## 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. The figure below 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).

Moving electron gaining velocity and energy.

As the figure below 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.

Moving electron losing velocity and energy.

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 the figure below 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.

View A: Electron gun with buncher grids.

View B: 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 the figure below 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 view closer together.

View A: Buncher cavity action BUNCHER-CAVITY.

View B: Buncher cavity action ELECTRON-1-DECELERATED.

View C: Buncher cavity action ELECTRON-2-VELOCITY-UNCHANGED.

View D: Buncher cavity action ELECTRON-3-ACCELERATED.

View E: 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 2-6A and B 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 figure 2-6B).

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.

Removing energy from a velocity modulated beam.

Removing energy from a velocity modulated beam.

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