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TECHNICAL REPORT

NASA Research Grant NAG-1-279 (UMass Account #5-28903)

"Near Millimeter Wave Imaging/Multi-Beam Integrated Antennas"

Period Covered: Principal Investigator: Co-Inv~stigators:

April 1, 1985 - September 30, 1985 Professor K. Sigfrid Yngvesson Assoc. Prof. Daniel H. Schaubert

Department of Electrical and Computer Engineer'ing UniversHy of Massachusetts

Amherst, MA 01003

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• 4'

The progress on Grant NAG-1-279, is described in:3everal attached

manuscripts. A comprehensive list of these manuscripts, and their status

with respect to publication, follows:

App. I: R. Janaswamy and D.H. Schaubert, "Additional Results on the Radiating Properties of LTSA's and CWSA's", a technical report.

App. II: R. Janaswamy and D.li. Schaubert, "Characteristic Impedance of a Wide Slot Line on Low Permittivity Substrates", submitted to the IEEE Trans. Microwave Theory and Techn.

App. III: R. Janaswamy, D.H. Schaube:--t, and D.M. Pozar, "Analysis of the TEM Mode Linearly TapElred Slot Antenna", submitted to Radio Science.

App. IV: K.S. Yngvesson, J. Johansson, and E.L. Kollberg, "MHl1meter Wave Imaging System with an Endfire Receptor Array", Accepted paper for the 10th International Conference on Infrared and Millimeter Waves, Orlando, Florida, December 1985.

App. V: K.S. Yngvesson, "Imagi,,;"; Front-End Systems for Millimeter Waves and Submillimeter Waves", Invited paper for the SPIE Conference on Submillimeter Spectroscopy, Cannes, France, December 5-6, 1985.

App. VI: J. Johansson, E.L. Kollberg, arj K.S. Yngvesson, "Model Experiments with Slot Antenna Arrays for Imaging", ibid.

App. VII: K.S. Yngvesson, J. Johansson, and E .L. Kollberg, "A New Integrated Slot Element Feed Array for Multi-Beam Systems", submitted to the IEEE Trans. Antennas and Propagat., Octo~er 1985.

App. VIII: T .L. Korzeniowski, "A 94 GHz Imaging Array Using Slot Line Radiators, Technical Report", (Ph.D. thesis).

The following papers, submitted in an earlier technical report, have

now been published or accepted tor publication:

1) R. Janaswamy and D.H. Sch"ubert, "Dispersion Characteristics for Wide Slotlines on Low-Permittivity Substrates", IEEE Trans. Microw. Theory Techn., MTT-33, 723-726 (Aug. 1985).

2) K.S. Yngvesson, D.H. Schaubert, T.L. Korzeniowski, E.L. Kollberg, and J. Johansson, uEndfire Tapered Slot Antennas on Dielectric Substrates", accepted for publication in the IEEE Trans. Antennas Propag., December Issue, 1985.

TECHNICAL REPORT

NASA Research Grant NAG-1-279 (UMass Account #5-28903)

5/;lll2-

( 1-16) "

"Near Millimeter Wave Imaging/Hulti-Beam Integrated Antennas"

PerIod Covered: PrIncIpal Investigator: Co-Investigators:

April 1, 1985 - September 30, 1985 Professor K. Sigfrid Yngvesson Assoc. Prof. DanIel H. Schaubert

Department of ElectrIcal and Computer EngIneerIng UnIversIty of Massachusetts

Amherst, HA 01003

The progress on Grant NAG-1-279, is described in several attached

manuscr Ipts. A comprehensive list of these manuscripts, and their status

with respect to publication, follows:

App. I: R. Janaswamy and D.H. Schaubert, "Additional Results on the Radiating Properties of LTSA's and CWSA's", a technical report.

App. II: R. Janaswamy and D.H. Schauber-t, "Characteristic Impedance of a Wide Slot Line on Low Permittivity Substrates", submitted to the IEEE Trans. M~~rowave Theory and Techn.

App. III: R. Janaswamy, D.H. Schaubert, and D.M. Pozar, "Analysis of the TEM Mode Linearly Tapered Slot Antenna", submitted to Radio Science.

App. IV: K.S. Yngvesson, .J. Johansson, and E.L. Kollberg, "Millimeter Wave Imaging System with an Endfire Receptor Array", Accepted paper tor the 10th International Conference on Infrared and Millimeter Waves, Orlando, Florida, December 1985.

App. V: K.S. Yngvesson, "Imaging Front-End Systems for Millimeter Waves and Submlllimeter Waves", Invited paper for the SPIE Conference on Submlllimeter Spectroscopy, Cannes, France, December 5-6, 1985.

App. VI: J. Johansson, E.L. Kollberg, and K.S. Yngvesson, "Model Experiments with Slot Antenna Arrays for- Imaging", ibid.

App. VII: K.S. Yngvesson, J. Johansson, and E.L. Kollberg, "A New Integra ted Slot Element Feed Array for Mult i-Beam Systems", submitted to the IEEE Trans. Antennas and Propagat., October 1985.

App. VIII: T.L. Korzeniowski, "A 9~ GHz Imaging Array Using Slot Line Radiators, Technical Report", (Ph.D. thesis).

The following papers, submitted in an earlier technical report, have

now been published or accepted for publication:

1) R. Janaswamy and D.H. Schaubert, "Dispersion Characteristics for Wide Slotl1nes on Low-Permittlvity Substrates", IEEE Trans. Microw. Theory Techn., MTT-33, 723-726 (Aug. 1985).

2) K.S. Yngvesson, D.H. Schaubert, T.L. Korzeniowski, E.L. Kollberg, and J. Johansson, "Endfire Tapered Slot Antennas on Dielectric Substrates", accepted for publication in the IEEE Trans. Antennas Propag., December Issue, 1985.

Appendices I-III describe the most recent work on the theory of single

element LTSAs and CWSAs. The radiation mechanism for these is presently

well understood and allows quantitative calculation of beamwidths and

sidelobe levels, provided that the antennas have a ~urriciently wide

conducting region on either side of the tapered slot.

Appendices IV-VII represent earlier work on the grant, as well as work

done during Professor Yngvesson's sabbatical visit to Chalmers University of

Technology, Gothenburg, Sweden, from Jan. 1, through Aug. 1, 1985 and work

done after Professor Yngvesson's return to the University of Massachusetts.

This work further elucidates the properties of arrays of CWSA elements, and

the effects of coupling on the beam-shape. It should be noted that typical

beam-efficiencies of 65% have been estimated, and that element spacings of

about one Rayleigh unit are possible. Further, two-point resolution at the

Rayleigh spacing has been demonstrated for a CWSA array in a 30.4 cm

paraboloid at 31GHz. These results underscore the interest in further

studies of the radiation mechanism of tapered slot arrays.

Appendix VII constitutes a final, detailed report on the "fork leading

to a 94 GHz seven element LTSA array imaging system, which has been reported

previously in less detan .•

~I

APPENDIX I ~~6-124?9 .-. "........ 4Il

Additional Results on the Radiating Properties of LTSAs and CWSAs

October 1985.

----,-----.-... ---'----~-~- ---~---

TABLE OF CONTENTS

I. Introduction

II. Formulation of the Problem

III. uiscussion of computed and Experimental Results

IV. Conclusion

Abstract: In this report, we present results on the theoretical and

experimental investigations of the radiating properties of Linearly

Tapered Slot Antennas (LTSAs) and Constant Width Slot Antennas

(CWSAs) carried out during April ~ August 1985. The antenna is

treated as a flared slot radiating in the presence of a conducting

half plane. The aperture distribution in the flared slot is

determined by approximating the tapered structure as a series of

short sections of parallel slots. The slot field of a uniform

slotline is determined by employing the spectral Galerkin's

technique and a power conservation criterion is employed to match

the fields at the step junction between two successive sections.

Comparison is made between theory and experiment for several LTSAs

and CWSAs etched on €~ ·2.22 and 2.55 substrates, and for flare

angles 40 < Y < 100• It is shown that the theory adequately

models the physics of the problem when the lateral dimension D of

the antenna is large and when the propagation constant of a

parallel slot line can be estimated very accurately. Newly

observed effects of the lateral truncation on the radiation pattern

of the antenna are discussed.

I. INTRODUCTION

A detailed desoription of the problem formulation and ~ome preliminary

results on CWSAs are given in the previous report under the Aperture Field

Model (AFM). We shall briefly summarize the key steps involved in the model

and discuss at length the results of the AFM on the LTSAs and CWSAs.

Fig. 1 shows the geometry of the LTSA. The method of analysis

essentially invol,ves two steps. In the first step, we determine the

aperture distribution (i.e., electric field distribution) in the tapered

slot region. In the second step, the equivalent magnetic current in the

slot is assumed to radiate in the presence of a conducting half plane and

the fa1"""field components of the antenna are obtained.

The aperture distribution in the slot region is obtained in the

following manner. The two lateral edges cd and c'd' are far enough from the

slot so that they have little effect on the field distribution in the slot.

The LTSA is consequently extended laterally in both directions to infinity.

Also, the slot truncation at bc and b'c' is assumed to result only in a

reflected wave of the dominant mode. (Note that this does not mean that we

are ignoring the important near field scattering due to the edges bc, b'c'.

This point will be clarified shortly.) Hence as far as finding the aperture

distribution is concerned. the LTSA, structure is reduced to a non.-uniform

(tapered) slot line. The aperture d,istribution of the tapered slot line is

determined by considering it as being comprised of short sections of

parallel slots of varying widths, connected end to end. The aperture field

ot a parallel slot line is obtained by employing the spectral Galerkin's

technique. For the purpose of radiation pattern computations, it is assumed

that the step discontinuity 1s "soft" enough so as to not result in any

.'

higher order modes of the slot line or in any reflections. A power )

continuity criterion across the junctions is enforced to determine the

amplitude distribution of the tapered structure. The phase distribution

(1.e., propagation constant) of the tapered slot line is considered to be

the same as that of the stepped approximation (valid for shallow taper

angles and when the dielectric substrate is thin enough). The validity of

the stepped approximation is verified by comparing the radiation pattern of

an air dielectric LTSA obtained using (i) the aperture distribution obtained

using the stepped approximation and (ii) the exact aperture distribution

for the tapered infinite structure obtained by using a conformal mapping

technique. A favorable comparison between the two justifies the stepped

approximation model.

Truncation of the aperture results in the edge cbb'c' and as a result,

diffraction currents are induced on the metallic portion of the structure.

As the slot is extended right onto the edge, the contribution to the

radiation pattern due to these induced currents is expected to be quite

Significant. (Indeed, it is shown in Section II, that the radiation pattern

in the E~plane (XZ plane) is entirely due to the edge diffraction). Effects

of the dielectric truncation on the radiation pattern of the antenna are

ignored. This should be a valid approximation for electrically thin

substrates. Near field scattering due to the metallic edge cbb'c' is then

rigdrously taken into account by treating the slots as radiating in the

presence of a conducting half plane.

In section II, we present the theoretical details of the analysis. In

section III, computed radiation patterns of LTSAs and CWSAs are discussed at

length vis~a~vis experimentally observed ones. Comparison with experiment

has revealed that the theory adequately models the physics of the problem

when the lateral dimensions of the LTSA and CWSA are large. However, new

trends in the radiation pattern have been observed experimentally, as the

lateral dimension 0 of the antenna is decreased. Lateral truncation effects

are more pronounced in the E~plane. These are discussed in detail in

section III.

II. FORMULATION OF·THE PROBLEM

Fig. 1 shows the geometry of the LTSA and the coordinate system

considered. As pointed out in section I, the tapered slot is replaced by a

stepped approximation. The field distribution of a uniform slot line is

determined by the spectral Galerkin's technique [1,2]. The unknown

longitudinal and transverse component.s of the electric field ES and ES

x z'

respectively, are expanded in terms of the basis functions (Tchebycheff

polynomials in the present case) as [2]

M Es _ LX b (1) U (z) (Z)2

m - - • I 1,., -W x. 1 wW 2m~1 W v m-

Where T.(·) and U.(·) are Tchebycheff polynomials of the first and the J J

second kind respetively and 2W is the width of the uniform slot. Mx and

(1)

(2)

Mz+l are the respective number of basis functions used for the x and z ;.,jk x

directed electric fields. The factor e x is suppressed in (1) and (2). , ,

kx is the propagation constant of the line. The ans, bms and 1\ are

obtained by solving the eigenvalue equation generated in the spectral

Galerkin's technique [2].

The characteristic impedaace Zo for a uniform slot line is defined as

[3,4]

Z -o

w s where V • f E (z) dz - Voltage across the slot in the y - 0 plane

o ... w z

and Pf is the power flow along the direction of propagation i.e., along the

Xt""axis. For the basis functions chosen, Vo - ao• We therefore have

P la \2 Z f - 0 0

(4)

Equations (1), (2) and (4) are utilized in defining the slot field for the

tapered structure. Enforcing the power continuity condition on the stepped

structure, we see that the slot field for the i,..th section may be defined as

(Z i)1/2 Mi ES \ _ 0 LX bi u (!...) z 2

'I1'Wi . .; 1..,(-)

x i-th section 1 m 2m" 1 Wi Wi (5)

(Z i)1/2 Mi T 2n(z/Wi )

ES

\

0 I Z a

i - 2 z i-th section 'I1'Wi o n .; 1-; (z/Wi ) (6)

Where z~ is the characteristic impedance of the slot line with a slot width

of 2Wi • Ti1e coefficients a~ and b; are normalized such that the impedance

brought out and a~ i dependence of a as per equation (4) has been explicitly o

- 1 for any i­

i terms of ao•

i i The remaining coefficients an and bm are all defined in

It can be shown following Tai's analysis [5] of infinitesimal slots

radiating in the presence of a conducting half plane that the longitudinal

slot field E: does not contribute to the far~field in either principal

plane. This may be explained intuitively as follows: E: is an odd function

s of z and hence the far-field due to Ex has a null in the plane of symmetry

i.e., XI plane (H~plane). The fa~field components in any plane have two

terms. The first term may be labelled the direct field ie~, field in the

absence of the edge cbb'c'. The second term arises as a result of

scattering due to the edge cbb'c'. Both the direct field and the scattered

field due to E~ are polarized normal to the edge i.e., along the y~axis and

hence contribute only to the crosspolarized component in the E-plane.

Indeed, the only copolar term appearing in the E-plane is due to the

radiation of the transverse slot field E: scattering from the edge cbb'c'.

