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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 37, NO. 12, DECEMBER 1989

A Feasibility Study of Stripline-Fed Slots Arranged

as a Planar Array with Circular Grid and Circular

Boundary

Abstmct- An

experimental study of the self-impedance of stripline-

fed slots has

been

undertaken, with slot length and slot offset relative

to the strip as parameters. The slot is cut in one wall of a parallel plate

waveguide and locally a cylindrical cavity is created around the slot by

two p =

constant walls and two

6 =

constant walls. Such cavities can

be used as modules to build a circular grid planar array. Anticipating

a corporate feed, it is demonstrated that sufficient dynamic range in

the self-impeda nce is achievable to overcome the effects of mutual cou-

pling, thereby opening up the prosp ect of an efficient circular grid array

for seeker antenna applications that require good sum and difference

patterns.

INTRODUCTION

ANAR ARRAYS possessing quadrantal symmetry and

p”

onfined within a circular boundary find wide application

as seeker antennas in radar systems, particularly those that

are airborne. The most commonly encountered type of such

array is shown in Fig. l(a ) and consists of a fam ily of rect-

angular waveguides into which sequ ences of long itudinal slots

have been cut. The design of these waveguide-fed slot arrays

has advanced to such a stage that no input experimental data

are needed [l] . Self-admittance, including the effect of wall

thickness, and mutual cou pling are both d etermined theoreti-

cally w ith the aid of efficient, affordable computer programs

Despite this high state of development, waveguide-fed slot

arrays suffer from several shortcomings. First, they do not

use the “real estate” along the circular periphery optimally,

resulting in some loss in aperture efficiency. Second, they

are narrow-band for two reasons: 1) the slots are inherently

frequency sensitive, and

2)

the slots are typically resonantly

spaced along each w aveguide, so the feeding structure is also

frequency sensitive.

Also,

the rectangular grid arrangement of

the slots is not the natural one if a symmetric sum pattern

is desired, as is usually the case

[3].

These shortcomings can be alleviated if on e adopts a circu-

lar grid arrangement for the slots, as shown in Fig. le), nd

also a corporate feed arrangement to provide the excitation.

121

b)

Fig. 1.

Planar arrays of collinear slots. Circular boundary. Only ne quad-

rant shown.) (a) Rectangular grid.

@)

Circular grid.

There is no wasted “real estate” at the periphery, the pattern

can be im proved, and the bandwidth is better because of the

frequency insensitivity

of

the feeding structure.

In 1981, Stem reported on a successful design of a

microstrip-fed collinear dipole array, arranged in a circiular

grid and employing a co rporate feed

[4].

The design had been

Manuscript received November 12, 1987; revised June 30, 1988.

R. I . Barnett, Jr. is with the Department of Electrical and Computer Engi-

R . S. Elliott is with the Department of Electrical Engineering. University

made difficult by the need to measure both self- and mutual

impedance as functions

Of

dipole length and Offset (the latter

also as a function of relative dipole position). Later, these dif-

ficulties were overcome by Katehi, w ho first obtained accurate

theoretical results for the self-impedance [5] and then the mu-

neering, California State University, Los A ngeles, CA 90032.

of California, Los Angeles, CA 90024.

IEEE Log Number 8929325.

0018-926X/89/1200-1510$01.00

989 IEEE



BARNETT, JR.

AND ELLIOTT: STUDY OF

STRIPLINE-FED SLOTS

1511

tual impedance [ 6 ] . t is now feasible to design a microstrip-

fed dipole array without the need to acquire any input data

experimentally. These are attractive antennas because of their

low profile, high-precision fabrication, and low manufactur-

ing cost. However, the dielectric contributes loss and weight.

Also, the presence of the microstrip corporate feed scatters

surface waves, an effect not included in Katehi's theory. This

causes some pattern degradation and input mismatch.

If slots in a ground plane are substituted for the dipoles, the

microstrip becomes stripline and we obtain the dual of Stern's

dipole array. This has some inherent advantages. External mu-

tual coupling can be calculated easily by using the half-space

Green's function, as was done in [I]. The slots need to be iso-

lated from each other internally by pin curtains, to insure that

only the transverse electromagnetic (TEM) mode propagates,

but this affords the opportunity to elim inate the dielectric (ex-

cept for small stanchions to hold the strips in place). Thus the

losses and weight become comparable to those of waveguide-

fed slot arrays, with the potential advantages of better ape rture

efficiency, better patterns, and an increased bandwidth.

