Choudhury, C

Khastgir, S R

English

IACS Institutional Repository

39 STUDIES IN ANTENNA RESISTANCE AND REACTANCE "" By S. R KHASTGIR, D.:c., ~EM. /. R. E. .~\ AND , ·t:: C. CHOUDHURY. ~.Sc. IRcl't'h'cti for rlf/J/iC<I/ioll, lit" 0, H).p.) t' ,bI, A~STRA.CT >::llt'asnrelll(,llts of antelllla resi~tall:c ~l1d r~artanre were carrierl (lut by folk~\\ng \\ l\lalls double-heat IIlltlJ<.d fer 11 rug£' of f'l<lut'IH'I(S frclll ahLut 330 k,',st'C'. to !IOOut 2300 kc/sec. ~ The theory uf the method of lIIeAsurements is clescribt!\d alld the t'''peril11ental results given in the paper. Measurements were made for three different types of receiving aerials 1 Iiz., (I) vntical aerial, (~) invertt'd I.-!Ierial and (3) T-acriat, eadl hdng earthed. The effect of varying the IUlgtlt of tlw }wrizollfa\ part of tIl(' last ho aerials wal' also studied. 1. IN l' R (I D (1 C l' r () N The Anteuna resistances aud reactances of three differellt types of receIving aerials Tiz. (I) vertical aerial, (2) T-aerial and (3) inverted L-aerial were measured by \ViJlallS' 1 method for different ratli0 freqnellcies within the tallgC from about 2300 kc/sec. to about 330 kc!sec. and the results of these measurements are recorded in this paper. Willans' method had already been applied to a detailed investigation of the variation with frequency of the resistance and reactance of an earthed receiving aerial of approximate I.-shape over a very "ide range of frequencies hy WiilJloite and Colcbrook,~ of the Radio Research Board, Great Britain. Antenna rcsistaun; IIH:Hsurelllellts hy other methods had also been carried out. by many il1vc~tigators, such as T. I •. Eckersley," J\Joullin/ Miller," Smith-Rose aud Colebrook I; aud others for different ranges of frequencies. All the three types ·of receiving aerials employed in this illvestigatioll were grounded. In the case of the T-type and the L-type of aerials, measurements were also carried out to fiud the dIed of the length of the horizontal parts of these aerials on the values of antenna resistance and reactance. 2. WI L LAN S' 1\1 F: THO 1> 0 F II. F. R US I S l' AN en lHEASURUMENTS The principle involved in the method of Willans is really au essential part of the method. The principle is the well known principle of transformer action * (ol11ll1unieated by the Indian Physical Society. 438 S R. Khastgir and C. Choudhury f.g. when a current flows in a secondary circuit, the resistance and reactallce of primary circuit apparently chan:;{e. Consider a secondary circuit havillg inductance I" resistance R and capacity C in the neighhourhood of an oscillating primary circl1it having inductance L1I resistHllcc R, and capacity C ,. Let M be the mutual inductance between the primary and the secondary in(hictances and (,' the angular frequency of the currents. If XII RJ and X, R be the values of the primary and secondary reactance and resi.st:lllce respectively \I ithont the secomlary cITed, thel1 calling X' and R' the cITectivc values of tile primary reactance and rcsistallcc, we can write and where 1{':::H +/H, X'=X·_'/X, The change ill the reactance means a cliange of the effective iuductance of the oscillator (primary) coil \vhich in t Ilrtl causes a chaugc in the emitted fre-queucy of the oscilJator. This change ill the freqnency of the oscillator is directly proportiolJal to the change of reactance which is )I"X,. The frequency-change is then giveu by Now it can be easily proved that for ("M=cOtlstallt, maximum, when R 2 = X 2 or wheu R = ± .l: the chUllge 111 freql1t'n(y is i.e. or R=(folL- Y, ) 1 we' . , I ( R=( .. 