Ultra High Frequency Oscillators Citation Haeff, Andrew Vasily (1932) Ultra High Frequency Oscillators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GAKG-W998. https://resolver.caltech.edu/CaltechTHESIS:09212010-105300778 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Electrical Engineering Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1932 Record Number: CaltechTHESIS:09212010-105300778 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09212010-105300778 DOI: 10.7907/GAKG-W998 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 6038 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 21 Sep 2010 18:42 Last Modified: 03 Oct 2019 23:48 Thesis Files Preview PDF - Final Version See Usage Policy. 29MB Repository Staff Only: item control page

ULTRA HIGH FREQUENCY OSCILLA~ORS Thesis by Andrew v. Haeff. In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California . 1932 . Contents . 1. Summary. 2 .Introduction. 3 3. Effect of the change of the position of electrodes with respect to the voltage wave. {a) • Description of the apparatus. 7 (b). Dependence of the amplitude of oscillations upon the position of the electrodes with respect to the voltage wave 9 (c). Dependence of the re quired mini mum grid current upon t he po siti on of electrodes. 13 (d). Dependence of the minimum grid current upon the v1avelengt h . 16 (e). Effect of the dissyrmnetry of the grid and plate circuits. 4 . Analysis of the experimental results. 16 20 (a). Distribution of standing waves along the wi res. 20 (b). Sffect of the grid to plate capacitance on the natural frequency of the oscillating circuit. 22 (c). Effect of lumped inductance in the Lecher system. 32 (d). Effect of' the distributed induct ance and capac itance . 33 5. Wavelength measurements . 43 6 . Energy measurements. (a) . Plate current. 47 (b). Thernocouple method . 49 (c). Abso lute value of energy output . 51 7. Dependence of energy output upon the emission current. (a). Limits of maximum energ<J output . 54 (b). Expe rience wi th water cooled grids . 57 (c). 1iinimum Vla.Velength as a function of tube constants . 57 8 . Conditions for maxi mum energy out_,ut . 60 9 . List of references. 62 (2) 1. SUlv'.'.MARY. The performance of three electrode tubes operating on the Barkhausen principle has been studied. Several tubes of different design have been constructed and tested. One particular desien in which two extra lead s >vere brought out from t he g rid and the plate, proved to be especially advantageous , because it s :n ini ~·1um g rid current was small, and the wavelength could be varied continuously throughout the region in which t he tube produced oscillations. liormal vraves and v;a.ves of t he hicher orders could be produce·d . The effect of changing the position of electrodes with respect to the standing voltage wave was studied. It was found t hat tubes oscillate mo re easily if the electrodes a re p laced in the loop of the voltage wave . This study was made possible by the design of a special tube and the use of a special circuit . 'l'he de_:iendence of the minimu.'!l gri d current upon t he v.ravelength has been studied and it was found. , that t:.ie t!leoretical relation lg =k.A 3 . is only ap1,roximate: the coefficient "k" increases as the wavelength decreases . The variation of t he energy out9ut vn th t he e~ission current was studied and it was found, that the maximum energy out1mt is / obtained ~1en the emission current re aches its static saturation value . Tests have shovm. that tubes with water cooled g rids have characteristics similar to those of tubes having grids cooled by radiation. (6) 2 . Il?l'RODUC'.;:'I01'I. J inc e the clisc overy by Barkhausen and Kurz in 1920 (Ref.l) of oscillations produced by a three electrode tube in v~1 ich the g rid has h i gh positive potential, a considerable amount of' wo rk on t he Barkhausen effect has been done by investigators in Germany, Russia, France and in this country. ,_._,_ very com:;:-Jlete outline of t he work done pp to 1930 was published by H. E. Hollmann (Ref . 2 ). This article contains also a very comp lete list of references. To make furt her discussion clearer, t ho essential features of t he Barkhausen oscilla tor will be considered here . Tho funda.-inental circuit is repr e sented in Fi g . l. The g rid is connect ed to the positive terminal of a D.c. generator or battery . -I,. p 6 F L,,. -4 Fzj. I. The l)late i s he l d at zero (negati ve end of the fila::i.en t) or neto,utive J.Jotential. ':.'he oscillating circuit, usually consisting of t'i7o par a llel u ire s, is c onnected. to the £;,rid and to the )late . S:!ie ci rcu it is te r.ni nated by a c ondenser "B", vmi ch for the high frequency used represents practically a short circuit . High frequency choke s are p laced in each le.'.ld , connecting the ~ube with t h e volt age su1)pl y . ( 4) Barkhausen found_ that the frequency of oscillations corresponds approximately to the frequency of electronic oscillations around the grid (Ref . l). This rule was later extended and modified {Ref.3,4) and can be stated as follows: The rnaxirmh!n energy output is obtained when t he natural frequency of the oscillating circuit corresponds to the electronic frequency or its multiple. \!hen the frequency is equal to the electronic frequency, the waves are called normal waves; when the frequency is some multiple of the electronic frequency, the waves are called high order waves (1st order, 2nd order, etc.) . The experiments of Kroebel (Ref.5) demonstrated that a considerable increase in the output was produced if the plate was made negative. ~...,aximum energy was obtained when the p late current was reduced to zero. Gill and i .. orell {Ref.6) were the first to observe the dependence of frequency upon the tuning of the external circuit. The so called "pure" Barl<.hausen oscillations, the frequency of which does not depend u1)on the tuning of the circuit, were later found to be produced only in exceptional cases. It is thow:;:ht that "pure" B-K oscillations occur only if there is a sharply tuned circuit inside the tube, wnich is formed by the electrodes and the leads inside the tube. During the present investigation in no case "pure" B-K oscillations were observed. '.i:he effect of symmetry in the arrangement of electrodes was studied by ..:,.. '.Jainberg {Ref. 7), w110 has shovm that with tu.bes havine the fila..'11ent or the grid displaced from the pos ition concentric with the plate, no waves of higher orders could be obtained, and that in general, the dissym'11etry re uuced the out1mt considerably both for normal and for hieh order waves . ( 5) The