INPUT INWEDANCQ MiiAESUREN‘VLENTS OF DESK CONE": ANTENNAS Thesis for the Degree of M. S. MICHIGAN STATE COLLEGE Harry De Vere Ruhl, Junior 1952 _‘_‘_,__ ‘ “:3: " _‘T_ -"' "‘ -‘fi~- _ _._'.'_ ‘- "' 0- ' " ._' " -' 4 ‘ ——'-—w— WW—h lHl"flfllfliflfiflflflifiififlmfllMINI 1774 9791 This is to certify that the thesis entitled INPUT IMPEMNCE MEASUREMENT.) OF DISK CONE ANTENNAS presented by Harry DeVore Ruhl, Junior has been accepted towards fulfillment of the requirements for MOS. degree in 312810! Major professor Date M ‘ '1 ‘ l q l \ l I l l I ‘M --' v" i. .‘ l l .5 i. .3, , c". l .' \ O \ 1", .- ’0 l -‘ :2 t , .- . ' .s' u . b l ' r. ’ ‘\ . "0 .‘-_ .‘ 4‘ t i I I l J .l 'f : a . . m _ r . w. . . Ym . .. md ‘ om fi _ mm _ is. om . . .mm . 8M mr _ .50 .. . . mm .-. .p. AVum om . me . s mr mm . . e on . . 3m 0 ; . W mm -.. m . ._ m . ,, m if requested. MAY BE RECALLED with earlier due date ' DATE DUE use clam-mu DATE DUE DATE DUE INPUT IMPEDANCE MEASUREMENTS OF ' ‘ EISK CONE ANTENNAS A D By Harry DeVere Ruhl, Junior A THESIS ' Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 1952 /O-/y7":LL (3 ) // TABLE OF CONTENTS Acknowlegements i Introduction ..................... 1 l1 Eethod of Calculation ........... 4 iiI Operating Conditions ............. 8 TV' Equipment ;.......................11 V Sources of Error .................24 VI Sample Calculation ...............28 ViI Results and Conclusions ..........32 Bibliography f}g§f“¢}(‘ P Sytfilfitil}{) ACKNOWLEDGMENTS I wish to express my sincere thanks to Dr. Alfred Ieitner and Dr. Robert D. Spence for their suggestions and assistance. I am also greatly indebted to Mr. Charles Kingston for his aid in construction details and to Mr. Robert Gault and Mr. Albert Smith for their help in photographic work. 1. INTRODUCTION The purpose of this thesis was to determine the input impedance of a disk cone antenna. The configu- ration in this experiment was a circular disk of finite extent as the ground plane, and a circular cone of wide angle with a flat base. The cone was located with its apex at the center of the disk and its axis coincident with the axis of the disk. See Figure l. .7. thure l The disk cone antenna belongs in a family gener- ally known as conical antennas. S.A. Schelkunofflgin his book, "Electromagnetic waves", considered and solved the problem for cones having half angles of less than two degrees. In later papersELflh Schelkunoff indicated a method of solution for the problem involving wide angle cones having spherical caps, from which P.D.P. SmithUiobtained an approximate solution. Both of these solutions are obtained for symmetrical biconical antennas, two cones having the same axis and touching at the apices. The impedance values found by these authors are twice the impedance of one cone perpen- dicular to, and with its apex touching, an infinite ground plane. The configuration of the disk cone, therefore, most nearly approaches that of Smith's work, with these exceptions: the ground plane, which is finite in the disk cone, and the base of the cone, which in Smith's paper had a spherical cap and in this experiment was flat. .VV . on . ma . m . 4 .3 Swans one? s m Ede .0 ‘00 “0 mmdwflm Hams w>d m>m£ mwfioo HH¢ . m... c pnwfih oaohpxo on» pm wdficcfiwom n.MMMWo onp omHBKOOHo wcfiumow. v.m oasmdm mocoo one we o>am .65 . IO.H "I Cl! ll» ‘ Illl‘llblllrln llln lll tllllll’. 