18968152 Introduction to Traveling Wave Antennas

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Introduction to Traveling-Wave antennasFabrizio Frezza March 19, 2006Traveling-wave antennas are a class of antennas that use a traveling wave on a guiding structure as the main radiating mechanism. Traveling-wave antennas fall into two general categories, slow-wave antennas and fast-wave antennas, which areusually referred to as leaky-wave antennas. In slow-wave antenna, the guided wa

ve is a slow wave, meaning a wave that propagates with a phase velocity that is

less than the speed of light in free space. Such a wave does not fundamentally radiate by its nature, and radiation occurs only at discontinuities (typically the feed and the termination regions). The propagation wavenumber of the travelingwave is therefore a real number (ignoring conductors or other losses). Because

the wave radiates only at the discontinuities, the radiation pattern physicallyarises from two equivalent sources, one at the beginning and one at the end of the structure. This makes it dicult to obtain highly-directive singlebeam radiation patterns. However, moderately directly patterns having a main beam near endre can be achieved, although with a signicant sidelobe level. For these antennas there is an optimum length depending on the desired location of the main beam. Examples include wires in free space or over a ground plane, helixes, dielectric slabs or rods, corrugated conductors. An independent control of the beam angle and t

he beam width is not possible. By contrast, the wave on a leaky-wave antenna (LWA) may be a fast wave, with a phase velocity greater than the speed of light. This type of wave radiates continuously along its length, and hence the propagation wavenumber kz is complex, consisting of both a phase and an attenuation constant. Highly-directive beams at an arbitrary specied angle can be achieved with this type of antenna, with a low sidelobe level. The phase constant β of the wave controls the

eam angle (and this can

e varied changing the frequency), while theattenuation constant α controls the be

¡ mwidth. The

¡ perture distribution c

¡ n

¡ lso

be e¡ sily t

¡ pered to control the sidelobe level or be

¡ m sh

¡ pe. Le

¡ ky-w

¡ ve

¡ ntenn

¡

s c¡

n be divided into two import¡

nt c¡

tegories, uniform¡

nd periodic, dependingon the type of guiding structure. A uniform structure h

¡

s¡

cross section th¡

tis uniform (const

¡ nt)

¡ long the length of the structure, usu

¡ lly in the form of

¡ w

¡ veguide th

¡ t h

¡ s been p

¡ rti

¡ lly opened to

¡ llow r

¡ di

¡ tion to occur. The guid

ed w ¡ ve on the uniform structure is ¡ f ¡ st w ¡ ve, ¡ nd thus r ¡ di ¡ tes ¡ s it prop ¡ g ¡

tes.

1



2

Introduction to TWA

A periodic le¡ ky-w

¡ ve

¡ ntenn

¡ structure is one th

¡ t consists of

¡ uniform struct

ure th¡

t supports¡

slow (non r¡

di¡

ting) w¡

ve th¡

t h¡

s been periodic¡

lly modul¡

ted in some f

¡ shion. Since

¡ slow w

¡ ve r

¡ di

¡ tes

¡ t discontinuities, the periodic

modul ¡ tions (discontinuities) c ¡ use the w ¡ ve to r ¡ di ¡ te continuously ¡ long the length of the structure. From

¡ more sophistic

¡ ted point of view, the periodic mo

dul¡

tion cre¡

tes¡

guided w¡

ve th¡

t consists of¡

n innite number of sp¡

ce h¡

rmonics (Floquet modes). Although the m

¡ in (n = 0) sp

¡ ce h

¡ rmonic is

¡ slow w

¡ ve, one

of the sp¡ ce h

¡ rmonics (usu

¡ lly the n = −1) is designed to

e a fast wave, and hence a radiating wave. A typical example of a uniform leaky

¢ wave antenna is a rec

tangular waveguide with a longitudinal slot. This simple structure illustrates the

asic properties common to all uniform leaky¢ wave antennas.