exiJerimental study of Barkhausen oscillators was undertaken with the purpose of fincling means of increasing the energy output in the shorter wave region. Ear ly in the course of investigation it was observed that t he capacitance between the electrodes and the wires forming the oscillati1-ig circuit had a consiclerable influence upon the oreratio\ of the tube . The distribution of standing waves along the oscillating circuit was then studied and. it was found that the smaller the ratio of the capacitance between the electrodes to the capacitance per unit length of the oscillating circuit, the easier it is to produce oscillations. To be able to displace the electrodes with res:pect to trie standing wave \'Ii thout cletuning the circuit, a S}Jecial tube was constructed . The results obt ained with this tube wi ll be described in the next paragraph . Since the principle of operation of the Barld1ausen oscillator differs radically from that of ordinary oscillators, special tubes were constructed. Part of the work i.ms been done with tubes connected. _permanent l ;/ to the evacuating system , consisting of a fore pump and a two stae;e mercury diffusion pump. The pressure was measured by means of a l.~acLeod gauge . The pre ssure of 10- 4 to l0- 5 rrnn.Hg . was usually maintained, between whi ch limits the operation of the tube was not affected by change s in pressure (Ref.8). The tubes \'1e re made so that they could be easily opened for re placing the filo.ment or for changing and adjusting: the electrodes. Several tubes were made wni ch after a thorougi1 baking and heating of electrodes were completely sealed off the pump. In these tubes an extremely hard vacuum was obtained, the :po sitive ion current at :naximum loading (about 100 ma , 800 volts,) being only a few microamperes. (6) Only cylindrical electrodes were used, the filament and t he grid being pl aced concentrically with the pl a te. P!llre tungs ten fils.ments we re used. Grids were made of tungsten wire wound in t ne form of a spiral. Tungsten was used for grids, because the heat produced by the electronic bombardment is sufficient to me lt metals with lower melting point {grids made of nickel melted rea4ily even at low loadi ng ). A 500-volt D. C. generator supplied the positive volta[e to the grid. The voltage was varied by means of a potentiometer. A 45-volt 11B11 battery was used for negat ive bias on the plate. A 6-volt storage battery was used for heating t he filament . The oscillating circuit usually consisted of a Lecher wire system on which standing waves were formed . The reflecting condenser bridge s were so designed that their natural fre quency was considerably above the frequency of the circuit (Ref.9). The methods used for measuring the wavelength and the amplitude of oscillations will be described in a later paragraph. ( 7) 3. Effect of the change of the position of electrodes with respect to the voltage wave. (a). Description of ap-oaratus . Fig . 2 and Fi g .3 respectively show the gene ral view of the apparatus and the construction of the tube. Fig .4 represents a schematic di ag rfu~ of the circuit. As can be seen from Figs . 3 and 4, connections to the pl a te and the grid are brought out at both ends of the tube, and are joined directly to the two oscillating circuits L1 and L2 • The filament leads are bent at right angle to the oscillating circuit Fig.2 . ( 8) Fzj.3. c; F2j. 4 . ( 9) and are connected directly to the chokes pl aced close to the tube. The Lecher system formed by the two circuits· L1 and L2 , is short circuited at the two ends by means of two condenser bridges 01 and 02. The grid and plate supply voltages (D.C.) are delivered to the circuit fhrough R.F. chokes and the connections are made at the ends of the Lecher wires 1 1 beyond the bridge c1 , where no standing waves are present. b). Dependence of the amplitude of oscillations upon the position of electrodes with respect to the standing wave. The following effect has been observed. With the voltage and the grid current constant and the bridges o1 and c2 moved in the s~~e direction along the wires so that their separation remained constant and the natural frequency of the circuit unchanged, the plate current was found to depend upon the position of t he bridges. The constancy of frequency was checked by means of an auxiliary Lecher wire system used for measuring the wavelength (see p.43). The results are shown on p .10. On the diagram the plate current Ip is plotted vertically, and the abscissar· represents the position of the middle of the oscillating circuit. The center line of electrodes is marked by a dotted line 63 cm. from an arbitrary zero. A marked decrease of the plate current occurs when the center line of the circuit is displaced from the center line of the electrodes. In other words, the plate current decreases when the A.O . voltage across the electrodes is less than the maximum A.O . voltage in the oscillating circuit.This result has been expected since the oscillations (11) of the electronic space charge which cause the tube to oscillate, are produced by the A.O . voltages between the grid and plate . Thus, the conditions for oscillations are most favourable when the electrodes are p laced in the loop · of the voltage wave . The same effect was observed for waves of different orders and for different wavelengths. For shorter waves, as for example for 30cm., the sharpness of the peak is very marked, and shows not only the importance of proper tuning of the circuit but also the necessity of placing the electrodes in the loop of the voltage wave. The method of doing this, as described above, using a special tube, is simple and effective, and of particular importance for short wavelengths . The curves on p.12 show the change of the plate current as a function of the displacement of electrodes with respect to the position of the loop of the voltage wave expressed in percent of wavelength. It should be noted, however, that the shape of these curves depends upon the ratio of the grid current at which the tube is operated to its minimum value at which the oscillations begin. (13) (c). Dependence of the reguired minimum grid current upon the position of electrodes. The importance of having electrodes in the loop of the voltage wave can be demonstrated in a striking manner by observing the minimum emission current at which the tube will oscillate . With constant grid voltage and frequency, this minimum grid current was observed for different positions of the bridges c1 and c2 , the distance between them being kept constant. The results are shown on p.14. The minimum grid current occurs when the