2.. -,OIL) i (oJC" j Here C'·t C" arc the values of the !>ec(JlJdary capacity for the h~o alternative conditions for maximullI challge of frequency as given in (3). Combiniug now the two altemative conditions, we get R= :hJ-(~/'''''t') (4) 3. G ENE R ALE X PER I 1\1 E N TAL PRO C Ii n [J R Ii J N W I I, LAN S' MET HOD The change in the emitted frequency due to the change in the effective reactance of the oscillator circuit can be discerned as an altematioll of the beat note in the telephones connected to an oscillating receiver. l.et us consider • Studies in A ntenna Resistance and Reactance 439 three circuits h), b) & (3) as shown in fig. 1. Circuit (t) is the measuring j:~ circuit which comprises an inductance L, a resistance R, a suitable standardised variable l:Ondensel' C and a switch K, circuit (2) • an oscillator circuit with an inductance L lJ a resistance R I and a suita~e standardised condenser C J' Circuit (3) is a detector-oscillator of the same') type us the circuit Cd with an inductance 1,2 a resistance R2 aud a variable couUtnser C~. A pair of telephones is it! the anode circllit of this detector osci11 attr . When the frequencies of the two oscillators are suitahly adjustt'd, it is possih}. to hear the lwterodyne beat-note in the telephones. The experimental procedure is as fo:lo\\,s: With the switch of circuit (1) open, the frequency of (3) is first adjusted to the desired value and the frequency of (2) is adjusted by varying C1 till no beat-note is heard. With the circuit (1) closed, the condenser C varied till the heat-noll.' again disappears; i.e. the fre-quency of 12) is back to its original value. This gives C r the resonance value of C. Next uisplacing C hy a ~tnall UIlJOlIlIt the heat-note is again heard due to a change ill the frequency of (2). C I is now challged till the heat-llott: disappears. If the plocess is repeated for other positiolls of C, it will be found that the variation of ('1 required to balatlcc the errect of variation 01 C is of tIlt' same forll1 as the variation of frequency shown ill fig. 2. Here the ordinate represents the heterodyne frequency (which depends on the value of el ) and abscissa, the value of C. Two peaks are observed 011 both sides of the C-value which corresponds to the original frequency and these peaks appear for two different values of C 'Viz., C'& C". 'fhe H.I<'. resistance R of tbe measuring circuit (1) can then be obtained frol11 equation (4). • 440 S. R. Khastgir and C. Choudhury The curve cuts across the horizontal li1le representing the rap!lcity ofC I co.rresponding to the initial frequency of (2), at a certain value of the capacity C whicb is the same as the resonance capacity Cr. 4 l\ X I' E R I l\1 1': N 'j' A L TEe H N 1 Q r I\ 1 NTH E P R H SEN 'J' INVESTIGATION The cOlllpkte arr,(ngclIleJlt of the apparatus is S}JO\llI 111 fig. 3. The oscillators ,\"t'le of till: Hartky type. A pail of tell:ph(lIl"~ 'las inserted ill th( Y CIRCUIT t I . . ~IRcur" .t F1C. 3 anode circuit of the detector-oscillating vain:. Whel] the fn.: 1jucl1cy of each ,,:1:0; adjusted, it "as possible to bear tile heterodyne "histle. The I..F. e.nd. developed across the telephone was theli fed into a 3-valve amplifier of the con-ventional type. A loudspeaker was cOlllwcted to the output of the amplifier. Through this loudspeaker was passed an audio-frequency current from the secondary circuit of an audio oscillator of a suitable constant frequency. A