f i ..

~~SE1~gtPJi }?!J!'~~,~~

Will VELOCITY CONCENTRIC FEEDER LllTES. ":.

~~r;r..TI-I ~):.9AL CENTRE CONDUQTORS

Report No. E.033 Serial No. 194-7/39

Research Department

Report vv.ritten by: S. F. Brownless ..

REPORT NO. E.033

Serial No. 1947/39 Fig .. Nos. 1 - 5

&9W VELOCITY CONCENTRIC F~ LOOS WITH J:IT!iliI9.AL CENTRE CONDUCTORS

SUMM.ARY

Filters using concentric lines as elernonts may have considerable application at televisicn and F~M~ frequencies. In particular, long line filters are being consid.ered for .use in the F.;M. band, to pe:r.rili t radiation f:;."om one aerial of the outputs, frarl1 a nU':1ber of transmitters,

The physical. length of such lines can be rerluced by decreasing their velocity of wave propagation; and. one oonvenient method of doing this is to use a helical centre conductor. This report gives the results of an apprOXll11ate theoretical ana~sis of such concentric lines. Velocity reductions of 5- 10 tunes would appear to be feasible, but w~th acco~anying increases of characteristic ippedance of the smne order. There is no well defined optimml ratio of diameter of inner helix to outer conductor for minimm,l n.ttenuation, corresponding to the ratio of 1:3.6 for a norr,ml concentric line. When used as a filter element, connected in parallel wi th nonaal 80 ohm concentric lines l h~we'ver, 'a ratio of 1:2 t61:2.5 gives best results. There is an optimUJn 'vvire diru:leter for the central helix~ depending on~ on ~he winding pitch_

Figs. 1 and 2 give the inpedance and' veloc:t ty ratio respectively as functions of the line proportions. Figs. 3 and 4 give the open and short-circuit impedances respective~ of long lines.~esigned for the filtering of frequencies spaced ~ at 90 Mc/s~ .

.. , A practical case has been considered in which tivo channels with

frequencies spaced ~ are asstmled, the proposed arrangement of lrrn velocity line 'filters being as sho~n in Fig. 5. The power loss in the fi;Lter in this case ls 0.3 db., and the smallest attenuation between trahsni tters' 16 db.· , " .

Appendix I derives' theforf,lulae from v/hich Figs. 1 - 4 have been drawn. AppendixII abstracts the published theoretioal and experllnental'work on low velocity concentric lines~

\

- 2 -

1. :qTTROnpCTION

Oonsideration is being given to the problem of combining the outputs from a number of high power FM transmitters, for radiation from a single aerial. For this purpose it is necessary to use a filter in conjunction with ,each transmitter which will introduce negligible loss at the wanted frequency, but a high loss at the tUnvanted frequency. One type of filter which has been considered is a long transmission line. A line 25\ long, for instance, would be an open circuit at a series of frequencies spaced 2~~, apart, and a short circuit at a series of intermediate fr?quencies.

Long lines of this type used on 90 MC/s would be approximately 270' long, v{hich is inconvenient. Consideration has, therefore, been given to methods of reducing the length by coiling up the central conductor in the form of a helix. It is nece ssary first to decide on the optimum dimensions in order to fulfil the necessary

. requirements, second, to consider how such filters would be used in . practice, and t,hird., to ascertain whether the power rating of the fil ter is satisfactory •.

No 'decision on the frequency spacing of the various channels. has yctbeen made, but it is thought that this vdll be bet\-,reen 1%, and 2J" of the· carrier frequency, .i.e,. approximately 1 - 2 Mc/s in . 90 MC/s. It is expected that it vo'1ll be necess'ary to deal 'with

. three transmissions, each of 25 kW. .

No attempt has yet been· made to assess the relative merits of methods of filtering other than that described in this report. 'It is hoped to do this ,in ,a further report.

2. THEORETIOAL ANALYSIS

2.1 Theoretical Characteristics of Low Velocity Lines

. The following assumptions have been made throughout, leading to simple, but. cru1y approximately correct expressions.