electrodes are in the center of the oscillating circuit, that is, in the loop of the voltage wave. T'ne rapid increase of the required minimum grid current with the displacement of the electrodes from this center shows the i mpo rtance of the proper tuning of the circuit, especially in the region of short waves. The change of the grid current with t he electrode displacement can be approximately expressed by the formula: where lg = the required minimum grid current for wavelength ;i , :1 l g'11in . ~l = minimum grid current for Al-= O. =the distance between the loop of the voltage wave and the center of electrodes, ) =the wavelength, and c) = coefficient depending upon A • The approximate value of this coefficient is <) = 1000, so that for a displacement of ,,1f /l -= 3,o' , the minimum grid current is t wi ce its value for the central r)osi tion of the electrodes. (16) (d). De·oendence of the minimum gri d current u pon the wavelength. From t he diag ram on p .14 it can be seen that the minimum grid current (poi nts mar ked "a") increases with decreasing wavelength . Minimum grid current as a function of wavelength is :plotted on di agram 5, p .17. In the middle region the curve can be approximately expressed by the followin equation: L. <.//Ylf/-1 This form of the function agrees with the one deduced from the theoretical considerations (Ref.10 and 11). The experimental curve, however, deviates from the theoretical curve especially in the region of short wavelengths, where the increase of the grid current is more rapid. In that region the i mportance of having the electrodes in the loop of the voltage wave is obvious, since for short wavelengtns the minimum grid currents are high and any means for reducing the grid current are very desirable . (e). Effect of the dissymmetry of the grid and plate circuits. Due to a very rapid increase of emission current for shorter waves, it has not been possible to obtain waves below A~ 25 cm. with the tube used in the experiments described above . This may be due to the dissymrnetry in the arrangement of electrodes, as at high emission the filament was slightly sagging . However, another peculiarity was also noticed, namely, the distribution of standing waves along the circuit was not syrrnnetrical. The position of nodes on the plate wire "P" did not exactly coincide with the nodes on the grid wire "G", nodes on "G" being farther (18) away f rom the tube, than t he nodes on the "P" wire. Since t ile "G" and 11 ? 11 circuits are identical except fQr the alectrodes, t h is eff ect must be caused by the grid, having an effective length which is evidently several times its actual length. By talcing into consideration the grid to plate capacitance and the inductance of the grid spiral the distance between the bridges \'Va s calcula ted . for different wavelengths and the results were found in agreement with the experimental values. However , the effective length of the grid circuit was greater than the length of the plate circuit, when the tuning bridges of the shape shown in Fig .4 were used. Hence, if the grid circuit is tuned sharply to the most probable electronic frequency or multiple thereof, the plate circuit is not so tuned, and vice-versa. The fact that one of the circuits is not tuned is very undesirable since . this condition requires more energy ex-pended in the circuit to produce a given voltage between the grid and plate, than is the case when the circuits are tuned simultaneously. This effect is much more pronounced for shorter wavelengths , and may wholly exp lain the rapid increase of the grid current with increasing frequency. To avoid this difficulty, the following remedi es can be used: (al Separate tuning of the grid and of the pl a te circuits, (b) Change in the construction of the grid by placing a supporting bar along the grid and welding it to t he grid, thus eff ectively short-circuiting the grid, so its effective length would be equal to that of the plate. The first method has been used by others for standard tubes with apparently good results (Ref.3), although the importance of the ( 19) separate tuning has not been explained. Por the special tube, described above, which has two circuits on either side for the pur 2ose of placing the electrodes in the loop of the voltage wave, the first method of obtaining synnnetrical "P" and "G" circuits is rather inconvenient. ~L'he dis1)lacement of the bridge C..t-11 with respect to Cgl (see Fig . 4), would affe ct the distribution of waves on 11 G0 , whi ch is undesirable • ..:',,nother disadvantage is that the distribution would still be unsymmetrical even i f both P and G circuits were tuned. J;nother modification of method (a) would be to make the 11 ? 11 and The "G" circuits intersect at right angles to each other (see F.5), but this would considerably increase the radiation resistance of the circuit. Fig.5. The second method , (b), will make it possible to obtain a symmetrical distribution of waves throughout the length of the circuit with the use of simple condenser bridges . At the present moment a special tube is being built with particular attention being gi~en to the symmetry of the electrodes inside the tube, and of the grid and plate circuits. (20) 4 . Analysis of the experimental results. The following analysis is an attempt to explain the very rapid increase of the grid current with shortening of the wavelength . The ex-perimental results presented, indicate that the minimum grid current depends upon the wavelength in the following manner: where k 1 , k 2 and k 3 are constants of the tube . This form of the equation has been obtained from the analysis of the curve Ignin. shown on Dia . 6 . The theoreti cal value of Ignin., derived on the assumption of the same effective .A.C. voltage throughout the length of the grid, (Ref . 10 ), differs from the above in that k 1= k3 = O. Hence it is desirable to analyze the conditions actually existing inside the tube, and to axplain why the theoretical ass$tion is not valid . Another object of this analysis is to show that the observed rapid increase of Ignin. with the displacement of electrodes from the central position with respect to the voltage wave, is actually caused bJ a decrease in the effective A. C. voltage across the electrodes and is not due to the detuning of the oscillating circuit ~ (a) . Distribution of standing waves along the wires . The distribution of waves along the wires forming the oscillating circuit is represented graphically on p . 