unit iv,sliet

8/13/2019 unit iv,sliet

1/9

754 I ANH:


2/9

Ir.-IS SURFACEWAVE AND LEAKY VAVi ANTENNAS 755

Medium 1 Eair)

H,. 90

o ection ofenergy f low

MedIum 2 (perfect conductor)~ ~

E,H,

MedIum 1(air)

O eclmn of~ r g y i l o wE, ---. . . . . . b)

E ~MedIum 2 (conductor wIlnfInite conductIVIty,,)

Figure 16-36 Vertically polarized wave travehng 10 nght al along surface of a perfectly ~ o n d U C l l n gmedium and b) along surface of medIum wah finite conductivity.

At the conducting surface the average power into the conductor - y direction) isSy = t Re ExH: (2)

This is power dissipated as heat in the conductor.The space relation of Ex, H= or H:) and Syis shown in Fig.

E ~ = ZH ,where Ze = intrinsic impedance of the conductorthen from 2) the power flow into the conductor can be written as

Sy = tH=H: Re Z, = -tH;o Re Zcwhere H. = H . o e j ~

H: = H , o e i ~ Y X = complex conjugate of Hz= phase lag of H. with respect to E ~

} = propagation constant = 11 + iPThe power flow parallel to the surface x direction) is

S ~ = t R e E H : (Wm-I)Medium 1

16-37a. Since

I L- 'hE.----C s._ - - - r = ; : : : : ~ S : t . : :,


3/9

756 16 ~ N T E N I I A S FOil S P E C I A ~ APPlICATIONS- FEEDING CONSIDHATIONSThe space relation of Ey, Hz and S is shown in Fig. 16-37b. Since

(6)where Zd = intrinsic impedance of the dielectric medium (air) above the conduc-

tOt Ithen from (5) the power flow along the conductor (x-di tection) can be written

(1)The total average Poynting vector is then

S . = x x + y ~ = H;o x Re ZJ - YRe Ze (8)Figure 16-37c shows the relation of Sa. to its X and y components. I t is apparentthat the average power flow is not parallel to the surface but downward at anangle t. This angle is the same as the forward tilt angle of the electric field seeFig. 16-36b . I f the conductivity of the conductor is infinite (0- = 00), the tilt iszero ( t = 0).

From (8) the tilt anglet = tan-1 Re Z


4/9

RelativeelectfIeld

' '

1 6 1 ~ SURFACE_WAVE AND LEAln_WAVE ANTENNAS 757

~ ~ .112.5 67.5

147.5 22.5

202.5 337.5

225 .2475. 292.5. 270

'Figure 16-38 (a) Magnitude variation with time of , and E. components o f in air at the surfaceof a copper region for a 3--GHz TEM wave t r a ~ e h n g paralle1to the surface. (b) Resultant values of E(space vector) at 22.5- intervals over one cy


5/9

758 16 ANTENNAS FOR SPECIAL APPLICATIONS, FEEDlNr. CONSIOF-RATIONS,147,5'

135 0112-5"

67.5" 9 0 ' ~ - < -

Figure 16-39 Poynting vector in air at a point on the surface of a copper region for a 3"GHz TEMw a ~ C traveling along the surface 110 rightl. The Poynting .ector IS shown al 22,)" intervals over at-cycle, The ordmate values are magnified 5000 times compared With the absei""a values. The tip ofIhc Poynllng vector travels around the ellip


6/9

,

'

16_,5 SURFACEWAVE ND LEAKY_WAVE ANTENNAS 759Wave

.... ::::= Oielectrlc Yd eCIlOn

E Tilt angle

0f 'o r ~

AConductor

Figure 16-41 Dielectric-slab surface-wave antenna wah horn wave_launcher.

where Zd = intrinsic impedance of medium filling the slots, ne = relative permittivity of the medium, dimensionlesso = free-space wavelength, m

= depth of slots, mFor air-filled slots Zd = 377 nand e = I), (12) reduces to

2ndZ jl20rr tan -) '

0) (13)

The slots store energy from the passing wave. When d < )_0/4, the plane along thetop of the teeth is inductively reactive. When = A0I4, Z = co and the planealong the top is like an open circuit (nothing below), while when = ;'0/2, Z = 0and the plane appears like the conducting sheet below it (a short circuit).