Henceforth we shall be concerned only with E~ and shall be referring to

it as the aperture distribution Ea. We shall also include the phase term in

it. With respect to the coorJinate system defined

distribution E! of the i~th section is given by

in fig. ), the aperture

jki(X'-L) (Zi)1/2 jki(X'-L) Ei ESt x 0 x • e - e a z i~th section ~Wi

The primed quantities stand for the source coordinates and

ki _ Cik _ propagation constant corresponding to the i~th section. x 0

L • total length of the LTSA

For the air dielectric case, we have

c i _ 1

Z1 • i Zi+1 - 1 (by appropriate normalization) - Z • •

0 0 0

Mi • 0 z jk (x'~L)

Ei , e 0

I£r • 2 a

• 1.0 ~Wi 1 1-(Z'/Wi )

(7)

(8)

For this case, however, the exact aperture field distribution for a flared

infinite structure can be found using a conformal mapping technique (6] and

may be shown to be

";jk 0'

E:xactt _ e 0,0 £ -1 r

cos I; , (9)

where (0',1;') are the polar coordinates in the plane of the slot with the

vertex of the LTSA at the origin and 2Y is the flare angle of the LTSA. The

LTSA width W(x') and the flare angle Yare related as W(x') - (L~x') tanY.

For shallow flare angles,

tan(~) ,:; t tanY

1;' 1 tan(-) = - tan I; , 2 2

0' ~ (L~x') in the amplitude part of (9)

cOSI;' =! 1.0

tan (1;2 , ) _ tanl; ,

---..,~~-

tan(~) tanY z'

W(x' )

"'jk 0' exact, 2e 0 Therefore Ea . .:r W(x')

£r - 1

We notice from equations (10) and

.; 1-[z'/w(x,)]2

(8) that Eexact and Ei a a

(10)

have the same

functional form except that the radial wave in (10) is replaced by a plane

wave in (8). This minor difference is expected to influence only the far

out angles off the end~fire for LTSAs with shallow taper angles.

Following Tai's [5] analysis of infinitesimal slots in the presence of

a conducting half plane, it can be shown that the fa~~field component of the

electric field due to an infinitesimal horizontal slot (i .e., z directed

electric field) is (for the coordinate system shown in fig. 1)

Eo. jk (xrsinecos~+zrcose) j 14 e e 0 Isin~1 e ~ F(v)

+ ~j~/4

e ~jk (xrsine~zrcose) eO. sin(i) , e ~ o,~

2

where v - kox'sine(cos~+l)

and F(v) • v -'jt

J e dt 12~t

° (Fresnel Integral)

Note that

lim ej~/4 F(v) ~ ~ v+<»

(11)

(12)

We observe from equation (11) that the magnitude of the second term decays

to zero as koX'+<» (e"O, ~t since the asymptotic expression is not valid for

e - 0, ~) and th~t E~ is dominated by the first term which, in this case,

reduces to the familar far field expression due to a slot in an infinite

ground plane. We may consequently interpret the first term as the 'direct

field' and the second term as the 'edge diffraction field'.

In the E~plana, ~.O, ~ and the first term vanishes, as it should for a

slot in an infinite ground plane. The E~plane pattern is hence governed

entirely by the edge diffracted field.

The fa.l"-\field components due to the i~th section are obtained by . 0

integrating (7) over the i~th aperture with Ee as the kernel. Integration

over z' with E~ as the kernel may be recognized as the Fourier transform .

(w.r.t. z') of th~ aperture distribution (7) and is known in closed form for

the ba~ls functions chosen. Integration over x' can also be effected in a

, ?

_._) Wi

closed form over each individual parallel section. Radiation from the LTSA

is finally obtained by summing the far-fields from all sections.

j i

I

III. DISCUSSION OF COMPtITED AND EXPERIMENTAL RESULTS

Using the foregoing theory, radiation patterns have been computed for

LTSAs and CWSAs with €r - 1.0, €r - 2.22 (substrate thicknesses d/Ao of

0.015, 0.02, 0.058) and €r • 2.55 (d/Ao • 0.04) for lengths varying over 3.0 o 0

~ L/Ao ~ 9.6 and flare angles varying over 8 ~ 2Y ~ 21 •

The aperture distribution given in equation (7) includes only the

forward travelling wave. It is expected that the truncation of the

structure to length L will alter the aperture distribution, at least by

introducing a reflected wave. To study the effects of the reflected wave on

the radiation pattern, a reflected wave was included in the aperture

distribution and the voltage reflection coefficient R was varied over -1 < R

< 1. Patterns were computed for various combinations of L, 2Y and €r' It

was found that for a long antenna the reflected wave affected the pattern

only at angles far away from the end-fire direction and had little influence

on the forward lobe. The front lobe is almost entirely decided by the

forward travelling wave. Figs. 2a and 2b show the typical behaviour

observed in the pattern by including a reflected wave in the aperture

distribution. o Patterns are shown for an LTSA with 2Y - 10 and L/Ao • 3 and

10 respectively, with R as a parameter. It is seen that the effect of the

reflected wave on the fr'ont lobe is not very critical and diminishes as the

length of the antenna is increased. In all the subsequent patterns, only a

forward wave as defined in (7) is considered for the aperture distribution.

Notice that the cases of R • ! 1 correspond to a uniform phase distribution

on the aperture (i.e., a pure standing wave on the slot) and would have

resulted in a broadside pattern (i.e., maximum along the y-axis) had the

slot been radiating in free space. However, currents are induced on the

...

metalization as a result of nea~field scattering off the edge cbb'c'.

These induced currents radiate with a maximum in the endfire direction as

evidenced by the second term in equation (11). The radiated fields of the

LTSA are dominated by those produced by the indll.Q~d currents and this is

clear from the end-fire nature of the H~plane patterns as shown in figs. 2a

and 2b.

Fig. 3a and 3b show the comparison for the E-plane pattern obtained by

using the exact aperture distribution given by equation (9) and th~ stepped ,

o approximation given in (8) for €r a 1.0, 2Y a 15 and. L/A o • 6.3. It was

found that five steps per wavelength gave convergent results on the

radiation pattern. In figure 3b, five steps per wavelength have been

chosen. The favorable comparison between the two justifies the use of the

stepped'approximation model in determining the aperture distribution for air

dielectric LTSA. The stepped approximation should be valid also for €r > 1

antennas. In all the subsequent computations, five steps per free space

wavelength have been chC'wen to model the continuous taper.

The computed patterns in the E and H planes for an air dielectric LTSA

are shown in fig. 4a. Corresponding experimental patterns are shown in

figs. 4b ~nd 40. o Comparison is shown for L a 19.0 cm, 2Y-15 and fa8.0 GHz.

The experimental model was built using a 5 mil brass sheet with 0-11.0 cm.

A microwave diode (HP~5082~2~15) was connected across the feed terminals to

detect the RF signal. The antenna was supported by using 1/2" styrofoam (€r

- 1.02) strips along the outer boundary. Table 1 summarizes the comparison

between the two. A similar agreement between the theory and experiment was

o 0 obtained on other LTSAs over the range 8 < 2Y < 21 and 3 < L/A < 9.6. In - - - 0-

all these cases, the LTSA height 0 satisfied 0 ~ 2.75 AO and O/Wo ~ 3.3,

where Wo • L tanY. The ripples observed in the experimental E-plane pattern

are due to finite D as will be discussed shortly. A summary of the

comparison of the 3 dB beamwidth between the theory and experiment over the

above range of taper angles is shown in figs. 4d and 4e for L/A - 5 and . 0

6.33 respectively. It i3 seen that the agreement between the two is very

good.

Figs. 5a~5d show the computed and experimental patterns fo~ an LTSA on

e: • r 2.55 and with d - 1.6 mm 2Y - 11.40 L a 22.7 cm, f - 8.0 GHz. The

computed patterns have been calculated using the slot line data obtained via

the spectral Galerkin technique. The experimental model was built with D •

9.7 cm. Table 2 summarizes the comparison and it is seen that the agreement

between the two is quite good. Note that we have D/Ao • 2.6 and D/Wo • 4.28

and the substrate is thick (d/Ao - 0.043).

It is expected that the theoretical model considered would correctly

predict both the E and the H-plane patterns for a large D (it may be

recalled that the model assumes that D+~) and this has indeed been

demonstrated by comparing theory with experiment for LTSAs on e: r - 1.0 for

which both the amplitude and phase of the dominant term (i.e., the TEM wave)

of the aperture distribution can be determined exactly. However, it has

been observed experimentally that the lateral truncation of the LTSA and

CWSA has a pronounced effect on the l'adiation pattern, particularly in the

E~p1ane, as the height D begins to decrease and approach Woe Ripples appear

in the E~plane pattern (as seen in fig. 4b) even for moderate D. The E~

plane beam narrows as D is decreased, reaching a minimum value before

beginning to broaden again. The H~plane beam, while being less sensitive to

D initially and having a low backlobe, begins to broaden with the backlobe

becoming more prominent. Both the E~plane and the HHplane patterns develop

a large backlobe and a poorly defined front lobe as D approaches Woe

Experimental patterns in both the E~plane and the H~plane for various values

of D ranging between 2.5 em ~ D ~ 15.24 cm are shown in Appendix A (Figs.

A1~A7) for an air dielectric LTSA at 9.0 GHz with L - 24 cm and Y - 5.9 0•

Figs. 6 and 7 summarize the results of the effect of lateral truncation on

the beamwidths (3 dB and 10 dB) of an air dielectric LTSA (2Y - 11.80) in

the E and H~plane respectively for L/Ao 8 6.4, 7.2 and 8.0. In figs. 6a and

7a beamwidths are plotted as a function of D/AO

' whereas in figs. 6b and 7b,

beamwidths are plotted as a function of WolD. It is ~een. from figs. 6b and

7b that the curves approach the theoretical values as WolD + O. Clearly the

H-plane beam is less sensitive to tha lateral truncation for sufficiently

large D and it is felt that the success of the foregoing analysis with

infinite D would be better evidenced in the H~plane.

Figs. 8a~8d show the computed and experimental patterns of a CWSA with

er - 2.22, d/Ao - 0.017, 2W/Ao - 0.67, L/Ao - 4.2. The tapered portion was

modeled by the stepped approximation. Experiments were conducted on a 20~

mil RT Duroid 5880 substrate at X~band with W - 1.0 cm and D - 5.0 cm. It

1s seen that there is a lot of discrepancy between the two in the E~plane.

o 0 The calculated 3 dB beamwidth of 42 is twice the exper~mental value of 21 •

The theoretical 3 dB beamwidth and the locations of the first minimum in the

H~plane, differ from experimental ones by about 25%. The H~plane pattern of

a CWSA is governed primarily by the wavelength ratio c (- kx/ko - Ao/A') and

the length of the antenna. (The antenna departs from behaving as a pure

surface wave linear antenna in the H~plane in that the diffraction due to

the edge cbb'c' narrows the H~plane beam noticeably hence the use of the

term primarily in the above sentence. In other words, the radiatio',l pattern

of the slot antenna has a narrower main beam in the H~plane than an

equivalent wire antenna of the same length and having the same dispersion

characteristic. Currents induced on the metalization due to the edge cbb'c'

tend to narrow the beam of the purely surface wave antenna.) It may be

recalled that the pattern of a surface wave antenna is highly sensitive to

'c' due to the phase accumulation of the wave as it progresses along the

structure. (Typically the beam width changes by about 20% for a 2~3% change

in 'c' for a 4Xo long antenna). The slot line wavelength as determined by

the spectral Galerkin's method is only within 2-2.5% of the measured value

as reported in [1J and this is expected to influence the radiation pattern.

The measured normalized wavelength for a slot line with the above parameters

was found to be 0.952 at 10 GHz compared to the computed value of 0.978

i.e., differing by 2.7%. The pattern of the CWSA computed using the

measured value of c is shown in figs. 9a and 9b. Table 3 shows the

comparison between theor'y and experiment wi th and wi thout the correction

factor for c. It is seen that there is good agreement in the H~plane

between the experiment and the theory based on the measured value of c. The

discrepancy in the E~plane is attributed to the lateral truncation effects.

,~owever, for the thick substrate case (d/Xo - 0.043) shown in fig. 5, a good

agreement with experiment is obtained for pattern computations based on the

calculated slot wavelength. Patterns corresponding to the CWSA at another

frequency (8.0 GHz) are plotted in Appendix B. (figs. B1~B4)

Figs. 10a and 10b show the computed H-plane patterns of an LTSA with E r o

• 2.22, d/Xo • 0.017, 2Y • 10 , L/Xo • 4.2at 10 GHz. In fig. 10a, the

computed slot wavelength is used whereas, in fig. lOb, the correction factor

------------..",.--,...--'------ . -.. ·---'''-----~-----_1IIiI .. ~.~ ... ~

of 2.7%, as discussed above is used over the entire length. Experiments

were conducted on a 20~mil Duroid substrate and D was set equal to 10 cm.

Fig .• 11 d shows the experimen.tally observed pattern. Table 4 summarizes the

comparison. Once again a very good agreement between theory and experiment

1s obtained when the correction factor of 2.7% for c is used. The

respective E-plane patterns are plotted in figs. 11a, 11b and 11c. We see

from Table 4 that there is a good agreement in the E~plane GOO and this is

expected since D is large in this case, i.e., D/Wo• 10.0 and D/Ao • 3.33.

However, the presence of ripples on the main beam seems to suggest that the

lateral truncation effects are not totally absent. Similar trends in

agreement have been found at other frequencies over the X-band. Comparison

at 8.0 GHz may be made from figs. 12a":'12f. Additional experimental plots

showing the dependence of patterns on D are plotted in Appendix B. Patterns

are shown at both 8.0 GHz and 10 GHz. (B5·-'B19)

An LTSA on a substrate with Er > 1 radiates all along its length

because the propagation constant and characteristic impedance of the slot

line change with slot width. In contrast, a CWSA radiates only from the

feed and terminal discontinuities as in the case of uniform dielectric rod

antennas. A forward travelling wave on a CWSA radiates primarily due to the

terminal discontinuity (edges bc and b'c'). We may therefore anticipate

that the lateral truncation effects are more severe in a CWSA than in an

LTSA with the same height and and length. To verify this notion, we may

compare the E--plane patterns of the CWSA shown in Figs. 8 and 9 with the E""

plane pattf~rns of the LTSA shown in Fig. B16. Both the antennas have

approximately the same length L/Ao - 4.2 and height D/Ao • 1.67

(corresponding D/Wo• 5) at 10 GHz. It is seen that the discrepancy with

r~spect to the theory in the 3dB beamwidth is • 100% in the case of CWSA and

only 65~ in the case of a LTSA. Comparison in other cases showed the same

effect.

