Improving efficiencies of superdirective arrays of monopoles over lossy groundplanes by using superconducting disc overlays

G .G. Cook S.K. Khamas D.R. Bowling

lndi,.ying tc~rnls: Antcwntr theory. Monopole urruys, Superconductive untenna, Superdirectirse arrays

Abstract: Electrically small perfectly conducting superdirective monopole arrays above lossy metal groundplanes are analysed at 5OOMHz using a moment method incorporating Sommerfeld terms. It is shown that significant improvements in efficiency are obtained when small perfectly conducting discs, which can be realised using high-temperature superconductors, are attached to the monopole bases, compared with the monopoles being directly connected to the groundplanes.

1 Introduction

The negation of ohmic losses in the radiating elements (as well as in the matching networks) of electrically small antennas can significantly increase radiation effi- ciencies [1,2], and is the reason for considering their fabrication using superconducting compounds. The advent of high-temperature superconductors (HTS) has now made deployment of such antennas more feasible. For dipole antenna arrays the entire radiating elements can be made superconducting, but for arrays of monopoles connected to groundplanes this may not be feasible, since the groundplane may form part of a vehicle on which the antenna is mounted. However, analysis of superconducting electrically small monopo- les and halfloops connected to groundplanes with nor- mal conductivities [3] suggests that significant efficiency improvements are still provided by making such monopoles and halfloops superconducting when it is not practical to make their groundplanes lossless. Nonetheless it may be practicable to increase the con- ductivities of small areas around the bases of monopo- les in an array by cooling the groundplane in the antenna's vicinity, or by overlaying discs of supercon- ductor to which the monopoles are connected. Since the highest groundplane current densities exist in these regions, conduction losses may be reduced to produce 0 IEE. 1995 I E E Procerdings online no. I9952358 Paper first received 26th April 1995 and in revised form 25th August 1995 G.G. Cook and S.K. Khamas are with the Department of Electronic and Electrical Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD. UK D.R. Bowling is with ONR, China Lake, CA 93555, USA

efficiencies which are significantly greater than for homogenously lossy groundplanes [4].

In this paper the analysis of a monopole at the centre of a circular disc over a flat earth plane [5] is modified and used to calculate the efficiencies of arrays of elec- trically small superconducting monopoles connected to lossless circular discs over lossy (e.g. copper) ground- planes, excited by Chebyshev superdirective driving- current functions. Results are compared to those when there are no discs, in which case the antenna elements are connected directly to the groundplanes. Dimensions and operating frequency for the arrays (500MHz) are taken from those suggested in the literature [6], where a UHF or microwave array will benefit most from the increase in conductivity obtained by using HTS, com- pared with lower operating frequencies. The analysis uses a moment method to determine the array-element driving point voltages and segment currents from spec- ified driving-point currents, in which standard free- space impedance terms coupling antenna segments are augmented by Sommerfeld-type integrals to account for the lossy groundplane. A two-fluid model [7] can be used to obtain values of superconductor conductivity, although this may be assumed infinite at the frequen- cies of interest.

i" I I

free space pn pn.1

lossy groundplane

Geometry of antenna array Fig. 1

2 Theory

The problem of a wire monopole antenna on a circular disc over a groundplane can be divided into two parts. The first is concerned with obtaining the moment method impedance terms Z,", in the absence of a groundplane, and the second is then the augmentation of these terms with additional terms Zrin to account for the groundplane, so that the final impedance terms are

(1) 0 Zm,= z,, + z;,

IEE Pioc - M K I O W Antenna, Piopag Vol 142 N o 6 Deccinhrr I Y Y S 462

The evaluation of the Z,", terms is straightforward [8]. Here there are three types of impedance elements: with respect to Fig. I , Zl,~$'+ couples wire expansion mode n to wire test mode nz, Z2idV' couples wire expansion mode n to disc test mode m and Z2f1 couples disc expansion mode n to disc test mode in. The corre- sponding impedance elements Z;, for the lossy groundplane involve the following improper Sommer- feld-type integrals [5 ] . The z-directed electric field due to a reflected z-directed sinusoidal current expansion pulse on a wire of radius a is