4. METHOD OF CALCULATION The method of determining the impedance of the antenna consisted of using it as the termination of a transmission line and measuring the terminating impedance. In using this method two quantities must be ac- curately measured; 1. The standing wave voltage ratio defined as : V'iagl Maul-n1 f. Voltage Minna-tin ( ) 2. The distance of the first voltage minimum from the terminal impedance. anuh) The terminal impedance is then given by = = 0' 19135115221 1"-"r 2AM '2“ (9-311” 31......) (2). where flit-“ézzgf: a?! , and where 2.1s the charac- teristic impedance of the line. «z, .h. i. filh¢y (3) where Evie the dielectric coefficient. Zawas equal to 79.2 Ohms for the transmission line used. The theoretical consideration of this antenna assumes that it is located in free space. This is Do difficult in practice, but it is possible to place the antenna sufficiently far from surrounding objects so that they will have very little effect. However, in doing this, some attenuation was introduced in the transmission line. For lines of small attenuation the phase constant (/3) is for practical purposes the same as that of a disSipationless line, hence the shift of the first minimum remains the same. The standing wave ratio is always decreased by attenuation, and the effect is greater for large standing wave ratios as shown below. The coefficient of attenuation (0C) was computed, and corrections were then made in the Standing wave ratio, in the following manner. For coaxial lines, '_ “El-til}? pig (t*%}' ‘4? -..-. frequency: 2.82 x lO’cycles/second, = conductivity of metal°'1.55 x 107 mho/meter, r. radius of outer conductor: 1.19 x lO'zmeters, radius of inner conductor = .318 x ldameters, l x 41Tx 10‘7 henrys/meter, f CF b a. :41, #flx 10.1 henrys/meter, f. e 103/36” farads/meter. The conductivity need here is an average value of that for brass. No information being available for brass tubing and rod used, an average was taken over .63? those values found in reference books , which was 6., ‘»&1$ :- found to be at a .0107 nepers/meter. .25 50"“, . The attenuation was then Voltage maxima in the standing wave pattern on a transmission line occur whenever the incident and reflected waves are in phase, and minima whenever they are 180° out of phase. Hence the standing wave ratio may be expressed as IV |+ IVgI : .3— /° Iva - ml ’ (5) where IVII is voltage of the incident wave and IV“! is the voltage of the reflected wave. _ Since the units of voltage are arbitrary, IVII may be taken as unity and the value of IVnI calcu- lated from the measured value of P . Since the re- flected wave has traveled from the detector to the antenna and back again, it has been attenuated by a factor of 6'“, where d is twice the distance from the detector to the antenna. In the present experi- ment,d :- 4.27 meters, «I 2- .0167. We designate the value of the reflected voltage which would have been present without attenuation as IV;|. It is seen that was W“ a“ and we find that IVs'I" 1.os|v‘|. This value is substituted in equation (6) and the corrected standing wave ratio {3' is used to calculate the antenna impedance: ,3": —___W1""' Mil (6) ml - w“ . where IVII” | . 7. From equation (5 ) we find that large standing. wave ratios occur when“ IVRI is large. From the devel- opment leading to equation (6) we find that IV“: #017 [V‘I , so that the difference-between IV“ and IV‘I is greater for large standing wave ratios. Since in equation (6) we add IV,” to IVII in the numerator, and subtract it from IVQIin the denominator, lo'is always larger than [J . The difference increases with larger standing wave ratio. The detector was located about twenty wave lengths from the terminal of the transmission line. The shift of the first minimum was determined by measuring the shift of the 41st minimum, the two be- ing essentially identical. Actually, three or four minima and four maxima could be observed in a slotted section of the transmission line, both with a shorted terminal and with an antenna. Altogether, eight values of the shift were observed, and each reading was re- peated several times. Separate observations of stand- ing wave ratios, voltage maximum to adjacent voltage minimum, were also taken, and then repeated. As a check, the sets of readings were repeated and averages were taken over all readings. Finally the standing wave ratio was corrected in accordance with equation (6). 