IV. CONCLUSION

Traveling wave slotline antennas have been analyzed in two steps. In

the first step, a wide uniform slot line is analyzed using a spectral

Galerkin's technique (i.e., wavelength, characteristic impedance and the

slot fields are obtained). The LTSA is approximated by a stepped model

consisting of short sections of uniform slot .line. Data on the uniform slot

line are utilized in determining the aperture distribution of the stepped

structure with a power continuity criterion employed at the step junction of

two adjacent sections. In the second step, the radiated field is obtained

by using a rigorous theory of slots radiating in the presence of a

conducting half plane to account for the important near field scattering due

to the edge of the conductor at the aperture and the far field components

are obtained.

Numerous experiments were conducted on LTSAs and CWSAs over the

range of parameters 3.0 ~ L/Ao ~ 9.6, 80 ~ 2Y ~ 21 0 and €r • 1.0, 2.22,

2.55. L and 2Y are the length and the flare angle of the LTSA. Comparison

between theory and experiment has indicated that the theory adequately

models the physics of the problem and predicts the radiation pattern of the

antenna with sufficient accuracy if the wavelength of the slot line is known

accurately (more accurately than the present 2 1/2~ discrepancy between the

computed and measured values) and the height 0 of th.~ antenna is large

enough (0 > 2.5A and O/W > 5). - 0 0 -

A systematic experimental study has, however, revealed that the

radiation pattern of the antenna is sensitive to the height 0 of the antenna

when it is no longer large. In particular, lateral truncation of the LTSA

'P'i

, I

iJ

can result in narrower beams in the E~plane than those obtained with

infinite D. The H~plane pattern is initially insensitive to 0 but

eventually broadens as 0 is decreased. Both E and H plane patterns

deteriorate and are poorly defined as 0 begins to approach Woe There is a

range of 0 over which the antenna exhibits the narrowest E~plane beam and a

satisfactory H~plane pattern. Clearly, 0 is one of the critical parameters

in the design of LTSAs and CWSAs. It is therefore desirable to include

truncation effects (i.e., finite D) in the theory. Work is presently

ongoing in treating this.

Table 1 Comparison of pattern between theory and experiment for an air dielectric LTSA

E~Plane

H .. Plane

L • 19.0 cm; f. 8.0 GHz; 2Y. 150

3 dB Beamwidth (deg) Theory Exp

37.4

46.5

34.2

45.5

10 dB SLL(dB) Beamwidth (deg) Theory Exp Theory Exp

53.4

64

55

70

Table 2

~15 ~13

"10 .. 9

Location of the first Minimum Theory Exp

42 35

35 42

Comparison of pattern between theory and experiment for an LTSA

E""Plane

H-Plane

L - 22.7 8m; £r - 2.55; d - 0.16 cm 2Y - 11.4 f - 8.0 GHz

3 dB BW(o) 1iO dB BW (0) SLLCdB) Theory Exp Theory Exp Theory

25 26.5 40 51 ';';17.2

21 24.6 NA NA "4 6.5

Location of the first minimum

Exp Theory Exp

~18 35 37

..l 6 20 20

E-plane

H-'plane

E~plane

H'" pi ane

Table 3

Comparison of pattern between theory and experiment for a CWSA

3 dB BW(o) SLL(dB)

Location of the first Minimum

Theory Using Exp Th90ry Using Exp Cth cmeas

Theory Using Exp Computed Measured

, c' C (C

th) (Cmeas )

42 38

40 32

21 ~11.5 ~11

32 ~ 9 .;; 8

Table 4

""'12

- 9

cth cmeas

36 33

33 28

Comparison of pattern between theory and experiment of an LTSA

L/)' - 4.2 o 2Y _ 10°

3 dB BW(o) Theory Using

Computed Measured , c' C

45.6 40

42.7 34.5

Exp

38

30

Location of the first

SLL(dB) Minimum Theory USing Exp Theory Using

Cth Cmeas cth cmeas

~13 -12 -10 38.6 36

;;111.5 ~10.5 f"!I10.5 36 31

34

27

Exp

32

30

..

References

[1] T. Itoh and R. Mittra, "Dispersion Characteristics of Slot Lines," Electron. Lett., Vol. 7, pp. 364~365, July 1971.

[2] R. Janaswamy and D.H'. Schaubert, "Dispersion Characteristics for Wide Slot Lines on Low Permittivity Substrates," IEEE Trans. Microwave Theor'y and Tech., Vol. MTT-;33 , No.8, pp. 723~726, Aug. 1985.

[3] R. Janaswamy and D.H. Schaubert, characteristic impedance of a Wide Slot Line on low Permittivity Substrates," submitted to the IEEE Trans. Microwave Theory and Tech. for publication.

[4] J.B. Knorr and K. Kuchler, "Analysis of Coupled Slots and Coplanar Strips on Dielectric Substrate," IEEE Trans. Microwave Theory and Tech., Vol. MTT-23, No.7, pp. 541~548, July 1975.

[5] C. T. Tai, Dyadic Green's Functions in Electromagnetic Theory, Intext Educational Pub. Scranton, Pennsylvania, 1971.

[6] R. L. Carrel, "The Characteristic Impedance of Two Infini te Cones of Arbitrary Cross Section," IRE Trans. Antennas Propagat., Vol AP , pp. 197-201, April 1958.

y

Fig. 1. Geometry of the LTSA and the coordinate system.

(a)

(b)

-t

... u

~

~ o ~

-20.0

Observotion Angl (Oeg)

r - -t'O(········· ·) - -0-'(-----) - 0.0(-)

. - Q.5(_._) \ • 1.0(--)

r. -1.0 ( ······ ··· ) • -0.5(------) • 0.0(--) • Q.5(-.~

- 1.0(---)

Fig. 2. Effect of the reflec ted wave on the radiation pattern of air dielectric LTSA • a) L/A - 3.0 b) L/ AO • 10.0

a

'-CD -,:, --IU -o a. CU-IU C o a: I -_ -lSI

4i-....... :~i

; .... ~ r!t;-' 4: -CD4 . ~ '-" _-12.0 o a._III

CU ,-- C

0-110

a: I -11.0

L&J

-27.0

-,I ., ~ I

Ex~t, TE~ ,rcl~ j , I,,' "': -:~':;!"' .. -T.; I .. ". _', -, I

1'1 = 15~' I

-Angle off Boresight

(a)

•

Angle 9ff Boresight, (b)

I

Fig. 3. Radiation Pattern of an Air Dielectric LTSA obtained by using a) the exact Aperture Distribution b) the Aperture Distributi on determined by the Stepped Approximation.

-10.0 en -,;,

l o "ii a::

-20.0

2'i : 15·

LII,.: s.O·

€;. = 1.0

-lO·~oiti.Q:;---::r.;---~--'O;;-----:::r::-...LL.-~--~

Observation Angle (De g)

(a)

Fig. 4'. Comparison of the radiation pattern between the theory and b experiment for an air dielectric LTSA with L/AO· 5.0; 2y • 15. a) Theory b) Experiment (E-Plane) c) Experiment (H-Plane)

-- --

#j " ''':;'.j, ..,-i. , ., ',"·!RE·fTA GULAR

.. '_ . o~~::". .. ,\ 0_-: ,:-; ,

. '.:0 .....

:, . o· • ' ''1'

"' ... : " '

"

,­.... :! •... p', , . '" -

'-..

, 'j "

PO ER PATTE dB

E- PLANE "

..J .~ .

U18

-------

(bj

RECTANGULAR POWER PATTERN I dB 0. :

,, '~------~~------~~------~----~---, ,~

H-PLANE

• '. J •• ,

(c)

'-.' .

r-.--------r-------~r_-------r-·------~

50

50

10

l/"- -5.0 01 A. -10 (Exp)

10

U.\o - 6.33 IY~ -3.7

+

15 '1.1 Oeg. (4)

•

., H-Plane

E-Plane

-TllIOIIY

o O~) + JIo__ liP. +

20

• H-Plane

o E-Plane

-TMIOIIY

o o I-PUIII

J • JIoI'UIli I I P. +

°r5~------tl0r_------_i15r-------~~~-------J 2."1 Oeg. 25

Oa)

Fig. 4. Comparison of the 3 dB beamwidth between the theory and experiment over 8 < 2y < 2l. d) L/Ao .. 5.0 e) Ll AO - 6.3

--.. CD -u '"0 J---J--~ '-" _-I o a.. -1

Q) c: . O-IU

a:: I -1f.D

W

-14.1

--.. '. CD -II

'"0 '-" _-111 o a.. -Is.a Q) c: 0-IU

a:: I -1I.D

I -lU

Angle off Boresight (a)

Angle off Boresight ,(b)

Fig . 5.

,1) Ii

Comparison of th radiation patt rn b tw en th th~o experiment f or an LTSA with L/'Ao· 6 .0; 2:( - 11. . ; ~ and d/'Ao. 0.043. a) Theory (E-Plane) b) Theory (H-P c) Experiment (E-Plane) d) Experiment (H-Plane)

y and 2.55

an )

e l)~

-to 1m

-all a.

G

RECTANGULAR POWER PATTERN IN dB

J\

(c)

RECTANGULAR

~:

-UIB

PO~~ER

e (d)

D/A =2.6 o

E-PLANE

PATTERN IN dB

2.4· , •

b2. ~o

D/l'o =2.8

H-PLANE

se 28B

OR\G\NAL PAGE \S Of POOR QUALITY

20

10

z-i,. 11.1,"

" = '·0

2'1,. /I.a';·

4= ,.0

E-Plane

<!) L/A. = G.4-

~ ,. 7.2-~ = 8.0

~

~

~

~

• •

E-Plane

CD L/A. = '.~ ~ = 7·2-

" .. &0

t:

O~~0'-~--~~~~S~-~--~O.5r---~--~O'~15~-L--~,,0~~ "l.l!) (b)

Fig. 6. Effect of the lateral truncation of the antenna on the E-Plane beamwidth. o.·f the air dielectric LTSA. (a) Beamwidth vs DO .. O (b) Beamwidth vs Wr/D

II

2'# = lI.a'· E~= 1.0

H-PLANE

(9 L/ >'. = , .• 4) 0: 7.:1.

~ = 8·0

°O~--~~--7---~3--~.~--~f----~6----~--~--~ 1)/).. 7.

III ... OIl II: '0 .. W Q

!!fO z ~ ~ .. Z < IU ..

50

I'

£,. = 1.0

21 = /I.aT·

, (a)

H-PLANE

(j) L/A. = 6.,. ® = 7.:1.

~ = e.o

0~o.~.--~--~o~.a~'--~---~~'~--~--~~7--' -~--,.~O--~ w./p (b)

Fig. 7. Effect of the lateral truncation of the antenna on the H-Plane beamwidth of the air dielectric LTSA. (a) Beamwidth vs D/ AQ ~(b) B'eamwidth vs WolD.

C = C. theory

L(> .. O= 4.2 2W/Ao- 0.67

Er - 2.22, d/AO- ["017

/'// /

!

~~~~~~.~~i~~f __ ~_ 4iIi sa; iU 1ilO iIlO •

-10

-CD....., "C -_ -Iz.o c:I a. -15.D

Go) c: c:I -110

a: I -11.0

::t: -24.0

-'0.0

Angle off Boresight (a)

eN = 4-0· C = C theory L/Ao = 4.2 2w/Ao= 0.67

€r = 2.22; 'd/Ao= 0.017

Angle off Boresight (b)

Fig. 8. Comparison of the radiation pattern between the theory and experiment. !a) Theory (E-Plane) b) Theory (H-PLane) c) Exp. (E-Plane) d) Exp. ( H-Plane)

---_ .. _--_ ... -

... RECTANGULAR POWER PATTERN IN dB i .--//

i • ________ ----- a DB

~---------------- - 3 !6 ------_. -.. ----------/-'\ -

'I.

E-PLANE

-211 GIl

I

I -'O»8~--------------~~--------------jSB -SB e ee 2138

(c)

RECTANGULAR POWER-PATTERN IN dB e DB

H-PLANE

D/Ao =1.87 -30»8~ ______________ ~ ____________ ~

-U!I -SB e ee U'B

(d)

-CD-u ~. _-12.1 C

Q.-IU CD c: c-IU

0: I -11.0

L&J

, -'c·;'6 = 1.027 C meas. theory

L/ "0- 4.2 2W/A~ 0.67

€ .. 2.22; d/Ao" 0.017 r

~~~~~~~~~r-~'~~ __ III '. aa:o ;,

-CC-u ~ _-12.0 o

Q. -15.0

CD c: 0-11.0 a: I -11.0 :x:

-27.0

Angle off Boresight

(a)

C .. C = 1.027 C meas. theory

L/Ao" 4.2

Angle off Boresight (b)

2W/AO" 0.67 €r= 2.22; 0.017

I I

Fig. 9. Computed radiation pattern of the CWSA using the measurea slot wavelength. a) E-Plane b) H-Plane.

-J.O -1----40.

.... 0 -. OJ-u "'0 ........ ..... -lz.o o

0.. -15.0 Q) C' 0-1&0

a: I -21.0

:I: -24.0

-%1.0

L/'Ao= 4.2 2y ... 10

Er= 2.22; d/Ao· 0.017 I

C ,. C theor

v (a) Angle off Boresight I

-OJ-t.O "'0 ........ ..... -lz.o o

0.. -15.0

Q) c: 0-1&0

a: I -21.0

:I: -24.0

-%1.0

(b) Angle off Boresigh

Fig. 10. Computed H-Plane pattern of LTSA using a) Computed slot wavelength b) Measured slot wavelength

LI Ao· 4.2 2y • 10

[

Er-:::; 2.22; d/Ao= 0.017

C ... Cmeas .= 1.027 Ctheory

.1

-u;----~

Lh .. o= 4.2 2y • 10 -CD-u

"0 E • 2.22; d/Ao. 0. 17 r

""" ~-I'.o o

Q...,U

CD c: O·IU

a: I .11.1

lAJ

-CD ... "0

C • C theory

Angle off Boresight (a)

.~ -

L/AO ~ 4.2 2y ... 10 I

E .. 2.221; d/Ao" r

. i.

