Design of Frequency Selective Surface Loaded toMultilayer Dielectric Plate for Loss Reduction over

Wide Incident AngleShota Ino, Tomihiro Ikegami, Kunio Sakakibara, Nobuyoshi Kikuma, and †Toshikazu Hori

Nagoya Institute of Technology, Nagoya, 466-8555 Japan† University of Fukui, Fukui, 910-8507 Japan

Email:sakaki@nitech.ac.jp

Abstract - Thickness of windshield, radomes, plastic cases ofwireless systems are comparable with a wavelength in themillimeter-wave band. In this case, the total reflection from theboundary surfaces of the dielectric plate increases depending onfrequency and input angle of incident wave. To solve theproblem increasing reflection, Frequency Selective Surface(FSS) is loaded to the dielectric plate. Transmission efficiency issignificantly improved by canceling the reflections. We proposethe design technique to find the required characteristics of FSSfrom the desired characteristic of whole multilayer dielectricplate with FSS. Reflection loss of the windshield was declined inthe range of incident angle from 30 to 60 degrees at 76.5GHz.

Index Terms — Frequency Selective Surface, equivalentcircuit, multiple reflections, wide incident angle.

1. Introduction

Antenna systems are generally housed in plastic cases orradomes to protect from moisture, and dust. When thedielectric plate is located in front of the antenna, it causesloss due to reflection from the surfaces. The thickness of thedielectric plate is small in low frequency band. Thereflections from the both surfaces are approximately 180degrees out of phase because the reflection coefficient isnegative when the wave incidents from the air to thedielectric and positive when incidents from the dielectric tothe air. However, in high frequency, although the reflectionphases of the both surfaces are still out of phase, a largephase shift by travelling through the electrically thickdielectric plate causes return loss. Therefore, the return lossof the dielectric plate cannot be ignored in the millimeter-wave band.

A windshield of a car is made of a laminated safety glasswhich consists of two sheets of glass with a plastic layerlaminated between them for safety. There are four boundarysurfaces with different dielectric constant. The totalreflection from the whole structure is formed by combiningreflected waves from the four boundary surfaces. Thus, thesignificantly fluctuated reflection loss depending on thefrequency and the incident angle are serious problems formillimeter-wave systems equipped in the car cabin.

The same square loop slot FSSs (SLS-FSS) are printed onthe both outer surfaces of the windshield as shown in Fig. 1.The SLS-FSSs are expected to work for a bandpass filterwhich operate to transmit at the design frequency. We

propose the simple and straight-forward design procedure ofFSS to obtain required reflection coefficient |R| of FSS fromthe desired characteristic of the whole multilayer dielectricplate with FSS. Equivalent circuit of the FSS and reflectioncoefficient |S11| including multiple reflections are simplyevaluated in this work.

Fig.1. FSS loaded to multilayer dielectric plate.

2. Equivalent Circuit of FSS and reflection coefficientincluding multiple reflections

FSS is designed to reduce return loss of the windshield.Dielectric constant, loss tangent and thickness of the glassare 6.15, 0.0038 and 2.286mm. Those of the laminate film inthe middle are 2.6, 0.0019 are 0.789mm. The characteristicsof the windshield with FSS printed on the both outer sidesare calculated by equivalent circuit.

(1) Equivalent circuit of FSSThe resonant frequency and the bandwidth of FSS can be

controlled by its parameters shown in Fig. 1 [1]. When theFSS with zero thickness is inserted on the boundary betweenthe different characteristic impedances Z1 and Z2, the FSScan be expressed by a shunt susceptance B as shown in Fig. 2[2]. Complex S-matrix of the FSS between Z1 and Z2 can beexpressed by a function of only a reflection amplitude |R| ofFSS by eliminating susceptance B and deriving the relationsbetween reflection and transmission amplitude and phase [3].When B is inductive, reflection phase is a positive value.When B is capacitive, reflection phase is a negative value.

Fig. 2. Equivalent circuit.

