Klystron

A klystron is a specialized linear-beam vacuum tube (evacuated electron tube). Klystrons are used as amplifiers at microwave and radio frequencies to produce both low-power reference signals for super heterodyne radar receivers and to produce high-power carrier waves for communications and the driving force for modern particle accelerators.

Klystron amplifiers have the advantage (over the magnetron) of coherently amplifying a reference signal so its output may be precisely controlled in amplitude, frequency and phase. Many klystrons have a waveguide for coupling microwave energy into and out of the device, although it is also quite common for lower power and lower frequency klystrons to use coaxial couplings instead. In some cases a coupling probe is used to couple the microwave energy from a klystron into a separate external waveguide.

All modern klystrons are amplifiers, since reflex klystrons, which were used as oscillators in the past, have been surpassed by alternative technologies.

The name klystron comes from the stem form κλυσ- (klys) of a Greek verb referring to the action of waves breaking against a shore, and the end of the word electron.

Klystrons produce microwave power far in excess of that developed by solid state. In modern systems, they are used in ultrahigh-frequency (UHF) television transmissions, which operate at power levels of less than 50 kilowatts. For ground-based communications, the range of

power levels is from 1 to 20 kilowatts. Pulsed klystrons are primarily used in radar and in scientific and medical linear accelerators. Some applications employ more than two cavities to obtain higher gain and more bandwidth. The power gain of the klystron is dependent on the voltage and current as well as on the number of cavities used. The larger the number of cavities employed, the larger the gain that can be obtained. There is, however, a practical limit imposed by the onset of RF instability.

History

The brothers Russell and Sigurd Varian of Stanford University are the inventors of the klystron. Their prototype was completed in August 1937. Upon publication in 1939,[1] news of the klystron immediately influenced the work of US and UK researchers working on radar equipment. The Varians went on to found Varian Associates to commercialize the technology (for example to make small linear accelerators to generate photons for external beam radiation therapy). In their 1939 paper, they acknowledged the contribution of A. Arsenjewa-Heil and Oskar Heil (wife and husband) for their velocity modulation theory in 1935.

The work of physicist W.W. Hansen was instrumental in the development of the klystron and was cited by the Varian brothers in their 1939 paper. His resonator analysis, which dealt with the problem of accelerating electrons toward a target, could be used just as well to decelerate electrons (i.e., transfer their kinetic energy to RF energy in a resonator). During the second World War, Hansen lectured at the MIT Radiation labs two days a week, commuting to Boston from Sperry gyroscope company on Long Island. His resonator, called a "hohlraum" by nuclear physicists and coined "rhumbatron" by the Varian brothers, is used in 2009 in the National Ignition Facility investigating nuclear fusion. Hansen died in 1949 as a result of exposure to beryllium oxide (BeO).

During the second World War, the Axis powers relied mostly on (then low-powered) klystron technology for their radar system microwave generation, while the Allies used the far more powerful but frequency-drifting technology of the cavity magnetron for microwave generation. Klystron tube technologies for very high-power applications, such as synchrotrons and radar systems, have since been developed.

Explanation

Klystrons amplify RF signals by converting the kinetic energy in a DC electron beam into radio frequency power. A beam of electrons is produced by a thermionic cathode (a heated pellet of low work function material), and accelerated by high-voltage electrodes (typically in the tens of kilovolts). This beam is then passed through an input cavity. RF energy is fed into the input cavity at, or near, its natural frequency to produce a voltage which acts on the electron beam. The electric field causes the electrons to bunch: electrons that pass through during an opposing electric field are accelerated and later electrons are slowed, causing the previously continuous electron beam to form bunches at the input frequency. To reinforce the bunching, a klystron may contain additional "buncher" cavities. The RF current carried by the

beam will produce an RF magnetic field, and this will in turn excite a voltage across the gap of subsequent resonant cavities. In the output cavity, the developed RF energy is coupled out. The spent electron beam, with reduced energy, is captured in a collector.

Velocity Modulation

The microwave tube was developed when the use of the frequency spectrum went beyond 1,000 megahertz and into the microwave range. The microwave tube uses transit time in the conversion of dc power to radio-frequency (rf) power. The interchange of power is accomplished by using the principle of electron VELOCITY MODULATION and low-loss resonant cavities in the microwave tube.

A clear understanding of microwave tubes must start with an understanding of how electrons and electric fields interact. An electron has mass and thus exhibits kinetic energy when in motion. The amount of kinetic energy in an electron is directly proportional to its velocity; that is, the higher the velocity, the higher the energy level. The basic concept of the electron energy level being directly related to electron velocity is the key principle of energy transfer and amplification in microwave tubes.