""" ~.'z.a o

C • C ~ 1.027 measo,

°to17 Cth ory

Q...,U CD C c·IU

a: I -21.11

lAJ

-27.0

Angle off Boresight (b)

Fig. 110 Computed E-Plane pattern of LTSA using a) Computed slot wavelength b) Measured slot wavelength

, .

'I

,-'..,

RECTANGULAR POWER PATTERN IN dB e D8

E-PLANE

-30~~ ______________ ~ ________________ ~.

-f8B ~B sa t8B.

. Fig. 't I c. Measured 'E-PLANE pattern of LTSA. L/Arr- 4.2 , 2y - 10, er- 2.22, d/Ao- 0.017

RECTANGULAR POWER PATTERN IN dB •

e D8 "~;-'-----'-----""';:------r----..,

-ll Q

~-------------4~+'-- 30.3 l

~I I

~( ~ H-PLANE

C:' -30D8~ ____________ ~ ________________ _

-fSD ~a e 80 tSB

Fig. lId .Measured H-Plane pat,tern. of LTSA. L/Ao· 4.2, 2Y • 10, er - 2.22, d/Art 0.017

'OW

.

-zu

-'011

L/Ao= 3.4 2y a 10

e: r'" 2.22; d/Ao· 0.01

C a Cthlry

~~~~~~r.-~--:~~----~'-------5d:O IlO ;a:a iiLi ta.o

-10

-&D' -CD-u '"0 -~.-t2.0 o ~

-1111 CD C 0-111

a:: : -2t.O ~

-'011

Angle off Bores;ght (a)

Angle off Boresight (b)

Fig. 12. Computed radiation pattern of LTSA. a) E-Plane. b) H-Plane.

L/AO= 3. 2y = 10

e: = 2. 2; r

C = Cthe ry

RECTANGULAR POWER PATTERN IN dB

-lO DB

E-PLANE

-USB 28B

(c)

L/ Arr 3.4, 2y .. 10, e:.,- 2.22; d/AO= 0.014

.,

RECTANGULAR POWER PATTERN IN dB o DB

~ :n.'! -iB DB

D/Ao = 2,87·

~I ~ H-PLANE -am ,,_ ~~./tlJV .J

c se JSB

(d)

Fig. 12. Measured radiation pattern of the LTSA. c) E-PLANE. d) H';'PLANE'.

__ , --

~

fIl-u ~ -_-12.0 o 0- -15.11

CD

a-laD

E I -11.0

Lt.J

-zu

(e)

-a:l-u ~ _-12.0 o 0- -15.11

CD C' 0-laD

a: I -21.11

:c

-27.0

(f)

L/'AO= 3.4 'C( = 10

e:r a 2.22;

C = C meas.

. ___ ~"""'...-ad.':--_

ORIGINAL PAGE IS OF. POOR QUALITY

d/'Ao = 0.014

,. 1.021 Cth eory

MOO iItO id.o

Angle off Boresight

• 42. L/'AO= 3.4 Z1 = 10

e: r = 2.22;

Angle off Boresight

.014

"

Fig. 12. Computed radiation pattern of the LTSA using the measured slot wavelength e) E-PLANE f) Ii-PLANE

\

A P PEN D I X A:

i ., EFFECT OF LATERAL HEIGHT 0 ON LTSA ~ATTERHS

FIGURES Al - A7 : E-PLANE, H-PLANE

L/>..o" 7.2

2y .. 11.9 Degrees.

------.~ ... _-

E - P LAN E PAT T ERN S

RECTANGULAR POWER PATTERN IN dB

30.2,.-

4-5.2·

~

II Dtli -ll 1m +-------

~------+~~---~~~

-III -tl • lell

(Ai)

RECTANGULAR POWER PATTERN IN dB eDIt

-lll 1m I--------+----l~- 4- 3. ~.

C .. ·1m

-lei e UIII

(A2)

RECTANGULAR POWER PATTERN IN dB e DtI +-______ ~

.. G

~·'

-sel -tl e sell

(AJ)

J) J Ao :: 4-. 5

Wol J) :: 0"7

E-PLANE

D/AO

=: 3.7'S

WolD = 0·2 E-PLANE

D/A O :: 3.0

W./D = O· 25

E-PLANE

ORIGINAl. r.".GZ fC Qf POOR QUALITY

RECTANGULAR POWER PATTERN IN dB \!Inti

z.e·s

'D/A o - 2.25 4-s' --LI n

Irv 'Wo/D - O· 33 -1$,3 -.... E-PLANE ,. '. \j

-tel -'1 e =- tel

.(A4)

H to IN dB RECTANGULAR POWER PATTERN II \;

entl r DJ Ao = 1·5" II

-LI n W.l]) - O.S - '~

V E-PLANE !~

G .... ~ i! fi if

~

i I -teB -81 e, Ml UII

'._·_4. _ * __

(AS)~ ~.

" RECTANGULAR P.OWER PATTERN IN dB , ~

aDB

I D / Ao - 1.125 -WolD = O. G7 ~

~ E-PLANE

~ il l' "

-tlB -'1 e tel r (" 'j (A6)

RECTANGULAR POWER PATTERN IN dB • DIJ ~ ______ ..........

•

o ... Im

-re. s. 1S1

(A7)

D/>-.o = 0·75

Wfj/D - \.0

I I I

I I i ,

.,.r ________ ~ __ ~

o

H-PLANE PATTERNS

RECTANGULAR f'OWER 1)D8

- 'i'.4 dS -(11m

~ ..... -ltl -1.11 IJ

(Al)

Re::CTANGULAR f'OWe::R ~ DII

.1.,J' -lilm

.... -til -1.11 e

(A2)

Re::CTANGULAR f'OWe::R eDIt

-'I D ~ ____ -=+-_~

... IDI

-III -Sl e

(AJ)

f'ATTe::RN IN dB

'; 2. •

'2. 0 '1;/)..,0 = 4. 5

WolD :: 0./7

H-PLANE

11)1

f'ATTe::RN IN dB

f'ATTe::RN IN

D / AD :. 3.75'

WolD = 0·2.0

H PLANE

Itl

dB

It I

D/)..,o = 3· 0

WolD = O· 25

H-PLANE

RECTANGULAR POWER PATTERN IN dB e DI

2.8.3'

-ll 0» 43.3-

~ (~l .... u

/---

U

-sel -Sl e 118 sel

(A4)

RECTANGULAR POWER PATTERN IN dB eDB

t--------I--4--- 4-1. S'

-La 01) 1-_____ +-_+-___ S3·

O~·U

-JIll -sa e 118 sea

(AS)

RECTANGULAR POWER PATTERN IN dB en

7-

-,a Q1) ~~.

G .... a ~ ~ -Sll -Sl e 118 sel

(A6)

J) / Ao = 2,. '2..!5'

WolD ::

H-PLANE

D/Ao= '.5 W./n :: 0·5 H-PLANE

D/Ao ::: 1·12S'

WolD = 0.'7

H-PLANE

0·33

~

"----

l

RECTANGULAR POWER PATTERN IN dB

~ __________ ~. __ ~~ __________ GZ O

(0 7 --i. n j------r-------+----~

... em

-"",-I <

~....J HI. -u e

(A7)

Dj AO = O· 75

WolD = I· 0

H-PLANE

t,

A P PEN D I X B:

ADDITIONAL. RADIATION PATTERNS AND LATERAL TRUNCATION EFFECTS ON LTSA PATTERNS

Figs. B1 - B4 : Comparison of the radiation pattern between the theory and experiment at 8.0 GHz.

Bl - Theory (E-PLANE) B2 - Theory (H-PLANE) B3 - Exp. (E-PLANE) B4 - Exp. (H-PLANE)

( C W SA)

Figs. B5 - B12 : Effect of the lateral height D on the patterns (L T SA) at 8.0 GHz ,

Lf.~o= 3.4, 2y = 10, €y = 2.22, d/ Ao= 0.014

Figs. B13 - B19 : Effect of the lateral height D on L T S A patterns at 10.0 GHz.

L/AO= 4.2, 2y = 10; €r= 2.22, d/ Ao= 0.017

.iAc'

......... CD -go "'0' ........ +J -12.0 o

0.. -15.0 Q,) c:: o -la.o

a:: I -21.0

La.J

-24JJ

-11.0

(Bl)

-3.0

......... C!J -9.0 "'0 ........ _-12.0 o

0..

Q)

-15.0

c: C -18.0

0.. I -21.0

:r: -24.0

-11.0

c = C .... ,.s = /'01'~ C~ -"I

. Angle off Boresight

8 W:. 4/. S'.

c= C~.s .. = I.02..S' C ... .... co.,.-

~.

-30.0 tn~I'iI"-;r.:--;;r:--o.::T:-~~--+---r---.--4dOO sa:o &eLi 1iiO aa:o id.o

(B2) Angle off Boresight

Computed patterns of CWSA at 8.0 GHz. L/AO. 3.4, 2w/Ao· 0.54, er .... 2.22, d/Ao· 0.014

RECTANGULAR POWER PATTERN IN dB

E-PLANE

-180 -90 a 90 leo

(B3)

RECTANGULAR POWER PATTERN IN dE eDa ~I ______________ (~\

.~ .

H-PLANE.'

-28a e 28a

(B4)

Measured r.adiation patterns of CWSA.

.oj

._4-----~--------------~------~~~~~~·

o

0

o

" DII

....

E-PLANE PAT T ERN S

RECTANGULAR POWER PATTERN IN dB,

(BS)

j)/Ao = 2.4-

Wo /'D = a.1I E-PLANE

RECTANGULAR POWER PATTERN IN dB

1)/)..0: 2.' 3

W,,! D = 0" '2. 5' E-PLANE

-'.1 ~I e '.1 (B6)

RECTANGULAR POWER eDlr

(B7)

PATTERN IN dB

D/ AI) = /·87

WolD : 0.14.3 E-PLANE

._-" _ ..

c···· ..

RECTANGULAR POWER PATTERN IN dB

t-------J~--. 2.2..7

... GIl

-1SI

(B8)

lsa

'Dj Ao= 1.6

Wo!D = 0-17 E-PLANE

RECTANGULAR POWER PATTERN IN dB e DII-+-___ . ___ ""7".

-II 0»

... GIl

lSI

(B9)

RECTANGULAR POWER PATTERN IN dB e D8,-+-______ ~

-ll 0»

... n

-lSI e lSI

(B10)

D/Ao = 1.33

WolD -= 0.2 E-PLANE

D/AO -= 0·8

WolD _ O· 33 E"'PLANE

! I ; j

0'·" .. '

o

RECTANGULAR POWER PATTERN IN dB e DB t-------

... a

-J18 11 JI8

(Bll)

RECTANGULAR POWER PATTERN IN dB

-II 1m

....

18 JI8

(B12)

]/>"0 = 0.53

WolD = 0·5

E-PLANE

1:>/)..0 = 0.4-

WolD = O. '7 E-PLANE

0

H-PLANE PATTERN S

RECTANGULAR POWER PATTERN IN dB "DII t-------~-

-LI Olt

.... em

-180 -90 o (BS)

36

90 180

RECTANGULAR POWER PATTERN IN dB

...--------,~_t_- 34-.0

-Lllm

.... em

D/ AI) = 2.4-

WolD: 0.11

H-PLANE

D/Ao = 2..13

WolD:: 0.1'1.5

H-PLANE

-~11-1------~-1-------0-------~.~------~ (B6)

RECTANGULAR- POWER PATTERN IN dB e DB t-------~

-lilm

TJ/)..o = \·87

W./D :: 0014-3 .... Im

H-PLANE

-III ~I • III

(B7)

____ 4-;----

I' I

i i

II<

c

C' '; ",

tC.' , V

RECTANGULAR POWER PATTERN IN dB eDI~ ______________ _

-lilm

... !III

-tel ~I e

(B8)

RECTANGULAR POWER PATTERN IN dB

e JIll -1-------_

-l108

... !III

" JeB

(B9} __

RECTANGULAR POWER PATTERN IN dB " DB +-______ _

~I e teB

(B10)

]/>'0 = J.G

WolD = 0./7

H-PLANE

D/>..o = /·33

Wo/'D = 0.2 H-PLANE

1)/Ao =0.8

Wo /:tJ = o· sa H-PLANE

RECTANGULAR POWER PATTERN IN dB 0) De \--_____ ---:_._-

... a

-tSI ISII

(Bll)

RECTANGULAR POWER PATTERN IN dB e~~ ____________ ~~

-LI em

-tSI -'SI lSI

(B12)

D/'A o = 0·53

Wa/D = O. 5'"

H-PLANE·

1)/ Ao = O·lt

WfJ/'J) = 0.67 H-PLANE

..u-rbI Y' dtlt' hOW ••

G ..

C· ." ·1

-J88 .it J81

(B13)

RECTANGULAR POWER PATTERN IN dB

-I.' 08

.~ ""I. IDI

-f81 -ell it

(B14)

RECTANGULAR POWER e DII

-II 08

.... aa

-,el e (B15J

PATTERN

'J)/>'r:, - 2.33 -WolD = 0"43

E-PLANE

f811

IN dB

USI

D/ >'0 = 2..0

Wo/r> = Q.17 E-PLANE

i -. I I

•

-LI ala

-aa GIl

o

-LI ala

RECTANGULAR POWER PATTERN IN dB

-tea

(B16)

tea

'X;/AO = 1.'7

Wolf) = 0.2

E-PLANE

RECTANGULAR POWER PATTERN IN dB

(B17)

RECTANGULAR POWER PATTERN IN dB

'D/AO = \.0

WolD = 0-33

E-PLANE

DIAo = 0.'7

WolD = 0·50

E-PLANE

-sel e sel

(B1S)

~ r,

I i

•

eN

-il aa

..... em

_7

RECTANGULAR POWER PATTERN IN dB

-%;., I

-sea

I I i u,.. !

(B19J

'.~ : ...

Jel

"'/ O. 5" .JJ ·'\0 = WolD = O. (,7

E-PLANE

..

• c: RECTRNGULAR POWER PATTERN IN dB

ORIGINAL PAGE IS Of. POOR QUALlTY

e DI

I J)I>-o = 3.33 -it 1m I

~ ,Wft'\! WolD = 0.1/

~ .. R-PLANE

-fel fel

(B13)

RECTANGULAR POWER PATTERN IN dB-e DB I----------,~-_

-111m !)/).,o = 2.33

WolD = 0"4-3

H-PLANE

o -fel e %el

(B14)

RECTRNGULAR POWER PATTERN IN dB ~H ~ _______ ~~ __

~ _____ -+--\ '30.3

-II D

o -1.1 lei

(B1Sr

D/ Ao = 2.0

Wo/l) = 0.11

H-PLANE

I 'I :: ··i • < I 'i

:~

•

c

RECTANGULAR POWER PATTERN IN dB e JIll +-______ ~_

~------f_-; 34-.'

-ll D

-SII -sa Sill

(B16)

RECTANGULAR POWER PATTERN IN dB a DB.

!J/ >"0 :: l.b7

WolD = 0·2

H-PLANE

D/ Ao :: '·0

WolD = 0.33

\'VVif\; H-pLANE

-sel -<!I 1111

(Bln

RECTANGULAR POWER PATTERN IN dB aDa ~ ______ ~~

-ll D

-III -Sll • (B1B)

JII

D/>.o:: O.b 7

WolD = 0·50

H-PLANE

~ .. " ~

1 I

1 i

'f

•

RECTANGULAR POWER PATTERN IN dB '" D8_.~ _____ --:~

-II n

o -till e till

(B19)

D/Ao = 0·5'

Wo /1) = O· b 7

H-PLANE

!\

I ~

I ., .li

1

. ...

-

APPENDIX II

N86-12480

Characteristic Impedance or a Wide Slot Line on Low PermIttivity Substrates*

R .. Janaswamy D.H. Schaubert

Department or Electrical and Computer Engineering UnIversity of Massachusetts

Amherst, MA 01003

July 1985

* This work was supported by NASA Langley Research Center under grant number NAG-1-279

I ~

[,

i l , . ,. I

~i '. '. ,;i , ,.

; " " f , ~

. t·

Abstract: Computed results on the characteristic impedance of wide slots

etched on an electrically thin substrate of.,low dielectric constant er are

presented. These results combined with t~ose in [1J provide design data for

these slot~ines. Results are given tor er - 2.22, 3:0' 3.8 and 9.8.

Comparison is shown tor the characteristic impedance between the present

calculations and those available in the literature for high-e r substrates.

I. Introduction

Impedance properties of a slot line shown in Fig. 1 have been

thoroughly treated in the literature by a number of authors [2,3]. All the

previous work has been contined to- slots on high-e substrates (e > 9.6), r r-

which are typically used tor circuit applications. No data have been

reported tor slots on' low-e r substrates, where slot lines have interesting

applications as antennas [4-6]. Knowledge of the characteristic impedance

ot· slot lines- on these low-e substrates is highly desirable in designing a r

proper teed and accompanying circuits tor· these antennas.

In this paper, computed. data are- presented for the character istic

impedance Zo tor slots on low-er substrates. The problem is formulated in , s

the spectral domain and the eigenvalue equation tor the eigen-palr (A , e ), , s

where A is the slot wavelength and e the slot tield, is solved by using

the spectral Galerkin's method [1]. The slot characteristic impedance Zo is

calculated from the slot tield in the spectral domain.

II. Formulation ot the Problem and Numerical Results

The characteristic impedance Zo ot the slot lIne shown in Fig. 1 is

defined as [2J

1Vol2 Pt

(1)

.~[_; •. J •. !ll!l!1.. • ..II"II"''''--.... · ... · --------------.:-..",-..... ,---"=""-=-.~'~ .. ~. --~.. - ..

2

,

where V is the voltage across the slot in the plane of the slot and is o

given in terms o~ the transverse electric field component Ex as