2 The fundamental TE10 waveguide mode is a fast wave, with β = ko − π a lower than ko. The radiation causes the wavenumber kz of the

£

ro£

agating mode within the o£

enwaveguide structure to become com

£

lex. By means of an a£ £

lication of the stationary-

£

hase£

rinci£

le, it can be found in fact that: 2

β c λo = = ko vph λg

sin θm

(1)

where θm is the ang¤ e of maximum radiation taken from broadside. As is typica

¤ for

a uniform LWA, the beam cannot be scanned too c¤ ose to broadside (θm = 0), since

this corresponds to the cuto fre¥

uency of the waveguide. In addition, the beam cannot be scanned too c

¤

ose to endre (θm = 90 ) since this re¥

uires operation at fre¥

uencies signicant ¤

y above cuto, where higher-order modes can propagate, at ¤ east fo

r an air- ¤ ¤ ed waveguide. Scanning is

¤ imited to the forward

¥

uadrant on¤ y (0 < θm <

π ), for a wave traveling in the£

ositive z direction. 2

Figure 1: Slotted guide (£

atented by W. W. Hansen in 1940) This one-dimensional(1D) leaky-wave a

£

erture distribution results in a “fan beam” having a narrow beam in the xz

£

lane (H£

lane), and a broad beam in the cross-£

lane. A£

encil beam canbe created by using an array of such 1D radiators. Unlike the slow-wave structu

re, a very narrow beam can be created at any angle by choosing a suciently smallvalue of α. A simple formul

¡ for the be

¡ m width, Europe

¡ n School of Antenn

¡ s



3

Introduction to TWA

me¡ sured between h

¡ lf power points (3dB), is: ∆θ

L λo

1 cos θm

(2)

where L is the¤ ength of the

¤ eaky-wave antenna, and ∆θ is expressed in radians. For

90% of the power radiated it can be assumed: L λo 0.18α ko

⇒ ∆θ ∝

α ko

Since le¡

k¡

ge occurs over the length of the slit in the w¡

veguiding structure, the whole length constitutes the¡

ntenn¡

’s eective ¡

perture unless the le¡

k¡

ge r¡

teis so gre

¡

t th¡

t the power h¡

s eectively le ¡

ked¡

w¡

y before re¡

ching the end of the slit. A l

¡ rge

¡ ttenu

¡ tion const

¡ nt implies

¡ short eective ¡

perture, so th¡ t t

he r¡ di

¡ ted be

¡ m h

¡ s

¡ l

¡ rge be

¡ mwidth. Conversely,

¡ low v

¡ lue of α results in

¡

long eective ¡

perture¡

nd¡

n¡

rrow be¡

m, provided the physic¡

l¡

perture is suciently long. Since power is r

¡

di¡

ted continuously¡

long the length, the¡

perture eldof

¡ le

¡ kyw

¡ ve

¡ ntenn

¡ with strictly uniform geometry h

¡ s

¡ n exponenti

¡ l dec

¡ y (

usu¡ lly slow), so th

¡ t the sidelobe beh

¡ vior is poor. The presence of the sidelo

bes is essenti¡

lly due to the f¡

ct th¡

t the structure is nite ¡

long z. When we ch

¡

nge the cross-section¡

l geometry of the guiding structure to modify the v¡

lue of α

¡ t some point z, however, it is likely th

¡ t the v

¡ lue of β at that point is also

modied slightly. However, since β must not

e changed, the geometry must

e furthe

r altered to restore the value of β, there

y changing α somewh ¡ t ¡ s well. In pr ¡ ctice, this diculty m ¡

y require¡

two-step process. The pr¡

ctice is then to v¡

ry thev

¡ lue of α slowly

¡ long the length in

¡ specied w ¡

y while m¡ int

¡ ining β constant (tha

t is the angle of maximum radiation), so as to adjust the amplitude of the aperture distri

ution A(z) to yield the desired sidelo

e performance. We can divide uniform leaky

¢ wave antennas into air

¢ lled ones and partially dielectric ¢ lled ones.In the rst case, since the transverse wavenum

er kt is then a constant with frequency, the

eamwidth of the radiation remains exactly constant as the

eam is scanned

y varying the frequency. In fact, since: β cos θm = 1 − ko2 2

(3)