8. OPERATING COND ITIONS A wave length of approximately ten centimeters was chosen primarily for three reasons; 1. It was short enough so that surrounding objects were electrically far enough away so as to have very little effect. (20Aor more) 2. It was large enough so that component parts could be machined while still maintaining necessary tolerances. 3. The antenna could be small enough so that no framework was needed to support the cone. The antenna was fed by a coaxial line, the out- side conductor ending in the disk and the center con- ductor supporting the cone. It was necessary therefore to have an aperture at the center of the disk and the apex of the cone could not be a point, so the field configuration was somewhat different from the theo- retical problem. Since it was necessary to place the antenna at some distance from all other equipment, the coaxial line of considerable strength was needed. The outside conductor was therefore made of l" brass tubing, and the inside conductor of l/h" brass rod. Styrofoam was used as a spacing material, in order to keep the conductors concentric and yet not introduce any appreciable error by changing the dielectric constant. Polystyrene spacers were used at two places along the transmission line where either the outer conductor was made larger or the inner conductor was made smaller so that the characteristic impedance of the line re- mained a constant. Near the terminal of the transmission line both the inside and outside conductors were tapered so that the aperture in the disk could be as small as possible. See Figure 3., The ratio of the two radii was kept constant along the tapered section, thus maintaining a constant characteristic impedance. This was checked by independently shorting both ends of the tapered section and observing the resulting standing wave pat- terns which were found to be the same in both cases. 10. Tapered SCCttfih And Termondtton --H--— .059 1V 5‘ II // | 3 -OI |.._ .2 58// '0 IHI // I :1) . " r' 'L" +1 I, __I;/ II " I g I I/i ' ’t 7 ’/ l I. I Lqr-—————-i A, A" 4 4‘ 0% / $ 41‘ g I 5/ 'I‘.“ , '4 ::5 ‘ ‘ I1P._.,\-PO"I‘t‘Ir."e In '15: 337 +11%.— .250 I fi'p— .H‘I II X-Surfaeo at wI'HCII short we: made Cone "tI‘F An I. 60' SInnt Ct‘ht ”4 6 ml Plow. "and Jun Kk Scale I ' I'I Enqure 3 JuLO EQUIPMENT The oscillator was the resonant cavity type employing a 2040 "light house" tube. It was modu- lated by a'bquare wave"pulse at a frequency of ap- proximately eight hundred cycles per second using a multivibrator, shaper. and modulator circuit, as in Figures Gand 7 . The multivibrator circuit was conventional, using a 6SN7 dual triode, and drove a 6V6 tube from saturation to cut-off, giving a fsquare" wave" output. The modulating unit used three SL6 I tubes in parallel. The screen grids and plates of the 6L6 tubes were connected together. This reduced the resistance of these tubes, and resulted in larger voltages from the plate to the cathode of the 2040 tube. Two separate regulated power supplies with separate grounds were used, one for the modulator and oscillator, and one for the multivibrator and shaper. The oscillator was placed