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Wednesday, 11 September 2019

Helical Slow Wave Structures

Travelling Wave Tube (TWT)

TWT is a high gain, low noise, wideband microwave amplifier. They work on the principle of interaction between electron beam and RF field. In TWT, slow wave structures are used instead of resonant cavities as in Klystrons.

Working Principle

TWT has an electron gun which produces and accelerates the electron beam along the axis of the tube. Surround magnet provides a magnetic field along the axis of tube to focus the electron beam. The slow wave structure at the centre of the tube provides a low impedance transmission path for the RF energy within the tube. The applied input signal which is to be amplified propagates along the slow wave structure. It produces an electric field at the centre of the helix directed along the axis. When the electron beam enters the tube the axial electric field and electron beam are interacted. The electrons entering the slow wave structures at zero electric field are not affected. Those entering at accelerating field are accelerated and those entering at retarding field are decelerated. Thus, velocity modulation takes place and electrons are bunched together and are collected at the collector. The microwave energy of electrons is transferred to slow wave structure and thus the signal is amplified.
Slow Wave Structures:

It reduces the velocity of the wave so that electron beam efficiently interacts with it. They are non resonant periodic circuits. In a normal resonant circuit as the operating frequency is increased both the inductance and capacitance of the resonant circuit must be decreased to maintain the resonance at the operating frequency. This limits the gain and reduces the output. Slow wave Structures compensate this limitation and produces large output over a wide bandwidth.

Various types of Slow wave structures are,

Helical Line
Folded Back Line
Zig Zag Line
Inter digital line
Corrugated waveguide

Helix Travelling Wave Tube (Helix TWT):

The TWT contains an electron gun which produces and accelerates the electron beam along the axis of the tube. The surrounding magnet provides a magnetic field along the axis of the tube to focus the electrons into a straight beam. A longitudinal helix slow wave structure is placed at the center of the tube which provides low impedance transmission path. The RF input and output are coupled on to and removed from the helix by directional couplers. The travelling wave tube is designed with helix delay structure to slow down the wave below or equal to the speed of electrons. The electrons of the beam are accelerated by interacting with positive value of the electric field through velocity modulation. This result in amplification and the electrons give up energy to the travelling wave. Thus, the energy of travelling wave is increased.

Amplification Process in TWT:

The phase shift of the fundamental wave on the helical slow wave structure is given by the equation,

θO = BzL

where, Bz – Phase constant
which is defined as Bz = ω/Vp
L is the period of the signal.

The equation for motion of electron is given by,

m(dv/dt) = -eE1Sin(ωt - Bzz) ------------------------- (1)

Let the velocity of electron be defined as,

v = vo + vecos(ωet + θe)

Therefore dv/dt = -veSin(ωet + θe) ωe -------------------- (2)

Sub eq (2) in (1)

mveSin(ωet + θe) ωe = eE1Sin(ωt - Bzz) ---------------------- (3)

ve is the magnitude of velocity fluctuation, ωe is the angular velocity
θe – Phase angle fluctuation
Let, the distance ‘z’ travelled by the electron is defined as,

z = vo(t - to) ----------------------- (4)

Where, vo is the ‘dc electron velocity’

Substitute eq (4) in (3)

mve ωeSin(ωet + θe) = eE1Sin(ωt - Bz vo(t - to))
= eE1Sin(ωt – Bz vot - Bz voto)

Equating LHS and RHS

we get, mve ωe = eE1


ve = eE1/mωe

That is, the magnitude of velocity fluctuation is directly proportional to the magnitude of electric field, E1.

Here, ωe = ω - Bz vo
ω = Bz vp - Bz vo
ωe = Bz (vp- vo)

where, vp – axial velocity.
Ie, the angular velocity, ωe is proportional to difference between axial and dc velocities.

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