Chowdhury, S K

Sarkar, D

Sarkar, P P

IACS Institutional Repository

Indian 1 Phys. 77B (4). 399-403 (2003)$ IJP\Theoretical and experim ental investigations on the frequency selective property o f an array o f slotted dipolesD Sarkar', P P Sarkar' and S K Chowdhury**' USIC, University of Kalyani. Kalyani-741 235, West Bengal, India ^Department of E&TC Engineering, Jadavpur University, Kolkata-700 032. IndiaE-mail ; skc_42®sify.comReceived 10 February 2003, accepted 8 May 2003Abstract : A frequency selective surface (PSS) comprising of a two dimensional array of slotted dipoles resonant at a single fitqueiicy is proposed. A computationally efficient method for analyzing this PSS is presented. The formulation is carried out in the spectral domain where the convoAmion form of the integral equation for the induced current reduces to an algebraic one and the Spectral-Oalefkin technique is used to solve the resutting equation. Entire- domain basis function that satisfies the edge condition is introduced to expand the unknown induced current on the ooiqpHinentary structure U .  an anay of metal printed dipoles. Using Babinct's principle for complementary screen, the transmitted electric field for (he structure of sloiicd dipoles have been calculated. This theoretical result has been compared with the experimental data also. The theoretical and experimental data indicate that this structure can be used as a band pass filter.Keywords : Frequency selective surface, slotted dipoles, spectral-Qalerkin technique, band pass filter PACS Nos. . S2.2S.Os, 84.30.Vn, 84.40.Ba1. IntroductionFrequency selective surfaces are often employed in the reflector anicnna system of a communication satellite [1-3] or a deep s^ ace exploration vehicle [4-7] for multi-frequency operations. Typically, an FSS consists of one or more grids supported by one layer or multiple layers of dielectrics. The grids are thin conducting periodic elements etched on thin substrates. As grids can be designed to resonate at specified frequencies, 'i'o FSS will reflect waves at these fiequencies and pass waves at other frequencies. Experimental investigations on the frequency selective property of an array of printed dipoles [8 ] •tave been carried out recently. In this paper, our goal is to design an FSS, which will act like a band pass filler and may be used in a multi-band reflector system. In the multi-band reflector antenna ‘Ppitcation [4], typkal[y <m PSS is employed as the subreflecu» •"‘I the different feequency ieeda are optimized independwttly ‘"<1 placed at the real and vimial foci o f the mainreflector. Hence, a single main teflectqr is required for inultifrequency’^ '•ponding Authoroperation. For example, the FSS on the high gain antenna (HGA) of the voyager spacecraft was designed to diplex S and X bands [4]. In that application the S band feed is placed at the prime focus of the main reflector and the X band feed is placed at the Cassegrain focal point. The main advantage is that only the main reflector is required for this dual band operation. Thus, tremendous reductions in mass, volume and cost of the antenna system are achieved with the FSS subreflector.2. Design of the FSSAn array of 7 x 5 aperture dipoles were fabricated within the copper screen on one side of a dielectric slab and the copper coating on the other side of the slab was completely removed (Figure 1. (a)). Dimensions of the dielectric slab were 140 mm x 140 mm X 3.16 mm. Its dielectric constent is 2.4. The FSS was designed in such a way that it may resonate at the ftequency of lOOHz without considering the dielectric loading effect Atthis frequency, die correqxmdingfiee space wavelength is 30 fum. For