in parallel with the cathode resistor of the 616 tubes, and the 616 tubes in turn were driven by application of the "square wave" volt- age. This drove them from near cut-off to saturation. As a result, a square wave voltage of approximately 12. two hundred volts was applied between the cathode and the plate of the oscillator. Since the charac- teristics of the 2040 tube show that oscillation ceases at plate voltages below 75 voltsLé', the oscillator was pulse modulated. Energy was taken from the cavity by a probe connected to the large coaxial line by way of a flex- ible coaxial line. The two coaxial sections were matched by double stub tuning, as shown in Figure II. Energy was extracted by a thin probe which traveled along a slotted section of the coaxial trans- mission line. The probe was inserted into the line a very small distance to insure loose coupling and min- imize the discontinuity it presented. The probe was connected to the center conductor of the detector unit, Figure I2, and could be raised or lowered into the main coaxial line. A moveable short was located in the detector unit between the cen- ter and outer conductor, with its position adjustable so it could be tuned to give a maximum of energy de- tected. A crystal was located perpendicular to, and between, the probe and short to detect the radio fre- quency energy. Essentially, the equivalent circuit was as shown below. I x.F.Condsnssr lf-ers*tl R.F. Ewart” —.' A.F. Ines-1t. —’ Failure, 4 13. Crystals have a square law response to voltage and since the voltage along the line, when shorted, varies as sinfi x, the detected signal should vary as sing/3x. (x being the distance from the terminal end) The crystal was calibrated by placing a short at the terminal and plotting voltage vs. distance, then comparing this with a sin‘f3x curve. These curves, as shown in Figure l3 corresponded so closely that the meter in the amplifier, which was designed and cali- brated to operate in conjunction with a square law detector, could be used to read standing wave voltage ratio. Actual voltage units were not important since they were used in a ratio. Minima and maxima were located by use of the same meter. A battery operated preamplifier, Figure #4, was used close to the probe to raise the signal level before noise was introduced. BIOCK 14. Dtaxram 0“ the. ExpcrzmentoI EQutpmeht : _-Ir Brass CourteI Cable Amplifier Pr. Amplifier 'OIOI‘ SI"I1 Power 5.;an _ _ _ _ IL II I I t ‘31... "alto uhmtor Shepcr Modulator Olenlletov .5). Q ULSr..& t-&d‘m Loy‘LD—>—u._,z — .OZ $C50h¢ IMIW: III—II A. I III. -I I - u SL950 fl .. .., 3 K. 1 am... I x8. 28. widJcm . i . II I M FuIL . / go (52...--. . II Seem. gal 3.3.“. (VQTIQ k $$Q. . .,IJII \ Ifil . III \ «T 1H \J _ _ x .3 gm tune Me. lmN xm 2m H, . r -.. my h -. (0.0.6.3qu .m .> +m £0541” at... scadsn—Izna—aZ F 0 L 3 P. l 32 n 12.0 A!“ u. t I: V: II, [I ~62 2.3.5 r b. ¥¢=.0.0 #510 «eczemoc W i i i. xn . _ . .02 3.3056 1.. O U L p ‘ ‘ i‘ U. I I K N N .D‘ \ \ .oo‘"” $1>1>1I ‘DDDI 111111I co.#e_srom Scarab!“ +0“ .ocHH Hoaxooo oHndonM one new onoaa on» op coupoodcoo one no; now one aw .LOpoHsuoa onp Home oaos anaboo onp.uo mono pmoa new unwaa oaoASKo onp pm ocodpoocdoo one .codpoom mmoaw o wefi>on onsp aoQDSL one go as; an uoaooo pan on: pH .quoHHHomo mpasno peacomoa one .m oasmam _ -I‘II IIIIIIII . u. \\ . x . < "F Figure 90 The experimental equipment showing flexible coaxial line, brass transmission line, antenna, detector, and amplifiers. -——'——- — ”— q ~“"“"’V .coESp one: nwcfinooa one moan: song aopoa can .aodmfiadeo name one .uonHHQBSIond one new hocfiopcoo one .coapoom noppoan one .aopoopoo o>o3 