v - f W/2 o -W/2

- -E dx • E (~)I a - E (0) x x ~- x

(2)

,-,. denotes quantit.ies Fourier transformed with respect to the x-ax.is and ~

1s the transform variable. P f is the real part of the complex power- flow .

(actually real in this case for a propagating mode) along the slot and is

given by

• • P • J J (E a - E H ) dxdy f x y plane x y y x

1 --. -"". - 2i f f (EXHy - EyHX ) dady (3) ~ y plane·

where Ex' E. , H , H are fields. tangential to the z-constant plane. The , y x. y

second equality in (3) follows from Parseval's theorem.

The fields E and H in the spectral domain pertaining to the air and

dielectric region of' the slot l1ne· can be related to the aperture field

(i.e.,. fIeld in. the slot), which is modeled by the method of' moments. As

was done 1n [1]. the- ~1eld

(5)

. •

1n the slot region 1s expanded as

or (~) e~-(~) 2nW n-O,l, •••

,,_(~)2 . w·

(4)

m-l,2, •••

where Tn and Un are Tchebychetf polynom1~ls of the I and II kind

respectively.

The Fourier transforms ot the above basis functions can be found

read1ly 1n closed form as C8]

"~-----'-----------' ... =-:,-... ::::C---.e::-.",-... ~. -_'-'.:'-'< ",.,-., ~

3

. , , a-x _ (_1)n J" (2l!) 0 1

n 2n 2 n - ~ , ••• (6 )

_ J (~!!) e-z •. j ( -1 ) m 2m 2m 2 , m _ 1,2, ••• m . (~)

2

(7)

The integration w.i th respect· to y in (3) can be done in closed form,

however, the integration on the a !ariable must be dnne numerically. The

slot wavelength A is stationary with respect to the slot field and,it was ,

tound that). converges: with only one baSis. function for the 10ng1 tudinal

field as repo~ted in [1]. s

However~ more than one basis function for Ez is

needed for the convergence ot· characteristic impedanceZo for a wide slot.

s s The maximum number o.r basis tunctions needed tor Ex and Ez during the

computation ot Zo was 5: and 3, respectively, when the slot width approached

one tree s'pace wavelength A,. .. o. f

Computer programs were developed to compute t and ~o for a specified

e A and d. As- a check ot these programs, Table 1 shows a comparison for r' 0

Z'o'"between these computations and those· in [3]. Characteristic impedances

tor' slot lines have been computed for e:r - 2.22,. 3.0, 3.8 and 9.8 and for

widths varying over 0.05 i W/Ao i. ~ .0. Computed values ot Zo vs. W/Ao with

d/Ao as a parameter are plotted in Figure 2.

III.. Conclusion

A spectral domain Galerkin method is used to compute the characteristic

impedance of wide slot lines on low e:r substrates. The data presented here

supplement data already available on high e:r substrates.

4

----------.--------

References

[1] R. Janaswamy and O.K. Schauber-t, "Disper-sion Characteristics for Wide Slot Lines on Low Permittivity Substrates," to appear- in IEEE Trans. Microwave Theory and Tech., Vol. MTT-33 p No.8, pp. 723-726, August 1985.

[2l J.B •. Knorr- and K. Kuchler-, "'Analysis of Coupled Slots and Coplanar Str-1ps on Dlelectr-la Substr-ate~" IEEE Trans. Microwave Theory and Tech." Vol. MTT-23p No.7, pp. 541-548,. July 1975.

[3l E.A. Mar-iani et al., "Slotl1ne Character-1stics,'" IEEE Tr-ans. Microwave Theory- and Tech., Vol. MT'l'-17, No. 12, pp. 1091-1096, December- 1969.

[4] E.L. Kollberg et al., "New Results on Tapered Slot Endf1re Antennas on D1electr-ic Substr-ate," presented at the 8th IEEE International Conference on Infrared and Ml111mete~ Waves, Miami, December 1983.

[51 S.N Pr-asad and S .. Mahapatr-a, "A New MIC Slot Line Aerial," IEEE Trans. Antennas and Pr-opagat.,. Vol.. AP-31, No.3, pp. 525-527, May 1983.

[6] J.F. Johansson, "Investigation of Some Slotllne Antennas," Ph.D. Dlssertatlonp Chalmers Universityp Gothenberg, Sweden, 1983.

[1] T. Itoh and R. Mittra,. "Dispersion Characteristics o~Slot Lines~" Electron Lett .. p Vol. Tp pp. 364-365,. July 1971.

[8] A. Erde-lyi et al •• TCi.Dles o~ Integr-al Transforms, Vol. 2, McGraw Hill Book Co., New York,. 1954.

5

6

Figures

Figure 1. Geometry ot slot line.

Figure 2. Characteristie. impedance-o~ slot line as a function of normalized slot width. a) e - 2.22 b) e - 3~O c) e - 3.8 d) e.z- _ 9.8.. ~ l"" r

Table 1.. Compa~1son o~ calculated characteristic impedance- Zo •

•

-.,,-.. --.~----------.-------

Table 1

Comparison or calculated slot characteristic impedance Zo.

E:r d/~ 0

W/a ZoCn) Present

From curves in [3]

9.6 0.06 1.0 140 141.87

11.0 0.04 1.5 160 159.8153

13.0 0.03 Q.4- 80 81.6118

16.0 0.025 2.0 150 151.0611

20.0 0.03 1.0 100 101.405

, ~1

-

. . ~ LC

·,

1.00

WI>" o

~ ___ ~~~'il~L. ____________ ~~~~~~----------_M~~._~ ~~~_'_ Y F ",_ !f.F1, Jib ¥'.-'. 1- JIt~.Ct . _;"':..;."; :~ . AAMJe, "'!!!.¥Ii

1.00

.~ -- -- ----

r •

800

• I

I

I ;

WI)", a

! ! L

..

o N

e = a.. r ;T.8

dl "0

0.75 1.00

W/~· '0

.'

APPENDIX III N86-12481

ANALYSIS OF THE TEM MODE

LINEARLY TAPERED SLOT ANTENNA

by

Ramakrishna Janaswamy

Daniel H. Schaubert

Dav id M. Pozar

Department of Electrical and Computer Engineering

University of Massachusetts

Amherst, MA 01003

OCtober 1985

This work was supported in part by NASA Langley Research Center under grant number NAG-1 -279.

In this paper we present the theoretical analysis of the radiation

characteristics of the TEM mode Linearly Tapered Slot Antenna (LTSA). The

theory presented is valid for antennas wi th afr dielectric and forms the

basis for analysis of the more popular dielectric-supported antennas. The

method of analysis involves two steps. In the first step, the aperture

distribution in the flared slot is determined. In the second step, the

equivalent magnetic current in the slot is treated as radiating in the

presence of a conducting half-plane and the far-field components are

obtained. Detailed comparison with experiment is made and excellent

agreement is obtained. Design curves for the variation of the 3 dB and 10 dB

beamwidths as a function of the antenna length, wi th the flare angle as a

parameter, are presented.

1. INTRODUCTION

Over the past few years there has been an increasing interest in the

use of planar antennas in microwave and millimeter wave integrated systems.

The various kinds of planar antennas presently in use may be b~oadly divided

into two classes; broadside and end-fire. Subsystems have been denveloped

using broadside rad5ating elements such as printed dipol~s and slots,

microstrip patches, etc. [Kerr et al., 1977; Carver and Mink, 1981; Parrish

et al., 1982; Rutledge, 1985]. These elements are all resonant structures

yielding a 3 dB bandwidth of 10 - 15 % maximum. The element gain for all of

these elements is fairly lOW, and does not suffice in applications where a o 0

10 dB beamwidth of 12 - 60 is required [Yngvesson, 1983]. End-fire

travelling wave antennas are included in the second class. Typical 10 dB o 0

beamwidths obtainable with these antennas range between 30 and 50 and thus

, f' ,

oan be used direotly in Cassegrain systems with f-numbers between 1 and 2

[Yngvesson, 1983]. The Linearly Tapered Slot Antenna (LTSA)e which will be

investigated here, belongs to the second class.

The tapered slot antenna consists of a tapered slot in a thin film of

metal with or without an electrically thin dielectric substrate on one side

of the film. The slot is very narrow towards one end for efficient ooupling

to devices such as mixer diodes. Away from this region, the slot is tapered

so that the travelling wave propagating along the slot gradually radiates in

the end-fire direction. Use of these antennas has so far been based on

empirioal designs. Gibson [1979] used an exponentially tapered slot antenna

(he named it the 'Vivaldi' antenna) on an Alumina substrate in an 8 - ~o GHz

video receiver module. He showed that the antenna is capable ~l'f producing a

symmetric beam over a very wlde bandwidth (3:1 bandwidth). Korzeniowski et

ale [1983], developed an imaging system at 94 GHz using LTSA elements on a

1-mil Kapton substrate. The LTSA was first introduced by Prasad and

Mahapatra [1979]. Their antenna was short (. Ao) and etched on an Alumina

substrate. Some preliminary experimental results on LTSAs were also

published by Kollberg et ale [1983]. All these workers based their deSigns

on empirical results, as no theory is yet available on these antennas. It is

highly desirable to develop a suitable theoretical model for these antennas

to facilitate successful designs. In this paper, we deal with the radiation

pattern analysis of the LTSA. The theory considered is applicable only to

the air dielectric LTSA (i.e., the TEM-LTSA). The case of an arbitrary taper

(i.e., exponential, linear, constant, etc.) and dielectric substrate (thin)

is also being treated by us and will be published in a future paper. The

TEM-LTSA is simpler and direct to treat analytically but will nevertheless

---------------------....----",. .. =',.;;;~"-.,.:~...,.,.-. ---

:.1 . . , .

'J

:_.,0< , ........

~ I

.' ~q

J ,.! I

"J

;.

shed light on the basic physics governing the radiation mechanism ot this

important class of end-fire travelling wave antennas. It forms the basis for

analysis of the more popular dielectric-supported antennas •

Fig. 1a shows the geometry of the TEM-LTSA. The antenna radiates in- the . end-fire direction, i.e., along the negative X-axiS with the E-tield

linearly polarized in the XZ-plane (copolar component). The method of

analysis involves two steps. In the first step, the aperture distribution (

i.e., electric field distribution) in the tapered slot is obtained. In the

second step, the slot is treated as radiating in the presence of a

conducting half plane (to account for the diffraction due to the edge cbb'c'

) and the far-field components are obtained.

The aperture distribution of the tapered slot is obtained in the

following manner. The lateral edges cd and c'd' are far enough from the slot

region that they have little effect on the field distribution in the slot.

Hence they are receded to infinity. In addition, we employ the usual

travelling wave antenna assumption that the aperture distribution on the

structure is essentially determined by the propagating modes corresponding

to the non-terminated structure. Note that this does not mean that we are

ignoring the important diffraction effects due to the edge cbb'c' on the

radiation pattern of the antenna. The effect of the termination of the

structure at cbb'c' is incorporated by adding a backward travelling wave.

The problem then reduces to finding the field distribution in the slot

region for a tapered fin structure shown in Fig. 1b. The resulting

structure, a pair of infinite coplanar "conical" tins, supports a spherical

TEM wave (and hence the name TEM-LTSA) tor which the scalar wave equation

~ . ----_ ..... ,,------------------_... .., ~...,.-.-

'I ,.

can be solved exactly by employing the conformal mapping technique (Carrel,

1958J.

The second step of the analysis is the determination of the fields

radiated by the aperture distribution determined in step 1. As the tapered

slot is extended right onto the edge cbb'c', it 1s expected that the edge

diffraction will play a dominant role on the radiation pattern of the

antenna. The edge diffraction is important because the radiation pattern of

a slot in an infinite ground plane (i.e., without the edge being considered)

has a null in the plane of the conductor (the E-plane). Hence, the E-plane

pattern of the antenna 1s governed entirely by the currents induced on the

metalization as a result of scattering off the edge. This important near

field scattering effect will be rigorously taken into account by treating