where:2 2 ko = k t + β 2 ⇒

β ko

2

=1−

kt ko

2

⇒ cos θm =



kt ⇒ ∆θ ko

2π λc = kt L L

European Schoo¤ of Antennas



4

Introduction to TWA

independent of fre¥

uency. On the contrary, when the guiding structure is part¤ y ¤

¤

ed with die¤

ectric, the transverse wavenumber kt is a function of fre¥

uency, sothat ∆θ changes as the beam is fre

¥

uency scanned. On the other hand, with respect t

o fre¥

uency sensitivity, i.e., how¥

uick ¤ y the beam ang ¤ e scans as the fre¥

uencyis varied, the part

¤ y die

¤ ectric-

¤ oaded structure can scan over a

¤ arger range

of ang¤

es for the same fre¥

uency change and is therefore preferred.

Figure 2: Dispersion Curves (eective refractive index) In response to re¥

uirements at mi

¤ ¤ imeter wave

¤ engths, the new antennas were genera

¤ ¤ y based on

¤ ower-

¤ oss

open waveguides. One possib¤

e mechanism to obtain radiation is foreshortening aside. Let us consider for examp

¤ e the nonradiative die

¤ ectric guide (NRD).

Figure 3: Non Radiative Die¤ ectric guide The spacing a between the meta

¤ p

¤ ates

is¤

ess than λo so that a¤ ¤

junctions and 2 discontinuities (a¤

so curves) that maintain symmetry become pure

¤ y reactive, instead of possessing radiative content.

When the vertica¤

meta¤

p¤

ates in the NRD guide are

European Schoo¤

of Antennas



5

Introduction to TWA

sucient ¤ y

¤ ong, the dominant mode e ¤

d is comp¤ ete

¤ y bound, since it has decayed to

neg¤

igib¤

e va¤

ues as it reaches the upper and¤

ower open ends. If the upper portion of the p

¤ ates is foreshortened, a trave

¤ ing-wave e ¤

d of nite amp ¤ itude then e

xists a ¤ ong the ¤ ength of the upper open end, and if the dominant NRD guide modeis fast (it can be fast or s

¤ ow depending on the fre

¥

uency), power wi¤ ¤

be radiated away at an ang

¤

e from this open end. Another possib¤

e mechanism is asymmetry. In the asymmetrica

¤ NRD guide antenna the structure is rst bisected horizonta ¤

¤ y to provide radiation from one end on

¤ y; since the e

¤ ectric e ¤

d is pure¤ y verti

ca¤ in this midp

¤ ane, the e ¤

d structure in not a¤ tered by the bisection.

Figure 4: Asymmetrica¤ Non Radiative Die

¤ ectric guide An air gap is then introdu

ced into the die¤ ectric region to produce asymmetry. As a resu

¤ t, a sma

¤ ¤ amount

of net horizonta¤ e

¤ ectric e ¤

d is created, which produces a mode in the para¤ ¤ e

¤

-p¤

ate air region, which is a TEM mode, which propagates at an ang¤

e between thepara

¤ ¤ e

¤ p

¤ ates unti

¤ it reaches the open end and

¤ eaks away. It is necessary t

o maintain the para¤ ¤

e¤

p¤

ates in the air region sucient

¤

y¤

ong that the vertica¤

e¤

ectric e ¤

d component of the origina¤

mode (represented in the stub guide by the be

¤

ow-cuto TM1 mode) has decayed to neg¤

igib¤

e va¤

ues at the open end. Then theTEM mode, with its horizonta

¤ e

¤ ectric e ¤

d, is the on¤ y e ¤

d¤ eft, and the e ¤

d po¤ a

rization is then essentia¤ ¤ y pure (the discontinuity at the open end does not in

troduce any cross-po¤

arized e ¤

d components). Groove guide is a¤

ow-¤

oss open waveguide for mi

¤ ¤

imeter waves, somewhat simi¤

ar to the NRD guide: the die¤

ectric centra

¤ region is rep

¤ aced by an air region of greater width. The e ¤

d again decaysexponentia

¤ ¤ y vertica

¤ ¤ y in the regions of narrower width above and be

¤ ow. The

¤

eaky-wave antenna is created by rst bisecting the oset groove guide horizonta ¤ ¤