An electron can be accelerated or decelerated by an electrostatic field. Figure 2-2 shows an electron moving in an electrostatic field. The direction of travel (shown by the heavy arrow) is against the electrostatic lines of force which are from positive to negative. The negatively charged electron will be attracted to the positively charged body and will increase in velocity. As its velocity increases, the energy level of the electron will also increase. Where does the electron acquire its additional energy? The only logical source is from the electrostatic field. Thus, the conclusion is clear. An electron traveling in a direction opposite to electrostatic lines of force will absorb energy and increase in velocity (accelerate).

Figure 2-2. - Moving electron gaining velocity and energy.

As figure 2-3 illustrates, the opposite condition is also true. An electron traveling in the same direction as the electrostatic lines of force will decelerate by giving up energy to the field. The negatively charged body will repel the electron and cause it to decrease in velocity. When the velocity is reduced, the energy level is also reduced. The energy lost by the electron is gained by the electrostatic field.

Figure 2-3. - Moving electron losing energy and velocity.

The operation of a velocity-modulated tube depends on a change in the velocity of the electrons passing through its electrostatic field. A change in electron velocity causes the tube to produce BUNCHES of electrons. These bunches are separated by spaces in which there are relatively few electrons. Velocity modulation is then defined as that variation in the velocity of a beam of electrons caused by the alternate speeding up and slowing down of the electrons in the beam. This variation is usually caused by a voltage signal applied between the grids through which the beam must pass.

The first requirement in obtaining velocity modulation is to produce a stream of electrons which are all traveling at the same speed. The electron stream is produced by an electron gun. A simplified version of an electron gun is shown in figure 2-4, view (A). Electrons emitted from the cathode are attracted toward the positive accelerator grid and all but a few of the electrons pass through the grid and form a beam. The electron beam then passes through a pair of closely spaced grids, called BUNCHER GRIDS. Each grid is connected to one side of a tuned circuit. The parallel-resonant tuned circuit (view (A)) in the illustration represents the doughnut-shaped resonant cavity surrounding the electron stream (view (B)). The buncher grids are the dashed lines at the center of the cavity and are at the same dc potential as the accelerator grid. The alternating voltage which exists across the resonant circuit causes the velocity of the electrons leaving the buncher grids to differ from the velocity of the electrons

arriving at the buncher grids. The amount of difference depends on the strength and direction of the electrostatic field within the resonant cavity as the electrons pass through the grids.

Figure 2-4A. - Electron gun with buncher grids.

Figure 2-4B. - Electron gun with buncher grids.

The manner in which the buncher produces bunches of electrons is better understood by considering the motions of individual electrons, as illustrated in figure 2-5 beginning with view (A).

When the voltage across the grids is negative, as shown in view (B), electron 1 crossing the gap at that time is slowed. View (C) shows the potential across the gap at 0 volts; electron 2 is not affected. Electron 3 enters the gap (view (D)) when the voltage across the gap is positive and its velocity is increased. The combined effect is shown in view (E). All of the electrons in the group have been bunched closer together.

Figure 2-5A. - Buncher cavity action. BUNCHER CAVITY

Figure 2-5B. - Buncher cavity action. ELECTRON #1 DECELERATED

Figure 2-5C. - Buncher cavity action. ELECTRON #2 VELOCITY UNCHANGED

Figure 2-5D. - Buncher cavity action. ELECTRON #3 ACCELERATED

Figure 2-5E. - Buncher cavity action. ELECTRONS BEGINNING TO BUNCH, DUE TO VELOCITY DIFFERENCES

The velocity modulation of the beam is merely a means to an end. No useful power has been produced at this point. The energy gained by the accelerated electrons is balanced by the energy lost by the decelerated electrons. However, a new and useful beam distribution will be formed if the velocity-modulated electrons are allowed to drift into an area that has no electrostatic field.

As the electrons drift into the field-free area beyond the buncher cavity, bunches continue to form because of the new velocity relationships between the electrons. Unless the beam is acted upon by some other force, these bunches will tend to form and disperse until the original beam distribution is eventually reformed. The net effect of velocity modulation is to form a current-density modulated beam that varies at the same rate as the grid-signal frequency. The next step is to take useful power from the beam.