21 . This distribution was found by determining the positions of voltage nodes and by wavelength measurements. Only the voltage W"dVe is shown . The standing (22) current wave would be displaced a quarter wavelength from the position of the voltage wave , because the d.Wlping is very small . Diagrarn 6 shows the distribution a long the grid wire only . The nodes on the plate wire, however , practically coincided with the nodes on the grid wire . (b). Effect of the grid to plate capacitance on the natural frequency of the oscillating circuit . The oscillating circuit consisting of the Lecher system, short circuited at the two ends and with the tube placed in the system, ,c. can be snematically represented as is shown in Fig . 6 . (-----____,,,.. .S. C . SC. .L., " c Fig . 6 . C0 represents the total grid to plate capacitance, L and C are the inductance and the capacit ance per unit length of the circuit. If 11 0 11 denotes the voltage between the wires at the point 11 0 11 of the system, the following d.onditions must be satisfied if the circuit is to oscilla te at its natural frequency ( the effect of damp i115 is here neglected): +I =O "j . (23) Eli:ninating e, 1 1 , Iz and 1 0 from the above equations, the following relation is obtained between the constants of the circuit L, C, and C0 , the lengths 11 and 12 and the angular frequency For two par a llel wires the following relations can be written: ~ / = -<., 7/'T r- ; w = 27T..r / = P' _) ,c;;c ......, ,- •_- ..??T/= 27/ v,,} r,(..~ Hence, the natural frequency of the circuit can be determined from the follo ~ing equation: J!'or special cases the above formula can be some vhat si:n11lified, as follows: Case 1. C0 ::: O. . {2) Case 2. 1 1 = 12 =1 (".,. .= - · c ...... f3J (24) 11 + 12 Case 3 . -=A =Const. To check the application of this sim:ple theory to the case of a tube :placed in the middle of the oscillating circuit, the value -to. was c alculated from the experimental results for different of values of A. The experimental data is shovm in Table I below. I. TABLE rf'c,., 109 102 92 82 60 48 38 30 Ac,,, 40 35 30 25 46 77 58 33 . 5 i';c,,., 20 17 . 5 15 12.5 9 26 19 16.75 t_ 20 17 . 5 15 12.5 37 51 39 16.75 •c1n Calculated values of 82 and 30, and formula ..go. using formula ( 3) for ;J =109, 102, 92 , ( 1) for ,1 = 60 , 48 , 38,cm. , are s.D.own in tables II, III , and IV. The values of in the region = 109 to 60 cm. of ..2.o c ) ..g.u. are almost equal for wavelengths For shorter wavelengths the vabe increases . '.i'his increase can not be attributed to inaccuracy of measurements but is probably due to the fact that at shorter wave lengths some factor other than the cap2.ci tance between t:i1e electrodes 1 lays an imvortant part , as for instance, brn inductance of' the grid spiral, which has been entirely neglected in the above discussion . l,Otwi thstandine the fact t!1at the theory- presented above is not directly a._9 licc:.ble to t11is case, the derived formulas will be used 1 (2o) TABLE II . ·- d _t. /l 109 t -~r ((,-t/1121/ ,,; .£ c_Ctf.h C-9fT" . 18035 66 . 0° . 445 . 0287 15 . 5 102 . 1715 61.7 .539 .0308 17 . 5 92 . 1630 58 . 7 .609 . 0340 17 . 9 82 . 1525 54 . 8 . 705 . 0383 18 . 4 30 .5490 197 . 5 3 .17 .10 47 30 . 3 /l TABLE III. d ft A -t2-.'17' u~'IT ) ) 4 ;? /,.271 ;/ c;~d,;1T" {,~~hr -r 2'// {#f,{ ,2-q -) c,. c ,A 60 . 150 54° . 726 .617 222° l.llO 1. 836 . 105 17 . 5 48 . 542 195 3 . 73 1.062 383 2 . 35 6 . 08 . 131 46 . 4 38 . 500 180 OQ 1.027 370 5 . 67 O<:> . 165 ~ TABLE rv. ;z -cc.. 109 15 . 5 102 17.5 92 17 . 9 82 18 . 4 60 17 . 5 48 46 . 4 38 <><::> 30 30 . 3 Ta6/eY c.. .277' _ /, 0 ;J , cc .. . ;; 277' - 5: 0 - , c.,_2;r _ 2 o c c ;I . ~" · ~r= IC'.O /,r~ .t;+~ !.:.% !:. .277' ~t~b /-{;t- ;Jt:21T ;1ft%" t+~ k'-C.,t- ;Jt!/ 21T )~z. T2 .f=-'6t: /lit,21T /IL-/, , T% /~-Co~ ,,/t7,2ff /1t't ,%" I+.!{% ;; " /I T~ ;J /I ,f'(J ..7. 17" - <><> .f'p -<'.F/ .J' ti /.88 ,?~ 15/ ..z 12>7 ,.;,;r (I " () fl.o -1.3/{ 2..376 . .JfS' ~-.J f' -r1.,;y .J'.676 - ..J2.i" /..?.?.> . b"'Y6 /'1.3 -ri1.3 ·7'1.r /.(' . .S .J,7,> " /~ .ff".Z. -7-26 /0 . b2# /.375 .J . ./If' J.o77 +~ " .zu (J n . ., +~ () () r:.>J' f"f":J'J' G".?7~ . / s-r Lf'7 jp . ., f"""' ~ c> j""tJ.u 'j'; .77 1/.37~ • 17~,J! /, 7"" ~/. 7" .2..3..?f ·~"7 ~-'YJ ,11.~J .f':.J2r , / J'.> 2.1r .12.j.r /tJ.3,i ~ . C?fl /,Pf .J/. r;/ ,yi;z. 71.1 .12.33 .r: i/11 (1 • /fc; .l. 1 2. ,tJf f /, J'7 2& .57 •7.> ·f77 / .J...> .J~r /.q..s . S'.fJ' /.rr 2J',S:r f',~7.r ,,; /ti ?.J.> L1.JJ t7.r • / 4'2 /. &2 2 /..: z. .M6 /ti. ~ ~,--;,., 'T.27Y ·.?.lo .J. rfb /,./. ~~ ;?:qy . l tJJ 17" l~-71.J .l. f 2f/ . 26J' .,,_ z 7 /~.;>l ff. l.2j/ , II'/ / .F'2. //, £'2.. . !t/..J 2. 2 ,r 72J' /," d -f; +~ ,?_{/ (J U /. 27f" ..Z J'. I i, / (1 ,(111(1 tf. l\:) ~f..z3 m l,.,. .'n / 1-1 . ;n/>-?. f n/n, J~.z 2 5,(1(1 12. 1"' {. :l Z. tJ1 ~ (26) to f ind hm'l much the natural frequency of the system ehanges if t iie condenser C0 is d isp laced from the middle position. :b'irst, the relation between 1 1 =j: 1 case p . 23 . and )::: const . 2 + 12 'I'his can be found from formula (1) , The results are sh mvn i n Tables V and VI , and are re p resented g r a11h ically on Diagrarn 7 . 11 11 and 1 2 will be found for the is e reater when In general, it can be said , that the sum 1 1 :f; l ,_ than when 11 = l~ . In the e xperiments of this thesis, the va lue of (1 1 + 1 ) 2 has been k e p t constant . let us find how much t he vrv.veleneth will be cha nged if the condenser C0 is displaced from t he central position . Formula (1) can be written as follows : 1 1 + 12 = 21 0 = const . of 2 x CotanJ 271' and the suJn Gf~ 41 ' Cotan _rl11, as functi on s of J_ .,,, ,l;r- 1 1 -= 12 (or t)t;=O ) , t he n fo r a g iven va lue of can find the value of Now, if we make change to /')\ ]" = 13 .. from t l-1e conditi on t hat .-1 • and """ vn 11 chan[;e to , fo il o···s · o( - 2C 0 c ·},, =~o, we tf ,.l71 :::-d., • A will Al 0 , the valu e of "< Ao so that °'•:::: T . 0 . 'i'he corres) ond1n_9 f=~·--;:d. · Knowing the v alue of r we can find fro:n c u rves on Dia . 8 the value of 3.S 12 = 1 0 1 1 = 1 0 +.A lo , and value of ~ wi 11 be: to ex) ress ,t, k~f;l?f.are ;il otted on Di agram 8 . If )., is t he wav elenct h corres1;ondine ) to tlie ca se The values f, and then tlie va l ue of f: f-f .. . e v:ant t in terms of the or i ginal waveJencth A,. ; this can be done ..6~• = ~P - .. · -;\ " • Ao A /\o = APo .J. T · "'o '.i:'hus assur:iing t he v a lue of' o<. , ·Ne can fin(:;_ L.e vc...lue of 'vile dis_1 luce·::e11L Ile., • .37 t~1 is :·ie thod the table VII has been com1.ut er" and (27) TABLE c.. ,~ VI. ,,,,7 t' 2 ?/' ,.L /! .o 1 . 57 . 250 .2 .1 1 . 475 . 234 .4 .2 1 . 370 .218 .6 .3 1. 280 . 204 .8 .4 1 . 190 . 189 1 .0 .5 1 . 107 . 176 1.2 .6 1. 029 . 164 1. 4 17 . 960 . 153 1. 6 .8 . 896 . 142 1.8 .9 . 838 . 