Because of the lure of these advantages, a series of prelim-

inary studies of stripline-fed slots has been pursued in recent

years. Park [7] investigated an array of nonoffset longitudi-

nal broadwall slots in a rectangular waveguide, made into a

boxed stripline by the addition of an internal meandering strip.

Park's strip passed centrally under each slot at angles that con-

trolled the amounts of coupling. Shavit

[8]

studied arrays of

transverse slots in the broadwall of a rectangular waveguide,

once again made into a boxed stripline by the inclusion of

an internal strip. For Shavit, the strip was straight and longi-

tudinal, but closer to one side wall. The degree of coupling

was controlled by transverse displacement of each slot. Shavit

needed transverse pin curtains to enclose each slot in a cavity

in order to prevent propagation of the TElo mode. Robert-

son [9] varied Shavit's geometry by using a meandering strip

that passed centrally under each transverse slot at angles that

controlled the couplings.

A common conclusion was reached in these three studies:

to lower the amount of coupling to

a

single slot to a value that

would permit use of a linear array of even a modest number

of slots, and still provide an input match, pushed one into the

region of light coupling where tolerances became critical. In

other words, slots excited by a centered inclined strip, or by a

transverse off-center strip were well suited for unity coupling

but not for light coupling. But this means that a corporate

stripline feed is ideal for the excitation of the slots, with the

proper level of coupling achieved by strip inclination, or off-

set, or a combination of the

two.

We have not yet mentioned mutual coupling. If 2 0 ~s the

characteristic impedance of the TEM mode associated with

the stripline exciting the nth slot, what we desire is that

Z i

=

Zo, ,

where

Z i

is the active impedance of the nth

slot. In other words,

2;

is the self-impedance of the nth slot

plus the weighted sum of its mutual im pedances with all other

slots in the array, these weights being related to the aper-

ture distribution. In order to satisfy 2; = Z O , ~ ,he latter

being a pure real number (neglecting losses), we must have

X;lf = -1m (MC,) and RS,If+Re (MCn) = 20 , where MCn

.

\

1 17/ B ,

I

1

L I - -

Pm

Fig. 2.

The

mth

ring

of

stripline-fed slots. Only one quadrant shown.)

is the complex mutual coupling term. This means that one re-

quires the dynamic range of both the real and imaginary parts

of P tfo be sufficient to compensate for the effects of m utual

coupling. It has been the purpose of the present investigation

to determine experimentally, for a typical practical case, the

extent of the dynamic range of elfor a single slot in vari-

ous cylindrical-section cavities, as functions of slot length and

stripline offset with a

90

crossing angle.

A

sufficient dynamic

range would permit use of the design procedure used in [ 2 ] .

THEDESIGNUNCTIONS

Imagine a circular grid array of collinear stripline-fed slots

for which part of one quadrant is depicted in Fig. 2 . We ob-

serve that a cavity has been constructed underneath each slot

by using pin curtains at the radii

P m

and P m + l and along the

angular directions

4,,

= n/2 . n l / N m ,with 4Nm the

number slots on the mth circle. One branch of the corpo-

rate stripline feed enters each cavity at a place where a pin

has been removed and crosses transversely under the slot, of

dimensions 21 by w , at a distance s from the end of the slot.

If the fields

of

the TEM mode are negligible at the four

pin curtain walls of the cavity, compared to their values in the

region between the strip and the upper ground plane, the slot

will scatter TEM modes asymmetrically in the two directions

along the strip, as a result of which the slot can be viewed

as a series impedance load on the TEM line. For this reason,

proper termination requires that the strip end (approximating

an open circuit) one quarter wavelength beyond the slot. This

is suggested in Fig. 2.

Let us define an input port at some convenient cross section

of the branch stripline which excites the mnth slot. Then we

can write

M

4N

p = l

q = l



1512 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.

