621.396.677.3Paper No. 1536

RADIO SECTION

A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYSBy A. BLOCH, Dr.-Ing., M.Sc, Member, R. G. MEDHURST, B.Sc, and

S. D. POOL, B.Sc.(Eng.), Associate Member.{The paper was first received \lth October, 1952, and in revised form 23rd April, 1953.)SUMMARY

The current distribution required for maximum directivity of anarray with a finite number of elements and any specified geometricalconfiguration is shown to be completely defined by the self- andmutual resistances of the elements and by a certain component of thevoltage (the "resistance voltage") across the terminals of each element.This voltage component is required to vary from element to elementin the same way as the instantaneous local values of a sinusoidaldisturbance travelling across the array, in the direction under con-sideration, with the velocity of an electromagnetic wave.

As a consequence, the maximum gain of the array is expressibleeither as a double sum containing only the mutual conductancesbetween the individual elements multiplied by trigonometrical factorsdepending on their spacing, or as an expression identical (except for anumerical factor) with that for the distant field of the array.

These theorems hold, slightly modified, for arrays of non-identicalelements.

The theory has been applied to the numerical calculation of certainsimple arrays. It appears that, for arrays of a given size, directivitiesgreater than those obtained by conventional design methods can beachieved without excessive losses.

This has been substantially confirmed by an experimental arrayof four elements operating at 75 Mc/s. The theoretical gain was10-ldb, while 8-7 db was measured. Of the discrepancy, 0-6 dbwas calculated to be due to losses in the feeder system and a further0-2 db to losses in the dipoles. The bandwidth was about +$ Mc/sfor a drop in gain of \ db. The degree of super-directivity is indicatedby the fact that a physically identical array fed with equal-amplitudecurrents phased for maximum field strength in the end-fire directionwould have a gain of 4- 6 db.

LIST OF PRINCIPAL SYMBOLSn Total number of elements in array.

Zmm = Rmm + J^mm Self-impedance of element m.Z/m = i?/m + jXlm = Mutual impedance between elements /

and m.Im = l'm + //^ = Current in mth element.

Vm = V'm + jV'n = Potential difference between the ter-minals of the mth element.

P = Radiated power.H = Received field strength at some distant

point in a direction of maximumradiation.

Is = Current in a reference element.Hs = Received field strength when the refer-

ence element is substituted for thearray.

Rs = Self-impedance of reference element.6m = Electrical angular distance from a

reference plane (perpendicular to thedirection in which the array is tohave maximum gain) to the mthelement. The positive direction isfrom the reference plane towards thereceiver.

Written contributions on papers published without being read at meetings areinvited for consideration with a view to publication.

The paper is a communication from the Staff of the Research Laboratories of TheGeneral Electric Company, Limited, Wembley, England.

2"

l=1

G = Power gain of the array with respect toreference element.

, = "Resistance" component of the totalvoltage across the /th element.

Zm = R

As As= Normalized mutual impedance between

elements / and m.+ jXm = Driving-point impedance of mth ele-

ment.

(1) INTRODUCTIONThe work described in the present paper had its origin in the

so-called "super gain" theorem relating to directional aerials.This states that it is possible to design an aerial of arbitrarilysmall dimensions with a directivity as high as desired. Thetheorem applies only when there is sufficient freedom to fill thefinite space occupied by the array with either a continuouscurrent distribution or an unlimited number of discrete radiators.

Closely connected is a second theorem which can be stated inthe following way:19 The bandwidth and radiation efficiency ofan aerial decrease if its gain is held constant while its size isreduced below that of a conventional aerial having this gain.

The concept of super-gain arrays apparently contradicts thecommon experience that an increase in the gain of an aerialmust be accompanied by an increase in its size, and is apt to beconsidered an academic curiosity. It is not therefore surprisingthat the super-gain theorem was forgotten and rediscovered6-9twice during the 24 years following its initial discovery.1 Mean-while, intermittent attempts8-11'13 were being made to calculate"optimum" current distribution for systems where there is, infact, no finite upper limit to the directivity.

The second of the two theorems stated above is of greatpractical importance to the aerial designer who wishes to knowwhether or not it is economical to use an aerial with a directivityhigher than normal.* Recent work20-23-26 on this aspect of theproblem has taken the form of computing current distributionsfor particular super-directive arrays, and pointing out that theseare associated with very large current amplitudes, and hencewith low efficiencies.

The methods used to find these current distributions do notconsider the radiation efficiency of the array, nor do they leadto maximum directivity, where the aerial system is so restrictedthat a maximum exists.

If one considers the current distribution required on an arrayof a finite number of fixed elements to produce an arbitrarilyselected directivity, less than the maximum directivity, one mayexpect to find an infinity of such distributions, many of whichmay be accompanied by low radiation efficiencies. This will betrue whether the selected directivity is greater or less thannormal. Consequently, to dismiss super-directive aerials asimpracticable23-26 merely because some extremely inefficient

Normal directivity is taken to mean that associated with an array of equal-amplitude currents, chosen so that the distant field components are in phase.

[303]

304 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYSsuper-directive current distributions have been found does notseem justifiable.

It is not yet known how rapidly the bandwidth and efficiencyof an array decrease when the directivity is increased abovenormal, so that it is of interest to seek a current distributionwhich, while having a usable bandwidth, combines super-directivity with an efficiency great enough to give an improvedpower gain over conventional designs.

To reduce the work to practicable proportions, the investiga-tion was restricted to the unique current distribution givingmaximum directivity with a particular configuration of radiatingelements.

Previous calculations of super-directive current distributionsfor discrete radiators have been based on the work of Schel-kunoff,6 on linear equispaced arrays. However, Schelkunoff'smethod does not, in general, lead to maximum gain; hence it isnot clear how much further improvement is possible by adjust-ment of the currents.

The only previous work concerned with maximum gains fromfinite numbers of elements appears to be that of Uzkov,12 whoconsiders omnidirectional sources. Explicit solutions are givenin two special cases: (a) for a linear array of n elements spacedA/2 apart, the maximum gain being shown to be n, and (b) foran end-fire linear array of equispaced elements as the lengthapproaches zero, in which case the maximum gain is shown toapproach n2. However, Uzkov says nothing about the relativeexcitations of the individual elements. Comparison of Uzkov'sresults with those for Schelkunoff arrays of three and fourcolinear equispaced elements (Fig. 22 of Reference 6) shows thatfor these simple arrays Schelkunoff's method leads to directivitieswhich are less than 1 db below the maximum.