0 where

B2 sin kAz Pn(r) =

and the piecewise sinusoidal along the wire are given by

F,L(z ' ) =

F,, (2') =

sin k ( z r - znP1) sin kAz

sin k(z, ,+l - z' ) sink&

F, ( z r , e 7" z' d z (3)

current expansion modes

which also serve as wire or disc test functions, where dimensions are defined in Fig. 1. The groundplane parameters are

g 2 = J2 - w ~ ~ ~ ~ , . E O E , + jwpop,a

The p-directed reflected electric field due to a z-directed wire expansion pulse of radius a is

and that due to a disc current expansion mode is M

where

(7)

The extra moment method impedance terms which account for the presence of the groundplane in the cou- pling of the antenna segments are therefore

Z:,;;t'" = E z , F m ( z ) d z ( 8 ) -.I 17L

(9) z;;p = -_ 71 EpzFm(a)dcud$ 27r

O m

If testing is done on a disc which is remote to the source wire or disc, a equals the local test-disc radius

I E E Pit11 -h-/iliou 4nrennrr~ Piopug Vol 142. No 6 Detemher IY95

vector, otherwise a = p. These impedance terms are used to formulate a set of linear equations which may be solved to obtain the driving point currents or volt- ages of each array element, defined at the junction of a wire monopole and disc (or groundplane if no disc), using standard moment methods. For superdirective arrays, Chebyshev driving source current excitations are specified [9], using the main lobe-to-sidelobe ratio (SLR) of the field pattern to denote the degree of superdirectivity, which is inversely proportional to the SLR. The linear equations are therefore used in an 'inverse' moment method calculation to obtain the cor- responding driving point voltages, and segmented antenna currents. In this procedure the A4 x M imped- ance matrix is inverted to produce an M x M admit- tance matrix, so that

[YIP1 = [I1 (11) However, the voltages away from the element feed points can be assumed zero, allowing reduction of the admittance matrix to N x N elements (for N feed points). The N feed-point Chebyshev currents are then used to obtain the N driving-point voltages. The full M x M impedance matrix may then be used to calcu- late the remaining segmented antenna currents. Con- sider as an example the three element array of Fig. 2,

Fig. 2 > = feed point

Hyyoihetical three-clipole arruy to explain inverse moment merhod

where each element supports three current basis func- tions, so that M = 9. Eqn. 11 can then be written

9 9

y y,,zK = I 3 (12) 3=1 z = 1

However, VI, V3, V4, V6, V7, V9 = 0 since they do not correspond to feed points, and one can therefore select a set of three equations ( N = 3 ) involving the known specified Chebyshev driving-point currents, and solve them simultaneously for the corresponding driving- point voltages, where

y 2 , 2 v 2 + y 2 , 5 v 5 + y 2 , 8 v 8 = 1 2

y 5 , 2 v 2 + y 5 , 5 v 5 + y 5 , 8 v 8 = 15 (13)

y 8 , 2 v 2 + y 8 , 5 v 5 f y 8 , 8 v 8 = 1 8

The efficiency of an array of N elements is then calcu- lated as

463

where V,, Vsn are ithe element driving-point voltages required to produce the same specified terminal cur- rents I, for lossless and lossy antennas, respectively. The groundplane current-density distribution is obtained from the component of total magnetic field of all the segment currents which is tangential to the groundplane.

3 Results

A typical requirement for a superdirective array sug- gested in the literature [6] might be a five-element array at 500MHz comprisiing L = 0.0% long monopoles with a = 10-3h radius separated by d = 0.12h. These dimen- sions have therefore been chosen for the analysis, with b = 0.06h-radius discs attached to the base of each monopole, at zero height (h-+O) above the ground- plane. Due to the electrically small size of the discs, a single radial half pulse is used as the disc current basis and testing function. In all cases the monopole ele- ments themselves arle perfectly conducting. Figs. 3 and 4 show surface plots of the current density distributions over a lossless groundplane for uniform broadside exci- tation of the array, and for superdirective broadside excitation with SLR = 100, respectively, where only a quadrant of groundplane is shown owing to symmetry. Here, the peak currents have been made equal to com- pare the shapes of tlhe distributions, and it can be seen that a higher relative current amplitude exists around the bases of the superdirective monopoles.