37,

NO. 12 DECEMBER 1989

where

V,,

,I,, are the TEM mode voltage and mode current

at the mnth port, with 2;: the mutual imped ance between the

mnth a nd pq th ports. It has been assumed in (1) that the array

consists of M concentric rings. The active impedance at the

mnth port is given by

where Z z : is the impedance seen at the mnth port when all

other ports are o pen circuited and Zb,, is the mode-current-

weighted sum of the mutual impedances. The prime on the

double summation means the term p =m , q

=

n is deleted.

If 2;: is negligibly affected by removal of all other slots

(usually a good assumption), then the first design equation

can be written in the form

z; =2:: +zb,,

(3)

where Zk is the characteristic impedance

of

the branch

stripline feeding the mnth slot and ;; is the isolated

impedance of that slot. Equation (3) imposes a match and

requires that the mnth slot be detuned so that

XR5f

= - X i , , ,

RZ5f

+

R i , =Zk . Equations (2) and

(3)

are useful because,

if all ch aracteristic impedances are the same (the commonly

encountered case), then

Zk,/Ziq

is the ratio of the powers

being fed to the mnth and pq th slots, which is necessary in-

formation when designing the power splitters in the corporate

feed.

Howev er, there is another equally useful form to the first

design equation. If the E-field distribution in a slot, induced

by a wave traveling externally across the ground plane from

another slot, is similar to the E-field distribution caused by a

TEM mode crossing under the slot internally,' then

m n = f m n ( s m n , 1mn)V;n (4)

where B,, is the total backscattering in the TEM mode, com-

posed of the linear sum of thre e parts:

1)

one due to the TEM

mode passing under the slot, traveling from the port to the

open circuit, 2) one due to the TEM mode passing under the

slot, traveling from the open circuit to the port, and 3) one

due to the composite of waves traveling externally across the

ground plane, originating at the other slots. Also in

(4), Vk,

is the slot voltage , defined such that

E,,

= V ,/W is the av-

erage value of the transverse electric field in the central cross

section of the slot. In parallel with the decomposition of Bm,

we can write

(5 )

In (4), the function

fmn smn,,,

indicates that the rela-

tion between slot voltage and TEM backscatter depends on

strip offset and slot length. This function can be d etermined

experimentally.2

VL, = V n, +

G n . 2

+ VLn,3-

This has already been found to be a g ood assumption

for

waveguide-fed

slots when

w << 21

and Z - ho/2, (see [lo]) and should be equally valid

here.

See [8] for how this was done for the case o f identical rectangular cavities.

Here, the function depends on which cavity one is considering because the

slot orientation relative to the pin curtain walls varies from cavity to cavity.

6)

with

I,,

the TEM mode current and Zkn the active

impedance of the mnth slot, both referenced at the slot center,

combining (4) and 6), one obtains an alternate form for the

first design equation, viz.,

1

m n = ZZmnz:,

We shall assume a comm on characteristic impedance ZO or

all branch striplines and write

7)

in ratio form for the mnth

and pq th slots:

(8)

;

ZO

n

VLnZpq

z;q

ZO

p q V Zmn *

This form of the first design equation is seen to be analogou s

to [ l eq. (lo)] when that equation is also written in ratio

form.

The second design equation can be derived in a manner

precisely analogous to what was done in [l] for waveguide-

fed slots. The details will not be repeated h ere, but if one uses

(4)-(7)

in conjunction with the reciprocity theorem, it can be

establishe d that3

in which

with K a geo metric constan t. MC,, is called the mutual cou-

pling term and

g m n p q

s a complex quantity resulting from a

double integration over points in the apertures of the mnth

and pqth slots. Its precise form appears (in single subscript

notation) as

[ I

eq. (30)]. It is an easily programmed function

that can be co mputed at low cost.

One uses the design equations (8) and

(9)

in the follow-

ing way:

1)

MC,, is calculate d for every slot in the array,

using the desired slot voltage ratios Viq, k,, hese being

determined from pattern considerations. Since the slots never

move, but their lengths change, one n eeds to assume starting

lengths in the

gmnpq

calcualtions. It should be adequate to

assume

U

= X0/2, a l l m , n . 2) Next, one searches for a

couplet s,,,, / that makes

Im

L)

Zj f /Z , = -Im(MC,,)

(1 1)

and that also makes Z:, /ZO

=

1. This process needs to be it-

erated because the length changes require up dated calculations

A similar derivation can also be found in [8] .



BARNETT.