y.It a

¤

so resemb¤

es a rectangu¤

ar waveguide stub¤

oaded. When the stub is o-centered, the structure wi

¤ ¤ radiate. When the oset is increased, the attenuation consta

nt α will incre¡ se

¡ nd the be

¡ mwidth will incre

¡ se too. When the stub is pl

¡ ced

¡ l

l the w ¡ y to one end, the result is ¡ n L-sh ¡ ped structure th ¡ t r ¡ di ¡ tes very strongly. In

¡

ddition, it is found th¡

t the v¡

lue of β changes very little as the

European School of Antennas



6

Introduction to TWA

Figure 5: Groove guide stu

is moved, and α v¡ ries over

¡ very l

¡ rge r

¡ nge. This f

e¡

ture¡

llows to t¡

per the¡

ntenn¡

¡

perture to control sidelobes. The f¡

ct th¡

tthe L-sh

¡ ped structure strongly le

¡ ks m

¡ y

¡ lso be rel

¡ ted to

¡ nother le

¡ k

¡ ge mec

h ¡ nism: the use of le ¡ ky higher modes. In p ¡ rticul ¡ r, it m ¡ y be found th ¡ t ¡ ll the groove-guide higher modes

¡ re le

¡ ky. For ex

¡ mple, let us consider the rst high

er¡

ntisymmetric mode. Bec¡

use of the symmetry of the structure¡

nd the directions of the electric-eld lines, the structure c ¡

n be bisected twice to yield the L-sh

¡ ped.

Figure 6: Sketches showing the tr¡

nsition from the T E20 mode in the full grooveguide, on the left, to the L-sh

¡ ped

¡ ntenn

¡ structure on the right. The tr

¡ nsit

ion involves two successive bisections, neither of which disturb the eld distribution. The

¡ rrows represent electric eld directions. The ¡

ntenn¡ m

¡ y be

¡ n

¡ lyzed u

sing¡

tr¡

nsverse equiv¡

lent network b¡

sed on¡

T-junction network. The expressions for the network elements

¡ re in simple closed forms

¡ nd yet

¡ re very

¡ ccur

¡ t

e. Usu¡

lly, the stub length needs only to be¡

bout¡

h¡

lf w¡

velength or less ifthe stub is n¡

rrow. To exploit the possibility of printed-circuit techniques,¡

printed-circuit version of the previous structure h

¡

s been developed. In this w¡

y the f¡ bric

¡ tion process could m

¡ ke use of photolithogr

¡ phy,

¡ nd the t

¡ per desi

gn for sidelobe control could be h¡ ndled

¡ utom

¡ tic

¡ lly in the f

¡ bric

¡ tion. The t

r¡

nsverse equiv¡

lent network for this new¡

ntenn¡

structure is slightly more complic

¡

ted th¡

n the previous,¡

nd the expressions for the network elements must bemodied ¡

ppropri¡ tely to t

¡ ke

Europe¡

n School of Antenn¡

s



7

Introduction to TWA

Figure 7: Equiv¡ lent Tr

¡ nsverse Tr

¡ nsmission Network of Groove guide the dielect

ric medium into¡

ccount. Moreover,¡

bove the tr¡

nsformer,¡

n¡

ddition¡

l suscept¡

nce Bs¡ ppe

¡ rs. The stub

¡ nd m

¡ in guides

¡ re no longer the s

¡ me, so their w

¡ venu

mbers ¡ nd ch ¡ r ¡ cteristic ¡ dmitt ¡ nces ¡ re ¡ lso dierent.