The current-modulated (bunched) electron beam in figure 2-6 is shown in various stages of formation and dispersion. A second cavity, called a CATCHER CAVITY, must be placed at a point of maximum bunching to take useful energy from the beam (shown in view (B)). The physical position of the catcher cavity is determined by the frequency of the buncher-grid signal because this signal determines the transit time of the electron bunches. Note also that both cavities are resonant at the buncher-grid frequency. The electron bunches will induce an rf voltage in the grid gap of the second cavity causing it to oscillate. Proper placement of the second cavity will cause the induced grid-gap voltage to decelerate the electron bunches as they arrive at the gap. Since the largest concentration of electrons is in the bunches, slowing the bunches causes a transfer of energy to the output cavity. The balance of energy has been disturbed because the placement of the catcher cavity is such that bunches are slowed down when they arrive at the cavity. The areas between bunches arrive at the cavity at just the right time. At this time the voltage is of the correct polarity to increase the velocity of the electrons and the beam absorbs energy. The areas between the bunches have very few electrons, so the energy removed from the beam is much greater than the energy required to speed up the electrons between the bunches. Therefore, if the second cavity is properly positioned, useful energy can be removed from a velocity-modulated electron beam.

Figure 2-6A. - Removing energy from a velocity-modulated beam.

Figure 2-6B. - Removing energy from a velocity-modulated beam.

The Basic Two-Cavity Klystron

Klystrons are velocity-modulated tubes that are used in radar and communications equipment as oscillators and amplifiers. Klystrons make use of the transit-time effect by varying the velocity of an electron beam in much the same manner as the previously discussed velocity-modulation process. Strong electrostatic fields are necessary in the klystron for efficient

operation. This is necessary because the interaction of the signal and the electron beam takes place in a very short distance.

The construction and essential components of a TWO-CAVITY KLYSTRON are shown in view (A) of figure 2-7. View (B) is a schematic representation of the same tube. When the tube is energized, the cathode emits electrons which are focused into a beam by a low positive voltage on the control grid. The beam is then accelerated by a very high positive dc potential that is applied in equal amplitude to both the accelerator grid and the buncher grids. The buncher grids are connected to a cavity resonator that superimposes an ac potential on the dc voltage. Ac potentials are produced by oscillations within the cavity that begin spontaneously when the tube is energized. The initial oscillations are caused by random fields and circuit imbalances that are present when the circuit is energized. The oscillations within the cavity produce an oscillating electrostatic field between the buncher grids that is at the same frequency as the natural frequency of the cavity. The direction of the field changes with the frequency of the cavity. These changes alternately accelerate and decelerate the electrons of the beam passing through the grids. The area beyond the buncher grids is called the DRIFT SPACE. The electrons form bunches in this area when the accelerated electrons overtake the decelerated electrons.

Figure 2-7B. - Functional and schematic diagram of a two-cavity klystron.

Figure 2-7A. - Functional and schematic diagram of a two-cavity klystron.

The function of the CATCHER GRIDS is to absorb energy from the electron beam. The catcher grids are placed along the beam at a point where the bunches are fully formed. The location is determined by the transit time of the bunches at the natural resonant frequency of the cavities (the resonant frequency of the catcher cavity is the same as the buncher cavity). The location is chosen because maximum energy transfer to the output (catcher) cavity occurs when the electrostatic field is of the correct polarity to slow down the electron bunches.

The two-cavity klystron in figure 2-7 may be used either as an oscillator or an amplifier. The configuration shown in the figure is correct for oscillator operation. The feedback path provides energy of the proper delay and phase relationship to sustain oscillations. A signal applied at the buncher grids will be amplified if the feedback path is removed.

TWO-CAVITY KLYSTRON AMPLIFIER

It is a µ wave amplifier with two cavities: one is input cavity known as buncher cavity and the other is output cavity known as catcher cavity.

The region in between the cavities is called drift region, which is a field-free space.

At one end exists an electron gun and at the other end electron collector, a metal plate grounded.

WORKING An uniform electron beam is formed from the divergent electrons emitted by

the cathode using a focusing grid and accelerated to high velocities by an accelerating voltage.

All the electrons enter the grid gap with one velocity v0 = √eV0/m).In the grid gap they encounter the signal voltage, which we assume a single sinusoid Vs = V1Sint of frequency resulting in ‘velocity modulation’ given by

v(t1) = v0[1+iV1/2V0 sin(t1-g/2)].

All the electrons which cross during positive half cycle of the gap voltage gets accelerated and that cross during the negative half cycle get decelerated.

Different electrons that enter the gap at different instants during the positive/negative half cycle get different amounts of acceleration.

