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Publication numberUS2957103 A
Publication typeGrant
Publication dateOct 18, 1960
Filing dateAug 19, 1954
Priority dateAug 19, 1954
Publication numberUS 2957103 A, US 2957103A, US-A-2957103, US2957103 A, US2957103A
InventorsBirdsall Charles K
Original AssigneeHughes Aircraft Co
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
High power microwave tube
US 2957103 A
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Description  (OCR text may contain errors)

Oct. 18, 1960 c. K. BIRDSALL HIGH POWER MICROWAVE TUBE 2 Sheets-Sheet 1 Filed Aug. 19, ,1954

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HIGH POWER MICROWAVE TUBE Filed Aug. 19. 1954 2 Sheets-Sheet 2 Irma/1% HIGH POWER MICROWAVE TUBE Filed Aug. 19, 1954, Ser. No. 450,987 11 claims. (C1. 31e- 3.6)

I This .invention relates to microwave tubes and more particularly to the slow-wave structure of a travellngwave tube.

As is well known, amplification is achieved in a traveling-wave tfube lby first launching an electromagnetic waveon a helical conductor whereby the wave is propagated along the helix at a velocity substantially less than the velocity of light. An electron stream is then projected through the helix at approximately the same velocity as that of the wave. Mutual interaction of the stream and the wave which is thus produced effects a transfer of energy from the stream to the wave causing the wave to grow or to be amplified.

The power gain of a traveling-wave tube is proportional to the stream current and the direct-current helix voltage. Both of these factors are limited by the practical dimensions of presently employed helices. v The stream current is limited by the available area within the helix and the stream voltage is limited by the helix pitch. If helices with larger pitches or diameters than those presently employed are utilized, a typeof self-oscillation called backward-wave oscillation is encountered which prohibits the use of a traveling-Wave tube as an amplifier. This is true because the gain of the forward wave is proportional to the forward wave impedance of the helix and the gain of the backward-Wave is proportional to the backward-wave impedance of the helix, the backwardwave impedance being relativelyhigh and the forwardwave impedance being relatively low for helices of larger pitches or diameters than those helices now employed.

A typical present day traveling-wave tube helix has the further disadvantage of being non-dispersive, i.e. waves having frequencies falling within a very broad band are propagated at substantially the same velocity as that of the electron stream whereby they are amplified. It is generally impossible to match the load impedance of the tube to the helix completely over the frequency band where substantial gain is produced and as a result of this unavoidable mismatch another type of self-oscillation is produced by the reflection of thermal noise at the output end of the helix. It is at present the practice to attenuate these reflected or circuit waves by covering the helix or its supports with a coating of a lossy material; however, this is not a satisfactory solution to the problem particularly because such a coating materially reduces the gain of a tube.

` It is also desirable that the interaction of the electron stream and the forward-wave in a traveling-wave tube amplifier be as complete as possible to attain maximum gain. To this end, it is necessary to accurately align the helix and the electron gun from which the stream is projected in order to maintain collimation of the paths of the stream electrons so that a maximum number of the electrons will travel through the helix without being intercepted, thus enabling the stream electrons to interact with the field of the wave over the complete length of the helix. Nevertheless, in la high power tube, e.g. a tube employing a direct-current helix voltage of 25,000 to nited States Patent 35,000 volts and a stream current of about ten amperes, it is impossible to keep some electrons from colliding with the helix when the stream is maintained contiguous to the helix for the efficient production of gain. This introduces another problem when the helix is constituted of the usual materials, such as, for example, tungsten or molybdenum. High speed electron bombardment of the helix generates heat which must be conducted away and dissipated. Although both tungsten and molybdenum are fair c-onductors of heat at high temperatures, stainless steel, copper or silver would definitely be more desirable if it were not for the low modulus of elasticity of the latter three metals. This consideration arises out of the fact that for the proper alignment of an electron gun and a traveling-wave tube helix, the helix must be rigid. Because of the inherent structural weaknesses of a helical configuration, the ,manufacture and assembly of this structure must be performed with delicate precision. A metal with a high modulus of elasticity such as tungsten or molybdenum is generally employed in order to prevent deformation by the forces Which are necessarily applied in the assembly of a traveling-wave tube. Tungsten and molybdenum are hard to work and are particularly hard to form into a helix. A structure constituted of these metals is consequently only moderately sturdy and can be manufactured only at considerable expense.