Figure 8: Eect of the structure¡

symmetry on the prop¡

g¡

tion ch¡

r¡

cteristics Ag¡

in, α c

¡ n be v

¡ ried by ch

¡ nging the slot loc

¡ tion d. However, it w

¡ s found th

¡ t

¡ i

s¡ lso

¡ good p

¡ r

¡ meter to ch

¡ nge for this purpose. An interesting v

¡ ri

¡ tion of

the previous structures h¡ s been developed

¡ nd

¡ n

¡ lyzed. It is b

¡ sed on

¡ ridge

w¡

veguide r¡

ther th¡

n¡

rect¡

ngul¡

r w¡

veguide. In the structures b¡

sed on rect¡

ngul

¡ r w

¡ veguide, the

¡ symmetry w

¡ s

¡ chieved by pl

¡ cing the stub guide, or loc

¡ ti

ng the longitudin¡ l slot, o-center on the top surf ¡

ce. Here the top surf¡ ce is sy

mmetric¡ l,

¡ nd the

¡ symmetry is cre

¡ ted by h

¡ ving unequ

¡ l stub lengths on e

¡ ch s

ide under the m¡

in-guide portion. The tr¡

nsverse equiv¡

lent networks, together with the

¡ ssoci

¡ ted expressions for the network elements, were

¡ d

¡ pted

¡ nd extend

ed to¡

pply to these new structures. Europe¡


s



8

Introduction to TWA

Figure 9: Eect of the stub width on the ph ¡ se

¡ nd the

¡ ttenu

¡ tion const

¡ nts An

¡ n

¡

lysis of the¡

ntenn¡

beh¡

vior indic¡

tes th¡

t this geometry eectively permits independent control of the

¡ ngle of m

¡ ximum r

¡ di

¡ tion θm and the beamwidth ∆θ. m Let us d

ene two geometric parameters: the re ¤ ative average arm ¤ ength ba where b ¤ −

r

l +

r ∆b bm = 2 ,¡ nd the rel

¡ tive unb

¡ l

¡ nce bm , where ∆b = 2 .

Figure 10: Ridge guide.β m It then turns out that

y changing

a one can adjust the value of ko without α α¡

ltering ko much¡ nd th

¡ t by ch

¡ nging ∆b one c

¡ n v

¡ ry ko over

¡ l

¡ rge r

¡ nge without

bm β aecting ko much. The taper design for controlling the sidelo

e level would therefore involve only the relative un

alance ∆b . The tr¡ nsverse equiv

¡ lent network

is slightly bm complic¡ ted by the presence of two

¡ ddition

¡ l ch

¡ nges in height

of the w¡ veguide, which c

¡ n be modeled by me

¡ ns of shunt suscept

¡ nces

¡ nd ide

¡ l

tr¡

nsformer. The ide¡

l tr¡

nsformer¡

ccounts for the ch¡

nge in the ch¡

r¡

cteristicimped

¡ nce, while the storing of re

¡ ctive energy is t

¡ ken into

¡ ccount through t

he suscept¡

nce. Sc¡

nning¡

rr¡

ys¡

chieve sc¡

nning in two dimensions by cre¡

ting¡

one-dimension¡

l ph¡

sed¡

rr¡

y of le¡

ky-w¡

ve line-source¡

ntenn¡

s. The individu¡

lline sources

¡

re

Europe¡ n School of Antenn

¡ s



9

Introduction to TWA

Figure 11: Equiv¡ lent Tr

¡ nsverse Tr

¡ nsmission Network of Ridge guide sc

¡ nned in

elev¡

tion by v¡

rying the frequency. Sc¡

nning in the cross pl¡

ne,¡

nd therefore in

¡ zimuth, is produced by ph

¡ se shifters

¡ rr

¡ nged in the feed structure of the o

ne-dimension ¡ l ¡ rr ¡ y of line sources. The r ¡ di ¡ tion will therefore occur in pencil-be

