation files. When originally de-signing the FSS structure, the surface was taken to be free standing in air. To incor-porate the effect of the dielectric, a layer of equal thickness to that of the prototypesubstrates was added. The thicknesses were obtained by carefully measuring thethickness of the prototypes using slide calipers.The conductive traces were previously modelled as perfect electric conductorsand therefore having infinite conductivity. These were replaced with the COMSOLtransition boundary layers. The transition boundary layer takes the thickness of thetraces and the bulk resistivity of the conducting material and converts it into a twodimensional conductive trace with equivalent surface resistivity. The bulk resistiv-ity and thickness in each case was set as to give an equivalent surface resistivityequal to the measured values from the four point probe machine.One other property that has to be given to the simulation file is the dielec-tric constant of the substrate materials. The dielectric constants of the substrateshowever were unavailable from the manufacturer. Other works which consider thedielectric constant of similar materials have a widely varying range and the rangesare also based on manufacturing process. So the value of the dielectric constant118Frequency (GHz)1 2 3 4 5 6 7 8Attenuation (dB)-45-40-35-30-25-20-15-10-50Measured TransmissionSimulated TransmissionSimulated Reflection(a)Frequency (GHz)1 2 3 4 5 6 7 8Attenuation (dB)-45-40-35-30-25-20-15-10-50Measured TransmissionSimulated TransmissionSimulated Reflection(b)Frequency (GHz)1 2 3 4 5 6 7 8Attenuation (dB)-45-40-35-30-25-20-15-10-50Measured TransmissionSimulated TransmissionSimulated Reflection(c)Figure 5.9: Plots comparing the simulated and measured transmission re-sponses through the (a) PET, (b) vinyl, and (c) paper FSS prototypes.The plots also show the simulated reflection from the prototypes.Table 5.4: The different property values used in the simulation files to com-pensate for the effect of dielectrics and conductivity on the transmissionresponse.Substrate Thickness ofdielectric layerDielectricconstantSurface resistanceof tracesPET sheet 150µm 3.3 200mΩ/sqVinyl sheet 192.5µm 4 250mΩ/sqSmooth paper 180µm 3.8 750mΩ/sq119was swept in a range consistent with the material until a match was found be-tween the simulated transmission response and the measured transmission. Thesimulation was not compensated for the rough paper substrate as it did not pro-duce a response due to the fabrication imperfections which cannot be accuratelyincorporated into the simulations. The simulations for the other three substratesare shown in Figure 5.9, with the parameters used for trace conductivity, substratethickness and substrate dielectric constant summarized in Table 5.4. The figuresfor the transmission through the prototypes also contain the simulated reflectionfrom the prototypes. The reflection measurement however could not be made inthe test setup in the lab. However the simulated reflection gives us a good idea ofthe operation of the prototypes at resonance. As can be seen the maxima frequencyof reflection corresponds to the minima frequency of transmission and vice versa.So it shows that the incident energy on the surface is either reflected or transmitted,a very small amount of it is absorbed by the prototypes.5.6 Off-normal measurementsDue to space constraints in the lab, The anechoic chamber turned out to be theexact size for doing normal incidence measurements on the prototypes. Due to thepresence of the thicker pyramidal foam behind the screen, the space requirementsfor off-normal measurements were slightly higher than available inside the cham-ber. As such, only off-normal measurements for a 30 degree incident wave werecarried out for TE polarization. The foam wall was rotated by the required anglewithin the chamber to create the off-normal incidence. The off-normal measure-ments were carried out for the clear PET prototype as it has deepest notch in thetransmission response and therefore easier to compare to the simulations.120Frequency (GHz)1 2 3 4 5 6 7 8Transmission (dB)-45-40-35-30-25-20-15-10-50MeasuredSimulatedFigure 5.10: A comparison between the simulated and measured transmis-sion responses of the prototype to a 30 degree off-normal TE incidentwave.The corresponding simulated response is shown in Figure 5.10. The simulationin this case considers the finite trace conductivity as well as the dielectric substrate.The off-normal characterization done previously in Section 4.3.2 did not considerthese effects. As can be seen in this case, the simulation very closely matchesthe measured response even for the off-normal case, justifying the simulation as asuitable design tool. Comparing to the normal incidence measurements, the off-normal response shows a shift of 50 MHz in the primary resonance frequency,while it shows a larger 240 MHz shift in the secondary resonance frequency. Interms of bandwidth though it shows very little degradation from the normal inci-dence case, with the primary bandwidth changing from 15.79% to 15.72% and thesecondary bandwidth changing from 3.30% to 3.02%.1215.7 SummaryIn this Chapter we have presented the experimental verification for the use of thedual band FSS designs on flexible substrates. The comparison between simula-tions and measurements shows that the fabricated designs are expected to behaveclosely to the simulations. The manufacturing process of screen printing conduc-tive traces on flexible dielectric substrates causes slight deviations in the transmis-sion response of the designs. However appropriate corrections can be made in thesimulations to compensate for their effects. Once the corresponding factors areadded in, the simulations and measurements show close agreement. There is stillsome further analysis which will have to be carried out regarding the off-normalperformance of the manufactured prototypes. For the normal incident case though,these analyses show that a prototype which produces stop bands at the Wi-Fi fre-quencies with wide bandwidths can be manufactured. A prototype with the stopbands at the appropriate frequencies can be designed by keeping all factors in thesimulations and it can be used to show the practical operation of the designs oncethey have been fabricated.122Chapter 6ConclusionWi-Fi communications have become an integral part of our daily lives. Almost alldigital devices these days come equipped with Wi-Fi connectivity. The prolifer-ation of Wi-Fi has been so wide spread we now have city scale Wi-Fi networks.This ease of access to the internet has also brought along its own set of problems.Security of information passed through the Wi-Fi network has become a sourceof concern. Keeping people off the network in certain situations has also becomea problem. In Chapter 1, we explore the idea of