US2492680A

US2492680A - Resonator

Info

Publication number: US2492680A
Application number: US588199A
Authority: US
Inventors: Arnold E Bowen
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1943-05-04
Filing date: 1945-04-13
Publication date: 1949-12-27
Anticipated expiration: 1966-12-27
Also published as: US2530373A; US2745039A; GB587775A

Description

Dec. 27, 1949 A; E. BOWEN 2,492,680

RESONATOR Original Filed May 4, 1945 4 Sheets-Sheet 1 l i 377a,

1 v VENTOR AEBOWEN @TMWM A TTORNE Y Dec. 27, 1949 An E.IBCDVVEHQ RESONATOR Original Filed May 4, 1943 4 Sheets-Sheet 2 FIG. 5

- //v l/EN TOR A. E. BOWEN Dec. 27, 1949 A, OWEN 2,492,680

RESONATOR Original Filed May 4, 1943 4 Sheets-Sheet 3 //vv/v TOR A. E. BOWEN ATTORNEY A. E. BOWEN Dec. 27, 1949 RESONATOR 4 Sheets-Sheet 4 Original Filed May 4, 1943 FIG. I/

lNVE/VTOR A. E. BOWEN ATTORNEX Patented Dec. 27, 1949 UNITED STATES PATENT I RESONATOR.

mnolfla-S. 2Red Bank,.fN.-;i., astringent ancirazeienhnnemcratories, Incnrnoratedrhlew York N. Y., a corporationef New'dtotk Original application Maya, r9 43, serlalflo." 1485.519. Divided and-this application April 13,

1945, Serial No. 588,199.

claim. (01. Lit-44;). f

This invention relates to a resonator or resonating structure particularly designed for microwaves, as tor *examplein the region of a 10- centimeter wavelength, more or less.

a This application is (a aiivision-of-any copending application Serial No. 485,579, filed May 4, 1943,

- and assigned to the sameassigneeas-the present particles such as electrons, and electromagnetic waves guided orienclo'sedihyrelectrical conductors.

The invention will be described asa component partial 3Q gp'art oft-aihighgrreguencyielectronicsclevicegofthe qf .--.a vibra in 13, c l nn- Th type disclosed in the parenttapnlication.

In devices of this type, it is common practice :to" determine theitraiectorieswithe charged particles either by means of an electric field alone or.by a combination of-electric and magnetic field components. Devices in which the combined type of trajectory control .is employed Care tccmmonly rcalled ,magnetrons. {In cone almown .classoflmagnetrons.anelectriefield is maintained jlemimpressinga potential hetweenfiparallel 'p1ane plates ,v.while-. atathe same .time ,aimagnetic field isL-m'aintai'ned parallel itovthe plates and hence p'erpendicular-itothe electric field. lit-is imown that electrically charged particles upon being exposed to the action in. mutually perpendicular electric and magnetic fields and having initial velocities confined to the direction perpendicular (to: both the electric andamagnetic field intensity vectors, move in cycloidal and trochoidal paths. Inmagnetrons with cycloidal or trochoidal electron trajectories, use'has been made, as far as I am aware, only of that part of the energy residing in the transverse component of the electron velocity. In other words, the energy utilized has been takeni'from "the electron 'during the :part of its 'motion p'erpendicular "to "the 1Dlanesbetween which it "moves.

- It is afeature of-the '-type of device IdlSCIOSGd in the arent application that energy is ab- :stracted from the electron when it is traveling parallel to the planes between which it moves. A device of this type may be embodied in an oscillator, an amplifiena repeater, and the like, particularly for high frequency and micrmvaae applications, wherever generation, repetition, control or ampliflcatienmfqelectromagnetic waves is an object. The '"resonator of the present invto In Canada April 12,

Mention anay 5116 .used .ith @the ideizicesdisclosed zin-fihe parent application izorein various other applications -.=for .ultrafi-hi h frequencies 'gand imicrowanes. v