2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

[FrF3-3]

539

(2) Reflection coefficient including multiple reflectionTotal reflection coefficient S11 of multilayer dielectric

plates with FSSs can be calculated by synthesizing reflectioncoefficients of dielectric surfaces and FSSs. SLS-FSSs areprinted on the both outer sides of the windshield as shown inFig. 1. In the three-layer windshield, four boundary surfacesexist between the air and the glass, and between the glass andthe film. Reflection coefficient S11 consists of multiplereflections and is calculated by using an infinite geometricseries of each layer shown in Fig. 3. Then, reflectioncoefficients of multilayer dielectric plates can be calculatedin order from the lower layer. The reflection coefficient φ0 ofthe lower glass layer terminated by the air boundary can becalculated including multiple reflections shown in Fig. 3(a).The reflection coefficient φ1 of the film terminated by φ0 canbe calculated as shown in Fig. 3(b). Reflection coefficient φ2

of whole structure can be calculated by termination of φ1 asshown in Fig. 3(c).

(a)Calculation of φ0 (b) Calculation of φ1 (c) Calculation of φ2

Fig. 3. Multiple reflection in each layer.

The reflection coefficient S11 of the whole structure iscomputed as function of the magnitude |R| of the reflectioncoefficient of the FSS and frequency, thus, characterized ascontour maps shown in Fig. 4. When the susceptance B isnegative value, the reflection phase is positive. Whensusceptance B is positive value, reflection phase is negative.Thus, two graphs are required to cover all conditions.Reflection amplitude |S11| of the whole structure can beobtained by superimposing the frequency dependency of thereflection coefficient |R| of the FSS on the contour map.

(a) B <0 (b) B >0Fig. 4. Contour map when FSS is loaded.

3. Design by using contour maps

(1) Normal IncidenceThe SLS-FSS was designed by the contour map so that the

reflection |S11| of the whole structure is reduced at 76.5GHz.Electromagnetic simulation of the isolated FSS betweendifferent dielectric materials was carried out under theinfinite periodic condition [4]. Reflection level |S11| of the

whole structure was improved below ,10dB at 76.5GHz byloading SLS-FSSs.

Fig. 5. Reflection |S11| of the whole structure innormal incidence.(2) Oblique Incidence

The SLS-FSS was designed to reduce |S11| of wholestructure in the incident angle from 30 to 60 degrees by usingcontour maps. The horizontal axis was replaced by theincident angle. Loading the designed FSS on the both sidesof the windshield, the reflection level was lower than ,10 dBbetween 30 and 60 degrees as shown in Fig. 6.

Fig. 6. Reflection |S11| of the whole structure inoblique incidence.

4. Conclusion

By calculating reflection coefficients including multiplereflections, FSS design was simplified by using contourmaps. Using these maps, reflection of the windshield isreduced to be less than ,10dB at the incident angle from 30to 60 degrees at 76.5GHz.

References[1] K. Sakakibara, M. Chiba, G. Nomoto, T. Ikegami, and N. Kikuma

"Reflection-Loss Reduction of Dielectric Plate by Reflection-PhaseControl of Freqency Selective Surface. " iWEM2017. MT-4.London,May 2017.

[2] G. H. Dadashzadeh, M. H. Amini and A. R. Mallahzadeh ,“Equivalent Circuit Model for Square Ring Slot Frequency SelectiveSurface” Journal of Commun. Eng., vol.3, no.1, pp.23-32, 2016.

[3] T. Ikegami, G. Nomoto, K. Sakakibara, N. Kikuma "Design ofFrequency Selective Surface by Matrix Transformation of LayerStructure to Reduce Return Loss of Thick Dielectric Plate", 2017IEEE CAMA, Japan, Dec. 2017.

[4] PT. Teo, K.S.Lee, C.K.Lee, "Analysis and design of band-passfrequency-selective surfaces using the FEM CAD tool" InternationalJournal of RF and Microwave Computer-Aided Engineering, Vol. 14Issue 5, pp. 391-397, Sep. 2004.

Incident Reflectionφ0

φ0

φ1 φ1

φ2

2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

540