As the amount of acceleration is equal to the deceleration the average acceleration or deceleration of the electrons is nil i.e. the average velocity of the electrons with which they leave the grid gap is same as that with which they entered.

While travelling through the drift region the beam under go ‘density modulation’. All the electrons that cross the gap during the gap voltage changes from negative peak to positive peak come together forming ‘bunch’, a thin dense electron cloud.

One bunch per cycle forms and the length of the drift region is selected so that bunch formation completes by the time it reaches the grid gap.

While crossing the grid gap, the bunch gives energy to the cavity to be taken out using a loop.

ANALYSIS

Let us suppose the device is along the z-axis with its first grid walls at z=0 and z=d. If v0

is the velocity of the electrons with which they enter the cavity gap then. It is given by v0

= √eV0/m) If the gap voltage due to the input signal is Vs = V1Sint, then the average gap voltage

during the transit of the reference electron is <V> = V1i sin(t0+g/2) where I is known as Beam coupling coefficient. It is the ratio of the alternating current

induced in the resonator to the alternating component of beam current that produces it. For the present case it is I = (sing/2)/ g/2

g is the average gap transit angle for the electrons = & is average gap transit time for the electrons = d/v0 ≈≈ t1-t0

Velocity with which the electrons leave the buncher gap v(t1) = v0[1+iV1/2V0 sin(t1-g/2)]. This is the equation of velocity modulation, which describes the variation of velocity of electrons in the drift space. The quantity iV1/V0 is known as the depth of velocity modulation.

If T is the transit time of the electrons in drift space then T =t2 – t1 = L/v(t1) = T0[1-iV1/2V0 sin(t1-g/2)].

The transit angle of the electron in drift space is T = 0[1-iV1/2V0 sin(t1-g/2)] or 0-X sin(t1-g/2) where

0 = L/v0 is the transit angle of the dc electron and X is Bunching parameter of the two cavity klystron

= (iV1/2V0) 0 = (iV1/2V0)L/v0

which determines the degree of bunching and the waveform of the density –modulated beam.

Optimum length of the drift space L0 = (3.6/(v0V0/iV1) Let i2 (t2) be the current at catcher cavity and from the principle of the charge

conservation i2 |dt2 |= I0 |dt0|i2 = I0 / (|dt0|/|dt2|)

t2 = t0 + T0 [1-iV1/2V0 sin (t1-g/2)] giving

dt2 = dt0 - T0 cos(t0+g/2) dt0

I0 / (dt0/dt2 ) = I0 /1-X cos (t0+g/2) = I0 /1-X cos (t2-0-g/2)

As i2 (t2) is a periodic current, it can be expanded in Fourier seriesi2 (t2) = I0 + [ ] n=1Σ∞ 2I0 Jn (nx) cos [n(t-0-g)]. Out of these infinite number of components only the primary or fundamental component that is useful to amplify the signal. The amplitude of the fundamental component I2 = 2I0 J1 (x) which assumes is maximum value when X = 1.841 = (iV1/2V0)L/v0 leading to the optimum length of the drift space L0 = (3.6/(v0V0/iV1).

Equivalent circuit

It consists of a parallel combination of wall resistance of the catcher cavity, beam loading resistance and external load resistance

Output power

Electronic efficiency =

If the coupling is perfect β0 = I1 , max I2 is 2I0 (0.58), and V2 = V0 , then the max electronic efficiency η = 58%, in practice it is 15 to 30%.

Voltage gain Av

Mutual conductance G m

PERFORMANCE

o Efficiency about 40% (58% max)

o Power output: CW power up to 500 kW

o Pulsed power up to 30 MW

o Power gain: about 30 db

Beam Loading

The production of an electronic admittance between two grids when an initially un-modulated beam of electrons is shot across the gap between them is called “Beam Loading”.

If the buncher cavity gap width is more, the gap transit angle will be large and the buncher cavity supplies energy to the beam to bunch. The power PB required to produce bunching action is given as PB = V1

2 GB where GB is known as beam loading conductance

equal to

The Conductive component of beam loading admittance is

Positive Gb indicates * Power is being delivered to the beam by the source of

alternating gap voltage. If the voltage source is resonator reduction in its Q broadening its tuning.

Negative Gb indicates * Beam is delivering power to the source of alternating gap voltage. If the source of alternating gap voltage is resonator, it may go into oscillations.

The susceptive component is

It affects the resonance frequency of a resonator connected across the gap and therefore cause the frequency of an oscillator to change with beam current and voltage.