(a)

(b)

The inductance/unit length is ,that of the central helix surrolmded by a cylindrical screen, the sldn' effect in both helix and screen being complete; the effect on the inductance of the amplitude and phase change along the line has here been neglected - (rough calculations indicate that it,is less than 10%).

The capacity/unit length is equal to that of a normal concentric feeder of equal outer diameter, and inner diameter equal to mean diameter of the helix.

- 3 -

( c)

( cl)

Dielectric losses are ~eglected.

·'Copper ,lo8ses are taken as those of the screened central helix at 90 l\~c/s ..

These assUi"aptions lead to the following formulae (see Appendix I for deri va t,ion) •

Let D d

- inner dianleter of~0uter conductor (cras) = mean diameter of' helix (ems).

c - vd~1diL1.g pi t?~ of .he~ix, ( 9ms) do = di8.t-neter of vJire of heliX (ems)

Inductance

Capacitance

Characteristic Irnpedance

Time Delay

Velocity ratio

opt:im1.1m wire , diame'ter. '

,A,ttenuation at 90 JlIc/s (Yli th optim1.1m do)

Attenuation per wavelength at 90 EC/s (vd th optimum do)

Cm, 2.42.10-5

= lOblOD)i ~F per netre.

, . d " % 2 ¥2 Zo ' =202 ('c) (loglOD/d ) (1':' d 1:02 ) ohms'.

d " -Y2 '::;. 07'2 Tm ,=' 4.89010-3 (c)(loglOD/d) (1.- d/n2)

microseconds per E1etre.; ,

= 0'.682 (£) (lOgl~/d)~ (1 -" d~)% (vc free space velocity)

,'.

(~depend~nt of' othervariablf.)s)

dbs. per netre'.

222*', 0/3 (?t +c{d ) , + ,2.19 (ID) ---.- ;., 2 --, , . (1 - d7rf):

dbs. per wavelength.

For comparinon, a ttenua tio:a per wavelength at -90 Mc/s for an 80 ohm normal ooncentric feeder.

- 4- -

dbs. per Wavelength

2.2 ,Discussion ~fTheoi-etical Formulae·

Figs. 1 and 2'shpw tho characteristic :impedonco and ve1ccity ratio computed from these formulae as functions of D/d'and cid. Interpolation in the region % )1 has been performed :with the aid of the dotted li.mi ting curve in Fig. 2, corresponding to free spaee , velocity along the 'wire of the helix. We sec thc ... t a low velocity ratio is accompanied by a high characteristic impedanqe.

. The min:im'tlln attenuatien per wavelength varies very 1i tt1e with cid or Did. It is approximately three t:imes as g;roat as that of a normal 80 ohm concentric line with the smue inner diameter d.

When used in a 'long line' filter, the quantities required are the resonant high and low input impedances of a long length of line short-circuited at the far end. These are plotted in Figs. 3 and 4-for a line 25~ long having an outer diameter of 10 ems, i.e. approximately the same oize as liIarconi No.O feeder; For comparison, the same quantities for a norraal 80 ohm concentric lino of the same outer diameter are also shovv.n.

Open circuit impedances appear very ~gh for all reasonable ~. lines, owing to their high characteristic :impedance, but the slwrt, ,., circui,t impedances increase steadily with reduction in voloei ty. This.mearis that ,the J:oss at the 'wanted f'requency I 'will be (lovV', but that the discrimination agains~ the 'ur~vanted frequency' ~iLll dccreaso "Vith the velocity ratic. '

. I,t wouidtherefore appear toot inner to outer d.iameter ratios in the region of 1.: 2 would be most sui table for 'long line r applica~ions.