selective blocking of the Wi-Finetwork and envision a Wi-Fi blocking wallpaper. This wallpaper could be madeusing frequency selective surfaces (FSS) to block the two Wi-Fi bands yet allowother communication frequencies to pass through. The Wi-Fi blocking wallpapercould be used to produce either Wi-Fi secure rooms or Wi-Fi free rooms, depend-ing on the required application. The control of propagation of the Wi-Fi signalcould also possibly improve the quality of individual networks by eliminating in-terference.In Chapter 2, we provide a detailed background description of FSS technology.123FSS design has been studied widely for applications in stealth and communica-tions. There are some factors in the performance of FSS which need to be con-sidered when designing for a specific application. These factors are also describedin the chapter. Since Wi-Fi blocking will require multiband filtering of waves, thedesign methods used for producing multiband FSS is given an overview. Finally,previous work done into producing designs for blocking communication signals isreviewed.While many FSS designs have been studied and described in previous litera-ture, we use Chapter 3 to compare their performance for our intended application.We choose -20 dB bandwidth in the stop band as measure of performance of the de-signs. The band stop type single resonance FSS are then standardized to the sameresonance frequency and their bandwidths tabulated. The trace and gap widths ofthe designs are also standardized to provide a comparison between designs, whilekeeping within required manufacturable dimensions. A simple equivalent circuitmodel is also used to describe the operation of the FSS filter in an intuitive manner.This model can be used to extract equivalent circuit parameters of the designs assupplemental data to the bandwidth.Based on the comparison done in Chapter 3, the best performing designs werechosen for modification to produce two stop bands. This modification was carriedout in Chapter 4. A second resonance path was added to the designs from the pre-vious chapter, while keeping the initial resonance as unaltered as possible. Thisalso allowed for independent tuning of the resonance frequencies, which was a de-sired characteristic. The off-normal response of the designs were simulated andpossible changes in the transmission response was noted. The performance of thedual band designs were compared according to the metric of bandwidth and the124superior performance was found. The interdigitated double hexapole with inter-mediate tripole showed the best performance of the studied designs. It shows stopband bandwidths of 24.75% and 10.5% in the primary and secondary stop bandsrespectively. This provides a minimum attenuation of -34.1 dB across the 2.4 GHzand -29.24 dB across the 5 GHz Wi-Fi band. Under off-normal illumination, thedesign performs well for TE polarization. At 60 degree off-normal incidence thedesign provides a minimum of -39.88 dB and -20.84 dB attenuation over the twoWi-Fi bands. However, for TM polarization the performance is slightly compro-mised. At 60 degree off-normal incidence it shows a maximum of -26.3 dB and-7.52 dB attenuation over the two Wi-Fi bands. In spite of this, it still shows mostpromise out of the designs for being able to produce a Wi-Fi blocking wallpaper.In Chapter 5, we provide experimental proof of performance of some of thedesigns from the previous chapter. Two of the designs were used to produce pro-totypes of the Wi-Fi wallpaper. The interleaved octopole design was fabricated ona foam board with copper tape. It was shown to produce two separate stop bandsin its transmission response. The interleaved double hexapole with intermediatetripoles was printed on flexible substrates using silver ink and screen printing tech-nology. This method was also able to produce two separate stop bands from thedesign showing the viability of printing FSS designs on paper substrates. Thisprototype was extensively tested to find the effect of the substrate and finite traceconductivity on the free-standing ideal FSS transmission response. The effect wasthen compensated in the simulation files and the close match between simulationand experiment was noted. The compensated simulation files were also brieflyused to characterize the off-normal behaviour of the prototype.1256.1 Future workThe designs in this thesis have been optimized for bandwidth at normal incidencein a free-standing situation. However, the presence of a dielectric substrate and theoff-normal incidence of waves causes the transmission response of the designs tochange. While the effect of substrate has been investigated in this thesis and com-pensated between simulations and measurements, the off-normal performance ofthe designs requires further studies. In the simulations done in this thesis, it can beseen that the performance of the designs suffer for the TM polarization off-normalincidence. The presence of the dielectric in fabricated prototypes should counter-act the effect of off-normal incidence, however this has to be tested extensively inlaboratory conditions. A complete off-normal characterization of prototypes has tobe carried out and included in the design process.The prototypes fabricated for this thesis were not necessarily the best perform-ing in simulations. The prototypes gave a verification of the dual band operationof the designs as well as providing data to incorporate the effect of dielectric sub-strates in simulations. The design with the best performance in simulations canbe fabricated using similar screen printing techniques. Having another design pro-totype on a dielectric substrate will provide further data to justify the simulationresults with substrate layers. The improved design can also be designed at the exactWi-Fi frequencies to see the effect on real Wi-Fi transmissions.In order to produce a Wi-Fi wallpaper, the effect of placing the prototypes onreal walls has to be studied as well. The wall will present a semi-infinite dielec-tric backing to the prototype modifying the transmission response of the FSS. Theeffect will vary between different wall constructions due to different effective di-126electric constants. However it should be possible to quantify the effects throughsimilar methods as utilized for the dielectric substrates of the prototypes. The ef-fect of placing the prototype on a wall can then be included in the simulation tocompensate during the design process.Finally once all factors affecting performance have been incorporated in thedesign process, a cost analysis can be carried out of producing the design as a massprinted wallpaper. 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Single-layer dual-wide-band frequency selective surfaces for Wi-Fi blocking in the built environment
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