Slow-wave structures are circuits used in microwave tubes that reduce wave velocity to allow interaction between an electron beam and signal wave. A commonly used structure is a helical coil inside a conducting cylinder. The phase velocity along the coil and pitch angle can be calculated from equations. A diagram shows the ω-β relation for a helical structure, with group velocity determined by the slope of the curve. Coupled cavity travelling wave tubes use slots to strongly couple adjacent cavities, with passband determined by the coupling. Two main coupled cavity circuits are forward-wave and first space-harmonic types with positive mutual coupling.

1. Slow-wave structures are special circuits that are used in microwave tubes to reduce the wave velocity in a certain
direction so that the electron beam and the signal wave can interact.
Slow-Wave Structures

2. The commonly used slow-wave structure is a helical coil with a concentric conducting cylinder that is shown below
The ratio of the phase velocity along the pitch to the phase velocity along the coil is given by the equation below
For a very small pitch angle, the phase velocity along the coil in free space is approximately represented by

3. The figure below shows the ω-β (or Brillouin) diagram for a helical slow-wave structure. The group velocity of the
wave is merely the slope of the curve.

4. Coupled-Cavity Travelling Wave Tubes
 The term coupled cavity means that a coupling is provided
by a long slot that strongly couples the magnetic
component of the field in adjacent cavities in such a manner
that the passband of the circuit is mainly a function of this
one variable.
 The adjacent figure shows two coupled-cavity circuits that
are principally used in travelling wave tubes.
 The first type consists of the fundamentally forward-wave
circuits.
 The second type is the first space-harmonic circuit, which
has positive mutual coupling between the cavities.