MULTICAVITY KLYSTRON

It gives more power gain than two-cavity Klystron. In a multi-cavity klystron each of the intermediate cavities, placed at a distance of the bunching parameter X of 1.841 away from the previous cavity acts as a buncher with the passing electron beam inducing a more enhanced RF voltage than the previous cavity, which in turn sets up an increased velocity modulation. The spacing between the consecutive cavities would therefore distinguish [From Lopt = (3.6/w)(0V0/iV1)]

The multi-cavity klystrons are often operated with their cavities stagger tuned to obtain greater bandwidth.Power gain: 40 to 50 dBBandwidth: several percentFrequency: 0.5 GHz to 14 GHzPower range: 25 kW to 40 MW

These are noisy because the bunching is never complete and so the electrons arrive at random at catcher cavity. So it is too noisy for use in receivers.

REFLEX KLYSTRON

Reflex Klystron is a low power, low efficiency µ-wave oscillator; used as signal source in Microwave generators, as local oscillator in microwave receivers, as pump oscillator in parametric amplifiers, as frequency modulated oscillators in portable microwave links. Its power output ranges from 10 mW to 3W and frequency from 4 to 200 GHz.

Its basic parts are one reentrant cavity, beam emitter, accelerator and repeller. The electron beam emitted is accelerated to high velocities by the accelerating voltage

and while passing through the grid gap the beam gets velocity modulated.

The velocity-modulated beam enters the repeller region to face repulsive field of the repeller region.

All the electrons, which cross the grid gap during the period from the positive peak to negative peak, come together forming a bunch after spending different amounts of time in the repeller region.

The thin dense electron cloud i.e. bunch crosses the gap giving energy to the gap. For maximum transfer of energy the gap voltage must be large and opposing the bunch movement.

Repeller protection: The voltage to repeller is always applied before the cathode and

A cathode resistor is often used to ensure that the repeller can never be more positive than the cathode.

Tuning: Frequency can be adjusted by adjustable screw , bellows or dielectric insert

(mechanical methods). Frequency can also be varied by adjusting the repeller voltage (electronic tuning). It is

an important feature of the reflex klystron because it provides a means of obtaining fine tuning and also a means of introducing frequency modulation. In a typical case, a total frequency variation of the order of 1 percent can be obtained.

ANALYSIS

Suppose the oscillator is lying along the z-axis with it grid walls at z=0 and z=d Let 0 t is the instant at which the reference electron enters the cavity gap at z = 0, t1 is the instant at which the electron leaves cavity gap at z = d and 2 t is the instant at which the same electron returned back to the gap by retarding field at z = d and collected by the walls of cavity.

Let v0 is the velocity with which the electrons enter the cavity gap after getting accelerated by potential V0 . Then it must be equal to √eV0/m). So the velocity with which the electron enters the cavity gap at t = t0 and z = 0 is √eV0/m).

The electrons while traversing the grid gap undergo a process known as ‘velocity modulation’ with the following features. Assuming the presence of single frequency component in the grid gap,

o The electrons that cross the gap during the positive half cycle of the gap

voltage get accelerated and those that cross during the negative half cycle undergoes deceleration.

o Different electrons that enter the gap at different instants during a half cycle

undergo different amounts of acceleration/deceleration.o The amount of acceleration is equal to the amount of deceleration during one

cycle of the gap voltage as the beam is uniform. So the average amount of acceleration/deceleration is zero.

o The average velocity of the electrons is same as the velocity with which they

enter the gap i.e.v0

o Different electrons leave the gap with different velocities Let vt1 is the

velocity with which the reference electron leaves the cavity gap at t1 = t and z d. Then it is equal to v(t1) = v0[1+iV1/2V0 sin(t1-g/2)].This is known as the equation of velocity modulation.

The electrons crossing the gap enter into the repeller region in the face of retarding force and spend different amounts of time before returning back to the gap. Electrons accelerated during the gap transit enter deep into the repeller region and hence require more time to come back to gap when compared to the electrons that got decelerated.

o E = Retarding electron field in the repeller space =

o The force equation for an electron in the repeller region is

Integrating this equation twice and applying the conditions

After the round trip the electron returns to the gap at t = t2, so at t = t2 , z = d giving

The transit time of the electron in the repeller region is

Form this

This equation for the repeller transit time can be put in the form of

all the electrons that cross the grid gap during the gap voltage variation from positive peak to negative peak spend different amounts of time in the repeller region and comeback to the gap at one instant forming into a ‘Bunch’. The electron bunch gives

maximum energy to the gap field when it faces maximum deceleration which is possible only when the transit time of electrons in the repeller space is

where n is a positive integer two onwards. So the round trip transit angle referring to the center of bunch electron

1 should be

o The transit time depends on the repeller and anode voltages

Power output of the RKOBy comparing with that of the two-cavity klystron the beam current of a reflex klystron oscillator can be writtenThe fundamental component of induced current isThe ac power delivered to the load

Efficiency of the RKO

Repeller voltage versus mode number

From the above relations

Power output versus repeller voltage

Frequency versus Repeller voltage

Electronic admittance Ye It is the ratio of the induced current i2 at t2 in phasor form to the voltage V2 across the gap at t2.