In :the aparticular .system-ciisclosedrherein and in themazrcnt application,- a stream at char d particles is vconstrairieil tor-move i3 raiec qry comprising a,iseriespf .cyclnidal ror, rtrochnida have. zmiqeressin ;.-a-1one ;-.a.;p ede erm n d alienationdscharact ri ed ahimth a ternate iintemz'als ;=e e1atwe1y hi h demand axia speed and aelativclyr v140w o ren wed j aisia sneed i11 other 1? :QYQLQEIQI .o. ;;t q hci almotion mi er subst nt all 5Q 1Sfii i1 fier st Th d si rel ti ely an 1 axial spee may con nien l nesi naredras ic ns. an the inte al 39 :e1.a- Finely-low o rererse a i aim i s-gin c ar e 1 parti le s hieQ1ie. to a F Y-QHQQ' A ui infla n JQH W b a fien a iq o a .:Qe. e t d a i tdecele ated-.qe eetren 13mm density varied stream which may be used tmeai- .cite ;oscil1ations in 1a resonator of .suitable iorm. The em d e e ia an o c tio exc t ien oper io arez arrie autat ioopsin th i le ie gpath whilegthe :stream .,-is1density varied by withdrawing asome vof the electrons drain the ;stream in .a tregion near a nodal point-pf thepath.

.Ithas already been proposed tp periorm upo n a stream of charged particles the operations-of velocity wariation, velocity :sort ing, tand -energy abstraction in that orderrindats ccessive points along I the pathiof the-.str.eam. It-i-is also knowr1 that 'velocityJwrtingnay be .efiected by curving or deflecting the stream. The arrange- ,ments disclosed hare an advantage not found in "prior devices, namely, that the path of the stream is kept away from the vicinity of the deflecting or controlling electrodes :except that those points where the operations of velocity variation, removal of unwanted --.part'icles;and abstraction of energy are to be effected. As a result, energy lossesiand noise cnrigents caused -,by charged-particles striking -,-the deflecting, ,or controlling electrodestare largely avoided.

the ;dr.awing, .Eigwl .is a somewhat diagrammatical cross-emotional -vie.w --zof a ,typical mechanism pior.icontipllir g-v the trajectorieslofea succession. -cf -.charged particles in -:ac.c01?.d%ll with the disclosure in the parent application;

Figs; 2, 3 and 4 are diaggams showing a variety o'f'proportionings, the essential parts of the trajectory control mechanism, including resonators in -.accordance with the present invention;

Fig. 3 is a perspective view, partly broken away respect to plate 2.

l 3 showing an oscillator employing a resonator in accordance with the invention;

Fig. 5-A is a plan View of the device of Fig. 5; Figs. 6 to 11, inclusive, are perspective views of various forms of resonators in accordance with the invention. I r

The principles underlying the invention disclosed in the parent application are conveniently explained with reference to Fig. 1 wherein are represented diagrammatically two parallel plane plates l and 2 separated a-distance a and maintained at a substantially constant potential difference V0, plate I being positive with respect" to plate 2. The resultant electric fieldintensity acts downward in the plane of the drawing as indicated by arrows in the figure. A cathode? is located in the plane of plate 2 and may be insulated from the plate so that the cathode may be a directly heated filament if desired. Slots or gaps 4 and 5 are made'in plate I on centers spaced apart a distance 1rd, the slot 4 being located a horizontal distance /21ra from the cathode 3. A collector plate 6 is located in the plane of plate" 2, insulated therefrom, and preferably maintained at a potential somewhat positive with A substantially uniform magnetic field of intensity H is maintained with-its lines of force directed perpendicular to the plane of the drawing in the sense away from the reader. It is assumed for the purpose of the explanation that the uniformity of the fields E and H is not materially disturbed by any edge efiects or by the presence of the cathode 3, the collector 6 or the slots 4 and '5. Assuming further that electrons are released with-zero velocity at the cathode 3, then, according to known principles the electrons will travel in trajectories such as that shown in the curve -l,' which is a common cycloid. The assumed conditions may readily be approximated in practice.