wcfiocoum on» pnwap on whoa Scam .dnooeom oboe wcfionopm on» ocfiaaopoo op oomz_enoenasuo one .oH enemas I I Ital L 6U. Ml‘LCIllvttl Stub q ‘ ‘ r ‘ ‘ ‘ ‘ 1 K I T... Stubs Used, Separated |.S"A‘I: Their Centers Fleur-e II 21. Standtnc' MIQve Detector POI o1 ‘t1l’8fl‘ \R. F. Condenser Soc to h T." 0 Cn‘stoI I Poln'stg'renc Probe thur'e I2. e a. TurtcaI Cr..3I,aI CnIcInaLIOv. Cur/e ? VIII. (1 T7... [51. (\quW LO Wlfooe .5 J no no 80.0 «a '0 I It 00 w thure I3 1.00.9079'4 5.». fix -—- I ----1- "Casual Voltoflca OUTPUT an van... out... Supplctd F‘qure. I4‘ 24. SOURCES OF ERROR There are several sources of error present, which come under five main headings. Concentricity of Conductors The inner conductor was held concentric by using styrofoam spacers. These were observed to contribute no detrimental effect by comparing the curves obtained when the end was shorted with and without the spacers. The effect of the single polystyrene spacer between the detector and the termination was checked in the same manner and found to contribute no observable effect. The dielectric coefficient 8,. of polystyrene is 2.55Lfl'. As a consequence, when it was used as a spacer, the inner conductor had to be undercut, or the outer conductor increased in size, to maintain the characteristic impedance of the line constant, of. equation (:3). When styrofoam was used as a spacer, it was found unnecessary to change the conductor sizes. Styrofoam, being such a large percentage of air by vol- ume, has a dielectric constant essentially equal to one, rendering changes of conductor sizes unnecessary. :3. Another precaution taken to maintain the center conductor concentric was to mount the entire brass section of the transmission line vertically. The line was maintained vertical by leveling screws, and as indicated, by the use of a level. Attenuation The attenuation due to the conductivity of brass has already been computed and corrected for, see page 5 . The spacers used to keep the center conductor concentric were unavoidable and probably contributed a negligibly small additional amount to the attenuation. The ratio of conductor sizes was very nearly the ratio giving minimum attenuation. Calibration of the Crystal This may introduce some error, though small, as indicated previously. See page ’3. Discontinuities Several of the discontinuities are unavoidable. The probe, the slot, the spacers, etc. were all neces- sary, but once again, the smoothness of the curve rep- resenting the standing wave pattern when the termination was a short indicated the minuteness of their contribu- tions. The probe was inserted in the line a very small distance to minimize its effect. 26. Measurements The errors in the location of the positions of maximum or minimum voltage were greatest for small standing wave ratios. As shown in Figure If, for small standing wave ratios the minima and maxima ap- pear much wider than they do for large standing wave ratios. As a consequence the exact positions of maxi- ma and minima were more difficult to locate, and greater errors were introduced when the standing wave ratios were small. The errors in reading standing wave ratios were greatest for large standing wave ratios. Figure I5 shows that a small error in the location of minima or maxima give larger deviations from the true station- ary value of voltage when standing wave ratios are large. This effect is due to the shape of the curve of voltage vs. distance along the transmission line. The error introduced by attenuation, as discussed on p. 5 , has a similar effect. It is not related to the error due to the shape of the curve. Both of these effects were minimized