In the present paper the approach is rather different from thatof Uzkov, who obtains his results by a process involving theresolution of the radiation patterns of the elements of the aerialarray into components which are orthogonal to each other inan n-dimensional complex space. Instead, by a variationalprocess a theorem is developedthe "travelling voltage wave"theoremfrom which the currents in the individual elementsrequired for maximum directivity can be derived simply by asolution of a system of linear equations. The theorem, slightlymodified, also applies to arrays in which the elements are not ofthe same kind or of the same orientation. It appears that usefulimprovements in gain over conventional arrays can be obtainedwithout a prohibitive loss of bandwidth or efficiency. Someexperimental results have been obtained which, while not com-pletely satisfactory, provide substantial confirmation of thetheoretical findings.

(2) THEORETICAL TREATMENT(2.1) Definition of "Resistance Voltage"

In an aerial array having n elements the relation between thecurrents and voltages at the terminals of the elements is given43by a system of equations of the form:

Vm = 2 J/S

BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS 305Comparing this equation with eqn. (3), it is clear that, since P

is real (see Section 8.1.1), the received field is real, and in thepresent system of units they have the same numerical value.

Eqn. (5) then simplifies toG=H=P . .

Substituting eqns. (7) and (9) into eqn. (4) gives

m = l /=1

(9)

(10)

Since every term in this expression has a conjugate counterpart,this simplifies to

= (11)If the array is made to have maximum gain in the opposite

direction the angles will be of the same magnitude but oppositesign; hence the maximum gain of an array is the same in any twoopposite directions, although, apart from symmetrical arrays, thetwo current distributions are not just the reverse of each other.

In Section 8.2 eqns. (6b) and (9) are converted into formswhich enable the values of the currents in the elements and thegain of the array to be conveniently computed on a desk-typecalculating machine.

(2.4) The Broadside ArrayThe foregoing theory applies to arrays having the maximum

gain in any chosen direction. The broadside array is a speciallysimple case, as all the angles 6m are equal. It follows that thisarray will have maximum gain if the resistance voltages at theindividual aerials are of equal magnitude and are in phase.

(3) LIMITATIONS ON THE APPLICATION OF THE THEORYTO PRACTICAL ARRAYS

(3.1) Values of Mutual ImpedanceWhen the elements of an array are omnidirectional sources

(the case studied by Schelkunoff6 and Uzkov12), the normalizedmutual resistances required, e.g. for eqn. (6b), take a very simpleform. It is easy to show that for this hypothetical type ofelement

sinrlm

where 6 is the angular distance between the elements.In practical arrays designed for the v.h.f. band the elements

commonly consist of thin rod dipoles, half a wavelength long,and the values of mutual impedance are not so unambiguous,since the current distribution is known only approximately.

It is usual, for lack of a better foundation, to assume that therods are infinitely thin and that the current distribution is sinu-soidal. For the case of most interest, i.e. when the elementsare parallel, the mutual impedances can be calculated (see, forexample, References 29 and 32) with a reasonable expenditureof labour; numerical values have also been tabulated over somelimited ranges.29"31

At first sight it might appear that calculations based on hypo-thetical arrays of infinitely thin dipoles could not be expectedto give a useful guide to the performance of practical arrays,since the changes in self- and mutual resistances when goingfrom infinitely thin elements to elements having thicknessesencountered in practice may be much greater than the terminalresistances found in super-gain arrays. To illustrate: an iso-lated element of the experimental array described in Section 4has a theoretical self-resistance36 about 13 ohms higher than that

of an infinitely thin half-wave dipole. The proximity of onesimilar parallel element at the spacing used in the array reducesthis value by 5 ohms. The mutual resistance between twoadjacent elements, ignoring effects of other elements, is about4 ohms higher than the value for infinitely thin elements. Sincewe shall find that the magnitude of the smallest driving-pointresistance encountered (1-6 ohms) is much less than thesevariations, it might be expected that the power relations in thearray, and hence its maximum directivity, would be criticallyaffected by the element thicknesses. However, these effectsshould not be severe, at least as far as the maximum gain isconcerned, for the following reasons:

This gain is merely the result of the concentration of the radiatedenergy into a small spatial angle, i.e. of the destructive interferenceof the radiation patterns of the individual elements. For super-directive arrays we may expect this interference to be substantiallydisturbed if, say, one of the individual patterns were changed.However, if all the radiation patterns are changed in the same way,the overall effect will be merely a multiplication, by a correspondingfactor, of the pattern previously produced. Now, if the array con-sists of identically similar elements, thickening of the elements willproduce changes in individual patterns which are to a first orderof approximation the same. It is only to the extent that the elementsdo not occupy equivalent positions in the array that this argumentis not conclusive.It would, of course, be even more satisfactory if it were possible

to use mutual impedances appropriate to thick aerials. Unfortu-nately, at present the necessary data do not appear to exist.Approximate values have been published for the case of twoaerials.36* However, mutual and self-impedances of thick rodaerials (unlike those of infinitely thin aerials) depend on thelocation of all other aerials in the vicinity, so that use of thesevalues for arrays containing more than two elements wouldprobably not give better results than one can obtain from thesimple thin-aerial approach.

It is interesting that the results of calculations37 on a pair ofelements (one fed and one parasitic), using the second-ordertheory, show little difference in maximum-gain values, as theaerial thicknesses increase, from the results of the simple thin-dipole theory.

(3.2) Tolerance on the Currents in the Elements of the ArrayConsider Ieff, the current required to flow in a single element,

to produce the same distant field as the array. If in eqn. (4) nis put equal to unity, it is apparent that Ieff has the samenumerical value as H, and also as G and P [eqn. (9)]. A com-parison of this current with the magnitude of the largest of thecurrents flowing in the elements of the array is of interest, sincea change of any current in the array by an amount Ieg- couldreduce the distant field to zero. We are thus given a measureof the practicability of constructing the array. For example,Jordan23 has designed, by means of Tchebyscheff polynomials,a super-gain array which has an Ie^ of 39 mA and an elementcurrent of 17 MA. The tolerance on the element current forthis design would consequently have to be much better than1 part in 4 x 108, which, as Jordan points out, is quite imprac-ticable. In the experimental array described in Section 4, Iejj isabout half the largest element current.