133 2. 0 1.0 . 785 . 125 2. 5 1. 25 . 675 . 107 3. 0 1.50 . 587 . 0935 3.5 1. 75 . 518 . 0826 4.0 2 . 00 . 462 . 0733 4. 5 2 . 25 .419 . 0668 5.0 2 . 50 . 380 . 0605 6. 0 3. 0 .320 .0508 7. 0 3. 5 . 277 . 0440 8. 0 4.0 . 244 . 0388 9. 0 4. 5 . 218 . 0347 10 . 0 5. 0 . 198 . 0316 c ;J Cc~_t..zr o.o TABL:S <X / / 4' / ~=;; / i::f/ J" ;8~;-0 "/ (30 ) VII. ,F di ,dI,, Af' <Y / -.::.-·J/ «., 4~ /JD 1.05 .953 .1858 .255 .069 6.58 1.10 .909 .195 .285 .090 8.17 1.15 .870 .204 .310 .106 9.22 1.177 .850 .208 .333 .121 10.30 1.25 .800 .221 .380 .159 12.70 1.33 .750 .236 .430 .194 14.50 1.41 .707 .250 .500 .250 17.70 2.11 .95 .132 .171 .059 5.60 2.22 .90 .139 .209 .070 6.30 2.35 .85 .147 .225 .078 6.63 2.50 . 80 .156 .255 .099 7.90 2.86 .70 .178 .313 .131 9.16 3.34 .60 .208 .380 .172 10.30 4.00 .50 .250 .500 .250 12.50 3.16 .95 .098 .126 .028 2.66 3.34 .90 .103 .148 .045 4.05 3.54 .85 .109 .168 .059 5 .00 3.75 .so .116 .187 .071 5.68 4.28 .70 .133 .233 .100 7.00 5.00 .60 .155 .285 .130 7.80 6.00 .50 .186 .351 .165 8.25 "' ~ - {'.,.!JI' .,- c',.J.,. :Jo ,/., /, =)" =/.77 ()/":: 2. () 13,,=,/25' oio=3.tJ ;S.=' (}_93 (32} the curves.on Diugram 9 represent the chu.nt;e of -.vavelen[th ~ \Jith I ~ e" for ti1e c ondition .i."or lart,e ,\ " 211' tne calculated values of the wnvelencths decrease 6 c.C. · Ao values of quite ra_Jidly with the disp l acement . ~he experimental results, however , increasing s~'low that the wavelent:;th is slightly instead of decreasing when the electrodes are di s~ilace<i from the central !>Osi ti on . This effect can be ex~>lained only by the presence of in<luctance as well as c e.1.'aci tm1ce in t110 :-:1icl<lle of tne circuit . This inductance is evidently- the induct~1nce of the .'.:.,l'id s~iral , :::.nd. its ei':i.'ect will be considered in the next (d} . =:ffect of lumped inductance in the Lecher system. If inductances Lo (see l<'ir; .7) are p l aced in each wire of a short circuiteci lecher system , the natural frequency of the circuit s. ~. 1 ~ I/ - c L., L,, f-:::f· L,,.. I,.. lu -~ ,L, c fzj . 7 can be found from the followint; conditions: ~ = 1:/·jf f-a/-7 £; IZC" w ez = -4..//f t-a n ~ yZC tu ~-e2 =;·z-..2L.,4.J :r -= -..r.. / .I,/ff CC/nL;ffe"' - Iz.~//F--Cctn t; IU- ~ /·z2L,, tv r!.}. ffew -/ ·12~ c.u ..z;/If tan t; ffe ~ = - .z/1 ·,!Z:z'Pl',H re: 1 .. ( 33) ill• Effect of a circuit of lengt4_ la, having distributed_ capacitance C0 and t h e inductance _1 0 ;Jer unit length, o laced in the Lecher ~~tern . ~he circuit is re~resented i n iig.B . ---- ~------ /,,___, _______ ~ ------ Fzj.8. '1.'l1e :t'o llowinc ec;_u.c.ticns cu.n be u sed t o find tlie ns.tura. l frequency of the circuit : c; =- .z;/·/§ /-t:? /7 t: /IC U' .. . (7) ~=~/·ff t-c/n /{tLC U/ .. . (8) /f! f//7 ~ ~ e2. = ~ L'cis ~ /Zj,, ~ + ./..Z: ?</ . . . . . (5!} c; = eL us~IZCo CV+J·.:z;.1~: J/n ~ IZZ cu . . . . . /lrj Jubstitutill[, (7) and (G) into (9) anC ( lJ) : (34) or, : : a iJ:linating I1 and 12 fro:·:1 ( 13) and ( 14) we [e t t.D following rela tion l;at· :eell :. ,o constants of tne circu it and t !1e frequency: t~n ~ }7/~n f,_ ,)-;;-/;- Cs'e',,!L(:. wl= L'-C/~ 2-tf42."' + ) ,J 1· +Jg.J,;, 1:12;<:, /f n: o- UJ "'J.C.L f;s-t; q,, 7""',/ "f 27 ,?;r +ifer nJ'".!!7·- :..·v/};N;/'ZZ,., -;fi[/,;., kf4 t£fi. w !:-,-t l'ZG ~ • . /Tern f 2r+Z7,_,; Lw;J. .. . .... . f?) # ~o check the correctness of tnis forr'.lulo., •.-,,_ '.ill cor s i c:er several s·,)ecial cases and com11a.re t .:ie resu lts with fornulas derived in the :•1recedii1g par agra~;hs . (35 ) his is e'd_uivcile1it to for:nula (1) on p . 23, where t 1"c tot:;;.l ca_1acik..nce 1 ·.;. 1 0 C0 was denoted bJ C0 . , - .... ·11.:Y This is equivn.lent to fonnula (6), p . 33, \here 21 0 , the total ir~d.ucto..nce ( 36) A co.se of particular interest to us is the following . Case 3 . 11 =lz - ,;z;c /z;:t , , ra .z w.. "'-' ; j,~/4"$ ?I /., f., -fhc> )h,;f ""Jel"? c~ o "z +/Ff {]fa-,_, / .. #:(i w; /, "/?/s ,4 7'je_ /,:/n,'/ .2 C,.,4 ... t':,_sx-/ == - kljt!-h .Le> -:? o ~-------,,,l> (;,f..,r - LSC'..,Y ,,,_ .s-~ .y z.f',,;_.z£ ;- Zt:1.n % .<~~~~ .z z z... . . .(2 o) .. t7 z -+ ,;T;i:" L!z'a- # I' ?;;Z ~ d;C w . . . . . p /) 2. (37) Now , using equation (21) let us calculate the value of ~ C....t.. from the experimental data shown in Table I, p .24, and then compate it vnth the theoretical value calculated from the dimensions of the circuit. To do this, let us rewrite equation (21) in the following fonn: where "v" is the velocity of p ropagation of waves along the paralle l wires (very nearly equal to the velocity of light i f the da.111ping is small). Denote the value ;§. Cran f f /i:c,27Ttr:::: ....( , t:i1en: = :t-~n;Jf 27/ . . . . . . . {22_) If we l::now "l" and '!1 " for two then: c,tqn F &zp.n ,,J~ from which "x" can be calculated, and then, if the value of "x" is substituted i nto ( 22), the value of /g can be calculated . However , this method is not ac curate , because a small error in measurements of ''l" or •/l" wi ll result in a considerable error in "x". We will use another method . We know that for 1 ;/-30 cm., =O; hence we can write from equation (22): Cotan .X = 0 · x = l.57 ~= 1. 57 x 30 = 47 . 2 ) ' Using this value of "x" the value of ,;:z;-;;- has been calculated fC:Z by means of equation ( 22 ). The results are shovm in Table VIII, p . 38. The average value of IN is about Let us now calculate the value of o. so . /g_ from tl1e di~nonsions c;..L. of the circuits (see Fig.9 and ¥ig . 10). ( 38 ) TABLE VIII . ;? 109 102 92 82 60 48 30 ~ 18. 7 16 . 2 13. 7 11 . 2 6. 5 3. 0 0 _£2'7T 1 .68 . 998 . 937 . 859 . 680 . 393 0 f'q/7 , / 2 1'7' 1. 868 1 . 55 1 . 36 1 . 16 . 809 . 414 0 /l . 43 . 462 . 513 . 576 . 785 . 983 1.57 {"oz'a-.n; 2 . 17 2 . 00 1 . 77 1 . 54 1 . 00 . 666 0 ~ . . 86 . 775 . 768 . 755 . 809 . 620 /1 ,.... ( 39) For t wo parallel wires, the capacitance and the inductance per unit iength are found from the followi11£ formulae: - - - d-· - -.i Fz5 . 9 . where p = 8 . 85 x lo- 14 and -8 /= 0. 4xl0. Substituting the above figures and the dimensions of the circuit in fonnulas (24) and (25), we find: -/-fl' C = _-h_r_. . _6'_.B_s-_,.._/_?'_ L.To check: (o./rj. The grid to plate capacitance can be calculated approximately if we assume that the plate and the grid form a cylindrical condenser of radii rp and rg. ~hen: -It' /' L. =271"? - 27T'-¥8J'5'.</() - ~7(5°..f/il1"7a'r. ··(ib) &¢ 'l - -t''}f.J.F · "' /j . Since the length of the plate is o I;= J.5" J eq_ual to 1 0 -::::: 2 . 