The equations of motion of an electron in the system of Fig. 1 are readily set up and the equations of the electron paths under given boundary conditions derived therefrom by conventional analytical methods. It is therefore deemed unnecessary to present a detailed solution and only fth'e'basic equations and final results are set down I lit mc d! where cis the velocity of light, and e, E, and H are to be taken as positive numbers. As the problem is fundamentally one of two dimensions only, itwill not be necessary to consider further the y-coordinate nor Equation 2. Additional simplification of the analysis may be had by introducing the following abbreviations:

the use of which makes Theequations to be solved then reduce g al f' dt dz d z do; =P o'- The complete solution of the simultaneous Equations '7 and 8 is from which the'following may be derived by diff erentiation for the constants of'integration. I

From the general solutions (9) and 10) a particular solution may be had for thecase of particles starting from restat the origin at the time when t is zero by usinlg the initial conditions represented by i dt dt (15) to determine the constants of integration. The

result is readily found to be a: =%(pt sin pt) (16) the standard equations of a common cycloid.

Referring to the curve"! in Fig. l'the left-hand portion of the curve represents the common cycloid of Equations 16 and 17. The curve will have a maximum value of a for the condition I pt=1r (18) and at this point it will be found that I Assuming that the spacing a has been so chosen that the cycloidal trajectory Twill just graze the plate l,'i-t will be evident that the maximum z-coordinate of the trajectory will be equal to a and it will be found that at pt=1r,

mummies with the iinvention; a may variation is impressed upon the particlescnsithey pass the first point of maximum z-coordinate, means of a variable potential difierence across the slot 4 which will be suitably superposed the initial potential V *of "the plate -I as a whole. Then the potential'wliich acts upen'a given electron causing it to pass the gap 4 may expressed as V: V0+6 V0 where '16 is a small factor which [in ordinaisy practice will-nsually lie within limits between eel and +1. If we assume that a given electron leaves the gap 4 with a speed -s determined by theipotential V as given in p26) thenthe'equa tion represents the relationshiplbetween V and s based upon the conversion of potential energy into kinetic energy. I solvin'g (2-7) iars and using 626-) gives VQ+6V0)6 T 't'flsing Vo=aE (29) together with and (.4), we have s=2sm/m The trajectory of an electron after "it leaves the gap 4 must' be suchasto' satisfythe eqnaticns of motion (1), (2) and (3) as well as the new initial conditions ,produced by the velocity variation. The latter conditions are such that when P =1 (31) then 'a:=" '1ra ('32) m/ =1/ +a tea and da e Under these conditions it is readily fourid th'at -=%[pi (M 54) r l "(3a 02(11 -vm %[1' 2 /f1-+8 1=-) cos mt] (ar Equations 36 and 3 7 willbe recognized as-the equations of 1a family of trochoidsszgenerated by amovable:point,-distant,

from the center of a circle of di ametertdwvhich is rollin .upon and above the line c t 1+ (as The .r-component of Velocity is -$=st1- mm -1- ws-p 1 (4 The 'trochoids corresponding irespectitrly to the values 6=0.5,,- 6=0, and-6=+0.5 are plotted as curves' 8, $9 and i0. Curve 9 is a common cycloid, which is a special case of a trochoid.