Equivalent circuit of the Reflex Klystron It consists of a parallel combination of one capacitor, one inductor both representing the energy storage elements of the cavity, three inductances representing copper losses, beam loading and load conductance.

The necessary condition for oscillations is that the magnitude of the negative real part of the electronic admittance should be greater than or equal to the total conductance of the cavity circuit. i.e.

TRAVELLING WAVE TUBE (TWT) TWT is a linear beam tube in which the interaction between the beam and the RF field

is continuous over a length.

Complete bunching results due to continuous interaction between axial RF field and

beam ultimately giving high gain.

TWT uses non-resonant microwave circuit and is capable of enormous bandwidths.

Slow-wave structures are special circuits used in microwave tubes to reduce the wave

velocity in a certain direction so that the electron beam and signal wave can interact; Ex: Helix, Folded back line, Zigzag line, inter-digital line, corrugated wave-guide and coupled cavities are slow-wave structures widely used.

HELIX When the signal is travelling along the coil with velocity C, the phase velocity of the wave in the axial direction is

The axial electric field E (x, y, z) is periodic along axial direction i.e z- direction withperiodicity equal to patch. This field can be expressed as linear combination of severalspatial harmonics using Fourier theorem.

PRINCIPLE OF WORKINGo There exists a spatially periodic travelling wave co-axial to the helix when the

signal is travelling along the length of its conductor.o The electron beam is accelerated to a velocity, which is slightly more than the

phase velocity of the axial wave.o The axial wave accelerates the electrons during one half cycle and decelerates

during the second half cycle but at any point of time there exists more electrons in the decelerating half cycle resulting in net transfer of energy from the electrons to the wave.

o The strengthened wave offers more deceleration to the incoming electrons,

increasing electron concentration in its region thereby increasing energy transfer to the beam manifold.

o It results in the exponential growth of the signal along the length of the helix.

Brillouin Diagram It is diagram for a helical slow-wave structure with several spatial harmonics. The second quadrant of the diagram indicates the negative phase velocity that corresponds to the negative n .The shaded areas are the forbidden regions for propagation. It is because if the axial phase velocity of any spatial harmonic exceeds the velocity of light, the structure radiates energy.

Attenuator Oscillations are possible in this high gain device, especially if poor load matching causes significant reflections along the slow wave structures very close coupling of slow-wave circuits further aggravates the problem. Attenuator is used to prevent oscillations in TWT and it has the subsidiary effect of reducing the gain. The attenuator may be a lossy metallic coating such as Aquadag or KANTHAL on the surface of the glass tube.Both forward and reverse waves are attenuated, but the forward wave is able to continue and grow past the attenuator because bunching is unaffected.

Electronic Equation It determines the convection current induced by the axial electric field.

Circuit Equation It determines how the spatial ac electron beam current affects the axial electric field of the slow-wave helix.

TWT gain parameter

Power gain

Propagation constants The four propagation constants represent four different modes of wave propagation in the O-type helical TWT.

It represents forward traveling wave. The beam velocity is slightly more than the phase velocity of this wave. Energy transfer takes place from the beam to the wave so its amplitude increases as it progresses.

It represents forward traveling wave. The beam velocity is slightly more than the phase velocity of this wave. Energy transfer takes place from the beam to the wave so its amplitude increases as it progresses.

It represents wave traveling in the forward direction. The beam velocity is less than the phase velocity of this wave. There exists no transfer of power between the beam and wave.

It represents a wave traveling in the reverse direction with no transfer of energy. The beam velocity is less than the phase velocity of the wave.