resonance to occur, the length of each dipole aperttueidioUld ‘ be equal to half of the free space wavelength [9]. Hence, the02OQ3MiCS400 D Sarkar, P P Sarkar and S K Chowdhurylength of each dipole aperture was made equal to 15mm. Its width was made l.Smm. The spacing between two rectangular dipole apertures was so chosen that the rule governing a conventional array antenna be maintained. Here> the spacing between two adjacent rectangular apertures was chosen to be 15mm (half wavelength) in a row and 7.5mm (quarter wavelength) in a column (Figure 1. (a)).1.5 mmFigure 1. (a). Frequency selective surface under investigation (All Dimensions are in rnai).3. Formulation for theoretical investigationIn this Section, the integral equation is developed for the scattering from a frequency selective surface of the type shown in Figure 1 (a). Let J be the current density induced on the FSS due to a given incident field and is the free space wave number. The scattered electric field in the transformed domain E \ a , P )  at z = 0 can be derived from [ 1 0 ]:Since the structure is periodic, J ( a , P )  has a discrete spectrum in the transformed domain Le, 7 {a , f i )  is non-zero for discrete value* of a ,/J viz. which correspondto the Floquet's modes. So while uking the inverse Fourier transform of ( 1 ), the integral form can be converted into a summation form.Putting £> _  and taking inverse Fourier transform of ( 1 ), we can getEy(x ,y )pine7inv■Ftt +a I 2I r i * Tus * 0 - 0 ^  - a .  AyOTEoxG {oc„,p„)wherea is the periodicity in x direction, b is the periodicity in y direction,2mnb y ’= ^osindcos0, k '^  = jig sindsin[where Q is an angle of incident wave with the Z-axis and  ^ isand we getEran + Etoh — 0 E tm ~ ~ E ^ .Next, our goal is to solve the eq. (2)using,QB|krkin'spi®‘^ '®‘ and to calculate J  in the transfonned domain. FcMr this, wer S " ”  “ '“ ” ” ” ■' “  “ ™ * » « -  F « .« , . ( 8 ) ,w . , «Basis function selection and solution :Let us write the matrix eq. (2) in the symbolic diadic form :401= g, where g  is the known matrix 4  *> r jand M is the matrix to be determined I ^and L  is the total operator involved in matrix eq. (2).Now we can write,+ iyL ^  + y iL ^  + +>>«,)= k x + h yI IS the basis function which is to be chosen. In generalisedmanner °^*  ^ **** written in the followingX “y =A 'y»i j.iwhere(3)orm:N" = X ( ^ c . , A + ; c , / J ./*! (4)From eq. (3), we can write+ L^Uy =N< = { h ’h x f x } b , P = ( ^ f ^ , L y y f y ^ y^ > { f x , . g x )  and ={ f y , , gy ) .As a whole, we can write in matrix form.^ " ^ ^ * J ' f * j ' ^ ^ X y ^ C y  f y  = g ^J ’ l y . |milarly,‘y*2^^x, fx j  + ^ y y ^ C y j f y  = g / " I  j~\a , , ... _ XJC6 iT - > 11_ Ajr «2 1 -(5) U/VI"'^  JCr■«AW b;5V- '^NN IIa , i .... • < * .T - ’^ \N ^ > 1“ 21 *".... -A A^ 2(6 ) ....J. (5), we get We shall have to calculate{ f x , ’Sx)-  (7 )Cx.-C^■*1 -*2 ' Ca '- . . . .c . and .....Then we can find out the function u a t j  from(11)(12)(13)(14)milarly, taking the inner product of fy^ and eq. (6 ), we get » = J  = ^ { x  + y  ). ^ / + ( / » > ^ > y 2 /y ,C ,.\  = ( / .  .gy).  faster calculation. Mittra era/ H i] suggested the/  \  > 1  \ J I ( )  basis functions for different FSS structures. For the FSS structurefronieq /7i »»•** ®°isistingofprinted dipoles. Basis function suggested by Mittra”1-V .fiwegei w/f/riiises«402 D Sarkar, P P Sarkar and S K ChawdhuryL -  Length of the dipole.P,(0 .L) = 1  for H S  I  s  0  otherwise.Considering this basis function, we have calculated and 7y(a ,P)  assuming and = 0 .Next, the values of (a,/3) and J y { a ,p )  have been put ineq. (2) to get the scattered electric field E i ( x , y )  and £ * (x ,> ) . Now