(3.3) Heat Losses in the Aerial ElementsThe theory given in Section 2 applies to loss-less aerials. In

practice, it is necessary to consider the effect of the resistanceof the elements.

Neglecting any effects of such losses on the current distri-* It should be noted that the earlier Tai values,3' which are reproduced without

indication of their approximate nature in Reference 39 (p. 266), are first-order valuesonly, and according to King^s "cannot be in good agreement with experimentalmeasurements."

306 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS

bution along the individual elements, it is possible to representtheir effect fully by the addition of a series resistance RL to thedriving-point impedance of the loss-less element. Hence thecurrents on the individual elements and the radiation patterncan be made the same as in the loss-less case. This leaves thedirectivity unchanged, although, of course, the gain of the arrayis reduced.

For cylindrical half-wave dipoles, assuming sinusoidal currentdistribution, it is easy to show that

. . . . (12)

where / = Frequency, Mc/s.p = Resistivity, ohm-cm.D Diameter of dipole rod, cm.A = Wavelength, cm.fi = Relative permeability.

The experimental array described in Section 4, which usedaluminium elements of |-in diameter, had an RL of 0 048 ohm.

The power lost in heating the dipoles can readily be calculatedfrom RL and the currents, and must be compared with the totalradiated power. In the experimental array the loss from thiscause was 0-2 db.

(4) DESIGN AND PERFORMANCE OF AN EXPERIMENTALSUPER-DIRECTIVE ARRAY(4.1) General Considerations

Taylor19 and others have shown generally that the bandwidthof an array decreases as the size is reduced if the gain is heldconstant, and it appears that the decrease is likely to be veryrapid. In fact, it has frequently been suggested that for thisand other reasons it is not worth while to push a design into thesuper-directive field. With this consideration in mind it wasdecided to build an experimental array, which, with optimumcurrent distribution, would give about 5 db more gain than thesame system fed as a conventional equal-amplitude end-fireaerial. It was felt that this represented a useful increase in gain,while at the same time there was still hope of retaining a sufficientbandwidth for some practical applications.

(4.2) Theoretical Performance Data of the Array SelectedThe array chosen was designed to operate at 75 Mc/s. It was

an end-fire array of four parallel half-wave dipoles, whosecentres were equally spaced along a line 0 6\ long.

The principal results of the numerical calculations are givenin Table 1. The theoretical maximum gain of the array isl O l d b over that of a single element. Some comparativefigures are offered to show the degree of super-directivity impliedby this gain value. A physically identical array fed with equal-amplitude currents phased for maximum field strength in theend-fire direction would have a gain of 4-6 db; a continuousarray of equal-amplitude doublets phased according to Reid's"optimum" distribution13 should produce 6-5 db gain over asingle doublet. The gain of four omnidirectional sources havingthe same spacing, and fed as described by Schelkunoff,6 isgiven in Fig. 22 of his paper. Using the same method asin Section 8.4, it is estimated that, if this array consisted ofhalf-wave dipoles the gain would be about 9 db. A 6-elementYagi array about 2\ times as long as the experimental arraywas found by Fishenden and Wiblin40 to have a gain of 9 db.

Fig. 1 shows the theoretical radiation pattern of the array, inthe plane at right angles to the elements. For comparison, themain lobe of a physically identical array fed with equal amplitudecurrents, having their respective distant field components in the

Table 1RESULTS OF THEORETICAL COMPUTATION

Element number1 2 3 4

Real parts of currents.. -2-157 +1-473 +1-473 -2-157Imaginary parts of cur-

rents -7-864 +18-327 -18-327 +7-864Moduli of currents .. 8-155 18-386 18-386 8-155Real parts of driving

point voltages .. 1-398 -12-694 +14-312 -2015Imaginary parts of driv-

ing point voltages .. -0-976 +2-729 +1-553 -2-878Driving-point resistances,

ohms +5-1 +6-8 -1-6 -20-1Driving-point reactances,

ohms +14-4 +51-2 +57-2 +24-2Input powers (relative) +340 +2288 -539 -1336

Power gain relative to A/2 dipole . . . 10-3 (10-1 db).Current in A/2 dipole to give same field as array in same units as

above currents, 10-3.Total radiated power (relative) . . . 73-1 x 10-3 = 753.Power lost as heat in elements (relative) . . . 38 (0-2 db).

end-fire direction in phase (i.e. an "orthodox" end-fire arrange-ment), is plotted on the same diagram. The scales of the twopatterns are such that the maximum field strengths are the same.

(4.3) Feeder SystemReference to Table 1 shows that, in order to maintain the

specified current distribution, elements 3 and 4 must deliverpower to the feeder system. To obtain the full gain this powermust be returned to elements 1 and 2. A loss-less feeder networksupplying the required driving-point voltages automaticallytakes care of this requirement. A discussion of the problem oftransmission lines terminated by impedances with negativeresistive parts will be found in Section 8.3.

Each element was fed through a network of lumped reactancesarranged as shown in Fig. 2. The networks were then connectedin parallel, using half-wavelengths of balanced twin feeder, andthe whole arrangement was fed with coaxial cable through abalance-to-unbalance transformer.

The values of XP and Xs must be chosen for each of the fournetworks so that, when the same input p.d. is applied to eachnetwork across the points T, the currents in the respectiveelements will be properly related to one another in magnitudeand phase. The number of ways in which this can be done istheoretically unlimited. In practice, the reactance had to bemade from small components. Furthermore, it was convenientto arrange that the admittance of the four elements in parallelwould approximately equal the characteristic admittance of thefeeder.

This method of feeding was selected for the ease with whichadjustments could be made. However, the values of the com-ponents chosen resulted in very high standing-wave ratios onthe half-wavelengths of feeder; in one case it was more than 80.

The components consisted of small coils or capacitors con-nected in parallel with trimming capacitors. Before the net-works were assembled the reactance of each group of com-ponents was measured at the design frequency of the array, usinga slotted coaxial line. The trimming adjustment was providedto allow for the difference between the actual driving-pointimpedances of the elements of the array and those calculatedon the basis of infinitely thin half-wave dipoles.