3. APPLICATIONS TO A PRACTICAL ~

3.1 Consider. two carriers only, vd th frequencies difforingby 21,S, and assuming .& single low velocity line for each frequency connected acrosn 80 ohm feeders. A suitable arrangemen~ in such a case would comprise an 80 ohm concentric line fr~ e~ch transmitter to Q junction point and thence to 'the aerial, the tv\1'O low-velocity lines being connected in po.rallel vd th these 80 ohm linos at a quarter-wo.volcngth f'rcm the junotiontowo.rds each transmitter. .For the pttrposos of

•

- 5 -

calculation, it ,viII be assumed that the impedancelookin[,: back into each transmitter is 80 ohmS at all operating frequencies. In practice, the impedance may be very different fror:l this value, since the class 0 output stage of the trpnsI:J.itter will not be matched. By suitable choice of the line le-ngth between each transmitter and the filter, it may be possible to obtain a areater attenuation between the transnutters than th~t calculated. .On the other hand, an .unsuitable line length vdll result in a smaller attenuation. The assumption of 80 ohm transmitter impedance thus gives a conservative estimate of the filter performance attainable in practice.

From Figs. 3 and 4 a velocity ratio of 0.1 and impedance of 400 oh~s seem to offer a reasonable' compromise. If D is [,}ade 25 cms~ d 12.5 cms, c 3.4 ems, and do 1.5 cms, the power loss-of such a simple filter at the vffinted frequenqy, considering copper loss only, is approximately 4% and the attenuation between the transmitters 29 db.

At ±o.l Mcls relative .to the carrier frequencies (thes~ limits corresponding to the extreme sidebands of the nonnal FM system) power loss at the wanted frequency 'willinc:::ease to 145'0, while the 'open-cireuited t line vdU present a reactance across the iine of· approximately 5,000 ohms. Much more serious, however, is the reduction of the attenuation betvreen the two transmitters to 9 db; this is accompanied by a standing wave ratio of 1.4/1 on the 80 oha line between the junction point and transmitter.

3.2 Single low-velocity line filter sections are evidently unsatisfactory. Two such lines connected across e['.ch transEutter feeder at a quarter-wavele-ngth and a half~vavelength respectivelyfram the junction point give a better perfon1ance~ At resonance the power loss of the filter is 4>S, and the attenuation betwQen tranSt:litters 58 db. A suitable arrangem.ent is shown in Fig. 5.

At !O·l Mc/s off tune, the 5,000 Ohml reactances of the open-circuited lines cancel each other. The power loss of the filter increases to 870, the attenuation betvieen transmitters becomes 16 .db.,. and the standing . wave rc..tio on the transmitter feeder 1'5/1. (The standing wave could be removed by a fifth Imv-velocity line connected at the main aerial junction, FiS. 5).

Such an arran,zement, though far from ideal, l'1ay be acceptable for an F.M serVice.

It should be stressed that the poor perfon.lance at the sideband frequencies is not due to loss in the resonant lines, but to their reactance, and is fun(1m~ental in requiring the transn1itter frequency

-- separation to be only ten times the transmitter bandwidth. ' \

- 6 -

3.3 The operating losses and voltages of both filters are very similar. For a filter using .double sections, the following values apply, for wvo FM transmitters, each of 25 ~v o~tput.

!>-~. ~J .. J·Fesu~pci~

Peak voltage· on 80· ohm ; line~ .from each transmitter to filter

Peak voltage on 80 ohm lines in filter and from filter to aerial

Both_.F~_s.!Pi tt~rs .. _ a t _c..?-!'rier_J.:r~SJ.Y.e~C':l.

Peak ~ol tage on 400 oh.ID io~r velocity line;. V4- from junction

Power dissipation in L.V. line

. Peak voltag~ on :400 ohm L~V. line V2 from junction

Power dissipation in L.V~ line

Unwanted transmitter O'l~ from carrier freguency

900 watts

70 watts

Peak voltage on 400 ohm L.V. line A/4- from junction towards· I wanted , transmitter 18·8 KY

Power dissipation in L.V. line 2,300 watts

Peak voltage on 400 ohm )~. V. line A/2 from junction

Power. dissipation in L.V. line

The critical disruptive voltage for the line~dimensions given in 3.1 is 34- ID!' or above, so that a fair, but not high factor of safety exists.

The physical size of the lines should permit satisfactory dissipation of the powers stated, although this power is g~nerated almost entirely in the inner conductor, ,and trouble with local overheat;ing may. occur.

e.