the tapered slot as radiating in the presence of a conducting half plane.

Tai (1971] developed the exact theory of infini tesimalslots radiating in

the presence of a conducting half plarie by using the dyadic Green's function

approach. Following hi.s approach, an expression shaH be obtained for the

far-field due to an infinitesimal slot located on a conduoting half plane.

The radiation pattern of the LTSA will be found by integrating the aperture

distribution found in step 1 over the slot region, with the expression found

in step 2 as the kernel.

In section 2, we present the key steps involved in the formulation of

the problem. In section 3, the computed radiation patterns of the LTSA are

compared with the experimental results and design curves tor the 3 dB and 10

dB beamwidths are presented.

2. FORMULATION OF THE PROBLEM

Fig. 1a shows the geometry of the TEM-LTSA and the coordinate system

cpnsidered. As pOinted out in section " the LTSA geometry is replaced by a

pair of coplanar fins (Fig. 'b) for determining the aperture distribution in

the slot. The resulting structure supports a spherical TEM wave [Carrel,

, 958]. Carrel determined the characterist.ic impedance of this TEM line by

employing a series of conformal transformations. Using the same

transformations, it can be shown (see Appendix A for details) that the x and

z-directed components of the electric field in the slot region are

approximately given by

e sina

R

s Ez (R,a) •

e COSa

R (2)

where (R,a) are the polar coordinates in the plane of the slot with the

vertex of the LTSA at the origin and 2~ is the flare angle of the LTSA. We

shall, however, be concerned with only the z-directed slot field for the

following reasons: It can be shown [Tai, '971] from the analysis of

infinitesimal slots radiating in the presence of a conducting half plane

that the longitudinal slot field E: does not contribute to the far-field in

either principal plane. This may be explained physically as follows. E~ is

an Odd function of z, hence the far-field due to it has a null in the XY-

plane (the H-Plane). The r~r-field component in any plane is composed of two

" f

terms. The first term may be labelled the 'direct field' i.e., field in the

absence of the edge cbb'c'. The second term arises as a result of scattering

due to the edge ebb' c'. Both the incident field and the scattered field due s to Ex are normal to the edge i.e., along the Y-axis and contribute only to

the cross-polarized component in the E-plane. Henceforth, we shall be

concerned with only the z-directed slot field and shall be referring to it

as the aperture distribution Ea i.e.,

-jkoR s e

EaCR,el) • Ez(R,el) - -----R

COSel

Employing the dyadic Green's function approach, it can be shown that

th.e far-field component e e( a, cp) at the observation angles (e, cp), due to a

horizontal infinitesimal slot located at (x',z') on a conducting half plane

1s given by

j~/4 +jko(x'sinacoscp+z'cose) eeCe,cp) - ISincple F(v)e +

-j[~/4 + ko(x's1ne-z'cose)J + sin(cp/2)e 7 {~kox'Sine, (e-O,~) (4)

where, ,

v -jt F(v) - f e dt (Fresnel Integral) (5)

o {2~t -

j~/4 ~ Note that Li~+we F(v) - 1/v~

Substituting z' - 0 and a • ~/2 in the expression for e a , it is seen that

(~) reduces to equation 35.11 of [Tai, 1971J.

We observe from (4) that the magnitude of the second term decays to

zero as k ox' •• (e-O, ~ as the asymptotic far-field expression is not valid

for e-O,~) and that ee is dominated by the first term, which in this case

reduces to the familiar far-field kernel due to a slot in an infinite ground

p1ane. Consequently, we may interpret the first term as the 'direct field'

and the second term as the 'edge diffracted field'. In the E-plane, ~ - ~.

and it is seen from (4) that the direct field is identically zero and the

far-field is contributed entirely by the edge diffracted field.

The far-zone field Ee of the LTSA is obtained by integrating the

aperture distribution Ea over the tapered slot S'. with ee as the kernel

i.e ••

Ee - II ee E dB' S' a

(6)

It is shown in Appendix B that for shallow taper angles Y, the two

dimensional integral in (~)may be reduced to a one dimensional integral.

The result (suppressing the common phase y

cosa

factor and constants) is given by

1 -jv1 - [F(v a) - e F(va(1-cose») v 1

* - F(v,(1-cose»)} ] (7)

where F(.) is the Fresnel integral given by (5) and

Va - koLsine(1+cos~)

v, - koLsece(1-sin(e+e»

and * denotes the complex conjugate.

Note that the E-plane pattern (cjl - 1T) is obtained from (7) by taking

the limit as cjl + ~. In this case, we also have va - 0 and Vl- v,cose. On

carrying out these steps, the E-plane electric field EE(e) is obtained as

Y 2cose(1-sin(e+e» -jv. * iEee) - I .e [F(v,) - F(v,(1-cose»)] de (8)

-Y tan 2 (~) tan

2 (~)

... . r

3. DISCUSSION OF THE COMPUTED AND THE EXPERIMENTAL RESULTS

The integral in (7) must be evaluated numerioally. The singularity in

the integrand as a ... ± Y is removable and poses no problems in the numerioal

integration. Radiation patterns for the LTSA have been oomputed for l~ngths o 0

L/Ao ranging between 3 and 10 and for flare angles between 8 and 21.

The aperture distribution given in (7) inoludes only the forward

travelling wave. To study the effeots of the wave refleoted at the aperture

termination X - 0 on the radiation pattern of the antenna, a refleoted wave

was introduoed in the aperture distribution and the voltage refleotion

coeffioient r was varied over all the possible values i.e., -1 ~ r ~ 1.

Patterns were oomputed for various oombinations of L and 2Y. Figs. 2a and 2b

illustrate the effeot of inoluding a refleoted wave on"the aperture

distribution for L/Ao - 3 and 10 respeotively, with r as a parameter. The

oases of r • ±1 oorrespond to a uniform phase distribution on the aperture

(i.e., a pure standing wave) and would have resulted in a broadside pattern

with the maximum ooouring along the Y-axis, had the aperture been radiating

in free spaoe. However, ourrents are induoed on the metalization as a result

of near-field soattering off' the edge obb'o'. These induoed ourrents radiate

in the end-fire direotion as evidenoed by the seoond term in equation (4).

The radiated fields of the LTSA are dominated by those produoed by the

induoed ourrents. This is clear from the end-fire nature of th H-plane

pattern of the antenna as shown in Figs. 2a and 2b. Also, it is seen that

the influenoe of the refleoted wave on the forward lobe is not very oritioal

and diminishes as the length of the antenna is inoreased. The front lobe of

the radiation pattern for a long antenna is almost entirely deoided by the

I ~

;fi "j

i

\, "" '" i'

,j ,il

",I

I . 'I

r '" " ~ .~

,;1

"

'. .

forward travelling wave. In all the subsequent patterns, only a forward

travelling wave, as given in (7), is assumed for the aperture distribution.

The computed patterns in the E and the H-planes with L/A o- 5 and 2Y -o

15 are shown in Fig. 3a. Corresponding experimental patterns are shown in

Figs. 3b and 3c. The experimental model was built using a 5-mil brass sheet

with D - 11.0cm (the LTSA half height). A microwave diode (HP-5082-2215) was

connected across the feed gap to detect the RF signal. The antenna ~as n

supported by using 1/2 styrofoam (£r- 1.02) strips along the outer boundary

dd'c'cd of the antenna. Table I summarizes the comparison between the theory

and experiment. It is seen that excellent agreement is obtained between the

two for all the important aspects of the pattern viz., the 3 dB and the 10

dB beamwidths, locations of the minima and the sidelobe level. Figs. ~a-~c

show the computed and the experimental patterns for a TEM~LTSA with 2Y -o

1'.9 and L/Ao - 8. Table II summarizes the comparison between the two. Again

there is a very good agreement between the two. Figs Sa and 5b show the

comparison of the 3 dB beamwidth between theory and e~periment for 2Y o 0

varying between 8 and 21 and for L/Ao - 5.0 and 6.33 respectively. The H-

plane beamwidth is relatively insensitive to the flare angle of the antenna.

The beamwidth can, however, be controlled by varying the length of the

antenna. In all the cases tested, the LTSA half height D satisfied D ~

2.75A oand D/Wo~ 3.3, where Wo· Lt~nY. Restriction is placed on D so that

comparison with the theory (which assumes infini te D) is meaningful. The

slight ripples seen in the E-plane experimental patterns are attributed to

the lateral truncation effects (1.e., finite D).

The computed 3 dB and '0 dB beamwidths of the LTSA in the E-plane and

the H-plane as a function of L/Ao and with 2Y as a parameter are plotted in

Figs. 6a and 6b respect1 vely. Important desl.gn parameters for the antenna

in the E-Plane are both the flare angle and the length, whereas in the H-

Plane, the pattern 1s relat1vely insensit1ve to the flare angle and is

controlled only by' varying the antenna length.

----~~-=-~-.. ----

· .

4. CONCLUSION

Radiation pattern analysis of the TEM-LTSA has been presented. The

method of analysis involves two steps: In the first step, the electric field

distribution in the tapered slot is determined by using the conformal

mapping technique. In the second step, the equivalent magnetic current in

the tapered slot is treated as radiating in the presen~e of a conducting

half plane to rigorously account for near field scattering by the edge, and

the far-fields are obtained .. Comparison is made between theory aild

experiment and it is shown that excellent agreement is obtained over the o 0-

entire range considered: 3 ~ L/Ao.~ 10 and 8 ~ 2Y ~ 21. Finally, design

curves for the var"iation of beamwidths as a function of the normalized

length, with the flare angle as a parameter, are presented.

lJIlI. ill .!·J!!!W

..

Appendix A:

DERIVATION OF THE APERTURE DISTRIBUTION FOR THE TAPERED SLOT

In this section, we shall obtain an expression for the aperture

distribution in the tapered slot region by first treating the assooiated

infinite ooplanar fin problem.

Fig. A1 shows the geometry of a ooplanar fin structure formed by a zero

thiokness perfeot electrio conductor. Note that the ooordinate system in

this seotion is different from the one introduced in the main text. We would

like to solve for the electrio and magnetio fields E and H for this

struoture and later specialize to the slot region to obtain the aperture

distribution in the tapered slot. Since the struoture is multiply conneoted

and has the same boundary for all 'r' (the spherioal ooordinate), it

supports a spherioal TEM wave. Adopting ejwt time oonvention, it follows

from Maxwell's equations that a spherical TEM wave oan be represented as -jk r

E • - e 0 Vt'l' (An 2

where the scalar potential '1' satisfies Vt'l' • 0 and the subscript 't' denotes

that the gradient operator is defined with respect to the tranverse

i.e.,(e,,) coordinates. ko is the free spaoe propagation oonstant. Following

Carrel, the soalar ·potential '1', af ~er dropping the constant factors, is

given by

'1' • a dq f /( 2 2 2 o ~1-a )('-~ a )

(A2)

1 where ~ • tan(Y/2) and a - - tan(ei2) e •

~

The eleotriC field d.istribution ES in the slot is obtained from (A1)

and (A2) and specializing to the case of , w O,1r. The final expression after

oarrying out the above operations is given by

-jkor -jkor 2

s .. sec ~9/2l Vt'I •• o,'Ir • - e E Cr,e) • - e e I 2 Y 2 9 r tan (-) - tan (-) 2 2

1 lei ~ Y (A3)

• /, 2 S - tan (2) ...

where S is the unit normal in the e-direction. In obtaining (A3), the