1, Y

Fig.3 uniform excitation

Surface plot of current density over quadrant of groundplane f o r

Fig.4 superdirective excitation ( S L R = 100)

464

Surface plot of current density over quadrant of groundplane for

Figs. 5 and 6 similarly compare cuts of the ground- plane current distributions along the line of the monop- oles, and normal to the monopole line, respectively. In this case however the total real power delivered to the uniform and superdirective arrays is made equal so that the same power is radiated for lossless antennas. Here

\ / \ I \ /

. 0 0.05 0.10 0.15 0.20 0.25 0.30

Xlh X-cut of groundplane current density for equal power input to loss- Fig.5

less uniform and superdirective arrays ( S L R = 100) _ _ _ _ uniform array __ superdirective array

Q . E look 10

Ylh Y-cut of groundplane current density for equal power input to loss- Fig.6

less unform and superdirective arrays ( S L R = 100) _ _ _ _ uniform array ~ superdirective array

the superdirective array has a significantly higher groundplane current density than the uniform array in the vicinity of the monopoles, and the H-plane radia- tion patterns are compared in Fig. 7. The directivities

0 30 6 0 9. deg

Fig. 7 tive arrays of Fig. 5 and 6 (@ = 90" corresponds to broadside direction) _ _ _ _ uniform array ~ superdirective array

H-plane radiation patterns for broadside uniform and superdirec-

of the superdirective array for dilferent SLRs is shown in Fig. 8, with that of the uniform array being 6.6dB. Fig. 9 shows the efficiency of the monopole array with

IEE Proc -Mzcrow Antennas Propag., Vol. 142, No 6, December 1995

"I--- 11

m

2: U .a .- 2 10- ?! .- U

-

1 10 100 lo00 10000 SLR

Directivities of superdirective monopole array with different SLRs Fig. 8

I i

10 100 1000 10000 SLR

Fig. 9 superdirective excitations (1) Cu groundplane (11) AI groundplane (in) brass groundplane

Efliciencies of monopole array over lossy groundplanes for various

perfectly conducting elements directly attached to vari- ous lossy groundplanes (no discs), when driven with different broadside Chebyshev superdirective functions [9] specified by their SLRs. Thus any superdirective improvement in directivity over uniform is considerably compromised by gain reduction owing to groundplane losses. Efficiencies are worst for the lowest SLRs which denote the most superdirective functions, and for the most lossy groundplane (brass). The efficiency of the uniform array is over 99% for all groundplanes. Fig. 10

.-

.- - .I .

----- ----- ---==I=

Fig. 10 Efliciency improvements obtained by connecting perfectly con- ducting discs to monopole bases compared with direct connection of mono- poles to groundplanes for various superdirective exitations ( b = 0.06A) (i) Cu groundplane (ii) AI groundplane (iii) brass groundplane

illustrates how these efficiencies can be significantly improved on by attaching perfectly conducting 0.062. radius discs to the monopole bases, and a typical value

of SLR = 100 is then chosen and the efficiency improvements are plotted as a function of disc radius in Fig. 11.

/ I

0 0.02 0.04 0.06 b lh

Fig. 1 1 Efficiency improvements obtained by connecting perfectly con- ducting discs to monopole bases compared with direct connection of mono- poles to groundplanes for various disc radii (SLR = 100) (i) Cu groundplane (ii) AI groundplane (iii) brass groundplane

4 Conclusions

The groundplane current density of a superdirective array is significantly higher in the region of the monop- oles, and decays less between the monopoles than that of a uniform array. Consequently a greater proportion of J2Rs-type losses can be negated by making the groundplane perfectly conducting in the immediate vicinity of the superdirective monopoles. This coupled with the inherent low radiation efficiencies of electri- cally small superdirective arrays produces significant efficiency improvements when perfectly conducting discs are attached to the monopole bases, and at higher microwave frequencies these improvements will be greater owing to the frequency dependence of the loss mechanism. An important consideration when improv- ing antenna efficiency however is the associated increase in Q factor, which may become practically unmanageable for highly superdirective arrays, and therefore retention of some loss may be an advantage. The size of the disc overlays could therefore be adjusted (indeed they need not be circular) to obtain a compromise between increased efficiency and (2 factor. The advantages in making electrically small antennas superconducting even when it is not practical to make their groundplanes lossless, such as when mounted on vehicles, have already been demonstrated 131.