•

- 7 -

40 FURTEER JNVESTIGATIONS

This re pert has dealt with ene particular type ef line used fer a 'long line' applicatien. The metheds used are enly approximate; a mere nearly exact approach with modified expressien fer inductance, capacity, and'cepper lo.ss is required fer satisfactory design, but the present treatment sheuld suffice to. decide the merits ef this type ef line. Other forms ef cencentric line, e.g. tvJO concentric cepper cylinders with a helix in the annular'space may be superior for certain requiremonts. It isnet'propesed to. do any further werk aleng these lines fer the time being, until a decisien is reached en the general line along which the investigation should be centinued. '

Other methods of using lines as filters m'ay be mere satisfactory fer the FMbandiwaveguide and cavity Tesonator technique is also. feasible at such frequencies. All these possibilities will be investigated as the work permits. '

IM (H. L. Kirk.e)

- 8 -

APPENDIX I

THEORETICAL C'HARACTERISTICS OF LOir VELOCITY LlNES

Let D ,: d : c : do:

inner diameter of outer conductor (ems) mean diameter of helix 'tems l 'iVinding pi tch of helix cms diaMeter of wire of helixcms

i.: nlDUCTANOE

~, For very long c16selywound sing1e-la,y:c;r coils in a cylindrical .screen the inductance per metre is given ~

2 . 1nl == 0'99. (~) (1 ...; d~) ~ per metre.

2. C.APACIT~

For, concentric tube,s, the capacitance per ,metre is equal to: +

2.42.10-5 Cm. = log10D/d !J.F per metre.

3. CHARAOTERISTIC D!PEDANCE

Zo = ~:V2

Zo : 202(~) (loelOD,i)~ (1 _ d7b2)lf2

4. TM DELAY

= CL C ) t'2 seconds per metre.

ohms.

mm

= It-'~9 .10-3(~) (lO~OD/a)-72 (1 _ d%z) 12 . microseconds per metre.

l! BogIe - "Effective Inductance and Resistance of Screened Coils" J.I.E.E., Vol.87 (1940) p.299.

+ Nottage - "The Calculation and Measurement of Inductance and Capacity" p.62.

...

\

- 9 -

The. veloci~ ratio is given by- the ratio of the free space t:j.me delay (3.33.10-5 micro~econds per metre) to the line time del~. -

- whence: ;c::: 0·682 (~) (loglOD/drh (1 - ~7f1)-*

This is assumed due entirely to the H.F. resistance of the hclical centre copper conductor. _

Rro :::

:::

:::

/

H.9.'_.0f. t'u£ps x. f.ep...s.th ,s>.f __ ~_.~..::_O.bm.sj21~ Cross~sectional-area'

- . ohms per metre.'

ornns per metre of line ~

6.2 !{atJ,Q..Qf_H.F. to D~C ._~§j...st~c;s:~. f9!_Uf!E2£"qEEcd .E2JJ.;.

At very high frequcnoies, when'skin'effect is .complete:

~ .. - 38 IF(MC/S)t2 ·do {l + ~(~~l

where u is a factor depending on the shape of ,the coil. For long helices, as in the'present'easo, at 90 1',1c/s, u = 9·87.

,." . ...

l!Tcrman"Radio Engineering Handbook ll - Sec .2.19, Eq. 93a.

r--'"

.. . '. - 10 -

R_ . '= R__ RrrF --ill' -W • Rro

, -4 2 2 2 ¥2 , Jf2' r.. . . . 21 = ,2.2 .. 10

0 i" 2 d + 0 l'x 38; (90) . do 11+ 4. 935 (~ \

. ".; ..0 :.' . ' '. ,"'1 . t.. '. -

1 ·4.935 rr'h1s is .of the f.oI'D.l K do' + . c'2 . - de I

~ J If de al.one is varied, this is a minimum when the t;,ie terms in the

, bracket are equal, ,:Thence:

6.3 ;J:?crease in H.P. resista,p.ce due'to screen

4 li P 1 (-Dd) RI_ - ::: 7illS"32 '. -1lF '.' c ol~ per unit length of line

'.\

vrhere p = resistivity of oOPPer; = 1.724~lO-6 'ohEls/cny3 .

s = effeotive skin depth for coppo:!:, :: 6·98.10-4 cms at 90 11.0/8."

whence: .ohbs per metro .of lino.

and tetal H.F. resistance .of line

RlJF = % i.356 (,,2d2;o2+ lr2.'.7i5-%,(%?l o~ perme~re of llne.