Two important characteristics of the trajecmes to :he deduced from the above analysis. mhe ifirst is that call the trajectories'a egarfilcss' iii tnezz-gap 't; 1 :The secondrlmportant aieii'uctfon ie that the average value of the -x=velocity et each particle iisiequal-tolso,independently ozf tliea va lue. In particular the result is :found that the transit time'between itheigaps 4 and 5 the same fe'rall ithe iparticles regardless-of theleng'th and shape of trajectory; 330th these-characteristics may be'verified by substituting 31r in I (36) =-atid G8 wliich lgive's which expressions-are independent of 6' and det'ei iiime "the above-mentioned common point "at the gap t. -"I-he average speed of any particle while itrayersing the instance between the gaps fl' and ti is the int'er'gap distance ir'a div-idefl hy the transit time from 2ft"=irt0 nt-=31, which-speed amomits -to /1112), or So. I l hepassage of charged particles across gap j in adensi-ty varied stream causes an alternating currentto'be"induced in the plate I. The stream is *g'iven a 'density-variation by the action (if the plate-Twhi'ch is so placed 'as to intercept particles 'ina group of trajectories represented by curve "It: while particles *in a group of "trajectories represented by curve 8 pass on 'uninter cepted. "The velocity variation *impressed upon me 'stream at 'the gap 4' produces a cyclical "variation in the trajectories 'o' f successive particles ranging in turn through trajectories of-the type of curve 8, the cycloidaltype 9, the type of curve It), the cycloidal type again and back to'the type of curve 8, etc. Only the particles following traj'e'ctories "ofthe'typ'et reachthe gap 5 and these form a density varied of intermittent stream at the gap 5. Plate 6 serves to "collect the spent particles after they leave'the gap 5. The parts of thecurves *9 and I0 which'are unoccupied'by particles because of interception "by plate 2 ar shownfdotted in Fig. '1. j 'j It-wil-l'be" noted; that the mechanism de'scr ea one "for "transforming a steady stream jffof charged particles into an intermittent -or density. varie'i'l stream. 'It wilhbe'hotecliurther'ithat the grou ing of the particles is not dependent'up'or'i' the -=principle of fast moving particles overtak in'g slower moving particles. The principle" employed is one of segregating 'th'ose'partioles which exceeda certain criticalvelooity. v H

It willbe noted "further that the charged pafrr; ticles approaching the gap 4'are' moving with'sfub stantially a uniform velocity and in a"'di rction parallel to the plate vI. This condition might lee-brought about in various Ways other than by locatingthe cathode 3 .in the plane ofsthe plate 2 "and using the mechanism described foraproe 1 ducing the cycloidal trajectory I. For example,

the stream of chargedtparticles might be made to -approach the gap -4 along a straight path parallel to the plate I under the influence of an electric fie'ldin "the absence of the magnetic field H. The mechanism shown and the use oithfe cyldidahtra'jectory '1 will ordinarily be simplest and most expedient'but it wil-l'be understood that it is within the scope of the invention to eifipiey any suitable means to, provide a stream of charged particles which approaches the gap 4 with substantially uniform velocity and charge density. I 1

In any case, after leaving the gap "4 the motion of the particles is characterized by a periodic the t-value pass through a common -poiiit u iear 13:5 component of motion in the direction of the electric field superposed upon a general proxression or drift in the direction perpendicular to theplane common to the electric and magnetic vectors. In the neighborhoods of ga 4 and gap the periodic component of motion in the direction of the electric force produces a maximum displacement in compliance with the electric field. In the region where certain of the trajectories meet the ground plate 2, the particles are movingg'in opposition to the electric field. In the casejof trajectories of the type of curve It there is superposed upon the drift motion an incidental periodic component which could be utilized if circumstances warranted;

The velocity variation at the gap 4 effects a control over the periodic motion in the direction of the electric force-,namely a control of the amplitude of such periodic motion. Under the variable amplitude condition, however, all the variation is confined to the region in which the particles move against the force of the electric field, as described, the excursion of the particles in compliance with the electric force being limited to the uniform maximum value a by the combined eil'ect of the electric and magnetic fields.

In the operation of the device as an amplifier, the potential of the gap 4 is varied by means of the wave to be amplified and the output resonator is connected across the gap 5. The spacing 1rd, between the gaps 4 and 5, as seen from (25), is a function of both E and H, varyin directly as E and inversely as the square of H. The transit time between the gaps is P and varies inversely with H, independently of E. There is, moreover, no critical transit time required in the amplifier case.