This paper has shown that further significant improvements in the efficiencies of superdirective monopole arrays can be obtained by reducing losses in only small regions around the monopole bases. Practi- cally this could correspond to HTS discs being laid over the paintwork of a metal vehicle. The cryogenic apparatus will be simpler to implement if only a small area of a groundplane needs to be cooled, and the cool- ing of a monopole radiator might in any case cause sig- nificant heat reduction in the region of the groundplane close to the antenna connection [lo].

The analysis presented here is intended to help in assessing the feasibility of electrically small HTS super- directive monopole-type arrays over groundplanes. The demonstrated benefits of making regions of a ground- plane lossless must of course be weighed against the engineering problems associated with cooling. Maxi-

IEE Proc.-Microw. Antennas Propag., Vol. 142, No. 6, December 1995 465

mum efficiency improvements for specific disc radii have been presented, assuming lossless matching cir- cuitry and perfectly conducting (HTS) discs. HTS RF losses. lossy matching networks, and inadequate cool- ing will all reduce the predicted efficiency improvement figures, but there are worthwhile advantages to be gained given the right technology.

5 References

I DINGER. R.J., BOWLING, D.R., and MARTIN, A.M.: ‘A sur- vey of possible passive antenna applications of high temperature superconductors’, IEEE Truns., 1991, MTT-39, pp. 1498-1507

2 LANCASTER, M.J., WU, Z., MACLEAN, T.S.M., and HUANG, Y .: ‘Supercooled and superconducting small-loop and dipole antennas’, IEE Proc. H , 1992, 139, ( 3 ) , pp. 264-270

FELT, P.L., and HAGEMAN, L.: ‘Predictions of the efficiencies of superconducting small antennas connected to lossy ground- planes using a Sommerfeld integral technique’, J. Appl. P/y.s.. 1994. 76. (2). pp. 1266---1268

3 COOK. G.G., KHAMAS, S.K., BOWLING,D.R. , OVER-

4 COOK, G.G., KHAMAS, S.K., and BOWLING, D.R.: ‘Effi- ciencies of superconducting small antennas connected to lossless disks over lossy groundplanes’, IEEE Truns., 1995, AP-43, (6), pp. 631-633

5 RICHMOND, J.H.: ‘Monopole antenna on circular disk over flat earth’, IEEE Truns., 1985, AP-33, (6), pp. 633-637

6 DINGER. R.J.: ’Some potential antenna applications of high temperature superconductors’, J . Supercwnd., 1990, 3, ( 3 ) , pp. 287-296

7 COOK, G.G., KHAMAS, S.K., KINGSLEY, S.P., and WOODS, R.C.: ‘Performance prediction of high Tc supercon- ducting small antennas using a two-fluid-moment method model’, Appl. Plzys. Lett., 1992, 60, ( I ) , pp. 123-125

8 RICHMOND, J.H.: ‘Monopole antenna on circular disk‘, IEEE Truns., 1984, AP-32, (2), pp. 1282--1287

9 DUHAMEL, R.H.: ‘Optimum patterns for endfire arrays’, Proc. IRE, 1953, 41, pt. I , pp. 652-659

I O DINGER, R.J., BOWLING, D.R., MARTIN, A.M., and TAL- VACCHIO, J.: ‘Radiation efficiency measurements of a thin film Y-BA-CU-0 superconducting half loop antenna a t 500 MHz’, Proceedings of IEEE MIT international microwave symposium digest, 1991, Vol. 3 , pp. 1243-1246

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