(.i:.4 1;, ttenua,tion. fer metre

At tenua tionc< nepcrs ~

whence: ilro

B Begle lac. cit. dbs. per metre.

-11

6.5 Attenuation per vvave1ength

A A. = Am·· • \n •

,,;hence: AA. - . -2 ·1· ).·72.10 • dO

dbs. per vrave1ength •.

6.6 Attenuation otnorma180 ohm concentric 1i~

dbs. per metre ~

For 80 ohm ~inc ,d.thD/d :::: 3.6, the attenuutionpcr wavelength becomes:

. dbs. per Y!D.ve1cngth.

!! 'Ladner and stoner - "S~W. Wireless Comr.mnication" Appendix IV'

-,12 ...

. APPENDIX II,

l.J3STRACTS OF PUBLISIED THEORETICAL JiJ\J"D' EXl?ERIMElfT1.L WORK' ON.

L0\! VELOCITY CONCENTRIC LmEfl

(1) "liigh ImpedanceCabJ,e" H.E. Kallman ••• Proc.I.R.E.,June 1946; p. 348. Discussion on this paper •••.•. ~ ••••..• Proc.I.R.E .• ,Oct., 194:7, ·p.1097.

Theoretical fo:tmulac are eiven for the characteristic impedances of concentric lines Yvi th helical centre conductcrs, [md for their inductance, capacitance and time delay per unit length. The effect on the inductance of the outer conductor is neelcctedj othervdse the formulae aeree :with those derived in Appendix I.

An experimental law power delay line for video applications is de scribed j its measured characteristios are:

Overall diameter ••.• 0.405 ins. Centre conductor.... 112 turns per inch on mean diameter of 0·12". Impedance ••• ~ ••••.•• 950 ohms. Oapaci tance ••.•.••• ', 42 pF per ft.

:'Velocity ratio •••..• O·024·,at 5 MC/s. Attenuation ••......• 1'3 db. ppr ft. at 5 'Mc/s.

These characteristics agree vd thin :!:20% with theory. In the discussion on the paper, correction of the :i.nduotanceformula by considerinG the effeot of the outer conductor (the theoretic,al A.' treatment then coinciding with th:.1.t in l~ppendix I) is shovm 'to 2.,ive • agreement "i thin :!:5% yofi th raeasured re suI ts. The approximate theory thus gives surprisinGly close predictions of experir.1ental re,sults, even in this extreme oase of velocity reduction.

(2) "&lualif3ed,D_c~ Lines" H.E. Kallman •.• Proc.I.R.E., Sept.1946, p.646. I

This paper discusses the, reduction in inductance and delay of very low velocity_lines of the type described in (1) at frequencies much abovo 1 Mc/s, owing to linkage betvvcen out-of-phase turns. Lines in which the delay reduction is compensated by capacitance loading comp:dsing "floating" patches of conducting material Whose effect increnses with froquency, are described, and sh~vn to give unifonn delay characteristics :up to 20 Mo/s. (This inductance reduction is discussed in Seotion 2.1(a) and is not serious at 90 MC/s for the velocity ratios proposed intbis report).

(3)

- 13 -

"Spiral Delay Lines ll F.T.T. Zi.r:Jmerm.an ••.• Electrical Communication, , Sept. 1~6.

This is a very similar paper to (1),. describing a similnr low power delay line; again reasonable agreement betrveen calculated and observed characteristics is obtained.

This paper describes a new microwave amplifier of wide bandwidth. lUl. electron beam is guided along Jche axis of a helix fonning the inner conductor of a concentric line, and carrying a travelling wave; interchange of energy betl-Jeen beam and 'iV8.Ve is the basis of operation. ~vo experimental lines, constructed on the ,assunlption of the wave follovdng the turns of the helix at the velocity of light, are described. (see limiting curve, Fig. 2). Their measured iLlpedances agree w:i thin 10% w:i th those computed from the published dimensions qy means of the formula in Appendix r.