(4.4) Gain and Bandwidth MeasurementsThe gain was measured by direct comparison between the

power delivered to the array and that delivered to a half-wavedipole to produce the same field at a receiving aerial. The

BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS 307

150 160 170 180 170 160 150( 140c

130c

Orthodox"end-fire arrayhaving- elements in same

position as \the "super gain"array

4-elementsuper gain

array

50' 50'

Fig. 1.Theoretical radiation pattern of the experimental 4-element super-gain array.

relative powers were measured with the slotted coaxial line anddue allowance was made for the losses in the coaxial cablesleading to the array and dipole respectively.

By systematic adjustments of the trimming capacitors of thematching networks a gain of 8 7 db was obtained. This wasconsidered to be satisfactory, since the calculated losses in thehalf-wavelength of twin feeder and in the dipoles themselveswere respectively 0-6 and 0-2 db. It seems probable that theremaining 0 6 db by which the measured performance fallsshort of the theoretical prediction could be largely accounted forby losses in the coils and capacitors of the matching sections.

Without making any further alterations to the matching net-works, the gain was measured over a frequency band. Theresults are shown graphically in Fig. 3. Although small, thisbandwidth is sufficient for some practical purposes, and may wellbe increased by changes in the feeder system.

Dipole arms

Balancedfeeder

Fig. 2.Matching arrangement for mth element.

(4.5) Possible DevelopmentsSeveral lines suggest themselves along which further develop-

ment could proceed. It is evident that for practical applicationsthe feeder system used in the experimental array is too cumber-

308 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS

74 75Frequency, Mc/s

Fig. 3.Variation of gain with frequency of 4-elementexperimental array.

some. Folding the dipoles would facilitate the design of suitablematching networks. Moreover, the lengths of the feeder sectionsconnecting successive dipoles could with advantage be reduced,and this might be done, e.g. by dielectric loading.

Another approach to the problem of improved design is sug-gested by Figs. 6 and 7, which show that the maximum gains of3-element and symmetrical 4-element linear arrays of constanttotal length change very little as the positions of the innerelements vary. Al though no computat ion has been done fornon-symmetrical 4-element arrays, one might expect that , ingeneral, the maximum gain of the present experimental arraywill be substantially independent of the positions of the two innerelements. If this is so, there may be considerable advantage invarying these positions, since the input powers and driving-pointimpedances required for max imum gain should alter considerablyas the configuration of elements changes. It might, for example,be possible to find an arrangement in which one of the elementsis parasitic, or in which two elements carry powers of equalmagnitude and opposite sign (in which case they could, of course,be connected together, forming a parasitic pair) . If both theseconditions could be obtained simultaneouslywhich is no t outof the question, since two degrees of freedom are involvedthefeeding problem would be greatly simplified, because only onefeed point would remain.

(5) SOME NUMERICAL RESULTS(5.1) Arrays of Three Parallel Half-Wave Dipoles: Length of

Array VaryingF o r three parallel equispaced half-wave dipoles arranged along

a line the maximum gain can be written in quite a simple form:

(2TT \ F /2TT \ ~|- y d c o s i/r J + y\ cos (-ydcos ipj . (13)

where d = Element spacing.tjj = Angle between line of array and line of shoot.

a, jS, y = Algebraic functions of the mutua l impedances.Fig. 4 shows the variation of maximum gain with the length

of array, in the broadside and end-fire cases, and Fig. 5 showsthe variation against angle when d is 0-15A. F o r the cases

.

N\ \x"\

y

\

\

\

\

\

\

\

| 7

h0 0-2 0-4 0-6 0-8 10 1-2 1-4 1-6 18 20

Total length of array, wavelengths

Fig. 4.Maximum gain of 3-element array of equispaced parallelhalf-wave dipoles.

End-fire.Broadside.

covered by these Figures it is clear tha t the max imum gain hasits largest value in the end-fire case, when the array lengthbecomes zero. I t can, in fact, be shown by direct computat ionthat this is generally t rue for the 3-element equispaced lineararray.

Fig. 6 shows the variation in max imum gain of the array oflength 0-3A as the inner element is displaced towards eitherend. Since the maximum gain of an array remains unchangedon reversal of direction of max imum radiat ion (see Section 2.3),the resulting curve is symmetrical abou t the central position.

It is seen that the maximum gain is a lmost independent ofthe position of the inner element, the extreme variation beingabou t 0 1 db. The largest value of max imum gain occurs whenthe inner element is central.

(5.2) Arrays of n Half-Wave Dipoles: Length of Array FixedAnother case that has been studied numerically is that of n

equispaced parallel half-wave dipoles, with the length of thearray equal to A. Values of the maximum gain are given inFig. 8. Also plotted in this Figure are the max imum gainsin the broadside direction, and in addit ion the gains whenthe array is fed in the or thodox end-fire manner , i.e. with equal-ampli tude currents, such that the distant field components in theend-fire direction are in phase. I t is interesting to notice thatthe maximum-gain curve (end-fire case) in this Figure approachesthe limiting curve of Fig. 9 (see Section 5.3) quite rapidly. F o rseven elements the respective gains are about 14-8 and 14-9 db .

(5.3) Limits of Maximum GainIt would be useful to know the maximum gain obtainable from

a particular number of elements arranged in any way, as thiswould set a limit to the possible improvement which might bemade .

The trend of numerical results suggests that this maximum isobtained when the elements are arranged as an end-fire arrayand the total length tends to zero. The full-line curve in Fig. 9shows this limit. This curve is derived from Uzkov 's expression,G n2, for the maximum gain of n equally spaced omnidirec-tional sources by a method described in Section 8.4.

BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS 309

140 150 160 170 180 170 160 150 140

130'

60'

50 50c

40 30 20 10 0 10 20 30 40

Fig. 5.Variation of maximum gain of a 3-element array with "angle of shoot."

d 8-3

"3 6

buojy

l'3-s

8-1 ^

1

V-o-

.