by care- fully making a large number of observations and taking an average. Vo/{nqc vs [Ir‘szfzon I on 6/76 T—ransmmsmn L/r/P. [0 e /.I u- \ \ \. Mp «“‘ > I ‘\ \~\ ‘/ \ 4.5 4.0 ‘.5 O .5 [.0 [.5 2.0 2.5 3.0 3.5 4.0 Position In Cm. Fleur-e I5 28. SAMPLE CALCULATION Readings of Position in Centimeters Short g3 Termination* Antenna as Termination Minima Maxims Minima Maxims 91.65 88.97 87.11 89.73 .51 .96 .14 .72 . .93 .11 .68 .92 .ll .70 .96 .14 .69 .91 .14 .70 .91 .ll .73 096 .12 071 3815.92 5 '76 322% W 9: 86.34 83.69 81.80 84.46 .31 .65 .79 .42 o 5 068 079 042 .68 .78 .43 .67 .81 .40 065 079 042 .66 .81 .43 .70 .79 .40 .20 .79 .41 o 9 o 9 9 3 83768 BTI? ' .4 .31 847% * .31 centimeters was added to the averages of readings taken when the termination was a short, in order to correct for the thickness of the ground plane. See Figure . This correction was added because high readings are towards the termination. 29. Minima Maxima Minima Maxima 81.02 78.38 76.50 79.20 031 041 050 014 81.33 .41 .49 .20 .43 .49 .20 .38 .50 .18 039 046 019 .36 .48 .17 oil-4 047 .15 .38 .50 .16 .40 .48 .14 78:71 75-13 73-18 76-gg 73-3; The :06 :49 :81 .00 .49 .86 007 050 080 .ll .46 .90 73 000 048 080 .02 .47 .89 7 '83 '50 Z72 20 o ' 0 73.21 76.49 . 73236 Readings 3; Standing Wave Ratio 3-8 3-8 3-7 3-8 3-9 3-7 .7 08 07 08 09 07 O7 O8 07 08 09 08 .7 08 07 08 97 -7 _:§. _;§ .;I _;Z _;2 ._£§ Total 112.9 for 30 readings. Average 3.76 30. Correction for Standing Wave Ratio IVItIV I- I+IVI : A- : —‘. ’0 3.76 I‘IVQI IWJ‘IWhI 2.76 - Ing= m‘.5.0 veltfie and; IV..|: I.03IVR|= Last .5803 .60, vo [feed u-n-‘l's -- «v.1 -w.'l - lo IWd'IVNI L60? = .4." Shift 2; the Standing Wave Pattern Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Short 91.96 89.25 86.65 83.99 81.33 78.71 76.01 73-35 ‘Antenna 89.71 87.12 84.42 81.79 79-17 76.49 73.84 Shifts of (X...,,) in Centimeters 4.86 .4.86 4.85 4.89 4.86 4.86 4.84 4.84 4.84 4.83 4.82 4.84 4.87 4.92 4.85 4.93 4.86 in: Total 87.45 for 18 readings. Average 4.86 cm. 31. Solution 9; the Problem 2 z 1 [Ti/0 7"" 16‘1"»: 7 o - ' Tan f I fl‘flun _ Z171 . _. . . - fix,” .. _.:\_m - £20455; ,7/377. [‘4 rs 7‘" flznuu = ".EBI /° ”"131... = 4” “-2011: “/- ’5 g . [*j/olf l, 7’2 4.”*".28’ .,_. 19.2w.” ”'4” 1.12 [g‘57’ = 29.4 (.707 +1370!) 37': (20.8 *1. 20. 7) 96m: 32. RESULTS AND CON CLUS IONS a. - It should be noted that for the disk cone an- tenna; there are three quantities which may be varied: the half angle of the cone, the slant height of the cone, and the radius of the ground plane, The results of these variations are shown in the accompanying graphs. The variations in the input impedance due to changes of slant height shown in Figure ILindicate in a very general way what happens. The resistance com- ponent appears to dip in the vicinity of 3/4 A . Ac- tually too few points were taken to give a conclusive picture. The reactive part represented a far more inter- eating variation. The reactance was inductive when the slant height was an odd multiple of quarter wave- lengths, and capacitive at even multiples of a quarter wavelength. These variations indicated some point of resonance between each change of one quarter wavelength. Exact locations of these points are not known because intermediate slant heights were not observed. The similarities and differences between the conical antenna as computed by P.D.P. Smith and the disk cone have already been discussed on page I . For purposes of comparison the results of his 33. ‘0'- / v. w < VQbU§ VTCSH V J“ urzws§¢\nl.un. 0" V 356‘ w. . 33.x . . 8% its... . 00%. fl QKR‘\\‘ \I/ 0&0“ hi\&QV.V \V\sb\ N&C\h. a.“ hQVdRC§ dexb I.