It is therefore an object of the invention to provide a traveling-wave tube slow-Wave structure having a relatively high forward-wave impedance and a relatively low backward-wave impedance to prevent backward-wave oscillations.

It is another object of this invention to provide a rugged slow-wave structure in combination with means for producing good impedance match thereto from a rectangular waveguide.

It is a further object of the invention to provide an unusually dispersive traveling-wave tube slow-wave structure whereby reflected wave self-oscillations are reduced and the necessity of employing a lossy attenuating material is obviated.

A further object of the invention is to provide a traveling-wave tube slow-wave Structure which is an especially good conductor of heat at high temperatures whereby the heat generated by electrons colliding therewith may be more readily conducted therefrom.

A still further object of the invention is to provide a traveling-wave tube slow-wave structure of unusual mechanical strength which may be manufactured by mass production techniques.

In accordance with the present invention, an integrated or unitary slow-wave structure for a traveling-wave tube is provided which simulates the impedance of ntermeshed contrawound helices of identical diameters. The slowwave structure of the present invention comprises simply a tublular conductive element having a plurality of transverse slots milled out at regular interv-als therealong, the particular configuration greatly simplifying and economizing the method of manufacture of the helical type of structure. The structure of .the present invention is also unusually dispersive and its forward-wave impedanceis more than two times as large as that of a conventional unifilar helix whereas the backward-wave impedance is smaller by a yfactor of more than eight, the problem of backward-wave self-oscillations being thereby substantially eliminated.

The novel features which are believed to be characteristic of the invention, both as to its organization andv method of operation, together with further o-bjects and advantages thereof, will be better understood from the following descripton considered in connection with the accompanying drawings in which several embodiments of the invention kare-illustrated by way of example. AI't'ttlt Patented Oct. 18, 1960.

be expressly understood, however, that the drawings are for the purpose of illustration and description only, and are not intended as a definition of the limits of the invention.

Fig. l is a sectional view of a traveling-wave amplifier embodying the present invention and associated circuits;

Fig. 2 is an oblique view of the slow-wave structure included in the amplifier of Fig. 1;

Fig. 3 is an oblique View, schematic in nature, of bililar contrawound helices to aid in the explanation of the invention;

Fig. 4 is a section on line 4-4 of Fig. 1 of -an external output waveguide segment `employed with the amplifier;

Fig. 5 is an oblique View of another embodiment of the slow-wave structure of the invention;

Fig. 6 is an oblique view of a portion of a half of the slow-wave structure of Fig. 5;

Fig. 7 is a plan view of a slow-wave structure ernbodying two half-sections of the type shown in Fig. 6;

Fig. 8 is an oblique view of a portion of another embodiment of a slow-wave structure in accordance with the invention; and

Fig. 9 is an oblique view of still another slow-wave structure in accordance with the invention.

Referring to Fig. l there is illustrated a travelingwave tube amplifier 10 having a cylindrical, conductive, non-magnetic envelope 12 which may be made of copper. An electron gun 14 is sealed in the left extremity of the envelope, as viewed in Fig. l. Electron gun 14 is employed to produce a stream of electrons which may be directed along the longitudinal axis of envelope 12.

A solenoid 16 is disposed concentrically about envelope 12 to provide an axial magnetic field along the envelope to prevent space charge spread of the electrons as they are directed along the stream path. Such a field may be of the order of 600 to 1200 gauss. In order to produce such a field, a direct current is maintained in solenoid 16 by means of a potential source 18.

Electron gun 14 essentially comprises a cathode cylinder 20, a heater 22, a focusing electrode 24, and an accelerating anode 26. Heater 22 is connected across a suitable source of potential 28 and the negative side of heater 22 is connected to cathode 210. The positive side of source 28 is then connected to the negative side of a potential source 33, the positive terminal of which is connected to ground in order to maintain cathode 20 about 30,000 to 35,000 volts below ground. Focusing electrode 24, which has a frustro-conical internal surface of revolution forming an angle of 671/2 degrees with its axis of revolution, is maintained at the same potential as the negative side of heater 22 by a suitable connection thereto. Anode 26 is maintained about 200 volts positive with respect to ground by a source 32 in order to produce an electron focusing effect.