8 0* 0 005 01 015 0-2 0-25 03

Distance of centre dipole from one end ofarray, wavelengths

Fig. 6.Variation of maximum gain of a 3-element end-fire arraywith position of middle element.

m 6 _0-6X

m e m

005 010 015 0-20 0-25Element spacing , 0, wavelengths

0-30

Fig. 7.Variation of maximum gain of a symmetrical 4-elementend-fire array with position of inner elements.

310 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS

16

^14

Il2'a!10to

o

/

/

11//////.

\Y

1

3 4 5 6 7Number of elements

9 10

Fig. 8.Array of equispaced parallel half-wave dipoles.End-fire; maximum gain.Broadside; maximum gain.

. . . . End-fire; field components in phase.

20

18

| 16^ 1 4

Il2

'I 2C5

// y

/ /

/ /

/ /

/

' A/ /

/ //

// ,

' /

///

/

//

/

///

/

/

/

/

/

/

2 3 4 5Number of elements

6 7 8 10

Fig. 9.Maximum end-fire gain of array of equispaced elements.Array of half-wave dipoles.Array of omnidirectional sources.

Although Uzkov's result applies only to equally spacedradiators, it is possible to show, by the method of the presentpaper, that for four symmetrically arranged end-fire elementsthe limiting gain is independent of the ratio of the spacings.

(6) CONCLUSIONSThe problem of designing aerial arrays with increased gain

has been approached afresh by an examination of the conditionunder which an array of a finite number of elements and offixed geometry has to be operated in order to have maximumgain in some specified direction. This condition has beenformulated so that the current distribution in the array can bereadily calculated from a knowledge of the mutual resistancesbetween the elements. The theory has been applied to thenumerical calculation of certain simple arrays. It appears thatfor arrays of a given size directivities greater than those obtainedby conventional design methods can be achieved without exces-

sive losses. An experimental array has substantially confirmedthese conclusions and has shown that the bandwidth of such anarray need not be prohibitively small.

(7) BIBLIOGRAPHYSuper-Gain Arrays(1) OSEEN, C. W.: "Die Einsteinsche Nadelstichstrahlung und die

Maxwellschen Gleichungen," Annalen der Physik, 1922, 69,p. 202.

(2) HOWELL, W. T.: "Electromagnetic Waves from a Point Source,"Philosophical Magazine, 1936, 21, p. 384.

(3) HANSEN, W. W., and WOODYARD, J. R.: "A New Principle inDirectional Antenna Design," Proceedings of the Institute ofRadio Engineers, 26, p. 333.

(4) FRANZ, K. "The Gain and the (Riidenberg) 'Absorption Surfaces'of Large Directive Arrays," Hochfrequenztechnik und Elek-troakustik, 1939, 54, p. 198.

(5) FRANZ, K.: "The Improvement of the Transmission Efficiencyby Directive Aerials," ibid., 1941, 57, p. 117.

(6) SCHELKUNOFF, S. A.: "A Mathematical Theory of LinearArrays," Bell System Technical Journal, 1943, 22, p. 80.

(7) FRANZ, K.: "Remarks on the Absorption Surfaces of DirectiveAerials," Hochfrequenztechnik und Elektroakustik, 1943, 61,p. 51.

(8) LA PAZ, L., and MILLER, G. A.: "Optimum Current Distributionson Vertical Antennas," Proceedings of the Institute of RadioEngineers, 1943, 31, p. 214.

(9) BOUWKAMP, C. J.: "Radiation Resistance of an Antenna withArbitrary Current Distribution," Philips Research Reports,1946, 1, p. 65.

(10) BOUWKAMP, C. J., and DE BRUIJN, N. G.: "The Problem ofOptimum Antenna Current Distribution," ibid., p. 135.

(11) DOLPH, C. L.: "A Current Distribution for Broadside Arrayswhich Optimizes the Relationship between Beam Width andSide-lobe Level," Proceedings of the Institute of Radio Engineers,1946, 34, p. 335.

(12) UZKOV, A. L: "An Approach to the Problem of OptimumDirective Antennae Design," Comptes Rendus de VAcademiedes Sciences de I'U.R.S.S., 1946, 53, p. 35.

(13) REID, D. G.: "The Gain of an Idealized Yagi Array," JournalI.E.E., 1946, 93, Part IIIA, p. 564.

(14) RIBLET, H. J.: Discussion, Reference 9, Proceedings of theInstitute of Radio Engineers, 1947, 35, p. 489.

(15) GILLETT, G. D.: "Analysis of Effect of Circulating Currents onthe Radiation Efficiency of Broadcast Directive AntennaDesigns" (summary only), ibid., 1948, 36, p. 372.

(16) RIBLET, H. J.: "Note on the Maximum Directivity of an Antenna,"ibid., p. 620.

(17) WiLMOTTE, R. M.: "Note on Practical Limitations in theDirectivity of Antennas," ibid., p. 878.

(18) BELL, D. A.: Discussion on Reference 14, ibid., p. 1134.(19) TAYLOR, T. T.: Discussion on Reference 14, ibid., p. 1134.(20) WOODWARD, P. M., and LAWSON, J. D.: "The Theoretical Pre-

cision with which an Arbitrary Radiation Pattern may beobtained from a Source of Finite Size," Journal I.E.E., 1948,95, Part III, p. 363.

(21) CHU, L. J.: "Physical Limitations of Omni-Directional Antennas,"Journal of Applied Physics, 1948, 19, p. 1163.

(22) BELL, D. A.: "Gain of Aerial Systems," Wireless Engineer, 1949,26, p. 306.

(23) JORDAN, E. C.: "Electromagnetic Waves and Radiating Systems"(Prentice-Hall, New York, 1950), p. 445.

(24) TAYLOR, T. T., and WHINNERY, J. R.: "Applications of PotentialTheory to the Design of Linear Arrays," Journal of AppliedPhysics, 1951, 22, p. 19.

(25) FREEDMAN, J.: "Resolution in Radar Systems," Proceedings ofthe Institution of Radio Engineers, 1951, 39, p. 813.

(26) YARU, N.: "A Note on Super-Gain Antenna Arrays," ibid.,p. 1081.