\...H S 0N on ow Po av on as nice 34. calculations were drawn on the graph of impedance vs. cone half angles. See Figure IT. The varia- tions for small angles, as calculated by Smith, were included to show the sharp rise at small angles, in- dicating no valid comparison can be made with Schelkunoff's solution for thin cones, but showing the results are not incompatible. The resistance components of the input impedance show the same trend and agree very well over most of the range. At small angles the work of Smith indica- ted there is a maximum at some position between 5' and 20". No conclusive data was taken in this range of angles. At angles larger than 70° the curve of measured values indicates that the resistive compon- ent of the input impedance of a disk cone approaches very small values. A cone having a half angle of 90. would be a disk. Since the apex of the cone touches the ground plane in the theoretical problem, a half angle of 90' degrees would result in a shorted termi- nation. These two results are in agreement. The close agreement of Smith's calculations and the measured values show that for these cone angles the effect of a finite ground plane on the resistive component is small. Since in either case the antenna is assumed to be a perfect conductor there are no 35- N : n:.\e.< utoxk \taes¢ v. .. uxkew 5 cl 0:90 on on o... c» on 2. Q N. oidr.h. Q / u/ / 4/ ./ / /. out o» 33% wuuk no.0 ox Art on.) g < {okeQ \ «Stow 2.. $33370 «him to .1 33.; Notice" I I I ox? .\ .t at .50 0 as 5.5 we . 35.x 23:. .5 .1... aces 05 .0 a. g D ON 0s _/ / 2.30 02. 329‘ 2:3ch 230 :3 mo ousdfiokth 2 {cassette 3 i :53 36. "Joule heat" losses. The resistive component is therefore the radiation resistance, and is directly prOportional to the energy radiated. As a consequence, the radiated energy per unit of current input to the antenna is very nearly the same for a finite or an infinite ground plane. The measured reactance decreases as the angle increases. This decrease is not as rapid as the de- crease for a conical antenna calculated by Smith. By the same reasoning followed for the resistance at I cone half angles of 900 , the reactance should de- crease to zero at 90°. It should be noted that the discrepancies between Smith's calculations and our measurements are greatest in the reactive component. Any discrepancy between the calculated and measured values of impedance should be due mainly to the fact that our ground plane is finite and not infinite, and that the base of our cone is flat and not spherically capped. Variations due to changes in ground plane radius indicated oscillations in the impedance between a max- imum and minimum approaching some limit at large ground planes. These variations have half period of one half a wavelength as shown in Figure [8. On the same graph the results of Meier and Summers are plotted. Their experimental data is for cylindrical dipoles with finite circular ground planes. No comparison of im- pedance values is intended since the cylindrical dipole 37- 0. 0L3r.u 315......) E 25.4 0...: 232.9 a h“ a he Qd m. I: «NM \r o \o /o\. /.\ /.\. M/ m Outdwud&\ O~ / _ m. . \ IO\( m 3 \\ ( an 25.6 0:; 2: . <¢N~.u.3ru._ 0.956 # k/ a on «38......5 3L5 \. ) \. m 1... 3.... .4”... \/ \ x \ / \ / 1. 0.0 .9 72532110 /. /\ /\ /\ 0.. tom. :3; v2.33! IIOIIOII... . .3 Coffin 3.4 .83! m .335 2... .5 .urrioi.»