Electrical analysis of light-weight, triangular weave reflector antennas

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Hortense McKinney
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1 Electrcal analyss of lght-weght, trangular weave reflector antennas Knud Pontoppdan TICRA Laederstraede 34 DK-121 Copenhagen K Denmark Emal: kp@tcra.com INTRODUCTION The new lght-weght reflector antenna technology beng developed by several spacecraft companes requres accurate electromagnetc modellng of the reflector surface propertes. In partcular, the new tr-axally woven fbre skns are of nterest. In a recent study for ESTEC a new computer program has been developed n a co-operaton between TICRA and Poltecnco d Torno. The name of the program s MESTIS (1), MEtallc STrIps Smulator, and by means of ths t s possble to model one or more layers of strp grds and each layer can consst of up to three strp grds makng arbtrary angles wth each other. In ths way t s possble n partcular to model the new trangular weave materals. MESTIS s developed entrely by Poltecnco d Torno and TICRA s role n the co-operaton has been to ensure that the output can be used for reflector antenna analyss software such as GRASP8. To ths end an auxlary program converts the scatterng matrx parameters from MESTIS nto the reflecton and transmsson coeffcents requred by GRASP8. In the followng sectons the electrcal propertes of the trangular weave wll be llustrated as a functon of some smple geometrcal parameters of the materal. The performance for a reflector antenna wth a typcal, trangular weave surface s calculated and the consequences are dentfed. MECHANICAL AND ELECTRICAL MODELLING OF THE TRIANGULAR WEAVE MATERIAL The geometrcal structure of the trangular weave s llustrated n Fg. 1. Three sets of parallel wre grds are tlted 12º wth each other. One notces that one set of wres passes alternately above and below the wres of the other sets. The ntersecton between one set and the two others takes place n the mddle between the ntersectons between these two other sets. The materal n Fg. 1 can easly be bent over a dual curved surface wth only a mnor deformaton of the mesh pattern. Once the wres are glued together a very lght weght but yet form stable reflector shell s obtaned. To arrve at the electrcal model t s assumed that all the wres are lyng n the same plane and that they are n electrcal contact at all ntersecton ponts. Wth ths assumpton we obtan the model shown n Fg. 2 whch we can consder as three co-planar strp grds each wth the spacng s and the strp wdth w. The reflecton and transmsson propertes of the structure n Fg. 2 can be analysed by MESTIS. It s possble to take nto account the fnte conductvty of the strp grd materal and also delectrc layers on both sdes of the strp grd can be consdered. In order to make the present nvestgaton smple t s assumed n the followng that the strp materal s a perfect conductor and no delectrcs are present. The structure n Fg. 2 can therefore be completely descrbed by the two parameters, s / λ and w / λ, where λ s the wavelength.

2 Fg. 1. The trangular mesh showng the nterleaved sets of carbon fbres W S Fg. 2 The electrcal model of the trangular weave. REFLECTION PROPERTIES OF THE TRIANGULAR WEAVE A planar sample of a general reflector materal s llustrated n Fg. 3. The drecton of an ncdent plane wave s gven by the sphercal coordnates(, φ ), where s measured from the postve z -axs and φ from the postve x -axs. The angle s lmted to the range < 9 o.

3 E r z E ˆφr ˆr ˆφ ˆ Surface materal φ y x ˆφt Fg. 3 E t ˆt Unt vectors for the defnton of reflecton and transmsson coeffcents n GRASP8. The ncdent plane wave can be decomposed as ˆ E = E + E ˆ φ (1) φ and s partly reflected and partly transmtted through the surface where the unt vectors of ncdence, ˆ and ˆ φ are the usual polar vectors shown n Fg. 3. The reflected feld s gven by where r r ˆ r E = E + E ˆ φ, (2) r φ r r E R R φ E r = E Rφ R φ φφ Eφ (3) and the unt vectors of reflecton, ˆr and ˆr φ are the negatve mrror mages of ˆ and ˆ φ, respectvely. Ths defnton mples for example that the reflecton coeffcents for a perfect conductor are R = R = + 1 and R = R =. Smlar relatons can be set up for the transmtted feld. φφ φ φ