6 cm . , this gives as the total grid to plate capacitance: Fzj. /(} . the ratio e/>7 0 0 10 = 115 x l0 - 14 farads, and 0§10 However, the experimental results interpreted on the basis of · (40) the assumption that the grid inductance is negligible, which is valid for long wavelengths , gave tne value of C:.t'., c = 18 . There- fore we will take C0 equal to: C0 :=;; 90 x lo- 14 far . /cm. Hote: Formula (24) gives the value of 0 0 too small because it neglects the end effects, which tend ~o increase the capacitance . To calculate the effective inductance of the grid spiral accurately is difficult, because it can not be treated as an ordinary inductance , since the current is dif:t'erent in different parts of the grid . \lhen the loop of the voltage wave coincides with the center of the grid , the current is positive in one half of the grid and negative in the other, thus ehe effective inductance of the grid spiral is diminished (see Fig . 11). It seems reasonable , then , to take as the value of the inductance of the grid per unit length the inductance of one turn times the nunber of turns per cm. z-r = . 05"' Ch? . io=Z.6ch7. The inductance of a single turn of radius R of wire of radius r, is expressed by the formula: cm. Or, since the value of •••• • •• ( 27) "!!/P!- is small: • •••••• ( 27) ' (41) r = . 05 cm., we get: Substituting the values of R ~ .25 cm. and The grid has 10 turns yer cm., so the inductance of the grid per centimeter: 1 = 6 x l0- 8henry /cm. In the above theor..r a symmetrical circuit has been asswjed. Therefore we must talce as the value of the inductance per unit length of the circuit 1 0 (Fig.8), L0 =1/2 = 3 x 10- 8 henry/cm. Using the values of 1, C, Lo and C0 calculated above , we find : Considering the roughness of approximations made in deriving this value, the agreement with the experimental value (0.8) is surprizingly good . The value of x = f" /L:(', ./-;rzr (see p .37) for the above values of L, C, 1 0 and c0 , becomes: 2 ·6 x 2 1T' x 3 x 10 10 / 3 x l0- 8 x 90 x 10- 14 x' = -yThe value found on p .37 vvas --t' ..Y7. 2 -=--:::: x = 47.2. The ratios: ' 8 0 and indicate that the true value of = 40.2 , G_;7 /./~ L0 must be: 1 0 ~ 3 x 10- s x ( 1.16 l2 <== 4 x 10 - 8 henry I cm. ( 42) The above presented analysis gives the explaination why the natural frequency of the circuit remained constant when the tube was displaced from the central position: the inductance of the grid neutralized the effect of the grid to plate capacity. Analysi ng the distribution of standing waves on the wires, shown on p .21, it can be concluded that when the frequency approached J~ 30 cm. the effective length of the grid was equal to half wavelength . For this wavelength, then, the A.C. voltage a~p litude was different for different positions along the grid. The average value of the voltage amplitude on the grid was less than its maxinrum value, while for longer wavelengths the A.C. voltage was very nearly the maximum throughout the length of the grid. Since the A.C. grid to plate voltage is the factor which produces oscillations of the space charge which supplies its energy to the oscilla ting circuit, the rapid increase of the minimum grid current when the wavelength approached ~ =- 30 cm., can be under/stood. A short circuited grid as a remedy for this undesirable phenomenon , was mentioned on p . 18. Comparing the circuit shovm in Fig.4, which can be called the "double" circuit, with the circuit shown in Fig .l, it can be said, that the average grid to plate voltage will be higher for the "double" circuit than for the "single" circu it, which will result in a greater a."Tlpli tude of oscilla tions for the sa."!le grid current for the double circuit. Another advantage in the use of this circuit is the possibility of studying the distribution of standing waves along the electrodes, which will aid in the study (43) of the mechanism of· the generation of Barkhausen oscillations. It also gives a simple method for the suppression of normal waves when shorter waves of higher order only are desired. 5. Wavelength measurements . The first evidence of the presence of oscillations in the circuit is the appearance of the plate current. ~nis current flows in the direction such as to charge the negative plate battery. This can happen only if the electrons gain more energy in the space filament-grid than what they loose in their path from grid to plate. If there were no oscillations the energ~ on the two sides is the sa.'1le and consequently no plate current flows. If the bridge "B" (F.l) is moved along the wires while the grid potential is kept constant, the grid current will be a maximum when the natural frequency of the circuit corresponds to the electronic frequency or its multiple. The distance along the wires between the maxima of the plate current will be then equal to one half wavelength . This is one of the most convenient methods of measuring the wavelength. If the p l a t e current is p lotted as a function of the position of the bridge , as shown on Diagram 10, and the waveleng t h is determined from t he curve, t he accuracy of this method is quite high ( a few millimeters). The above described method was used together with another, which consisted in bringing close to the oscillating circuit an auxiliary Lecher system. Vlhen the natural frequency of the auxiliary system was the same as that of the first circuit, a decrease of the plate current was observed, because the auxiliary circuit then absorbed energy from the primary circuit. For small amplitudes of oscillations the frequency of the circuit for maximum output was found to correspond to the theoretical value of the electronic frequency or its multi ple, calculated from the dimensions of the tube. Scheibe's formula (Ref. 12 ) for cylindrical electrodes "Wa.S used for calculating the wavelength: In all practical cases the value of function f(x) rg/rf > 10 so that the is the same for all tubes and is equal to F(x) :::=: .620 . For convenience in using the above formula, it can be rewritten as follows: J =: /"ou~. If } .,!fff-J+J~/ J ~r ~=6 (~}// / J:/ /=.62o The value of the second term is plotted on Dia. 11 , p . 46, as a function of the ratio ~/dg • Knowing thms ratio the value of the cons tant "A" can be easily detenni ned from t he cu rve. The use of t h is me t hod make s the applica tion of Scheibe's formula pr a ctica l. The expression: can be called t he "wavelength constant" of the tube, lmowing which the volt age f or normal waves and f or higher order waves can be calcula ted from a simple formula: where "n" stands for the order of the wave . For small amplitudes this formula gives the wavelength within 5%. The explaination why this formula does not hold for large amplitudes can be found in Ref . 