Riemann sheet corresponding to Ii. +' 1s chosen. The term under the first

radical sign in (A3) arises as a result of the edges at 9 - Y and the second

is due to those at e - ~/2. For shallow taper angles Y, the edges at 9 - ~/2

do not effect the field distribution in the tapered slot much and the

following approximations are valid,

sec2

(9/2) ., and JIc,-tan 2(SI21 . ,

Using these in (A3), and decomposing the resulting slot field into x

and z components in the coordinate system introduced in section 2, we get,

-jkoR s e

Ex (R,a) • Sing

ES (R,a) • z

R I 2 Y 1 a tan (-) - tan (-) 2 2

-jkoR e cosa

I ! Y .! R tan (-) - tan (~) 2 2

(A4)

(AS)

... - - ,,>,.~-... ~,.><.,. ' .. l!WSiJii;4 ""

-,.

Appendix B:

DERIVATION OF THE FAR-ZONE ELECTRIC FIELD OF THE !EM-LTSA

We have trom equation (6) ot seotion 2,

Ee- .r 1 ee E ds' S' a

(g1)

where S' is the area oooupied by the tapered slot. For shallow taper angles,

the triangular region S' may be approximated by the oiroular seotor ot

roadi us L and inol uded angle 2Y. Hence ,

Y L Ee • 1 1 ee E R dR de

_Y 0 a (B2)

The polar coordinates (R,a) referred to the vertex of the LTSA and the

souroe ooordinates (x' ,z') with respeot to the coordinate system shown in

Fig. 1a are related as x' - L - R cosa, z, • R sina. Combining (3), (4) and

•

-jkoRC1-sin(e+a» • e } dR (B3)

where v - kosine(1+cos,) (L-Roosa) v -jt

and F(v) - f e dt (B4 ) o {2,..t

The integral over R in (B3) can be evaluated in closed form. Consider

:first the integral Il of the first term in the inner integral of (B3),

jkoLsineo\)s~ L -jkoR(' +!~in,ooseoosa-ooses1nCl) II - Is1n~1 e • J F(v) e dR

o

We integrate II by parts and cast the resulting integral in a form

suitable for defining it in terms of the Fresnel integral. The final result

atter carrying out the required manipulations is

jkoLslnecos, -jVl ;v;--jLlsin,1 e [F(v 2 ) - e F(V 2 (1-cosa») - I(i)'

-jv 1seca * .e {F(v,) - F(v,(1-cosa»)} )

} (B5)

The integral 12 involving the second term in (B3) may also be evaluated

in closed form as follows:

-jk oLsln8 L jkoR( l-sin (8+a» 12 • -j sin(,/2) e f e clR

{~kosine 0 { L - R cos a

Letting L-Rcosa • u and simplifying, we get,

-jkoL(1-cos8sina)seca L jkou(1-sin(e+a)seca e I

z • _j sin(,/2) e • f du

cosa{~kosine L(1-cos(l) ru Introducing a second change of variable p • kou(1-sin(8+a»seca, and

evaluating the resulting integral, Iz may be expressed in a closed form as

-j(koLsln8+v,) .r;-- * I z • -jLsln,seoae /(-) • [F(v,) - F( v, (1-cosa»)]

vzv,

Substituting for II and 12 in (B3) and noting that IsIn,1 • sIn" 0 ~ ~

S· 11', and simplifying the resulting expression, we get, for 0 ~ , ~ 11',

jkoLsln8oos, Y cos a da 1 Ee'e,,) • -jL e sln~ f [ F(V2) -

-Y/ tan \1) _ tan:1 (9) VI 2 2

-jv1 ~ -jv1seoa e F(vz(1-00sa») + /(v;)e •

* .{F(v~) - F(v,(1-oosa»)} ] (B6)

• • i-

where F(.) is the Fresnel integral defined in (B4) and Vl, V2 and Va are

given in (B5)

REFERENCES

Carrel, R.L., The Charaoteristio Impedanoe of Two Infinite Cones of

Arbitrary Cross Seotion, IRE Trans. Antennas Propogat, Vol. AP-6(2),

197-20'1, 1958.

Carver, K.R. and Mink, J.W., Miorostrip Antenna Teohnology, IEEE Trans.

Antennas Propagat;, Vol. AP-29 (1 ), 2-24, 1981.

Gibson, P.J., The Vivaldi Aerial, Proo. Eur. Miorowave Conf., 2!h,

Brighton, U.K., 101-105, 1979.

Kerr, A. R., et al., A S.imple Quasi-optioal GaAs Monoli thio Mixer at 110

GHz, 1977 IEEE MTT-S International Miorowave Symposium Digest, San Diego,

CA., 96-98, 1977.

Kollberg, E.L., et al., New Results on Tapered Slot Endfire Antennas on

Dieleotric Substrates, 1983 I.EEE Int. Conference on Infrared and

Millimeter Waves Digest, Miami Beach, FLA., F3.6, 1983.

Korzeiowski, T. L. et al., Imaging System at 911 GHz Using Tapered Slot

Antenna Elements, paper presented at the 8th IEEE Int. Conference on

Infrared and Millimeter Waves, Miami Beaoh, FLA. I' i 983.

Parrish, P.T. et al., Printed Dipole-Schottky Diode Millimeter Wave Antenna

Array, SPIE Proc., 337, !'!1:llimeter Wave '!;hnology,49-52, 1982.

Prasad, S.N. and Mahapatra l S., A novel MIC slot-line Aerial, Proc. Eur.

Microwave ~., ~, Brighton, U.K., 120-1211, 1979.

Rutledge, D.B., (Feature Article), IEEE Antennas Propagate Soc. Newsletter,

Vol. 27(~), 1985.

Tai, C.T., Dyadic Green's Functions in Eleotromagnetio Theory, Intext

Eduoational Pulishers, Soranton, Pennsylvania, 1971.

Yngvesson, K.S, Near-Millimeter Imaging with Integrated Planar Receptors:

General Requirements and Constraints in Infrared and Millimeter Waves,

vol. 10, edited by K.J. Button, Academic Press, New York, 1919.

· .

FIGURE TITLES

1a. Geometry of the TEM-LTSA and the coordinate system.

1b. Geometry of the coplanar fin structure.

2. Variation of the pr.incipal plane patterns as a function of the load

reflection coefficient r. a) L/Ao • 3.0 b) L/A o• 10.0

3. Comparison of the radiation pattern between the theory and experiment. o

L/Ao • 5.0, 2Y • 15.0 • a) Theory. b) E-Plane(Exp.) c) H-Plane (Exp.).

4. Comparison of the radiation pattern between the theory and experiment. o

L/Ao - 8.0, 2Y - 11.9. a) Theory. b) E-Plane (Exp.). c) H-Plane (Exp.).

5. Comparison of the 3 dB beamwidth between the theory and experiment.

6. Variation of the beamwidths of the TEM-LTSA asa function of the

antenna length, with the flare angle as a parameter. a) E-Plane b) H-

Plane.

A1. Geometry of the coplanar fin structure and the coordinate system.

E-Plane

Theory

Exp.

H-Plane

Theory

Exp.

E-Plane

Theory

Exp.

H-Plane Theory

Exp.

Table I

Comparison or Pattern Between the Theory and Experiment

L/A - 5.0 o

Beamwidth ( Deg) Side Lobe Level I Looation or the

3dB 10dS (dB) !='irst Minimum (Deg)

36.5 55 -15 38

34.2 57 -14 3~

47.0 67 -9.0 34.5

45.5 72 -9.5 35.0

Table n Comparison of Pattern Between the Theory and Experiment

L/A • 8.0 o

Beamwld th (Deg)

3dB 10dS

29 43

30 45

38 51.4

35 47.0

Side

o 2'Y • 11.9

Lobe Level (dB)

-16

-15

-9.0

-7.5

Looation of the First Minimum (Deg)

33 30

32

30

'. "' '

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ORI~INAL PAGE IS OF POOR QUALITY

II.

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N86-12482 APPENDIX VI

1 e10 o eon rraye for 1 qinq

J .t'. Jo neson, B.L. Itoll

• Del)&rtlllen of Electron Phy. e Ind. 1 pac 0 rvatory , Cha~ra OnLveralty of Teehnol~y. 5-412 96 Gothenburq, Svei1.en.

A /.) /-'oJ!)/>(

44=S­.5 t.7fI r .orO

•• Oepartlllent of UnLvereLty ot

In reduction

Enqlne.e.rlnq. a. 01002. U

,4/;1/1

It h • b n d tor) wlth a h1qh f parabolold c

aq1nq eyatems requlre a foeu.1nq e l ement (len. or r eflec­r of elements that can be placed at the focus of a

uted u. q a fOr1llula 'l1ven by Ruz • S The nUilbu of 3 dB be_ 'dth. that c be a lth a qa1ft loe. of 1 dB .I.a

" - O. , • 22('/D)'

'1'h.1. 1 it th about -10 dB for a be overlap at 3 dB. of rec ptor. that can be plac at th focal plan v1thout appr clabl e aberr t!.Orta lncr a •• harply wh n th f >1. undred. of r ceptor. coald be u.ed wl an f -1 two-dimen.lonal imagin'l .y.t , wl out ny la 'ler deqrad tion of th 'ling capabill-tre •• Thi. _ lie. that elth l' a pr ry-fed paraboloid vlth an f.>-l or a Ca. rain ay. i. preferred for 1n'l u.ln'l reflector ••

Anoth l' par tel' that affects the .y.e. do nc 1. bloc:lta'le caua d by the laa91nq array. 0 qat a l~ r sld 10 lev 1 the bloc age • ould be small, or entirely 41-.pen e4 vl by ua1ft9 an of teet .y. •

The .-in requ1r ent fo r th receptors i . that they .hould provide .ymmetrieal be ... with a de. ired reflector edge i " lUlll1nation of about -10 to -13 dB even when they are aen.ely packed. The power radiated cut a1da the ol1d an'l a whleh 1. .ubtended by the reflector, a. Men frClla the teed, .hould 0 • 11. The ratio of thl. power and the total rad1ated power , denoed ap111-o l' efflciency 1.

e, 2. • 2. n.1 • f f F(e •• ).I" d d. 1 f f F(e •• )./n d ~

o 0 0 0

Tb coupl1n'l betw.en the receptors .hould al.o b h ld at a 1 talk.

(2)

level to inim1ze cro •• -

A n._ type of planar reeept.or that bel',jnq. to the ela •• of uavol11nq-wa.ve antenna. ha. recently been In,·eet.1qated.' Thi. anten'::.a type con.late ot a eneleetrie aut.trate w. t:h a

1 I n (p 0 n_ - Th Viva 4

bro&dh.nd. Me Mve eXper~nted lilly with two other t ype •• the COn t.an

and the LineAr Taper Sl ot Antenn. ( loTSA) . The •• type. are • bro t. ... , c:c.pared wlth a Vi ' a ld! a.ntenna of th . .... l ength. '1'he 9 antenna t~. ue .hown in Fl gure 1.

Vivaldi USA ONSA E H

Piqur 1. '1'hr antenn

t of fir. alo lin Piqur. %. d l a on ttem of a CIf a 31 t. 10 dB/div.

r

t ern. for a • t .re I In P19. %. 31 GHa, • Ilot wldth 110 l.n th .. 10 lID.

Duroid 5880 (c -%.22). enna. for our ginq array., . inc. they pro d to • ee.y to

ch 4eqradaUon 0 th be_ pett.rn.. w. f ound it po .. 1ble to UI. both aul)ltrat. by intul avinq the el_nta. Th.y could then be even IDOre den •• l y

cU.t.urblnqth alot field of the ir n.i9hbours. (S .. Piqur. 3.)

Figure 4. The 5xS array with 1ta v ide fixture.

TO facil1tate asuraments we .. • alotl1n -finlin -wavequid tr&nattiOR. Iub-. trat •• could then ea.U y be fi tted lnto wavequide fixtur •• A avequl de det Cltor or

er w • bolt. d to th. b lock .t the .el cted el nt ln the arr.y. (Se !'iqure • • ) In a real .y. lt woul d of cour_ be preferable to e full u •• of the planar geo.etrY and 1ntegr a te the e r w1th th. antenna. Thi. 4e.19n lend. its.lf to • two-d1:aenaion.l a rray, .1ace the lub.trate. c.n be den.ely p ClJced ln th -plan wlthout .i9nlficant. be_ pattern degrade 10n.

Ante nn. array llU!.a.ure nt.

TO .... ur. the antenna pat t.r n. we built. alnl.tur & an.cho i c chamber at Chalmer. Oniv. The c:baIIber h.. a crol.-a.ctlon of 1xl a .nd • dilt.nce of 2 .0 _t.ra betwee n the trana­II1ttln9 ·.nd th. r.ce1vln9 antenn •• The antenna to be _a.ured il plac ed on a turntable,

ORI INAL OF POO ITY

P19U%'. S. Th. X-plane (laft) and th. R-plan. (ri,ht) patt.rn. of 9 of the al.-.nta in a 5&5 array. El ... nt .pacin9 18 13 _ and tha frequency 18 31 CHI:. Loq .cal. w th 10 dB/dJ.v.

The .pill-ovar .ffici.ncy, •• d.f1D • lc:ally caaputed. Th •• ffici.ncy 1. in the region o~ 60-65 t, ic i. (corru,ated horn. of cour •• exe.pt'~).

o th t. of ord11\U'Y wav89U1de born f .. d. pat.tarn. f or a 10 _ .pacing,

bUt the pat. .bowed IIIOr. a. oy.r .~flciency.

, an4 ne. l ower .pill

rat. 68 .. a function of a lateral f ed. off •• t. 4& • glven in

•• ret ((I ').4x/')

Th ..... D.viat.ion ractor (BOP) 1. clo • to 1 for .y.t ... with t >1 at ... 11 off •• ta. Th. be .. dJ..plac_nt: La thu. ••••• nti.lly a linear fUnction of tJ;. lateral f.ed off •• t:. OU!, _aaur .. nt.. of the array wi t.h 13 _ .1 ... 1\ t .pacinq gav. be .. cU.plac .. nta 1n t.M rancj. of 2.1-2.' degr .... 'l'hi. coniOJ:'ll. vell wlth tM tbaoreUcal valu. of 2.33 degr •••• With •• tapp1D9 .otor po.1t1oniD9 accuracy of about +/- 0.2 cSeqr ... the dl.cr.paney 1. acc.ptabl ••

,;.

(3)

,

-I

'\ I \ I \ I I , I ,

I I I \ , I I I \ \ \ -

Plquz. 6. E-plan. pattern. fpr 3 .1 ... 4 ln the aid row of a lx5 array with 10 .l ... !)t .pac inc; • L:inJ ar acal.. Horizon axl. l&be~led n eqr...

lon

pattern. for 5 ~ ftta of a 3x 5 array with 13 _

1\11. L inear cal • Hor1zon~ ln dec;r ••••

Vl..U

Hi.toric 1.. 9 .thora ot r.aolu l on crit.ria for optical sy.tea.. Th we lIO.t _11- Rayl.J.9 Nil Sparrow criteria.' I. I I Both th ••• aitarl. ar. b •• ed on the Airy cUo ,

I(r) I , It J,( 1(1'·)]1 * ( 4 )

r/(lfJ

which 1 dJ:.tanc Thi. dJ..

J.nated cir~ar apertur •• The Rayl e1q • pe ftd the fir . t null ot the Airy dlsc.

4 , 1. C;1 by

1r 11tude. ar. added with a pha •• ln flgure I. b.r_ c •• _ of .peclt1c in,;"