(27) "Supergain Antennas," QST, 1951, 35, p. 46.(28) AIGRAIN, P.: "Les antennes super-directives," L'Onde Electrique,

1952, 32, p. 51.General References(29) BARZILAI, G.: "Mutual Impedance of Parallel Aerials," Wireless

Engineer, 1948, 25, p. 347.(30) SMITH, R. A.: "Aerials for Metre and Decimetre Wavelengths"

(University Press, Cambridge, 1949), p. 43.(31) MEDHURST, R. G., and POOL, S. D.: "Mutual Impedance of

Parallel Aerials," Wireless Engineer, 1951, 28, p. 67.

BLOCH, MEDHURST AND POOL: A NEW APPROACH TO

(32) CARTER, P. S.: "Circuit Relations in Radiating Systems and Appli-cations to Antenna Problems," Proceedings of the Institute ofRadio Engineers, 1932, 20, p. 1004 (see also 1948, 36, p. 1003).

(33) MILNE, W. E.: "Numerical Calculus" (University Press, Princeton,1949), pp. 15-35.

(34) KING, R., and MIDDLETON, D.: "The Cylindrical Antenna;Current and Impedance," Quarterly of Applied Mathematics,1946, 3, p. 302; 1946, 4, p. 199; and 1948, 6, p. 192.

(35) TAI, C. T.: "Coupled Antennas," Proceedings of the Institute ofRadio Engineers, 1948, 36, p. 487.

(36) KING, R.: "Self- and Mutual Impedance of Parallel IdenticalAntennas," Cruft Laboratory, Harvard University, TechnicalReport No. 118, 1950 (shortened version in Proceedings of theInstitute of Radio Engineers, 1952, 40, p. 981).

(37) KING, R.: "A Dipole with a Tuned Parasitic Radiator," Pro-'ceedings I.E.E., 1952, 99, Part III, p. 6.

(38) CROUT, P. D.: "A Short Method for Evaluating Determinantsand Solving Systems of Linear Equations with Real or ComplexCoefficients," Transactions of the American I.E.E., 1941, 60,p. 1235.

(39) KRAUS, J. D.: "Antennas" (McGraw-Hill, New York, 1950).(40) FISHENDEN, R. M., and WIBLIN, E. R.: "Design of Yagi Aerials,"

Proceedings I.E.E., 1949, 96, Part III, p. 5.(41) SAXTON, J. A.: "Determination of Aerial Gain from its Polar

Diagram," Wireless Engineer, 1948, 25, p. 110.(42) LAMONT, H. R. L., ROBERTSHAW, R. G., and HAMMERTON, T. G.:

"Microwave Communication Link," Wireless Engineer, 1947,24, p. 323.

(43) TERMAN, F. E.: "Radio Engineers' Handbook" (McGraw-Hill,New York, 1943).

(8) APPENDICES(8.1) Derivation of the Condition for Maximum Gain

(8.1.1) The Power Radiated.The radiated power is given by

P = [V'J'm + V ' ^ ] . . . . ( 1 4 )Substituting from eqn. (1)

P = U'nJUirlm - I','xln) + /;; (V{rlm + /Jm = \ 1=1

= [(/;/; + W H J7 7 1 = 1 1 = 1

since xlm = xmli ltnhrlm (15)

m=\ 1=1

= i*mrm 0)m = l

Eqn. (15) follows since rlm = rml and

[(W-h,] = 0i /

Note that the power input to the zwth terminal is the real part ofImVm, and not of J j , ^ . The latter expression omits all thosecontributions to the power input which are due to mutualreactance and which cancel in the summation over the wholearray.

(8.1.2) The Received Field.Select a reference plane perpendicular to the direction in

which the array is to have maximum gain.The received field at a distant point in this direction is given

by eqn. (4).If the array is replaced by a reference element similar in all

respects to the elements of the array and situated in the reference

THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS 311

plane, the received field is, making the same simplification asfor eqn. (4),

HS = IS (16)The radiated power from the reference element is

nr = I2

since in the normalization adopted, rs is unity.

(8.1.3) The Voltage Theorem for Maximum Gain for n Equal andIndentically Oriented Elements.

The power gain of the array with respect to the referenceelement is

iHl2 I1 \H\2

\HS\2P~ p u/;

Write U=\H\2 (18)

so that GP= U (19)If the currents in each element are slightly perturbed from the

values which makes G a maximum,

8G = 0 (20)hence G8P = 8U (21)From eqn. (18) U = HH* (22)Therefore 8U = H&H* + H*8H

= 2&H8H* (23)Limiting the variation to the current Ir, it follows from

eqn. (4) that SH = 8 l r e ^ ;hence 8 U = i M H h l U ' ^ . . . . ( 2 4 )Again from eqn. (15),

P= l*m%hr,m+ 8l*mIirlm . (25)m = i 1=1 m=l 1=1

= r?8it + rm8i*m (26)/ = 1 m = l

If the variation is again limited to Jr,

8 P = r * S l r + r r S l * . . . . ( 2 7 )= 2 T r 8 l * r (28)

Substituting eqns. (24) and (28) into eqn. (21),GMTr8l* = &H8l*~JOr (29)

Since eqn. (29) must be valid for any 8lr let 8lr first be chosenso that T*8lr is imaginary. The left-hand side of eqn. (29) willthen be zero, and hence also the right-hand side, i.e. bothexpressions following the^? sign will be purely imaginary. Then,advancing the argument of 8lr by 77/2 will make both expres-sions real, allowing t h e ^ signs to be removed from the equation.

It follows that

Tr = ~e-J0r (30)

Since the gain of the array is independent of the power level,the modulus of eqn. (30) may be made unity, and eqn. (6a)follows.

312 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS

wherecos 6{

(8.1.4) Generalization to Elements Different in Form or Orientation.Eqn. (15) for the power radiated is still valid, and, by defini-

tion, so is eqn. (16). By introducing suitable factors, hm, thedistant field can still be expressed in the form

= 2 '

7 7 1 = 1

(3D

hm can always be made real by ascribing to each element anappropriate position value 6m.

Now, introducing new currents by the relationsIt

= AT (32)

eqn. (31) can be rewritten as

and eqn. (15) as

with

m=\

P = S 2771 = 1 l = \

(33)

(34)

r]m = rlm\hmh{ (35)The problem is now reduced to the same form as that dis-

cussed in Section 2. The maximum gain of the array, and themodified currents Pm, can be calculated using the relations givenin that Section.