...u 2:... \v. 334$ VP... .3! * 3..de 2;: 33.2.6 .2. cocdwopiH 2.5 x20 38. is similiar to the conical antenna of small angle discussed above. There is, however, qualitative agree- ment. Changes of the ground plane radius caused the resistive and reactive components of the input imped- ance to oscillate with a period of 'g for both types of antennas. For the disk cone the oscillations ap- proached a limit more rapidly. At very small ground planes the information was lacking so that the effects in that domain could not be given. At large ground planes the information was also incomplete. The 60. cones of slant height 3/%.\and A , were made hollow, with removable flat caps. They were placed over a ground plane with a radius of‘5Q. No change was noted in the input impedance when the flat cap was removed. The results show that a variation in any one of the parameters changed the input impedance. The largest variations of impedance were observed with changes in cone half angle, second largest with changes in slant height, and smallest with changes in ground plane radius. These graphs clearly show the general trends. There remain points which would be interest- ing to investigate, especially slant heights and ground plane radii less than one quarter of a wavelength, and the vicinity of zero reactive component in slant height variations. 39- The difficulties of measuring the input imped- ance of a disk cone have already been pointed out. With further investigations on the effect of sur-. rounding objects, it might be found that the support- ing line could be shortened. The conductors could be silver plated. Further improvements in the equip- ment such as detector, the oscillator, or any associ- ated equipment, would make more accurate the measure- ments on the disk cone antenna input impedance. 9. 10. 11. 12. 13. BIBLIOGRAPHY Schelkunoff, S.A., Theory of Antennas of Arbitrary Size and Shape, Proc. of I.R.E., 22, 4937521, 1941. Schelkunoff, S.A., Electroma {etic waves, D. Van- Nostrand Co., New York,.194%. s. , n. - Schelkunoff, S.A., Principal and Complementary Waves in Antennas, Proc. 2: I.R.E., 4, 23-32, 1946. Schelkunoff, S.A.,'Genera19Theofy of Symmetric Bi- conical Antennas, Jour. Appl. Phys., 22, 1330- 1332, 1951. Smith, P.D.P., The Conical Dipole of Wide Angle, Ji—uro A221. H1280, 42, 11-23, 19480 Eshbach, W'.D. (Editor), Handbook Lf En ineerin Fun- damentals, Wiley and Sons Inc., New York, 19 7. Handbook of Chemistr and Physics, 31st Edition, Chimical— Ru b ishing Co., Cleveland, 1979, 19 9. Martin, R. L., A Ten Centimeter Oscillator, Un- published M. S. Thesis, Michigan State College, 1948, 27 numb. leaves, 8 figures. Mann, F. J. (Editor), Reference Data for Radio En- gineers, 3rd Edition, FEderal TeIeEEo one ma Radio Corp., New York, 1949. Meier and Summers, Measured Impedance of Vertical Antennas Over Finite Ground Planes, Proc. Lf I. R. E., 21, 609-616, 1949. Ryder, J.D., Networks Lines and Fields, Prentice- Hall Inc., New York, Terman, R.E., Radio En ineers Handbook, McGraw-Hill Book Co. Inc., New York, I943. Montgomery C. G., Technique Lf Microwave Measure- ments, McGraw-Hill Book Co. Inc., New York, 1947. l4. Bronwell, A.B. and Beam, R.E., Theor and Appli- .cation of Microwaves, McGraw-Hi .Book.Co. Inc., New York: 1947. - . '-v' (.PJ‘ - 1Mfl‘?‘w* 'v O O ‘y‘ u . fl '- \ .27“ {L.{L ‘ #3} .- JP". "3"" ‘0‘ 4' t. - “31:" V “3" 4 I'. "fl-bu}: ’ ' I ..' ' x ‘ fiflifiiVJA " 7 . 8' _ - . '1' I L ‘3‘ . , ‘, sir: 4 " Q . v S v I 19' ‘tf'i’J-‘é .’n‘. b .‘_51',“ “1‘ ‘ . a . ’ .r. n ,a 1:. ‘ 1", u .I t,“ .)‘ '. .. . . A .w ;- .-, \ >-- , 3.571.» ,' ~. ., ' 3,; . J} .- ., sQf‘g ‘ . . 1 . -. -. it? ‘ ”' " ' fit‘ {1” 4“” ‘ . - t. ~ -‘ .s-e» . ‘- . . ’3; ' - x ‘ . ~ I a I It ‘. I no "e ‘ , H" - § .. c a .‘ ‘ J . . . ,.' . I' n I I. .I ' .I I; . ‘ I Wit uh a‘ a» 5' «s w- ”- 'axj' l-'Q . Y- ' ’c‘éo " ‘. , fr 4. O<" ._ _' . w I. . s )5 - - ; ' . - A" 7 . 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