The guiding action of a flat condUcting surface can also be enhanced byadding a dielectric coaling or slab of thickness d. With a launcher, as in Fig.16-41, the combination forms another type of surface-wave antenna. The electricfield is vertically polarized but has a small forward tilt at the dielectric surface.For a sufficient thickness d, the fields attenuate perpendicular to the surface ydirection) as e - ~ ~ where

(14)

For e = 2, the attenuation is over 50 dB ;, - 1 . Thus, the fields are confined closeto the surface.

Corrugated and dielectric slab surface-wave antennas, as in Figs. 16-40 and16-41, with a length of several A and, a width of 1 1 or more (into page), produceend-fire beams with gain proportional to their .length and width. It is assumedthat the conducting surface (ground plane) extends beyond the end of the corru_gations or slab. I f not, the beam direction tends to be off end-fire (elevated). Foroptimum patterns. the depth of the slots or thickness of the slab may be taperedat both ends.Although sur/ace-wave antennas take many fonns, the ones described aboveare typical. They are traveling-wave antennas carrying a bound wave with theenergy flowing above the guiding surface and with velocity v < c slow wave). Ewould be perpendicular to the surface except for its forward tilt.


7/9

760 16 ANTf_NNAS O ~ SPECIAL APPLICATIONS, FEEDING CONSIDERATIONSBeam

EOpe/IOPm - - ~ ' - - = ' = - - - ' ~ - ,E d \ G U ' , , _ , . . . . , ~ _ - - - C S i ' d ; ' - - - - - _ . . . J r.gun 16-42 Open-top wavegUIdeantenna with continuous energyleakage_Leaky wave antennas are also traveling-wave types but ones in which radiating energy leaks continuously or periodicaliy from along the length of the

guiqing structure, with most of the energy flow wilhin the structure. Typically,but not necessarily, the structure carries a ast wave v > c). A hollow metal waveguide is an example. With one wall removed, energy can leak out continuously allalong the guide.

A leaky-waveguide antenna of this type is shown in Fig. 16-42. Since thewave velocity v in the guide is faster than the velocity c of light, the radiationforms a beam inclined at an angle t with the guide as given by

IS)

For v = 1.5c, t = 48. Since v is a function of the frequency, the beam angle tmay be scanned by a change in frequency.A leaky-wave antenna may also be constructed by cutting holes or slots ata regular spacing along the waveguide wall as in Fig. 16-43 (see also the slottedwaveguide of Fig. 13-5). Leakage may be controlled by the slot or hole size. For aslot or hole perimeter of ... 1..1. leakage is large but decreases rapidly with adecrease in perimeter. This periodic structure radiates at a beam angle t givenfrom 7-11-8) by

where s = hole or slot spacing, m1.0 = free-space wavelength, m1.9 = wavelength in guide, mm = mode number, 0, t, I,Example. Find the beam angle t for II = t.SAo, s = Ao and m = 1.So/ tiQII. Frorn.. 16),

in back-fire direction)

16)


8/9

eam

Fi&me 16 43 Slotted-waveguIdeantenna with leakage at penodic(discrete) intervals.

f the slots are spaced )./2 instead of tJ., proper phasing requires that alternate ones be placed on opposite sides of the centerline. For this case m = - in16). The beam angle > may be scanned by a change in frequency. Although

described here as a leaky-wave antenna, the antenna of Fig. 16-43 may also beconsidered as simply an array of waveguide slots.Consider now a dielectric slab waveguide of thickness d with wave injectedat small enough (below the critical angle) so that the wave is totally internally

reflected and propagates by multiple reflections inside the slab. The situation issimilar to that for the submerged radio transmitter in Sec. 16-14, except that herethe denser medium has upper nd lower boundaries and a thickness of the orderof 1 1 0 . Although the energy is transmitted inside the slab, fields exist above andbelow. These, however, are evanescent and decay exponentially away from theslab. They convey no energy. (Recall the evanescent wave above the water surfacein Sec. 16-14.)