Coupled-cavity TWT

Helix TWTs are limited in peak RF power by the current handling (and therefore thickness) of the helix wire. As power level increases, the wire can overheat and cause the helix geometry to warp. Wire thickness can be increased to improve matters, but if the wire is too thick it becomes impossible to obtain the required helix pitch for proper operation. Typically helix TWTs achieve less than 2.5 kW output power.The coupled-cavity TWT overcomes this limit by replacing the helix with a series of coupled cavities arranged axially along the beam. Conceptually, this structure provides a helical waveguide and hence amplification can occur via velocity modulation. Helical waveguides have very nonlinear dispersion and thus are only narrowband (but wider than klystron). A coupled-cavity TWT can achieve 60 kW output power.Operation is similar to that of a klystron, except that coupled-cavity TWTs are designed with attenuation between the slow-wave structure instead of a drift tube. The slow-wave structure gives the TWT its wide bandwidth. A free electron laser allows higher frequencies.

MAGNETRON

The cavity magnetron is a high-powered vacuum tube that generates microwaves using the interaction of a stream of electrons with a magnetic field. The 'resonant' cavity magnetron variant of the earlier magnetron tube was invented by Randall and Boot in 1940. The high power of pulses from the cavity magnetron made centimetre-band radar practical. Shorter wavelength radars allowed detection of smaller objects. The compact cavity magnetron tube drastically reduced the size of radar sets so that they could be installed in anti-submarine aircraft and escort ships. At present, cavity magnetrons are commonly used in microwave ovens and in various radar applications.

Construction and operation

All cavity magnetrons consist of a hot cathode with a high (continuous or pulsed) negative potential by a high-voltage, direct-current power supply. The cathode is built into the center of an evacuated, lobed, circular chamber. A magnetic field parallel to the filament is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced around the rim of the chamber are cylindrical cavities. The cavities are open along their length and connect the common cavity space. As electrons sweep past these openings, they induce a resonant, high-frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular

cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high-gain antenna in the case of radar.

A cross-sectional diagram of a resonant cavity magnetron. Magnetic lines of force are parallel to the geometric axis of this structure.

The sizes of the cavities determine the resonant frequency, and thereby the frequency of emitted microwaves. However, the frequency is not precisely controllable. The operating frequency varies with changes in load impedance, with changes in the supply current, and with the temperature of the tube. This is not a problem in uses such as heating, or in some forms of radar where the receiver can be synchronized with an imprecise magnetron frequency. Where precise frequencies are needed, other devices such as the klystron are used.

The magnetron is a self-oscillating device requiring no external elements other than a power supply. A well-defined threshold anode voltage must be applied before oscillation will build up; this voltage is a function of the dimensions of the resonant cavity, and the applied magnetic field. In pulsed applications there is a delay of several cycles before the oscillator achieves full peak power, and the build-up of anode voltage must be coordinated with the build-up of oscillator output.

The magnetron is a fairly efficient device. In a microwave oven, for instance, a 1.1 kilowatt input will generally create about 700 watt of microwave power, an efficiency of around 65%. (The high-voltage and the properties of the cathode determine the power of a magnetron.) Large S-band magnetrons can produce up to 2.5 megawatts peak power with an average power of 3.75 kW.Large magnetrons can be water cooled. The magnetron remains in widespread use in roles which require high power, but where precise frequency control is unimportant.

Cavity Magnetron is a high power, high efficiency microwave oscillator which depends upon the interaction of electrons with a traveling electromagnetic wave for its operation.

It is a diode with several connected re-entrant cavities in the anode structure. The connected re-entrant cavities results in the existence of a rotating rf field in the interaction region whose angular frequency is

It is a crossed – field device as it employs axial dc magnetic field and radial dc

voltage. If the values these fields are adjusted property, the electrons follow cycloid paths in the interaction space.

In total there exists three fields in the interaction region of magnetron.

Hull Cut-off field is the magnetic field/electric field required to return the electrons to the cathode after they have just grazed the anode in the absence of RF field.

Mode π oscillations: Self-consistent oscillations can exist only if the phase difference between the adjoining anode poles is nπ / 4 where n =1,2,3 etc. For best results n = 4 is used in practice which gives a phase difference of π between two successive poles and the resulting mode is known as π - mode.

Strapping: Magnetrons using identical cavities in the anode block employs strapping to prevent mode jumping. For π mode of operation it consists of two rings of heavy gauge wire connecting alternate anode poles.π At very high frequencies, rising–sun anode structure is used to prevent mode jumping.

Frequency pulling: The resonant frequency of the magnetron alters with the changes in the load admittance. Such frequency variation is known as frequency - pulling.

Frequency Pushing: It is the variation of the frequency of the magnetron due to the changes in anode voltage.