In the operation of-the device as an oscillator, the available values "of H are limited once the frequency of th desired oscillation is determined. It has been shown above that the particles which pass the gap 5 when the plate 2 is in place are those which are dcelerated at the gap 4. In

order for these particles to contribute energy to the field at the gap 5 the particles must pass gap 5 while the field is opposing their motion. In a case where the gaps 4 and 5 are excited in such manner that the fields at the two gaps are poled in the same direction, an integral number of periods of the oscillation should elapse between the passage of a particle across the gap 4 and its subsequent passage across the gap 5.

In terms of the frequency, f, the relation n 21' 2mm: 7 43) must hold, where n is any integer, or, in terms of the free space wavelength, x,

in which formula i is to be expressed in centimeters and H and whichformula is applicable either to an amplifier or an oscillator. Since in the case of the electron oscillator )\H is given by (45), the spacing will be W a 2 m centimeters where V0 and are in electromagnetic units, A is in centimeters, and c=3 10 centimeter/seconds, or

centimeters (50) where A is in centimeters and V0 in volts.

A number of examples coming out of Formula 50 have been computed and are shown diagrammatically in Figs. 2, 3 and 4. It will be noted that for given values of 7x and V0, the spacing a is proportional to n. Thus if, as in Fig. 2, a has the value an corresponding to 11:1; then for the same wavelength and same voltage, the spacing is 2ao for 11.:2, which case is shown in Fig. 3; and 3am for 12:3, as shown in Fig. 4. The spacing of the gaps is equal to 1rd in every case. For a wavelength of 10 centimeters and a voltage V0 of 1,000 volts, the value of ac comes out approximately 1 millimeter.

Various changes in the values of V0 and K may be made, at the same time changing n so that the required spacing remains the same. For example, in Fig. 2 if n is made 2 and the wavelength and spacing remain unchanged, the voltage must be reduced to one-fourth its former value. The change in 11. also requires that H be reduced to one-half its former value, in order that (4'7) may be satisfied.

Several possible combinations of values for a 10 centimeter wavelength in the diagram of Fig. 2 are tabulated in Table I.

2 Several possible combinations for a 10 centimeter wavelength in the diagram of Fig. 3 are given in Table II.

aneacso Combinations for the diagram of Fig. 4 are given in Table III.

Table III 41, cm. n V0, volts H, oersteds I, cm.

Conductors I4, I5 and I6 of a resonant circuit are shown schematically, connecting the plate segments I in Fig. 2. To indicate resonance at the same wavelength in Figs. 3 and 4 as in Fig. 2, the areas enclosed by the conductors are shown approximately equal in all three figures.

Fig. 5 represents an embodiment of the invention in an oscillator complete with a resonating circuit, an output coupling device and means for supplying the requisite electric and magnetic field intensities. The equivalent of the plate I of Fig. 1 is represented in Fig. 5 by a threesegment anode having segments II, I2 and I3 connected together by conductors I4, I5 and I6, the latter, together with the anode segments, comprising a resonant circuit. The inductance of the resonant circuit resides mainly in the conductors I4, I5 and I6 while the capacitance is mainly between segments II and I2 at the gap 4 and between segments I2 and I3 at the gap 5. The negative or ground plate 2 has a depression in which the cathode 3 is insulatingly mounted. These parts, together with the collector plate 6,

are supported by rods held in a press I1 of conventional type formed in the wall of a vacuumtight container I8, which wall may, for example, be of glass. The supporting rods may serve also as electrical connections from the plates to the sources of electromotive .force. The latter sources may constitute batteries or other suitable devices of which I9 serves to heat the cathode, 20 to polarize the anode segments II, I2, I3 positively with respect to the

ground plate

2, and 2| serves to maintain the collector 6 preferably at a somewhat positive potential with respect to the plate 2. Coupled to the conductors I4 and I6 is a coupling loop 22 the ends of which may project through the envelope I8 and be connected to any suitable load device for transmitting or utilizing the generated oscillations, the load circuit here being represented by a resistor 23. An electromagnet comprising pole-pieces 24, winding 25, a yoke 26 and energized by suitable means such as a battery 21, is provided preferably external to the envelope I8 and is set up in such a position (Fig. 5A) as to provide a magnetic field having lines of force substantially parallel to the cathode 3 and the several plates.