t might be supposed that any wave injected into the slab at an angle belowthe critical value will propagate, but, because of multiple-reflection interference,waves will only propagate at certain angles (eigenvalues). Figure 16-44 is an endview of a dielectric slab waveguide carrying a wave with electric field parallel to

Evanescentfield Air Slab

EAir

Figure 16 44 End view of dielectric slab waveguideWIth E parallel to the slab surfaces. Propagation IS tntothe page. Arrows and graph (at left) indicate variallonin magmlude of E across the thickness d of the slab. Thefield outside the slab is evanescent and transmits noenergy.

I J. D. Kraus. Electromtl{l elics, Jrd cd., McGraw-Hili, 1984. p. 590.D. Marcuse, Theor} fJj Dieleclric Optical WalJeguides, Academic Press, 1974.


9/9

762 16 ~ N T E N N S fOI. SI'ECI"L "PPUC"T ONS FEEDING CONSIDER"TlONSthe surfaces (perpendicular to the plane of incidence). In the notation of Sec.16-14 this is an E L field. Propagation is into the page. The evanescent field aboveand below the slab matches the field inside but carries no energy. However, discontinuities on the slab surface can cause energy leakage from inside and radiation. Thus, a dielectric slab with surface discontinuities can act as a leaky-waveantenna.A dielectric cylinder can also serve as a guide in the same manner as a slab.At or near optical wavelengths the cylinder diameter can be physically small orthreadlike. Such guides, or Optical fibers. consist typically of a transparent glasscore surrounded by a glass sheath or cladding of slightly lower index of refraction,with the ~ h e t h enclosed in an opaque protective jacket. A typical core fiber5 m in diameter is as fine as a human hair and can carry one thousand 2-way

voice communication channels with an attenuation as small as 1 dB km - atlight or infrared wavelengths t to 1 }lm .The literature on surface- and leaky-wave antennas is extensive. Summarytreatments are given by Zucker and by Mittra.'

16-16 ANTENNA DESIGN CONSIDERATIONS FOR SATELLITECOMMUNICATION. In 1945 while a radar officer in the Royal Air Force,Arthur C. Clarke published an article in Wire/ess World in which he proposedthe use of artificial satellites and, in particular, those in a geostationary orbit, as asolution to the world's communication problem. The idea then seemed farfetched to many but 12 years later Sputnik went up and only 6 years after that, in1963 the first successrul geostationary satellite, Syncom 2 was put into orbit andClarkes proposal became a reality. Now there are hundreds of satellites l in thegeostationary or Clarke orbit with more being added at frequent intervals. Thesatei ites move with the earth as though attached to it so that from the earth eachappears to remain stationary above a fixed point on the equator. These satellitesform a ring around the earth at a height of 36000 km above the equator, puttingthe earth in the company of other ringed planets, Saturn and Uranus, with thedifference that the earth's ring is man-made and not natural. Arthur Clarke hasobserved that the ancient superstition that our destinies are controlled by celestial bodies has al last come true, except that the bodies are ones we have put upthere ourselves.Having a transmitting (transponder) antenna on a Clarke-orbit satellite islike having it on an invisible tower 36000 km high. Since earth-station disheslook upward at the sky, ground reflections are eliminated but the ground is still

F. J Zucker (cllap. (2) and R. Mittra (chap. 10), in Ame . Engineering Handbook McGraw_Hili,1984., A. C. Clarke, "Extra-terrestrial Relays H Wireless World 51, 305--308. October 1945.] Nearly 500 al the end of t986.

Jj

unit iv,sliet

Documents

Transcript of unit iv,sliet