A plurality of disc-shaped dielectric spacers 34 are employed to maintain the cylindrical appendage 3S of anode 26 in alignment with the longitudinal axis of envelope 12. A glass cylinder 36, which is sealed to the stem leads 37, and spacers 34 comprise the support of gun 14, stem leads 37 being welded to the electrode leads of gun 14.

Within envelope 12, adjacent to electron gun 14, a simulated contrawound helical slow-wave structure 40 is provided. A portion of the slow-wave structure 4t) is also shown in Fig. 2 and has a relatively long end cylinder 41 and a plurality of relatively short intermediate cylinders such as 43, -44 and 45. Each cylinder 41, 43, 44, 45 is connected to an adjacent cylinder by a pair of straight axial segments 46, 47; 48, 49; 50, 51; and 52. A first set of adjacent pairs of cylinders is connected by axial segments at a first set of diametrically opposed points and a second or subsequent set of adjacent pairs of cylinders connected by axial segments disposed at a second and different set of diametrically opposed points,

4- a plane intersecting the second set of points being disposed 90 mechanical degrees with respect to the plane intersecting the first set of points. For example, segments 46 and 47 connecting cylinders 41 and 43 are disposed along the same line, respectively, as segments 50 and S1 connecting cylinders 44 and 45. Likewise segment 49 and segment 52 are disposed along the same line.

The conductive tubular element comprising the slowwave structure 40 may consist of any conductive material, such as, for example, stainless steel, copper or silver. The slow-wave structure 40 is electrically equivalent to two intermeshed biilar contrawound helices because the slow-wave structure 40 can be considered as the path of four substantially helically disposed wires. The cylinder 41 is the equivalent of four wires in physical contact, each of the wires having a cross-section equal to a one-quarter arcuate segment of the cylinder 41. The slow-wave structure 40 may be compared to the schematic helical slowwave structure shown in Fig. 3. The first and second wires 132 and 134 of the four wires 132, 134, 136 and 138 can be visualized as emanating together in electrical contact as the axial segment 46 of slowwave structure 40. The first wire 132 may then be visualized as traveling to the right and the second wire as traveling to the left about cylinder 43. The third and fourth 136 and 138 wires are likewise thought of las emanating from axial segment 47, the third wire 136 traveling to the left about cylinder 43 and the fourth Wire 138 traveling to the right about cylinder 43. The first and third wires 132 and 136 are then deemed to have emanated from cylinder 43 at axial segment 49 where they may be considered to have crossed. The first wire 132 then continues to the right about cylinder 44 and the third wire 136 continues to the left about cylinder 44. Likewise the second and fourth wires 134 `and 138 emanate from cylinder 43 at axial segment 48 and cross, the second wire 134 proceeding toward the left about cylinder y44 `and the fourth wire 138 continuing toward the right about cylinder 44. The first and second wires 132 and 134 thus meet again and cross at axial segment 49 and the third and fourth wires 136 and 138 meet again and cross at axial segment 50. From the right edge of cylinder 41 to the right edge of cylinder 44 the wires have thus made one-half of one turn. The pitch of each of the four helices, which is then twice this distance, is.

indicated by 53 in Fig. 1.

A unifilar helix must be wound on a mandrel with extreme precision; however, the manufacture of the slowwave struct-ure 40 may be accomplished with considerable facility simply by mounting a hollow conductive cylinder in a suitable jig, making one pass with a plurality of milling machine wheels transverse to the axis of the cylinder, rotating the cylinder degrees, and making a second pass with the milling machine wheels.

In the embodiment o'f the present invention shown in Fig. l, 207 mils is representative of the magnitude of the outside diameter of the tubular element comprising the slow-wave structure 40. The -pitch 54 may be 89 mils for an inside diameter of the slow-wave structure equal to 167 mils. The entire length of the structure 40 may be 2.5 to 3.0 inches. None of the dimensions are particularly critical, for example, the pitch 53 may be between 70 and 130 mils dependent on the operating voltage or phase velocity reduction to be effected. For ease of manufacture and for suitably launching a traveling-wave, the