from this scattered electric field, the transmission coefficients of the structure of mode m. n due to incident mode k, I may be readily calculated [10,12]. From the transmission coefficients transmitted electric field have been calculated for the array of printed dipoles. Then following Babinet's principle for complementary screen [ 1 2 ], the transmission coefficients for the array of slotted dipoles have been calculated and normalized transmitted electric fields in dB vs. frequency have been plotted as shown in Figure 2.a.s 7.5 asFigure 2. Normalized transmitted electric field vs. frequency.4. Dielectric loading effectDielectrics are often used for structural support. A number of papers describing dielectric loading effects have been published. The resonant frequencies decrease as the dielectric thickness increases [9]. If be the resonant frequency of the slotted dipoles etched on a thin copper sheet supported by thin dielectricsubstrate of dielectric constant Cj then its effective resonantfrequency/ is f r2air. This formula is valid for normal Incidence o f theelectromagnetic wave. Here, = l,e^ «2 .4  a h d /s  ioqHj so, 4 =  7.7 GHz.5. MeamrefnentTransmission and reflection tests for the FSS (Figure 1 . (aj were performed at J and X bands using standard microwave tes bench. The FSS was placed between the transmitting am receiving horn antennas (Figure 3). The distance between thes' two horns is 25 times of the wavelength corresponding to th. centre frequency (10 GHz). The transmitting horn antenna wa connected to a Marconi microwave source. The receiving hon antenna was connected to a VSWR meter. Measurements havi been made in the frequency range of 6  GFf  ^to 9 GHz with ai intervai of 0.1 GHz. From these measured ^kta, the normalise) transmitted electric fields versus frequency'were plotted in ihi same Figure 2 for comparison. \Transmitting HornFSS under InvestigationMlcronl Microwave SourceFigure 3. Experimental setup.Receiving HornVSWR/Power Meter)where e .  = dielectric constant of6. ConclusionThe experimental results show that the maximum transmission through the FSS occurs at the frequency range of 7.7GHz to 7.95GHz and almost total reflection from the FSS occurs ai ih frequencies above 8 .T GHz and below 70Hz. Theoretic investigation shows that maximum transmission occurs in ihi frequency rangeof 7,68GHz to 8 .1 CHIz. However, the plot oft! computed result is not so steep as the plot of the measu result. This may be due to the fact that in eq. (13), the matrix sia has been taken 20 X 20 instead of infinity-References(1 ] N D Agnwal aiul W A Imbraile IE£E 7)w«, Anumui Fn 27 463 (1979)12] S WUeeiatPaperpreaeniedBttlie/itt (Ontario, Canada) p 666 (199!)(31 K Ueno et at Paper pmemed at the M- ViEE AF-S (Ontario* Canada) (1991)[4] G H Setennum Mieromm J W J5 (1973)[5J T K Wu Paper presented «  die iSEE AP-S (Qbh^ .  Caeada) (199.1) .W Ltt^  iFFF n-«„ A .^___»|7] T  K Wu er a/ P»p« presented at the Int. IEEE APS Symposium (Chicago) (1992) y ^ iu m .|8] P P Sarkar, D Sorkar. S Das and 5 K Chowdhuiy Pror. Nat. Conf.Propaialion (Jaipur, India) p 115403[11] J j j  Mittra. C H Chan and Tbm Cwik. Pmc. IEEE 76 p 1593 DecVnrir^ij n®***" Elerlromagnetic Fields (NewYork ; MaOraw Hill) p 130 and p 365 (1961)

Theoretical and Experimental Investigations on the Frequency Selective Property of an Array of Slotted Dipoles

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/6780/1/Theoretical%20and%20Experimental%20Investigations_D%20Sarkar.pdf

Theoretical and Experimental Investigations on the Frequency Selective Property of an Array of Slotted Dipoles

Abstract

Similar works

Full text

Available Versions

IACS Institutional Repository