JR. A N D

ELLIOTT:

STUDY OF STRIPLINE-FED SLOTS

1513

Fig.

3 .

Test module. Top plate removed.

of MC,,. Fin ally ,

(8)

is used to determine the necessary ratio

of I,, / I , , , thus providing information needed in the design

of the power splitters.

It can now be appreciated what is crucial to the success of

this design procedure. An adequate dynamic range of ZEl,f/Zo

must be available to insure satisfaction of (1 1). Experien ce

with waveguide-fed slot arrays, and with the studies by Park,

Shavit, and Robertson of slots fed by boxed stripline, suggest

that if XEl,f/Z, is found to vary in the range

=

0.4 as strip

offset and slot length are varied, (1

1)

can be satisfied. Before

attempting a full design of the circular grid, stripline-fed slot

array shown in Fig. l( b) , it seems prudent to undertake first a

feasibility study of Zself(s, /Zo. This has been done for the

four cavity arrangements shown in Fig. 2.

EXPERIMENTALTUDY

In order to determine the dynamic range of

P e l f

for each

of the four modules shown in Fig. 2 we constructed one basic

cavity with interchangeable top plates. All parts were brass,

and on a solid bottom plate, we erected one solid radial wall

and two solid azimuthal walls, one at

p =

6.200 in and the

other at p = 10.335 in. The second radial “wall,” 22.5”

distant, consisted of seven pins, composed of 0.185-in rod

stock, 112-in on centers. For each module, two of these rods

would be removed to permit entry of the strip. The upper

and lower plates were 114-in apart and the strip, composed

of 1132-in flat stock 0.279-in wide, was positioned halfway

between the plates. This gave a TEM characteristic impedance

of

50

ohms, a figure for which theory and experiment were

in agreement.4 The only support for the strip inside the cavity

was a slitted 1/4-in cube of lucite, slipped onto the open-

‘The experiment was conducted with the slot absent.

circuited end of the strip. This lucite cube can be represented

by a small reactance that becomes part of

P e l f .

The external coaxial transition to the strip utilized an SMA

male fitting and a time-domain reflectometer measurement

verified that we had a well-matched transition at the design

frequency of 2.5 GHz.

All four top plates were 6-in by 7.5-in and 1132-in thick.

Each contained a slot of width 1/4 in whose central point lay

on the

p =

8.268-in circle, but the slot orientations differed,

in conformance with Fig. 2. In all cases the slot ends were

square, and in the course of the experiments, the lengths were

steadily increased by filing out both ends.

The place where the strip crossed under the slot was con-

trolled by changing where the strip entered the cavity. This

required changing the strip length in order to maintain exactly

one-quarter wavelength of strip beyond the slot. A photograph

of the test module, without an upper plate, is shown in Fig.

3 .

Input impedance data was recorded for all four modules as

the slot length 21 and strip offset s were varied. A reference

plane was established by shorting the coax-strip transition,

measuring the distance along the strip from the transition to

the slot, and rereferencing the impedance data to the slot cen-

ter line. For the modules labeled A,

B ,

C, and D in Fig.

2 , smoothed curves through the experimental data points are

shown in Figs. 4-7.

DISCUSSION

Not surprisingly, the grid of lines for which

U

= constant

or

s =

constant that one sees in Figs. 4-7 are quite similar to

what Stern obtained for the microstrip dipole case, as can be

appreciated by studying [4, fig. 21. The dynamic ranges are

similar, which is encouraging. However, it should be pointed

out the Stern’s results apply for

any

microstrip dipole in the



1514

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL.

31, NO.

12, DECEMBER

1989

RIZ,

R I Z ,

X I Z ,

Fig. 6.

. P e l f@ /V for module C.

XIZ,

Zself s,) / ZO or module

B .

ig. 5.

1.0

array, whereas ou r results for a stripline-fed slot differ some-

what from module to mo dule, since the orientation of the slot

changes incrementally as one moves from module A to module

D. This implies that, in designing a stripline-fed circular grid

array, one would need to m easure

Zself s,

1 for each module

in a quad rant. For a small array, such as the one depicted in

Fig. 1, this is not too dem anding a task. For very large ar-

rays, however, it could become a problem. O ne can hope that

ultimately ZseIf(s, 1 will be obtain able via theory and

I I

1 I I I

-1.0 -0.8 -0.6 -0.4 0.2 0 0.2 0.4 0.6

0.8

1.0

X/Z,

P I f @

O/Z

for

module

D .

ig. 7.

data taking. This would seem to be a fruitful area for further

research.