intermediate cylinders, such as cylinders 43, 44 and 45, are preferably equal in axial length, 22 mils in the embodiment shown, to the length ofV each axial segment 48, 49, 50, 51 and 52. Each of `the end slots in the structure 40, formed, for example, between short axial segments 46 and 47 is equal to one-'half the axial length o'f one of the segments 48, 49, 50, 51 and 52. The length of end cylinder 41 is not material except that it need not be longer than the width of the end portion S4 of a rectanguessaies' lar internal input waveguide segment 55 which is incidentally employed to support one end of the slow-wave structure 40. To this end, the end portion 54 is provided with a circular o'pening 63 through which slow-wave structure 40 extends. The right end of slow-wave structure 40 is supported by the end portion 56 of a rectangular internal output waveguide segment 47 which is provided with an aperture `65. The end portions 54 and 56 extend at right angles to their waveguide segments 55 and 57. Waveguide segments 55 and 57 are also made of a conductive material such as copper and, since the waveguide segments 55 and 57 and slow-wave structure 40 are in physical and electrical contact, they are maintained at ground potential by a connection `58 from waveguide segment 55 to the envelope 12 w `ch has a connection 59 to ground.

The dimension indicated by 60 in waveguide portions 54 `and 56 should be as small as practicable in order to produce a broadband match to slow-wave structure 40. The `circular opening 61 in waveguide portion 54 should be about equal in magnitude to the sum of the outside diameter of the slow-wave structure 40 plus one-half of the pitch of the structure. The same is true of aperture 67 in waveguide portion 56. The particular conguration of ithe slow-wave and Wageguiding structures shown and described provide a good impedance match, the ampliiier being rated as having a ten percent bandwith at 9 l09 cycles per second. The good match is evident from the fact that the voltage standing wave ratio in the absence of an electron stream is 1.2 near the center frequency of the operating band.

The stream electrons projected through the slow-wave structure 40 are intercepted by a collector electrode 62 which projects otutwards of the envelope 12 at the opposite extremity of the envelope with respect to electron gun 14. Collector 62 is supported by a disc-shaped dielectric spacer 64 so as to have a large surface external to the evacuated chamber for heat dissipation purposes and may be provided with fins to aid in conducting away the heat that is generated by the stream electrons when they are collected. Accordingly, collector 62 is preferably fabricated of a metal having good electrical Iand heat conducting properties, such as, for example, copper or silver. A potential of the order of 200 vol-ts positive with respect to structure 40 is applied to collector 62 in order to prevent secondary electrons, which may be produced by the stream electrons impinging upon its surface, from reaching slow-wave structure 40. This po-tential is applied by means of .a connection from collector 62 to the positive terminal of a source 66, the negative terminal of which is grounded.

Also supported in appropriate openings in spacer 64 are an external rectangular input waveguide segment 68 and an external rectangular output waveguide segment 70. Both of the external waveguide segments have mica windows 72 and 73, respectively, at their outer ends which provide vacuum seals. A vacuum is thus maintained from the windows 72 and 73 to the opposite extremity of envelope 12 at the end of glass cylinder 36.

External Waveguide'segment 68 has a uniform width 80 shown in Fig. 4 equal to abo'ut 900 mils. The segment 68 increases in height from left to right from a minimum height 74 equal to 90 mils to a maximum height 78 equal to 400 mils. The length of the increase in height 76 may be 1900 mils. yDesign considerations for producing a good impedance match in the reduction in height of a rectangular waveguide are well known in the art, e.g. dimension 76 should be about mtg where n is any positive odd integer and kg is a guide wavelength. Wavelength segment 70 may be similarly constructed.

In the operation of amplier 10, an input signal to be ,y conductors of segments 190 and 200 wave propagation, it is easy amplied is impressed upon input waveguide segments 68 and 55. A traveling wave is subsequently launched on the slow-wave structure 40 and the iield of the wave interacts with the electron stream projected from gun 14. This interaction results in a transfer of energy from the stream to the wave causing the wave to' grow or increase in amplitude as it progresses along the slow-wave structure 40. At the end of the slow-wave structure, the amplified wave energy is coupled from output waveguide segments 57 and 70 to a utilization device, not shown.