13 . (47) 6. Energy measurements. (a). Plate current. It was mentioned above that the appearance of the plate current indicates the presence of oscillations in the circuit. The shape of the curves showing the plate current as a function of the tuning of the circuit resembles the shape of resonance curves (see Dia.10). Let us consider more c&osely in w't!f manner the plate current varies with the change in the A.O.potential on the plate which is superimposed on D.C. potential when oscillations are present. In an ideal case, if the qathode represented an equipotential surface, all electrons would move in straight paths radially and approach infinitely close to the plate, then the plate current could be represented by a blocked wave, as shovm in Fig .12. The shaded area would represent half the number of electrons which passed the grid, and the average value of tho of the current would be independent of the A.O. volt age. However, in ' ;_____ ~ the actual case, the A.O. field acts on electro nE Fzj. 12. throughout the time of their motion f rom the ' !_. - - - - _J filament to the plate; there exists a drop of potential along the filrunent and the electrons have different radial velocities due to deflections from t heir radial paths caused by the grid spiral. ~ 11 t hese factors would tend to make the pl ate ·current de pendent upon the magnitude of the plate potential (A.O.). As a first approximation we would expect that the plate current will be proporti onal to the voltage ~p litude. This rela tion is conf irmed by the experiment. The current in an aperiodi' (49) circuit coupled loosely with the Lecher system is found to be proportional to the plate current. Since t he current in such an a~eriodic circuit is proportional to t he A.O. current in the oscillating circuit, it means then, that t he pl a te current is proportional to the a.~p litade of oscilla ti ons in the circuit. The curves on Dia.12, p. 48, show the plate current Ip , the grid curr ent I g and t h e current in the arieriodic circuit l o<. , as functions of the grid voltage Eg • The cur rent i n t h e aperiodic circu it has been ~e a sure d by means of a t hermoc ouJ> l e and a e:;a l vanometer 7 a s sh ovm i n .l!'i g . 13 . F'zj . 13. The cu rves on Dia .12 siiow t hat the shage s of the _)l at e current curve and and of the current in the aperiodic circuit are a like. Thus the mea surement of the p l a te current gives t he relative value of t he a..m111itude of oscillations. The grid current (Ig l follows t he (I o1. l curve more closely than does the (Ipl curve, but it is diff icu l t to mea sure accura tely small variations in the grid current caused by oscilla tions . (b) . Thermocouple ~ethod. As was mentioned above the relative value of t he intensity of oscillati ons can be measured by a the rmocou9le in the aperiodic circuit. The absolute value of the energJ can not be found by t h is meth od, because the coeff icient of coupling between t he aperiodic circuit and t he os cillating circuit, and t he constant of the aperiodic circuit is difficult even to estimate, as they depend not only uvon the dimensions and distances of t h e two circuits, ( 51) but vary also with the frequency. The thermocouple could be placed directly in the oscillating circuit but this would introduce a considerable resist ance in the system and change its characteristics, which is undesirable especially because it is difficult to calculate the constants. Thus the thermocouple methods give only the measure of the relative change in the intensity of oscillations. (c). Absolute value of energy output. Some idea of what the absolute value of the energy is, can be obtained by the following method. It was shown that the plate current is caused by the A.C. potential on the plate. Onl11 those electrons will reach the plate which acquired more than zero energy in passing from the filament to the plate. This energy has been taken from the A.C. energy. W'nat becomes of this surplus energy of the electrons which reach the plate? They strike the plate and their energy is dissipated in the form of heat at the plate.'Thus the plate current represents loss of energy. This was first demonstrated by Kroebel (Ref.5). been obtained by the author. Similar relults have The curves shown on Dia.13, p.50, were obtained when the plate potential was made negative. Here we see that while the plate current decreases with increasing negative plate potential, the current in the aperiodic circuit increases. This happens because the energy which was lost at the plate is now delivered to the oscillating circuit . The plate loss can be measured as follows. The plate current giving the number of electrons per second which loose their energy at the plate is measured by the galvanometer in the plate circuit. The energy (53) distribution amongst the individual electrons must also be known to find the total pl a te loss. If we apply a negative potential to the plate , at the sa~e time keeping the A.O. p late potential the same, the plate current will gradually decrease . The negative potential at which the plate current becomes zero will represent the maximum energy of the electrons . The energy distribution will be represented by a curve shown on Dia .14, p . 52; by integrating this curve the total energy loss at the plate (WP} can be found. The plate loss is not the only loss. Some power is expended due to resistance and radiation of the circuit. The theoretical considerations of the mechanism of oscilla tions of the Barkhausen tube lead one to believe that there exists an energy loss at the grid. By the grid loss here is meant not the loss Ig Eg, but a loss similar to the plate loss due to the oscilla tions. For practical purposes the radiation loss may be consi dered t he only useful energy, so that it is desirable to elimina te all other losses a s completely as possib le. T'De ohmic resist ance of the circuit i s usually very small. The grid loss can be decreased b~r making t he grid of thin wires, althogh the grid loss can not be eliminated completely. The plate loss is decreased by a9pl y i ng negative potential to the plate. The curves on Dia.13 show the increase of the intensity of oscillations when the plate loss is decreased . The maximum of intensity is reached when the plate current is reduced to zero. With further increase in voltage the intensity of oscillations decreases because the oscillating space charge is farther away from the plate and the voltage induced by it on the plate is smaller. The ratio I ,;. /I._ 0 represents the increas e (54) in the amplitude of oscillations which can be obtained with optimum value of' the plate voltage. I f the plate loss is measured for zero plate voltage, the