variable resista11ce '" as inserted to adjust the umpiitude of this audio-frequency current so that the hderodYllc \\hi~tje and the ~ound due tu the audio-frequency current from the audio-oscillator cou;d be ll:ade of the saml: order of intensity. As a rcsult of the superposition of the~e t\\'o audio-frequency currents through the loudspeaker, heats couid be heard. The tuning condenser l\ or C" of either oscillator could be adjusted tillllo beats were heard. This double-heat tecJmi4ue increased the accuracy of the condenser settings to a consiaerable extent. All the condensers were properly shielded and calibrated VCI Y Hccun,teJy. A mercury-link was included in the measuring circuit. l'sually Illore than one condensers fitted with slow-motion dials "ere used ill )Jaralld both for C and ('1' Long glass rods fixed to the condenser knobs were employed for turuin~ ~he condensers. Studies in Antenna Resistance and Reactance 441 5. MFA SUR It MIt N T 0 F THE ANT It N N A R It SIS TAN C E AND REA eTA NeE AND THE THE 0 R Y 0 F T H. E l\f E THO ~ First, the measuring circuit consisted of an inductance L and a standardised variable capacity ('. The H. F. resistance R of tbis circuit was measured by the method of \ViIlans. The reSlJnance value of C was C'r. N exf, the aerial under investigation was connected to one end of the indllctance and the other end was put to the earth. Similar procedure was foll~I\\'ed to measure the equivalent resistance R' of the complex circuit. The res~ance capacity of the variable condenser in this case was Cl,. which was different from Cr. Measurements of Rand R' weI e made succesiively and the coupling between the coil of the oscillator and the coil of the Illef,suring circuit was kept fixed fo), each frequency. The thec))'y of the method is indicated below.;: If R " be the effective antenna resistance, it can he shown that R' = R + ___ R , (",zr.C',.. R =R' - --~-. t' I -- (,)'!I.,.('f /" Since w2 LC,. = I, we can write R = R' - R. C_,~ __ , C,.-C',. The effective reactance X, of the antenna can be obtained in the following • manner· 1£ X' he the reactance of the complex circuit when the ante11na is connected ;11 the maimer shown in fig. 3, the condition of resonance is given by X. + X'= 0, l'nder the conditions of the experiment, it can he shown so that the &lltenna reactance will he given by X I C,. ..; (' = -(I).,. _ .-C, -e'l' (6) The values of the antenna resistance and reactance lIen: obtained with the' help of (5) and (6). 6. EXPERIMENTAL RESrL'J'S--VARIATION OF ANTENNA RHS1STANCE AND REACTANCE WITH FREQUENCY The results of meaSllr('ments for the ealthed vertical aerial, the inverted L·aerial and the T-nerial are given in figs. 4. 4(a), S. S(Il).and 6, 6(a). 6-1 387P-Vl 442 S. R. Khastgir and C. Choudhury '160 JNITIALv..WI ore:..,' r-----..!::=-= 120 III 100 i ! 80 60 " --+ C IN,.I¥Ar llJO 160 200 2~0 40 FIG. S(Ll) OJ /0 ./ " hlQUINCY IN Itc.JSlt, 301) 1'10) FIG, 4 '!f)u 210 J'.!{J 2(10 '0 ''''' 1(,11 "7 ,14Q .. E 12 i ! JOO I So " f!(l .. .. I. t 20 I -8 I I .. ·9 \ E \ 5 \ .10 , ! I .. \ ·11 \ ~ \ I ,~ \ ~ -\I l '0 l • -II ,l r -II /,.'''IQUENC.V IN K..JIlC, II 10 I~ II FIG. 6 ~ *I '0 ~ I I .. 60 ! 10 ! i 10 i Ii !O J I It t -II 10 t 18 -. ,. .... 11141' INC./.n, :I " FIG. S FIG. Q(a) Studies in Antenna Hesistance and Reactance 443 7. V A R I A T 1(' N n FAN T g N N A R H S r S TAN C P. AND REA C T-A N C H. WIT Il T II H I, H N l~ T II II II 'J' II E II II R I Z 0 N TAL I' 1\ R TOIl l' II H T-A H R I .