In Fig. 5, an alternative slow-wave structure is shown which sirnilates the structure of unilar contrawound helices. Slow-wave structure 160 consequently co'mprises a plurality of conductive cylinders 160, 166, and 168 which are respectively connected by single axial segments 162, i168, and 172. The third and fourth wires 136 and 13S in Fig. 3 which are deemed to emanate from axial segment 47 in Fig. 2 thus have no simulated existence in the slow-wave structure 160 in Fig. 5. The pitch of the helices `of slow-wave structure 160 is indicated by 164. The two wires 132 and 134 may be visualized emanating or crossing at axial segment 162 and traveling degrees in opposite directions about a iirst intermediate cylinder 166. They are deemed to cross at axial segment 168, travel another 180 degrees inopposite directions about a second intermediate cylinder 170, and cross again at a third axial segment 172, each wire having made one complete turn.

lin Fig. 6, a segment having the shape of the structure 160 of Fig. 5 is illustrated. Segment 190 may be stamped out of stainless steel and joined together with a similarly stamped section as shown in Fig. 7 forming a structure equivalent to that olf Fig. 5 where a half-section 200 is shown welded at points 202 to section 190.

Fig. 8 is a view of a portion of te slow-wave structure of Fig. 7 wherein the axial slits 212, between the segments 190 and 200 are iilled with a lossy attenuating material 218. In the absence of the lossy material 218, the slow-wave structure comprising segments 190' and 200 has substantially the same propagating characteristics asl sldw-wave structure 160 of Fig. 5 because the impedance of the capacitive coupling between the contiguous axial is substantially the same as that of a conductor. In the absence of the lossy material 218 currents may therefore ow either according to the direction of arrows 214 o'r 216 at slit 212. Since both sets of arrows 214 and 216 show different modes of to see that the slower mode exhibited by arrows 214 nray be suppressed by employing lossy material 218. The wave phase velocity on the circuit, the direct-current voltage of the structure and therefore the power of the tube may be increased.

Fig. 9 shows how the construction ,of biiilar contra-.

wound helices similar to the slow-wave structure 40 of Figs. l and 2 may be simplified in that four quarter-sections 220 may be stamped from sheet steel and joined together in a relationship analogous to that of sections 190 and 200 of Fig. 7.

In some applications, it may be desirable to couple one slow-wave structure 40 to a similar one or a slowwave structure 160' to one of like construction. This can be accomplished in a ymanner analogous to that-` shown -in U.S. Patent No. 2,588,832 granted March ll,

1952 to Clarence W. Hansell where one unifilar helix isV disposed concentrically about another.

What is claimed is:

l. A slow-wave structure for use in connection with a traveling-wave tube comprising a conductive tubular element having a ii-rst set of rectangularly shaped transverse slots disposed in the Same arcuate position at periodic intervals therealong, said tubular element having a second set of transverse slots disposed intermediate said first set of slots on the side of said tubular element one-half' Opposite said first set of slots, whereby the electrical equivalent of at least two contrawound helices is simulated.

2. A slow-wave structure for use in connection with a traveling-wave tube comprising a conductive tubular element having a first set of transverse slots disposed in the same arcuate position therealong, a second set of slots disposed diametrically opposite said first set of slots, a third set of slots disposed in quadrature with and intermediate said first and second sets of slots, and a fourth set of slots disposed diametrically opposite said third set of slots, whereby the electrical equivalent of bifilar contrawound helices is simulated.

3. A slow-wave structure for use in connection with a traveling-wave tube comprising a plurality of conductive cylinders axially aligned with each other about a predetermined path, and a plurality of axial conductors, each being connected between an adjacent pair of said cylinders, the conductors connecting alternate pairs of said cylinders being disposed at diametrically opposed points about said cylinders to maintain said cylinders in a predetermined spaced relationshi whereby the electrical equivalent of at least two contrawound helices is simulated.

4. A slow-wave structure for use in connection with a traveling-wave tube comprising a plurality of conductive cylinders axially aligned with each other along a predetermined path, conductive means connecting a first set of alternate adjacent pairs of said cylinders at two first diametrically opposed points about their periphery, and conductive means disposed at a second plurality of diametrically opposed points arcuately intermediate said first points connecting a different set of alternate adjacent pairs of said cylinders, whereby the electrical equivalent of contrawound helices is simulated.