4 The coeffcents R represent the couplng from the ncdent to the reflected - and φ -components, respectvely. These components are also referred to as R TMTM and R TETE, respectvely. Typcal values for the trangular grd n Fg. 2 can be s / λ = 1/2 and w/ s = 1/1. The MESTIS software has been used to calculate the four reflecton coeffcents for these values and for the ncdence angles 6 and φ 36. The results for R are presented by the plots n Fg. 4. The results for the off-dagonal elements are not shown because they are very small, more than 8 down. Two mportant characterstcs are readly dentfed from Fg. 4. The trangular grd n Fg. 2 s very regular wth symmetry planes every 3º n φ. Ths wll lmt the possble varaton n φ and the results n Fg. 4 show that n practce the reflecton coeffcents are constant n φ. Ths s a very useful concluson snce t means that t s only necessary to nvestgate the varaton wth. The other observaton from Fg. 4 s that R decreases wth ncreasng whereas R φφ ncreases. Ths can have an effect n crcular polarsaton for offset reflector antennas, as wll be demonstrated n the next secton. At normal ncdence, =, R = Rφφ =.6. Ths s due to a small amount of transmsson through the grd. When the trangular weave s used for a reflector antenna the peak gan wll be reduced by the same amount. If the grd spacng, s / λ, s ncreased the mesh becomes more open and the reflecton coeffcents wll decrease. Ths s llustrated n Fg. 5 whch shows R as functons of for dfferent values of s / λ. In ths graph the strp wdth relatve to the spacng s kept constant, w/ s =.1. Fg. 5 shows for example that f the strp spacng s ncreased to /.2 s λ = the transmsson loss ncreases to about.9. The varaton wth the strp wdth s shown n Fg. 6 for the constant value of the strp spacng, s / λ = 1/2. ampltude R-TMTM ampltude R-TETE φ φ 2 3 Fg. 4 The reflecton coeffcents R (left) (rght) versus the angle of ncdence (, φ )

5 s/λ = 1/4 s/λ = 1/2 s/λ = 1/ s/λ = 1/ Fg. 5 The reflecton coeffcents R (full lne) (dotted lne) versus the angle of ncdence from the normal wth the strp spacng relatve to the wavelength, s / λ, as parameter. The strp wdth relatve to the strp spacng s constant w/s = 1/5 w/s = 1/1 -.1 w/s = 1/ w/s = 1/ Fg. 6 The reflecton coeffcents R (full lne) (dotted lne) versus the angle of ncdence from the normal wth the strp wdth relatve to the spacng, w/ s, as parameter. The strp spacng relatve to the wavelength s constant 1/2.

6 APPLICATIONAL EXAMPLE In ths secton we wll llustrate the nfluence of the trangular weave materal for a sngle offset reflector antenna. The dameter s D = 5λ and the focal length s f = D. The feed s located at the focus and t s a smple Gaussan beam operatng n crcular polarsaton. The antenna s llustrated n Fg. 7. Fg. 7 Offset reflector antenna Fg. 8 shows the radaton pattern n the plane of asymmetry both for a sold reflector and for a reflector constructed as a trangular weave wth the typcal parameters, s / λ = 1/2 and w/ s = 1/1. For the sold reflector the co-polar component exhbts the typcal beam squnt n crcular polarsaton and the cross-polar lobes are very low, about 6 below the co-polar beam peak. For the trangular weave the co-polar component n Fg. 8 s ndstngushable from the sold reflector (although there s a transmsson loss of.6 ). However, the dfference between R generates a cross-polar component wth the same shape as the co-polar beam and the maxmum cross-polar lobe s now only about 45 below the co-polar peak. Ths result shows that wth a slghtly larger s / λ the cross-polar performance could soon become crtcal.

7 deg 6 Fg. 8 The radaton pattern n the plane of asymmetry for the antenna n Fg. 7. The full lne curve shows the co-polarsaton for both the sold reflector and the trangular weave. The curves wth short dots and long dots s the cross polarsaton for the sold reflector and the trangular weave, respectvely. CONCLUSIONS Ths paper has demonstrated how the reflecton propertes of a trangular weave can be determned by the MESTIS software developed by Poltecnco d Torno. It s shown that the reflecton coeffcents are almost ndependent of the azmuthal varaton of the angle of ncdence but they do depend on the angle from normal ncdence. It s demonstrated by an example how ths can affect the cross polarsaton performance for an offset reflector system operatng n crcular polarsaton. REFERENCES [1] R. Orta, R. Tascone, and D.Trnchero, USER MANUAL, Metallc Strp Smulator, Dpartmento d Elettronca and IRITI-CNR, Poltecnco d Torno, October 21.

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes

R s s f. m y s. SPH3UW Unit 7.3 Spherical Concave Mirrors Page 1 of 12. Notes SPH3UW Unt 7.3 Sphercal Concave Mrrors Page 1 of 1 Notes Physcs Tool box Concave Mrror If the reflectng surface takes place on the nner surface of the sphercal shape so that the centre of the mrror bulges