\ I, AN)) T II H L-A H R I A L The cxperiuJents 011 the variation of the antl'J1IlU resistance and reactance with the horizontal tOlJ length were carried ,,·ith freq : 045 kc/sec. (A. = 355m). 'flte results of measurements with a "T "-acrial,re given in table IV. TABtE IV Earthed T-aerial: Frequency: 845~c/sec. ('\=355111) . Top length \metres) 1I.0 IU·S IO.n 9·5 8·5 i Without aerial i---,------ ! : c' i C" r.. 1 Ric' \ lp.p./l : (p.p.f) (p.p./l (ohtm<) I (p.p./) 2<)2 3"5 57Y (Joo SS9 5·j 31:/ 3J 2 321l ... ~, ._._-_ .... _---_. ---~-~-. 1 \\,it~ aerial . ~ . I ! e" :,'i e'r i (p.p./I> I (p.p.I) 350 31<) 36.5 332 370 I 339 I 366 I 344 I 3112 I i 354 i , R' ((ohms! . 54.2 50 4) 46.y \ 4.HS I I 39.R R . (oh11ls) 4I.1l 37·4 33·5 ~9'i 25·5 X. (ohms) -7.U1)( 102 -7·36 -7·57 " -7·72 " -8.05 " Similar experiments were performed with an I.-aerial of different hori1:ontal top-lengths for a definite fn·qucI1CY. The results of lI)(.:aSlll cments an:: given ill table V. These are illustrated in fig. i. T .. AI .... L ("SIC.) I! ,~o .11/' I '·10 i . ! -"r. I! ~ to/ ! oS'O 30 ,-' , I. t ftoi 7~'i ! I x~._·· I .... ~ ............... . t - TO. UN.TII '" IIITIIII t no 140 100 • • I" II 11 ,. FUl 7 444 S. R. Khastgir and C. Choudhury TABl.E V Earthed I.-aerial (in verted). Freql1ency; 857 kc/sec. (A=3501l1). 'fop lengtll ;metr€'~) Without af'rial ! I c' I C" I c, R I (1'-/41 ! (p.}J-tJ : (p.}J-!) I ((lh!ll~) I , I With aerial co. ~ C' ' (" I R' (l'o}J-fl 'I'ol'o/i: \1'01'01 ! I (llnlls , 11.75 123 IS() 137 150 .:2 1466 - 288s x w' II.O 124 lSI 138 1482 144·1l -2.888 " 10.25 778 , 788 783 3·(l 12S : 152 I.W LIS <; 142.2S - 2.893 " 9·5 126 I i 153 140 "1.1·5 139.85 -2·[-;97 " 8·75 I 13S .() ]~7 , lSI III , 14 I 7 I -2.90 2 " S. DrS C t' s s rON 0 F TIlE EX]> E R I ~l r.: N T ;\ 1. R H S tJ 1.( T f: In the case of the earthed vertical aerial and thc earthed inverted I.-aerial, the effective antenna resistance R, was found to increase steadily with freql1ency as can be seen from figs. 4 & 6. The smallest wavelength in the il1\'estigatiol1 was hmvcver larger than the natural iundanlcrltal wavelength of the antenna.) In the cuse of the T-aerial, 011 the other hand. the n:sistancc at first decreased steadily with the incrt!ase of frequency alJd attained a minimullJ value hut subsequcntly it increased with furthel in(['ca!:>e of freql1Clll'Y. The minimum value of the antenna resistance appeared at 750 l:c/~ec- The existence of snch a minjmul11 in tIlt! value of anten11a resistance had also been previously observed . by earlier investigators. There had been attempts also to explain the nature of the variation of the antenna resistance with frequency. All approximate theory for the case of a perfectly conducting straight vertical wire cOlJl1ected to hOl1JOgelJeOllS earth with a horizontal surface, had been \Im-ked out by EccJc.s.; It had hecn shown that if R is the antenna resistance at any \\·ave.!t!l1gth A, then Ro-H. _ 3'\0(A-Ao) Ro - .... A· where Ao is the \wtural \\,avelellgth (fundamental) of the 3nte11n3 and Ro is the antenna resistance at that wavelength. The equation shows that if the resistance R be plotted against fn:quel1cy, tlle curve is a parabola. It can he seen that the minimum resistance is Ro! 4 and occurs at A = 2'\0 and that when'\ = 3Ao. the curve is straight and directed through the origin. The r€sistallce is Ro/3 for ,\= 3'\0. This ideal curve was, of COlUSC, departed in mallY practiclll clises. According to Colebrook's R theory, the antenna resistance of a vertical or an L-aerial should Studies in A ntenna Resistance and Reactance 445 vary much in the same way as in our experiments. The observed variation of the antenna resistance of aT-aerial resemhled EccJe's theot etical cllt\'e to a certain extent. Referring to the anteD11a reactance of a vertical earthed aerial. it l'an be seen from fig-. 