(8.2) Computation Procedure(8.2.1) Separation of Equations into Real and Imaginary Parts.

In numerical work it will usually be convenient to solve theset of equations (6b) directly for the currents, rather than tocarry out the intermediate operation of evaluating the invertedmatrix glm. The procedure for identical elements is as follows.

Separating eqn. (6b) into real and imaginary parts gives thesystems of equations

2 rlrlm = cos 0ni=i

n

2 r,'rlm= - s i n

Then, from eqns. (4) and (9)

m = l(l)n .

; ;(-sin 0 j ]

. (36)

(37)

For arrays of not more than about ten elements, eqns. (36)can readily be solved on a desk-type calculating machine, using,for example, Crout's method.33'38

If the array consists of elements symmetrically spaced along astraight line, it is advantageous to choose the reference plane sothat it passes through the centre of the array. The values takenby the cosine and sine functions in eqn. (36) are then respectivelysymmetrical and skew symmetrical. It follows that the valuesof /,' and 1'^ show the same symmetries, and the number ofsimultaneous equations is halved.

(8.2.2) An Alternative Expression for Gain.From eqns. (36) and (37) the gain could, of course, be written

explicitly in terms of the mutual resistances rlm and the angles6m. In fact, with a little rearrangement, we obtain the followingform:

& (38)

A = -

'21 '22'In

c o s &)

' T 1

COS d{

'11

'21

rn2

cos 62 .

'12

'22

',,

. . COS0rt

' 1 7 ,

r2

cosC

sinsin

sin

and A =

' , ,2

s i n $>

r22

sin

r\nr2n

sin c0

rn\ rn2 rt

('ii = '22 = = rnn = 1)

When the currents are required as well as the gain, eqn. (38)has no particular merit, since the right-hand side of eqn. (37)can be evaluated in a single operation on a calculating machine.If, however, the gain only is required and the current magnitudesare not of interest, e.g. if it is desired to examine the trend ofthe gain as the element spacing or the number of elementsvaries, there is some advantage in using eqn. (38). It is notnecessary in a particular case to evaluate the denominatorsseparately, since in Crout's method the values of the two termsof G come out directly as the bottom right-hand terms of themodified matrices obtained from the respective numerators.33Eqn. (38) is particularly useful for dealing with limiting cases inwhich elements coalesce, e.g. in the 3-element case shown inFig. 6, where the inner element coalesces with either of the outerelements.

The approximations to the mutual resistances required forthis computation are reproduced here because they seem not tobe generally known:

m&2l-sinmp + sin [m ohms

(39)to second order in S,

where i?p = Mutual resistance when spacing is p.i?P+s = Mutual resistance when spacing is p + 8.

m = 2TT/A/=A/2

BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS 313

If Rl2 is the mutual resistance when the spacing approacheszero,

i?12 = 2 9 - 9 7 9 ^ - ^ - + ^ 4 . . .)ohms (40)where p Spacing

cj> = 2-nplXr = 2 - 4 3 7 6 5 . . .

K= HL + A/16TT2 = 0 0271659 . . .

As far as the square term, eqn. (40) is given in Reference 39(p. 267).(8.2.3) Driving-Point Impedance.

Driving-point impedances are required for the design of afeeder system and for the estimation of the heat losses in theoperation of the array.

Dividing both sides of eqn. (1) by Im we obtain the driving-point impedance offered by the mth element as

1 "rm +JXm = 7 ~ 2 hZlm . . . . (41)

Then it is readily shown, using eqn. (36), thatn n

Urn CS " f f l - 4 S I'l'Xim ~ Im Sin em + I'm 2 I'iX,m]1 m ' tn

. . . . (42)and

[Im 2 I Mm ~ Im Sm 8m - lm COS dm + Im 2 11 Xim]x = ' - ' '= '

'" (/'2 +1"2). . . . (43)

In these equations the impedances are normalized and mustbe multiplied by Rs to convert the units to ohms.

(8.3) Transmission Lines Terminated by Negative ResistancesWhen optimum current distributions for arrays of aerials are

worked out it frequently happens that the driving-point resistanceof one or more of the aerials is found to be negative, i.e. theseelements are drawing power from the array. For maximumgain this power has to be fed back to the other elements.*Suppose that each element is connected to a transmission line,possibly through a network of some sort, and that these trans-mission lines run to a common feed point.

When the standing-wave pattern on these transmission linesis considered a difficulty appears in connection with those lineswhich feed power from the array towards the feed point. It isusual to determine the standing-wave pattern from the "load"end of the line and work back towards the generator. It wouldtherefore seem that in those cases just mentioned further analysiswould be required in order to find the load presented to the lineat this common feed point. However, this is not so; the standingwave pattern on all transmission lines is uniquely determined bythe load impedance (here, the aerial driving-point impedance)even if the real part of this quantity turns out to be negative,and transmission-line equations can be applied in the usual way,as can be seen from the following analysis of transmission linefundamentals.

If the aerial is to be designed only for maximum directivity, without regard to thelosses incurred, it is, of course, much simpler to dissipate this energy by terminatingthe elements concerned with impedances equal to the negative of their respectivedriving-point impedances.

Denoting the components of forward and backward travellingwaves by the subscripts / and b, we have

E=Ef + Eb (44)I=Ir-h (45)

hence, defining the ratio Ejl as the load impedance Z,,IZ,= Ef + Eb (46)

IZ0 = IfZ0-lbZ0=Ef-Eb . . . (47)and / = i / ( Z / + Z0) (48)

Eb = y(Z,-ZQ) (49)The reflection factor is then

? (50)Ewith no restriction on the value of Zt. From Fig. 10 it followsthat, when Z, has a negative real part, |p| is greater than unity,

Fig. 10.Vector diagram to show that impedances in the left-handplane are associated with reflection factors

Zi - Z0+Z0

> 1

i.e. the reflected wave is larger than the incident wave, and thusmore energy is returned to the line than has arrived. This, ofcourse, is in agreement with the fact that for such values of Zlthe energy consumption is negative.