The cycloidal path of a typical electron leaving the cathode 3 and approaching the gap 4 is shown at 1. The path of this electron, should it be decelerated at the gap 4, is indicated at 8 showing that its trajectory continues past the gap 5 and preferably. ends upon the collector plate 6. Should. the same electron instead be accelerated at the gap 4 its path is indicated at I0, ending upon the ground plate 2 and not. reaching the p 5.

' The spacing between the ground plate and the anode is. determinedv as. described hereinbefore in connection with. Fig 1,. for a desired operating wavelength at a given voltage and for a chosen value of It, according. to The resonator is proportioned" to be resonant to the operating wavelength. Furthendeta ilszofz the operation of the system of Fig. Swill be e ident from the explanation given hereinabove' in connection with Fi 1. i

Fig. 6 shows a modification of the tuned circuit of Fig. 5. The anode segments II and I3 of Fig. 5 are merged into a single segment I00 which may surround a middle segment IOI as shown. The inductive connection between the segments I00 and I 0| comprises the conductors I4, I5 and I6 corresponding to those similarly numbered in Fig. 5.

Fig. 7 shows a tuned circuit similar to that of Fig. 6 but with the inductive connection between the plates I00 and IOI simplified so as to eliminate the conductor I4.

Figs. 8 and 9 show tuned circuits similar in principle respectively to the tuned circuits of Figs. 6 and 7.

In the arrangement of Fig. 8, a conductive bar I02 takes the place of the conductors I4, I5, I6, inclusive, of Fig. 6. In this kind of structure there is less inductance in the connector I02 and resonance is determined to a greater extent by distributed inductance in the segments I00 and IN.

In the arrangement of Fig. 9 the inductive connection I5, I6 is replaced by a bar I03. Here again the inductance relied upon for resonance resides mainly in the distributed inductance of the segments I00 and IIII.

.Fig. 10 shows a tuned circuit comprising a pair of anode segments I04 and I05 joined by an inductive conductor I06. The arrangement is mounted so that the plates I04 and I05 are coplanar with a guard plate I01 and are positioned in an opening therein. The conductor I06 is conductively connected to and supported by a conductor I08 which is in turn conductively connected to and supported by the plate I01. The conductor I08, while it may represent an appreciable inductance can still serve as an untuned connection between the conductor I06 and the plate I01. It is only necessary that the system I01, I08 shall not support electromagnetic oscillations at a frequency in the neighborhood of the desired operating frequency. Under this condition, the anode segments I04 and I05 may sustain an alternating potential, while the plate I01 and connector I08 will remain at a substantially unvarying potential.

Fig. 11 shows a tuned circuit which is a modification of that shown in Fig. 10. A guard plate I01 has two openings within which the plates I04 and I05 are positioned respectively. The conductor I06 connects the plates I04 and I05 as in Fig. 10 and a conductor I08 connects the middle of the conductor I06 to the portion of the plate I01 between the two openings.

What is claimed is:

A resonator comprising a conductive guard plate having a closed-slot therein, a pair of conductive plates mounted coplanarly with each other and with said guard plate within the slot 11 in said uard plate, a first inductive conductor connecting said pair. of conductive plates and lying in a plane perpendicular to'the plane of said guard plate, and a second inductive conductor lying in a plane perpendicular to the plane of said guard plate, said second inductive conductor connecting said first inductive conductor to said guard plate and thereby supporting said pair of conductive plates within the slot in said guard plate.

ARNOLD E. BOWEN.

REFERENCES CITED The following references are of record in the file of this patent:

12 UNITED STATES PATENTS Number Name Date Lindenblad May 26, 1936 Hollmann Apr. 2, 1940 Mouromtseff et a1. Oct. 8, 1940 Fiske Sept. 3, 1946 Fox Dec. 9, 1947 Dallenbach Mar. 9, 1948