5. A slow-wave structure for use in connection with a traveling-wave tube for simulating the microwave transmission properties of bifilar contrawound conductive helices, said slow-wave structure comprising a plurality of conductive cylinders aligned axially about a predetermined path of travel for charged particles, and conductive means electrically interconnecting alternate adjacent pairs of said cylinders at two pairs of diametrically opposed points, said pairs of points being displaced 90 mechanical degrees with respect to each other about said path.

6. The slow-wave structure as defined in claim 5, wherein each of the cylinders disposed at the outer ends of said slow-wave structure is spaced apart from its adjacent cylinder a first predetermined distance, and the remainder of said cylinders are spaced a second predetermined distance apart equal to two times said first predetermined distance.

7. The slow-wave structure as defined in claim 6, wherein each of the cylinders disposed at the outer ends of said slow-wave structure are longer than the remainder of said cylinders, the remainder of said cylinders having a length equal to said second predetermined distance.

8. A slow-wave structure for use in connection with a traveling-wave tube comprising a first set of semicircular conductors disposed in the same arcuate position perpendicularly to and sequentially along a predetermined axis, a second set of semiparallel conductors disposed perpendicularly to and sequentially along said axis having their arcuate extremities disposed contiguous to said first set of semicircular conductors, a first set of straight axial segments connecting one extremity of a first set of successive adjacent pairs of said first set of semicircular conductors at the same arcuate position, a second set of straight axial segments disposed contiguous to said first set of straight axial segments connecting one extremity and different set of successive adjacent pairs of said first set of semicircular conductors, and a fourth set of straight axial segments disposed contiguous to said third set of straight axial segments connecting one extremity of successive adjacent pairs of said second set of semicircular conductors, whereby the electrical equivalent of contrawound helices is simulated.

9. The slow-wave structure as defined in claim 8, wherein a lossy material is deposited between said contiguous axial segments.

l0. A traveling-wave tube comprising an evacuated envelope; an electron gun disposed at one end of said envelope for producing an electron stream; means for directing said stream along the longitudinal axis of said envelope; a collector electrode disposed at the opposite end of said envelope for intercepting the stream electrons; an input waveguide having an end portion disposed transversely to said path adjacent said electron gun, said end portion of said input waveguide having a first aperture in the wall facing said electron gun and a second aperture in the opposite wall, said first and second apertures in the end portion of said input waveguide being disposed concentrically about said path; an output waveguide having an end portion disposed transversely to said path adjacent said collector, said output waveguide having a first aperture in the wall facing said collector and a second aperture in. the opposite wall, said first and second apertures in the end portion of said output waveguide being disposed concentrically about said path, said first apertures of each of said waveguides being equal in diameter and said second apertures of each of said waveguides being equal in diameter, said second apertures being larger than said first apertures; a conductive non-magnetic tubular element extending through said first apertures of said waveguides for providing a slow-'wave structure, said tubular element having a plurality of rectangularly shaped transverse slots relieved at periodic intervals therealong, each slot having arcuate edges perpendicular to said longitudinal axis whereby the electrical equivalent of contrawound conductive helices is simulated.

l1. The traveling-wave tube as defined in claim 10, wherein said second apertures of each of said waveguides have a diameter larger than that of said tubular element by an amount equal to four times the width of the transverse slots of said tubular element, each of said waveguides having a shorted termination disposed at a distance from said tubular elementl approximately equal to two times the width of the slots of said tubular element.

References Cited in the le of this patent UNITED STATES PATENTS Great Britain Mar. 12, 1952v Patent No 2,957,103 October 18, 1960 Charles K Birdsall It is hereby certified'that erIoI" ent requiring correction and that the s corrected below.

appears in the bove numbered pataid Letters Patent should read as Column 4, line 5% for "54 read e@ 53 g column 6, line 36, for "LeM read e: the QC- Signed and sealed this 27th day of June 1961o SEA L) Attest; A* ERNEST W. SWIDER DAVID L. LADD Attesting Officer Commissioner of Patents

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Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US3069588 *Sep 26, 1958Dec 18, 1962Raytheon CoTraveling wave tubes
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US3335314 *Sep 4, 1963Aug 8, 1967Varian AssociatesHigh frequency electron discharge device having oscillation suppression means
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Classifications
U.S. Classification315/3.6, 315/39.3, 333/157, 313/44, 313/45, 333/162
International ClassificationH01J23/27, H01J23/16
Cooperative ClassificationH01J23/27
European ClassificationH01J23/27