Charts and formulae for transformation of impedances alongtransmission lines are usually designed for use with values of\p\ less than unity, so that, at first sight, values of |p| greaterthan unity might appear inconvenient. But if a transmission lineis cut at any point and it is found, say, looking to the right ofthe cut, that the line is here working into an impedance Zhthere will be at the left of the cut an impedance Zt. This isa simple consequence of the fact that impedance, in the senseused here, is merely the ratio of voltage to current* and thatboth pairs of terminals have the same voltage across them butthe currents, while equal, are of opposite sign; if the currentflows into one pair of terminals it must flow out of the other pair.If the impedance Z7 is terminating the line and has a reflectioncoefficient \p\ greater than unity, it is clear from eqn. (50) thatthe impedance Zt to the left of the cut has a reflection co-efficient, \\\p\, less than unity.

The transformation of the nominal load Z; along a trans-mission line towards the nominal generator (transformationfrom loading-end impedance towards sending-end impedance)can thus be solved by inserting the impedance Z/ in a formulaor chart intended for transformation from the actual generatortowards the load (transformation from sending-end impedancetowards load impedance).

* This impedance must not be confused with the "internal" impedance whichinforms us of the change in voltage associated with a change of current.

314 BLOCH, MEDHURST AND POOL: A NEW APPROACH TO THE DESIGN OF SUPER-DIRECTIVE AERIAL ARRAYS(8.4) Method of Deducing the Gain of Zero-Length Arrays ofHalf-Wave Dipoles from Uzkov's Result for Omnidirectional

SourcesAn exact result found by Uzkov for linear end-fire arrays of

equispaced omnidirectional sources states that the limiting valueof maximum power gain is n2, with respect to a single omni-directional source, where n is the number of elements. Thedotted line in Fig. 9 is based on this expression. For half-wavedipoles the corresponding values can fairly easily be obtainedby the method developed in the present paper, for a smallnumber of elements. The limiting maximum power gains fortwo and three elements (with respect to a half-wave dipole) are,respectively,

1 + r (51)

r -(1 -

1 - 2AKr (52)

where r and K have the same significance as in eqn. (40).Unfortunately, the algebra needed for a larger number of

elements becomes very tedious. However, a good approxima-tion for the half-wave dipole system can be obtained fromUzkov's omnidirectional-source expression as follows: Saxton'sformula41 gives an approximate value for the half-power beamwidth of the Uzkov array. On the assumption that the slope ofthe pattern in this region is given closely enough by Lamont'sformula,42 the modification of this half-power beam width whenthe omnidirectional pattern is multiplied by the half-wave dipolepattern can be calculated. Were it assumed that in every planecontaining the direction of maximum radiation the pattern ischanged in the same fashion, renewed application of the Saxtonformula would give the gain of the array thus modified. How-ever, since the pattern remains unchanged in the plane at rightangles to the plane of polarization, the final approximation isobtained by taking the mean of this and Uzkov's result.

Since the error in the final result should decrease as the beamwidth decreases, a stringent test of this device is to compare theresult so obtained for three elements with the exact value givenby eqn. (52). The figures are respectively 8-2 and 8-4 db.

Values so obtained are plotted in Fig. 9.

"RECENT PROGRESS IN RADAR DUPLEXERS, WITH SPECIALREFERENCE TO GAS-DISCHARGE TUBES"

RADIO SECTION INFORMAL LECTURE, 24TH NOVEMBER, 1952Mr. P. O. Hawkins began his lecture by saying that the

function of a microwave radar duplexing circuit was to permitthe use of a single aerial for both transmission and reception.Since the radar system performance would be impaired if energywere lost into the receiver during transmission, the isolationbetween transmitter and receiver had to be of a high order. Itwas possible to achieve this isolation even though the transmitterand receiver were simultaneously connected to the aerial.The duplexing action was then achieved by means of polariza-tion-sensitive duplexers, which were passive circuits and did notuse gas-filled tubes. The polarization-sensitive systems might inspecial cases be used with advantage in pulsed radar systems,even though the transmitter and receiver functioning was time-separated. In general, however, the use of microwave gas-filledswitches [transmit-receive (t.r.) switches] led to simpler duplexingsystems. The lecture was concerned with advances in duplexersusing t.r. switches, i.e. active duplexers.

Although, in principle, for most applications a wide-band t.r.switch used with a balanced duplexer was satisfactory, in practiceit was difficult to maintain the requisite degree of isolationbetween transmitter and receiver.

Some of the reasons for this were now understood, and it wasshown that the difficulties were due to compressing three distinctduplexing functions into one switch. The operation of the t.r.switch and the physical processes that led to imperfect operationwere described. It was suggested that the passive t.r. switchwas not the best form of valve for duplexing, and that a systemin which the three functions were separated and in whichsynchronous attenuation was introduced into the duplexer wassuperior.

A number of experimental solutions to this problem were beingtried. An experiment with switching tubes, in which the threefunctions were physically isolated, was described. Attenuationsynchronized with the transmitter was introduced into thesystem with one of these tubes. This work had shown that it

might be possible to derive improved performance with balancedduplexers.

In the discussion which followed, some speakers confinedthemselves to seeking further elucidation of points raised in thelecture, while the majority indicated the lines of their ownthought on the problems and their particular experience in thedevelopment of various aspects of design. More time wasdevoted to discussion of the improvement of conventionalarrangement in particular respects, such as in the choice of gas-filling or of priming-electrode material, than to the more radicalmethods outlined in the latter part of the lecture; these werenevertheless generally regarded as being promising.

Much importance was attached to reliability of system opera-tion and to satisfactory life of mixer crystals and t.r. switches.A variety of expedients were indicated for limiting the trans-mitter power from the transmitter which reached the mixercrystal of the receiver and for minimizing deterioration in thedischarge gaps, owing to sputtering and detuning, with conse-quent unreliability of operation.

For the order of transmitter power used in the more con-ventional pulsed equipments, the problem of providing suitabletypes of t.r. switch giving adequate protection of the crystalmixer was not considered to present undue difficulty. Wherehigher powers were required, however, improvements becameextremely valuable, particularly where exceptional reliabilityand continuity of operation were desired. Increasing interestin broad-band operation and the consequent need for relativelylow-Q-factor resonators meant that special attention needed tobe given to reliable means of initiating the discharge, whichset up the reflection barrier against energy from the trans-mitter.

The improvement in performance and reliability offered by themore complex arrangements envisaged in the lecture, however,needed to be sufficient to justify the excess bulk and weight