ISSUE

2~-2 r--r--.-----r--------.--------.--,---,----.---------r-------~ eooo

tooo

4--4---4-----r----~~~~--~~ '00

2.00

~~--~----+--------4~------~~~~--_,~--------r- ----~ 40

L.IMI'TINO L.INE FO~ " OPT!M M WIIltE c)IAM!''T!''

" " d.o & 0·4-5 C;.

20 " " DOTT~I) pa~TION5 VALID

~~--~----+-------~L-------~~--~-----~OA .MAL.L.ER wl~E ,/ " OIAM!TKItI.

---10 & 6

-'" - " .,.

" 2

" "

/ /

/

1 0'. 0·. PITCH 0" HEI.I)( e

RATIO = MEAN OIAMETER OF HaLI)( ; er-

F'G.1.

0·2

CHARACTERISTIC IMPEDANCE OF CONCENTIrIC '-INE WITH HSL.ICAL. INNE~ CONDUCTOR.

10 O·f

Ul U Z < o w a.. ~

BBC ~~:,O~:1.~~~~yWlc,.~N~:~~~...--~r------~-----i CENTRE CONDUCTORS.

ISSUE

23-2-48.

•

--

CURVES IHOWN DOTTeD • avoNO ~IMITING ... IN' O~ PIG.'. lVALID Po" , SMA""LI,. Will. DIAM.TI.S).

~IM'TING CAtS A •• UMt .... Q

"ltOPAGATION AT 111: ••• tPAt.' VELOCITV At.oNCI WIRE OF HIiLI)(, (IN OapI'NO_NT OF 0).

FIG.2. VEL.OCITY RATiQ OF CONtENT"UC f..INe

WiTH "'SLICAL INNER CONDUCTOR.

1

0·'

0·,

0· ....

o·z

0·, '08

·0.

-04-

'Ot

>I~

•• >-r

E u 0 ..I

U ... 0> .J ... > u

\la ~ .. Z

'" ~ tal If u.

I' 0

~ It )-

t u 0 ..I \U >

OPtliN - CIRCUIT" II\It~OANc.s IN OHM'5

FIG.3 . OP N - CIRCUI 'MPEOANCE AT 90 Mc/s OP CONC.E~TfIt'c: . l-lNE WITH HeL.ICAl-

ceNTRE CONOUCTO El-SeT lCA.... L..&NGT.... &5 ~ J OUTER OlAM TeR 10 '''' •.

RIiPO .... T

E. 033 .3. L.OW VELOCITY CO CENTRIC FEeCeR. L-lNES WlTH HEt..,-~, .. J!=.~~

CEI\ITRE CONOUCTOA.S. • SHEETS

, FIG.4.

HaRT - C'RCUrr tMPeDANCE AT 90 Mc/s OF CONCENT' le '-'NE Wtl:H . H5L...lCAL.. CENTRE CONOUC;-O~ eLeCTRICAL L-.ENGTH 2.5", OU E

LOW VELOCITY HELICAL

CONCENTRIC FEEDER LINES WITH CENTRE CONDUCTORS.

ISSUE

23-2 - 48

t-----------f5FEET'----- - -+-I APPROX ,

I 124' A at fl } ,z.f ;>.. at fa '

ADJUSTABLE SHORT CIRCUITIN~ END SECTION

4000nm LOW VELOCITY LINES.

FIG.5.

COMBINING UNIT FOR TWO F.M. TRANSM~ITTERS SEPARATED BY 2. M s IN THE 90Mc/s BAND,U IN~ LOW VeLOCITY LINES WITH HELICAL CENTRE CONDUCTORS.

I FROM TRANSMlTTE2 FREQUENCY.ft.

~-- 80 ohm. CON­CENTJ<.lC LlN~S.

TO AE~IAL--

F ~OM TT<ANSMITTEI2 2 FREQUENC.Y'2.