The most notable feature of the data represented in Figs.

4-7

is that an adequate dynamic range for

Xself

is obtainable

through modest variations of

s

and

21.

It seems reasonable

to assume that this would also be true for other modules on

different rings in a circular grid array.

CONCLUSION

A theory has been described which provides the design

equations for a circular grid array of stripline-fed collinear

slots. The theory indicates that a dynamic range of the self-

impedance of a slot, as a function of slot length

21

and strip

offse ts, is needed to com pensate for external mutual coupling.

An experimental study of

Zself(s,

1 has been undertaken for

four typical mo dules in such an array. The experimental data

strongly suggest that an adequate dynamic range exists, clear-

ing the way for the design, fabrication, and testing

of

an actual

array of this type.

REFERENCES

[ l ]

R.

S .

Elliott, “An improved design procedure for arrays of shunt

slots,” IEEE Trans.

Antennas Propagat.,

vol. AP-31, pp. 48-53,

Jan. 1983.

G. J. Stem and R. S.Elliott, “R esonant length of longitudinal slots

and validity

of

circuit representation: Theory and experiment,” IEEE

Tmns.

Antennas Propagat.,

vol. AP-33, pp. 1264-1271, Nov. 1985.

For

a case study comparing the

sum

patterns prod uced by a 20 by

20 array (lopped comers) with the elements in a rectangular grid ver-

sus a circular grid, see R. S . Elliott,

Antenna

Theory and

Design.

Englewood Cliffs, NJ: Prentice-Hall, 1981, pp. 225-237.

G.

J Stem and R. S. Elliott, “The design of microstrip dipole ar-

rays including mutual coupling, Part 11: Experiment,” IEEE Trans.

Antennas Propagat.,

vol. AP-29, pp. 761-765, Sept. 1981.

P.

B.

Katehi and N .

G.

Alexopoulos, “On the modeling of electro-

magnetically couple d microstrip antennas-the printed dipo le,”

IEEE

[2]

[3]

[4]

[SI

I

computations, thus eliminating the need for ex perimental input

Tm-ns.

Antenna; Propagat.,

vol. AP-32, pp. 1’179-1188, Nov. 1984.



BARNETT.

JR.

AND ELLIOTT: STUDY OF STRIPLINE-FED SLOTS

1515

P. B. Katehi, “A generalized method for the evaluation of mutual

coupling in microstrip arrays,” IEEE

Trans. Antennas Propagat.,

P.

K.

Park and R. S . Elliott, “Design of collinear longitudinal slot

arrays fed by boxed stripline,” IEEE


vol. AP-29, pp. 135-140, Jan. 1981.

R. Shavit and R. S . Elliott, “Design of transverse slot arrays fed by

boxed stripline,” IEEE


vol. AP-31, pp.

R. S. Robertson and R. S . Elliott, “The design of transverse slot

arrays fed by the meandering strip of a boxed stripline,” IEEE Trans.

Antennas Propagat., vol. AP-35, pp. 252-257, Mar. 1 987.

S . Hashemi-Yeganeh, “External excitation of a slot in the broadwall of

a rectangular waveguide,” M.S . thesis, Univ. California, Los Angeles,

Aug. 1983.

vol. AP-35, pp. 125-133, Feb. 1987.

545-552, July 1983.

Roy I. Barnett, Jr. (S’85-M’87) received the

B . S .

degree in electrical engineering and the B . S . de-

gree in engineerin g physics from Lehigh University,

Bethlehem, and the M.S. and Ph.D. degrees from

The O hio State University, C olumbus , in electrical

engineering, in 195 3 and 1 963, respectively.

He is an Associate Profes sor of Electrical Engi-

neering at the California State University, Los An-

geles.

Dr. Barnett is a member of Eta Kappa

Nu.

Robert

S.

Elliott

S’46-A’52-SM’54-F’6l-LF’87),or a photograph and

biography please see page 1271 of the Novem ber 19 85 issue of this

TRANSACTIONS.

1989 12 feasibility study of stripline-fed slots arranged as planar array with circular grid and...

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