Phase–focusing effect: In cavity magnetron the electrons are bunched by an effect known as phase – focusing effect without it, the favoured electrons (i.e. which contribute energy to the RF field) would fall behind the phase changes of the electric field across the gaps, since such electrons are retarded at teach interaction with the RF field. The wheel spoke bunches rotate counter clockwise with correct velocity allowing continuous interchange of energy. In this interchange, the RF field receives much more than it gives.

FUNCTIONING The dc field strengths are to be adjusted to cut-off values i.e. V0 should be set to

For a given V0

Under the influence of the dc fields and the rotating rf field the emitted electrons from the cathode revolve around the cathode with a cyclotron angular frequency

When the cyclotron frequency of the electrons is equal to the angular frequencyof the field i.e.

the interactions between the field and electron occurs and the energy is transferred .

ANALYSISEquations of Electron motion

The Lorenz force acting on an electron because of the presence of both the electric field E and the magnetic flux B is given by

In Cylindrical-coordinate system the general expression for the acceleration is a =

Uses: It is a high power microwave source used in Radar transmitters Linear particle accelerators.

Performance chart: It is a chart containing the contours of constant power output, constant efficiency, constant flux density and occasionally constant frequency. Plotted on coordinates of direct anode voltage Vs direct anode current at a specified load admittance.

Load admittance diagrams: it is a chart containing contours of constant power or efficiency and of constant frequency plotted in coordinates of load resistance and load reactance. When polar coordinates are used these diagrams are called “Rieke Diagrams”

The Backward-Wave Oscillator

The BACKWARD-WAVE OSCILLATOR (bwo) is a microwave-frequency, velocity-modulated tube that operates on the same principle as the twt. However, a traveling wave that moves from the electron gun end of the tube toward the collector is not used in the bwo. Instead, the bwo extracts energy from the electron. beam by using a backward wave that travels from the collector toward the electron gun (cathode). Otherwise, the electron bunching action and energy extraction from the electron beam is very similar to the actions in a twt. The typical bwo is constructed from a folded transmission line or waveguide that winds back and forth across the path of the electron beam, as shown in figure 2-16.

The folded waveguide in the illustration serves the same purpose as the helix in a twt. The fixed spacing of the folded waveguide limits the bandwidth of the bwo. Since the frequency of a given waveguide is constant, the frequency of the bwo is controlled by the transit time of the electron beam. The transit time is controlled by the collector potential. Thus, the output frequency can be changed by varying the collector voltage, which is a definite advantage. As in the twt, the electron beam in the bwo is focused by a magnet placed around the body of tube

M-type BWO :

Schematic of an M-BWO

The M-type carcinotron, or M-type backward wave oscillator, uses crossed static electric field E and magnetic field B, similar to the magnetron, for focusing an electron sheet beam drifting perpendicularly to E and B, along a slow-wave circuit, with a velocity E/B. Strong interaction occurs when the phase velocity of one space harmonic of the wave is equal to the electron velocity. Both Ez and Ey components of

the RF field are involved in the interaction (Ey parallel to the static E field). Electrons which are in a decelerating Ez electric field of the slow-wave, lose the potential energy they have in the static electric field E and reach the circuit. The sole electrode is more negative than the cathode, in order to avoid collecting those electrons having gained energy while interacting with the slow-wave space harmonic.

O-type BWO :The O-type carcinotron, or O-type backward wave oscillator, uses an electron beam longitudinally focused by a magnetic field, and a slow-wave circuit interacting with the beam. A collector collects the beam at the end of the tube.

The Crossed-Field Amplifier (Amplitron)

The CROSSED-FIELD AMPLIFIER (cfa), commonly known as an AMPLITRON and sometimes referred to as a PLATINOTRON, is a broadband microwave amplifier that can also be used as an oscillator. The cfa is similar in operation to the magnetron and is capable of providing relatively large amounts of power with high efficiency. The bandwidth of the cfa, at any given instant, is approximately plus or minus 5 percent of the rated center frequency. Any incoming signals within this bandwidth are amplified. Peak power levels of many megawatts and average power levels of tens of kilowatts average are, with efficiency ratings in excess of 70 percent, possible with crossed-field amplifiers. Because of the desirable characteristics of wide bandwidth, high efficiency, and the ability to handle large amounts of power, the cfa is used in many applications in

microwave electronic systems. This high efficiency has made the cfa useful for space-telemetry applications, and the high power and stability have made it useful in high-energy, linear atomic accelerators. When used as the intermediate or final stage in high-power radar systems, all of the advantages of the cfa are used. Since the cfa operates in a manner so similar to the magnetron, the detailed theory is not presented in this module.