¡ m form

¡ nd will sc

¡ n in both elev

¡ tion

¡ nd

¡ zimuth in

¡ conic

¡ l-sc

¡ n m

¡ nne

r. The sp¡

cing between the line sources is chosen such th¡

t no gr¡

ting lobes occur,

¡ nd

¡ ccur

¡ te

¡ n

¡ lyses show th

¡ t no blind spots

¡ ppe

¡ r

¡ nywhere. The describe

d¡ rr

¡ ys h

¡ ve been

¡ n

¡ lyzed

¡ ccur

¡ tely by unit-cell

¡ ppro

¡ ch th

¡ t t

¡ kes into

¡ cc

ount¡ ll mutu

¡ l-coupling eects. E ¡

ch unit cell incorpor¡ tes

¡ n individu

¡ l line-so

urce¡

ntenn¡

, but in the presence of¡

ll the others. The r¡

di¡

ting termin¡

tion on the unit cell modies the tr ¡

nsverse equiv¡ lent network. A key new fe

¡ ture of th

e¡ rr

¡ y

¡ n

¡ lysis is therefore the determin

¡ tion of the

¡ ctive

¡ dmitt

¡ nce of the

unit cell in the two-dimension¡ l environment

¡ s

¡ function of sc

¡ n

¡ ngle. If the

v¡

lues of β and α did not ch¡

nge with ph¡

se shift, the sc¡

n would be ex¡

ctly conic¡

l. However, it is found th¡ t these v

¡ lues ch

¡ nge only

¡ little, so th

¡ t the devi

¡

tion from conic¡

l sc¡

n is sm¡

ll. We next consider whether or not blind spots¡

re present. Blind spots refer to¡

ngles¡

t which the¡

rr¡

y c¡

nnot r¡

di¡

te or receive

¡

ny power; if¡

blind spot occurred¡

t some¡

ngle, therefore, the v¡

lue of α would r

¡ pidly go to zero

¡ t th

¡ t

¡ ngle of sc

¡ n. To check for blind spots, we woul

d then α look for¡ ny sh

¡ rp dips in the curves of ko

¡ s

¡ function of sc

¡ n

¡ ngle.

No such dips α were ever found. Typic¡

l d¡

t¡

of this type exhibit f¡

irly ¡

t beh¡

vior for ko until the curves drop quickly to zero

¡

s they re¡

ch the end of the conic

¡ l sc

¡ n r

¡ nge, where the be

¡ m hits the ground.

Europe¡


s



10

Introduction to TWA

References[1] C. H. W

¡

lter: Tr¡

veling W¡

ve Antenn¡

s, McGr¡

w Hill, Dover, 1965-1970, reprinted by Peninsul

¡ Publishing, Los Altos C

¡ liforni

¡ , 1990. [2] N. M

¡ rcuvitz: W

¡ veg

uide H ¡ ndbook, MCGr ¡ w Hill, 1951, reprinted by Peter Peregrinus Ltd, London, 1986. [3] V. V. Shevchenko, Continous tr

¡ nsitions in open w

¡ veguides: introduction

to the theory, The Golden Press, Boulder, Color¡

do 1971; Russi¡

n Edition, Moscow, 1969. [4] T. Rozzi

¡ nd M. Mongi

¡ rdo, Open Electrom

¡ gnetic W

¡ veguides, The Inst

itution of Electric¡ l Engeneers, London, 1997. [5] M. J. Ablowitz

¡ nd A. S. Foke

s, Complex v¡ ri

¡ bles: Introduction

¡ nd Applic

¡ tions, second edition, C

¡ mbridge U

niversity Press, 2003. [6] A. A. Oliner (princip¡

l investig¡

tor), Sc¡

nn¡

ble millimeter w

¡ ve

¡ rr

¡ ys, Fin

¡ l Report on RADC Contr

¡ ct No. F19628-84-K-0025, Polytech

nic University, New York, 1988. [7] A. A. Oliner, R¡ di

¡ ting periodic structures:

¡ n

¡ lysis in terms of k vs. β diagrams, short course on Microwave Field and Networ

k Techniques, Polytechnic Institute of Brooklyn, New York, 1963. [8] A. A. Oliner (principal investigator), Lumped

¢ Element and Leaky

¢ Wave Antennas for Millimete

r Waves, Final Report on RADC Contract No. F19628¢

81¢

K¢

0044, Polytechnic Institute of New York, 1984. [9] F. J. Zucker, Surface and leaky¢

wave antennas, Chapter16.

European School of Antennas

18968152 Introduction to Traveling Wave Antennas

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Transcript of 18968152 Introduction to Traveling Wave Antennas