maximum energy output of the tube can be approximately calculated from the formula: VI (I c< p \I o\o )z 7. Dependence of energy output upon the emission current . a) Limits of maximum energy output. The above derived relations are applicable to cases when the tube is operated with constant emission current. The increase in emission current increases the intensity of oscillations . The curves on Diagram 15 and Dia.16 are typical curves re presenting the change of the intensity of oscillations with t he emission. T'ney show t hat t he oscillations begin only at a certain minimum gri d current. The intensity increase s very r apidly at first and then reaches saturation. This effect is quite important since it shows that the energy output of the Barkhausen oscillator can not be increased indef;ini tely by increasing the emission. The voltage at which the saturation is reached is approximately the voltage corresponding to the saturation current on the static characteristic. This then, represents the upper limit of energy which can be obtained with a given tube. This saturation effect can be explained by the screening action of electrons which do not deliver energy to the circuit but form a dense space chargg around the electrodes, tnus disturbing the oscillations. One interesting feature of these curves (Dia.15) is that the minimum grid current does not depend u _ion the plate voltage. Another (57) important point is that the optimum negative plate voltage is not directly proportional to the amplitude of oscillations, but seems to be also a function of the grid voltage and the emission current. (b). Ex.)erience with water cooled grids. Results similar to those shown on Dia .15, were obtained for tubes with water cooled grids . Figures 14 and 15 show the general view of the construction of the tubes. The saturation was also reached at voltages corres~onding to the static saturation curves. In most cases, however, the minimum grid current \V8.S considerably higher than for radiation cooled grids , which can be explained by the coarseness of the grid which had to be made of tubing of larger diameter than the dia~eter of wire used for radiation cooled grids. The maximum intensity of oscillations that could be obtained with these tubes was usually smaller than for ordinary tubes. Thus, in general, it can be said, that the use of water cooled grids is not a solution for increasing the energy output of the Barkhausen oscillator, since other factors, such as symmetry, proper design of electrodes and sharp tuning of the circuit, are of a greater importance than the excessive heating of the grid. (c). Minimum wavelength as a function of tube constants. The above tests demonstrated the existance of the lower (Ignin) and the upper (Igmaxl limits of the grid current (the latter corresponding to the maximum of energy output). Obviously, the tube will produce oscillations only if Igmax)> Igmmn. The dependence of rgnax upon the voltage can be approximately expressed as follows: Ignax = lcs Eg~ (58) (59) where the constant "ks " can be called the saturation constant of the tube. It depends in a known manner upon the dimensions of the electrodes and can be calculated . In the short wave reg ion the value of Igmin can be expressed as (see p .20): ·where "ks" can be called the excitation constant of the tube. The condition for oscillations requires that: I gnin < rgnax, or: Expressing the voltage Eg in terms of the wavelength and the wavelength constant (see p.45), we get : A similar expression for waves of order "n" wi ll be: L . = Keh , '-fmm ~?" . .- L~"714,r - ~- h1/h. ~ ;!;~ %. ffer. K.3 ~ ;J ~ ; . . ~ - cJ+o//z; _, / (J-r1-n_J3 These relations show that shorter wavelengths can be obtained for higher order waves. However, the excitation coefficient for high orders "ken 11 depends a great deal upon the symmetry, so that higher order waves are obtained only when t he tube is symmetrical. The value of the excitation coefficient depends not only u;ion the design of the tube, but also upon the nature of the oscillating circuit. (60) 8. Conditions for maximum energ;y output. The conditions for obtaining maximum energ;.J output from the Barkhausen oscillator will be here summarized: a) The oscillating circuit must be tuned to the most probable electronic frequency or its multiple (Ref. 1,3,4). b) The emission current must be high , aL111ost reaching its saturation value. c) The plate voltage must be :negative and adjusted for maximu.111 am_;_1li tude so as to eliminate the pl a te loss (Ref. 5). d) 1r11e tube must be symmetrical in order that higher order wt;.ves could be obtained (Ref.7). e) The A.C . volt [lge betv1een the electrodes must be a maximum, which can be obtained by placing the electrodes in the loop of the voltage wave, as has been described in paragraph 3 of this paper . The above are the most essential requirements. Other factors, such as the construction of the grid, the ratio of the diameters of the p late and grid, their size (diameter and lencth), the size and the material of t:ie fila.'Tient, the degree of vacuu.111 in the tube , and many other factors i1ave effect U)On the operation of t!~e tube. But a systematic study of their effects has been very d.ifficult , since they were usually masked by t he more ir12ortant ones . It is hoped that this work r:iay aid in the further stud.f of the Barkhnusen oscillator by reducing the nu-nber of the "unJrnowns" . ( 61) In conclusion, the author wishes to ex.!.Jress his ap1)reciation for the assistance rendered by :t:r. William Clancy in the construction of the tubes , t he advice and suggestion:;; by Dr . s . s .Mackeovm , and the interest in this work shown by Professor R.'J . Sorensen and Dr . R.A .11illi1rnn. Kelloee Radiation Labor~tory, Lay, 1932 . (62) Refe rences: 1. H. Bar:imausen and h . irnrz , ?hys.ZS, 21, 1, 1920. 2. :-r .E•.Hollmann, ZS i'Ur Hochf requenztechnik, 33, 1929, :JP • 27, 66, 101. 3. G. ? otapen1co, ZS f. T. Phys ., 1929, p .542. 4 . G. Potap eruco, Phys. Rev., Vol .39, 4 , 19 32 , p . 625 , 638. 5 . ".'. Kro ebe l, ZS f. Phys. ,61 , 3 ,4. 6 . :C . Gill and J.Morrell, Phil.liag ., 44, 161, 1922. 7 • .1:H 1.!ainberg, Journal of Applied Phy sics, Vo l. VII , I, 1930. (Russ .). 8 . Ii . Kapzov, ZS f. Phys., 129, 1925. 9. F .Ollendo rff, Die Grundlag en der Hochfrequenzt e chnik, Berlin , 1926 . 10. H . G . ~- ~ller, S lekt rische Nachrichtentechnik, April 5 , 19 30 . 11. H. :..:: . IIoll.>nann, .Ann . cl . ?hys., 86 , 1928, p . 1062 . 12. """.;:;cheibe, . ~nn . d • ..-hys., 73, 54, 1925 . 13 . G. ?otapenlco , _llJs . 71.ev., Vol.39, 3 , i) • 547, (Abst ract ). ( 63) (64) (65) llij . 2 / .