4 that its value was lIegative and that it increased steadily with fre-quency, tending to pass through the zero value. In the case of the earthed inverted L aerial, the alltenna reactance (wIdell was also negative) increased with freqUEncy and in the region of 900 kc/sel'., i* suddenly began to decrease with the increase of frequency, as is evident froll! fig. 6. III the case of tbe T-aerial, the antenna reactance was found to fall sudfenly in the frequency region of minimullI antenlla resistance; otherwise, on Ih~ whole, the antenna reactance sllo\\'(:d 8n increase with the increase of fn.:quen1" (See fig. 5 ) Regarding (he variation of thc antellIJa reii!'tam'e and reactance with the horizontal top-lel1gth of the T-aerial or that of ihe inverted L-aeria1 for a definite frequ(:ucy, the (,xperilllcntal results showed tlia. hoth resistanc(' and reactance il1crea~(·d steadily WIth the lel1gth of the horizontal part. (Sec fig. 7.) LJ S I, l\J J\1 A R Y Expel iJlIcnts to study the variatioll of thc total-loss-resistance and reactance of receivillg aerials with frequency were carrico out following Willans' doublc-beat method of measuriug H.F. resistance. Three different types oi aerials were employed Tiz. the vertical aerial, 1'-aerial aud the inverted L-aerial each being grounded. It appears that in the case uf the vertical aerial and the inverted L-aerial, the antenna resistallce steadily illcreased \\ ith frequency. The range of frequencies did 110t however include the natlll'a1 fundamental frequency of the aerial or its harmonics. III the case of the T-aerial a definite miuimum for the ante11na resistallce appeared to exist within tJ"e nl11ge of fn:qnencies employed in these llIeasuremeuts. The autelllHl leactallCC was found, ill gl'llcraJ, to illcreasc with the jJ1crea~e of frcquel1cy. 111 the case of the invertEd I.-aerial the rise was foHowed hy a sudden decrease with the increase of frequency at a celtain frequency, In the case of the 1'-acrial, thelC apvearcd a sudden dilJJinutioll in the value of the antenna reactance in the region \vhere the minimum antenna resistance was observed. The experiments also showed that the antenna resistance and reactance of a T-aerial and an inverted L-aerial increased with the increase of the top-length of the horizontal part of each aeria1. PHYSICS LABORAtORY, DAcCA UNIVERSITY 446 S. R. khasigir and C. choudhury REF Ii R ENe I·: S ... I Willans t'idc Turner's paper, Experilllt'ntnl Wireless & Wireless Engineer, p. 348, ~IaTeh, 1925. 2 Will110tte & Co1t:brook JOII/, 11";{, " Eke. l\llgillet'rs ,·Ide nxp. WireJ(·ss & W.E." p. 83 (193 1). 3 T. L. Ikkerslcv, JOIl/,. 1.IU.I., 9, 58 (1922). 4 :'IIoulin, High Fr~qul'\I('Y l\lensun:lJcllh, 1'. ·1<:h (1')~\1). 6 Millt-r,)lurcau uf Standards, 13, 1916-17. 6 Smith·Rose & Colebrook, Exp. Wireless & W.E. 2, ~(j7 (r()2S), 7 Hccl~s, Handbook of Wirdess Tl'Il'!~raphy & Telephuny, 2nd edition, p. 129. ~ Colebmok, Hxp(,rilllt'utal Wirell'ss and Wireless Enginel'T, p. 657, 1\0". 1927. 

Studies in Antenna Resistance and Reactance

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Studies in Antenna Resistance and Reactance

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