o~ 0 r • • 90 CSeqr ••••

1110 cSecJr ••• ,

(5)

t.r for th~ quadrature ca •• than the In-pha •• • quadrature ca.. 1. equlva~.nt to the ca ••

-2 2

r19ur. a, . Int.nsity pattern ot two p('lnt­aourc •••• parated by ~ yle19h d1.tanc~ . In-pha •• (--), quadrature (---) and out-of-~e •• (~ •• -). ~lled 1n Rayl.19h d1st.un1ta.

-10 10 -1 0 o 10

- 10 10 -10

Plqur 9. -1'1 pa t rna for two polnt-aourc ... s .. .,uat1o 1. 0.77 (top left), 1.0 (top rlqht), 1.2 (bo taD l.ft), 1.'5 a (bo eo. r19ht). Th. curv ••• ow p a diff.r e. of O' (--), 90 ' (---), 110' ( •• ). Lin ar c 1 •• orlzon 1 axis 1a l1ed In 4eqr a .

Th. aource. are r ao1 (90') for parat10 9r.at.r til or '~1 to 1. 0 • In fae , the theory pred eta for a un1fonaly l11-JIIl!.-nat.d dla • b oc:k 9 91 • a narr r in 10, an iner a 81 -10 le 1 1. traded for thl. 1JIprov~t in two-polnt r •• olution. JIt. !DO ~l obj.ct 'IOU d thu. be hard to re.olve.

Plot. of the apparent pea); .. .,.ration ... function o f r •• l .. paration fOT: • thr .. cu •• U.ted above' are <Jlven 1n riCJ"m 10.

~ .. _.- --- ... . ~. .~ -------

3 3 c: c: 0 0 -.. .. .. ..

2 I.. 2 I.. 2 • .. ~ Q. u u

VI VI

+# .. c: .. c: c: u

/ u

I.. I.. I..

• .. .. ~ a. a. a. a. tr a:

0

" 2 3 2 3 " 2 Re. 1 Sep.,.at lor. Rea l Sepa,.at l on eal Sepa,.at lon

Flqur. 10.Apparent v.. r.al peak .eparation for • tvo-P9lnt .oure • Th. thre. c ••••• rel in-pha •• (l.tt), quadrature (middle), and out-of-pha •• (r19ht). The axe. are labell.d in Rayl.iqh di.tanc. unit •• Hea.ured polnt. ar •• 1.0 plotted in the Uqur ••

1

J

Data the 5 leal

Which 1a treqUJ IICY

I) - I/(U )

-~J «I (>1

11. _ that the is ~ ro outside a l' cS1 a o f spatial

l'h1. i. the cut-ott frequ.ncy ot the elrcular aperture s yat , 1 ••• spatial trequencl •• higher than this U.a1t are irretrlevably lo.t in the 1m4ging proe ....

HIU, I OTF

u y

Pique 12. O'1'Pa for annular a "ure. with

(6)

(7)

Pl na

11. The O\'P for a Wliformly l11uai­c i rc:ular perture. incre .. inq ob cura tioD (0-90 ". No 3.1.ed

a.

a clrcular aperture with . a central circular 0 scuratlon, gi".. t of hiqh .patial tr cie •• This give. antenna

I\&lI:'rC~r IUlJ.n 10 and an iIIereHe<! ai4 -lobe 1 1. O'H'. for annular aper­tur a with differ nt eqre. of obacuration are plotted 1n Piqure 12, to ab th enhance-

o h19b apatial tr ncie ••

LV

'l'b Pouler tr for. of th OTP qiv • the point Spread FuDct:1on (PSP), hieh repruanta die r e.pona in the 1II&qe pune to a point . ource ill the fa.r-n.ld. With anqulAr eoord~ate. 1ft.tead o t lin ar, t:b1. PS i . a good approx t10n ot the antanna radiatJ.oD pattern. if a hlgh t. i . a.au.ed. 1 a 'l'bia . 1 •• u. to pute the OTJ' tor an antenna ay.t-. ju.t by Pouler tr .fo antann pa tt.rn. For the eireula.rly .~trlc ca •• th1a .. an. t:&k1nq th el t:r fom of ant nna pattern , -6(p) - C 2. ! '(.)J,(2 p. lnt) .ln8d(.ln8) (8)

o

A nlllMlrlcally effiCient Hanke l tranaform method 1s due to saraJcat1' , and e trans tom torm a 1. ql v n by (9).

t 'fhrouCilhOut thi. paper it i. a •• llIMId that the OTP is real and non-neqat:1ve. The 0'fF i. then equlvalent to the Modulation Tranat.r Functlon (MTP). whlch 1. the lIIOcSulus of the O'fl'.

-- - Flo /(2 »)

B(It). I: / I: -","---, , (J,(on')'

0'1'1' r tr a. fo ot the _' ••• u; . ...

UTa,. w th 13 • ftt . ciD9 1 •• hovn in P1CJUr. 3. "lOS _ parabolold 1 . alao plotted 1ft the cUaqr_ tor 1D tile 0Tr .tor the __ urad pattern. 'ftl1. 18 evidently aClOQDtere4 1A th.1. c ....

2

.. · ~

:. l

~ i .. · ii ,

· co:

-------------"""" t .. •• r , 5 ... '1 1 lol . "

Co 0'.'"

/

5 ... .. 1 lol ...

--n----:--- f co. - • o . ~ , , ... Gul'"

........-- Clrell' ... Guide -- I,b' Ito .... • ~--------------+--8 Z 3 • , r t f. r .1 41 Tapor

", dlp

Pipre 13. C&lculate4 0'1'1' ( - ) tor an . 1 Pi9UJ:'e U. Ccmp&xi.oll ot packing aaAdty tor -.at: in the 3x5 array with 13 _ ap&cing. d1fteren antaNl& feeda. tcSeu 0'1'1' with cut-off .t 1 (noauliae4) 1a .~.o plotted (---) •

• U /2 (10)

II • a fllID

.....

5S1020

Piqur. 15. Th. inte9rated .ile.l' circuit. A slnql. CWSA el...nt i. shown •

Conclu.ion

• \ned a two-d~na1onal 5x5 aua of A .lotlin. antenna. tor 1a&CJinCJ in e c ranCJ.. The receptors showed &c:c p 1'fo .ance when used tOCJethe1' with an

f.-l loid. The achieved packinCJ den.ity i. rior to conventiona l ante • tor the .... pel:foraane.. rellUlt. are encour&'1i nq and _ intend t o continu. the r esearch in this aree.

Th SVe41. would 1 • chus. U .

1.

1.

3.

4.

5.

6.

7. I.

t. 10.

11.

12.

13.

14 .

15.

16.

ation 1 e4ish Board for Technic 1 Develo nt and the ActiviUe. i. 9ratefully acknovled9ed. On of u. (X.S Yngve.son)

support for hi. .abb Ucal leav frca Univ 1'. y of Ka •• a-r s bo per. onnel for 1r help with .. ch ic 1 detail ••

It ference.

-Array Detector. tor Killlll ter L1n Aatroft y. , 13, pp. 14-18, 1979.

a, - 9in9 Antenna Arrays- , I T-AP-30, pp." 535-540,

trat_L n. COUpled Antennas for K1ll al.tter, pp. 5-8, Auq. 19.5.

nt 1n a ParabOloid-,

utton. ed.), Vol. 10. pp. 91-

T-AP-13, pp. 660-'65.

06 Dielectric Sub. trat;e.·, To

Itib

flector.-,

Diffrac t i on Theory- .

Astronomy·, Australia

dio Astronc.y·, Au.traUa J.

tor Mult1be .. Reflector

• N86-12483

APPENDIX VII

Arrar(or

ember,.

K.S. n esaOD iswith the-Depa.rtmen.tofElectrica! and Computer Engineering, tT niversity o(Maaachusetts,. Amhers Mas,,: 01003':

I. Iohan.soIl-and E'.L. Kolloerg,' are-with Space: Obsern.tor]"j Chalmers tTniversity 0

Aft.t9"f'-l""'en 0 Electron Physics I and Onsal& echnology; 8-41296 Gothenburg, Sweden

anTi~enm!L$ (CWS .'), fed from block

b o-dime1'.sional COll:

ff",'t_ti-on wi hnv eIemen each.on.fiv parallel ubstrates Beam.-widthsare-compatible

with. u.sein. flD = 1.0 multi-beam system3',. with. optimum taper. Array element spacings

are elOISe to factor of two smaller than for other typica:i urays>~ and spill-over efficiency is about. 65%.

Introduc 0

p entl bein d eIop (0 lug number of appU-

hich fi reftecto or lens, Som exceptions c b

end!re tapered slot element.

yo by Ru led et a1 [2). ,bu not given any resu1 on a:1s ta of b . g fully o-dimensional.

Su ork report d here, and h b adapted

fo flD of abou on. This is common.f'-

numb 0 imagin d communication tellit antenn ppUcatio , since i allow

• convenientl I numb 0 b Cons ant • dth. slo elements- (CWSA's) have been

employed, ho in Flgtm 1. sign.iiican advantage 0 the CWSA array is that the

sp' • g between elements-can be made small by bon a factor of two, compared with &

waveguide array used in a. system with h ame {-numb •

31' D fgn design w b ed 0 wor wi single el men 0 en tapered lot

antennas, d crib in other publications [4}, [5}. Such antennaa achieve a somewha

enlarged g&in. due to the traveling-wave nature of the radiation mechanism, compared

with what one would expect. £rom the croea-s tiona! dimensioIlS'. It is important to note

1

that;i 0 p obi

tctlle

width tap

'!lut

at [4J

dimensio

b

valu

o bo t

dicuIa.r

studied in

pA1"t1:11''''

bolic. dish 0 f­

of approximate1Y-10

b mstched

idth eetion. In 0 ca.se~ in Ie elemen

..... tI .. - 0 e specific a ·ons; for an y to b ed 3-1. GHz: Radiation patterns 0 mgl elements. are or caUl'S modified. when the elemen~

are placed: in.. the array" but caI1 still 0 ed & rough g\llde to the beamwidths one can.

expect ill' th arra.yenmonm nt-

J!iX1Der1D1ental De

feedin

spectrum analyzer i~ or by modu-

kRz'. and usin narro band ampllfl th de ctor. A • th form 0 box with trapezoid tion for the source, and

employed. The tes antenna. or gr&ywu tumed by teppin mo 0 und control by Hewlett-Packard 9816 computer.

Data. were KCes ed d plo b utomatically. The linear dynamic range

attained was typica.lly 25-30 dB. ....~ ...... ta

T radiatio p ttems in th E- and R-plan for single elemen are shown in Figure

2'. Sing! CWSA elemen can sho houlde on the E-plane patt m. Th amplitude and

loc:&t'on 0 th ould depend on. the size and shape of' th block, as well as the frequ ncy.

While such interaction: effect" with. the fixture are presently not. exactly predictable, it is

poaible to empirically e1iminate any undesirable shoulders- on the beam, for example by

changing the frequencyo

while - °

etc. OnI quadran

whi

from

o quare ma ement 13: is' the central element,

iven,. sine da. or the other

b

to this are th to - dB on. th id 0 a; ay

,. b nonnal aper 0 th oth ide o th beam. Also a.symm.e -c:. T asymmetry b easily exptain~ since thes4f

are 0 QUtermoet sub tra e'. I - e to emedr the asymmetry, if desired, ~ ainc 1m extra. -crumm,-- substrate O~ id 0 array.

A IxS eIemen a.rrq w also. measured -th imil resulb see Figure _

D 1 A.1"'Pj,,-v. or line 11' t p ed

to achiev quit small element o taken. (Of' CWS array ith ·e beamwidths in E- and H­

an.""°ITlea.tion,· 0 our leno ledge the

'!f, m tch d to (/D - 1 dish. Th ° on with dat (or arrays constructed

ds hich would inside perture aveguid walls,

it ia HeD ay the compa.rable conical horn. array_ The crou-sectiona o( the two a15 compa.red in Figure 5.

m & recent publicatiou-, Rabmat-Samii et al havecompa.red the gain or difrerent types of reed element. which might be used in arrays [6] (cigar antennu, rectangular and. circular

W&~egulo.e,..

distance",. 6R.1Sthe elemm spacing. whiclt.co

which canlusi: be' resolved. &Cco~din Q h

in.i images 0 . twopoint-sources-,

criteno [7} rt is given by::

( )

spacln

b includ and of elemen • Equally

tapered slot-an enna.

bearin on th utility of the CWS arra;

SJ'fI

the :y~

thespilI-o

IDlOO

e ha.ve timated

o a.rra; ha~ spill-o er efficiencies cIes to

off"erin ignificantly cIo er beam spac­and deer as d cost of fabrication,. as well 80S'

lower weight,. CWSA ancf other tapered slo antenn. elements: can thus be considered. as.

[LJ Ko • T.L.,. Po , D.M.~ Schaubert, D.H.,. and Yngvesson, KoS., "Imaging 5yst G& U: in T pered. Slo Antenn& Elements"', 8th Intern. Con! .. Infr. Millim Waves- (1983).

[2} Rutl d D.B. and uha, .S.~ "Imagin .An.tenna Arrays, IEEE Trans. Antennas. and Prop ., P-30 535-540 (1 2).

[S] Farr~ E.,. W. bb, K.. and ·ttr R&d Applications, Arch. Elec

tudi in Fin-Lin Antenn Design for Imaging Ub ., b T- 9 (1985).

["I. Yn.gvesaon, K.5.,. Schaubert D.lr., Korzenio ki, T.L., Kollberg, E.L., Thungren, r.~, and Johansson, J., I&Endfire- Tapered Slot Antennas on Dielectric Substrates" I accepted for publlcation-,. December 1985 issue, IEEE Trans. Antennas and Propag.

[5

Introduction

and Lee-, S.W., "Realizable. Feed.­aIys~, IEEE Trans· Antennas

eG ;w-Hill, ew York. 968

gur. :ptlou.

Figure ~ Radi • pattenlS measured 0 o

lFi&Ure X. MeUU:rect rIW.la.JOlWU

Fi&me $. Compam· ron hom:

i1&1U8 6'. prot 0 rt . oy e elemen :-spa.cin 0 arra 0

fOllowing en () C (this paper) (b) LTSA [11 ~ (e) Cigar antenna. 6), (d) Rectangular guide [6J,. (e} Circular guide' [6J, (f) pyramJdal horn. 6}. The: array elemanta are: assumed, to illuminate' & reftect~r with f-# given. on: the horizontal azis., anei with.. -10. dB taper~

~igure t

I'

E ·H Figure 2

ORI_ .. _ ......

Of. POOR U

Figure- 3a

E-P an e P att er ns

Figure- 3b

H- P a n e a t e n s

Figure- 3c

•

E-Ptane Pa terns

H-Pl ane Pat'te ·rns

Figure 4

(b).

Fi r S

•

2

LTSA. a ,

' . CHSR.

CI a "

\ Diffractfon L imited R"eso J uti on

:- Ci 9 ar Anten"~ • .

: • • • • • • • f r Rectar.tgu 1 at" Gu i d ' :- ,-

t. # : . • . :-. ..

----------------------------------~:.' ~ / _-Cit"cuJat" Guide ,. ~---------------------------------~ ... -- '. ",

Fyram i d 1 HOt"n

0~--------~·~·--------~--~----+---------~--------~f-----~ tel 4 S

Ft, for-: 10' dB Tapet"

Pigure 6