## Travelling Wave Tube Amplifiers

#### Theory The essential principle of operation of a TWT lies in the interaction between an electron beam and an RF signal. The velocity, v, of an electron beam is given by:

An anode voltage of 5 kV gives an electron velocity of 4.2 x 107 m/s. The signal would normally travel at c, the velocity of light (3x108 m/s), which is much faster than any 'reasonable' electron beam (relativistic effects mean that the electron mass actually increases as its velocity approaches c, so that achieving electron velocities approaching c is a complicated business), If, however, the signal can be slowed down to the same velocity as the electron beam, it is possible to obtain amplification of the signal by virtue of its interaction with the beam. This is usually achieved using the helix electrode, which is simply a spiral of wire around the electron beam,

###### The geometry of the helix Without the helix, the signal would travel at a velocity c. With the helix, the axial signal velocity is approximately c x (p /2πa) where a, p are shown above, so the signal is slowed by the factor p/2πa. Note that this is independent of signal frequency. The signal travelling along the helix is known as a slow wave, and the helix is referred to as a slow-wave structure, The condition for equal slow-wave and electron-beam velocities is therefore approximately

The interaction between the beam and the slow wave takes the form of 'velocity modulation' of the beam (i.e. some electrons are accelerated and some retarded) forming electron bunches within the beam. The beam current therefore becomes modulated by the RF signal, and the bunches react with the RF fields associated with the slow wave travelling down the helix, resulting in a net transfer of energy from the beam to the signal, and consequent amplification. Since there are no resonant structures involved in this interaction, amplification is obtained over a wide bandwidth. In fact the principal factors which limit bandwidth are the input/output coupling arrangements.

It should also be mentioned that it is possible to construct an oscillator, utilizing the so-called backward wave, whose energy travels in the reverse direction to the electron beam. These tubes are known as backward wave oscillators (BWOs) and have the advantage of a very wide tunable range (an octave or more). They have been used extensively in swept frequency sources (sweepers), but are rapidly being displaced by Gunn diodes and, more recently, transistor sources.

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