Microwave Tube Research & Development Centre, Bangalore-560 013.
Nomenclaturea
Helix tunnel radius
α0Maximum growth-rate of the device
αnGrowth-rate of the nth taper section
bRadius of the electron beam
β0Propagation constant of a uniform circuit
β0nPropagation constant of the nth taper section
βeBeam propagation constant
βpPlasma propagation constant
βqReduced plasma propagation constant
CPierce's gain parameter
CNNormalised circuit length
(CN)criticalNormalised critical length of the circuit for oscillation to start
DNormalised taper strength
ε0Permittivity of free-space
ηeCharge-to-mass ratio of an electron at rest
GBackward-wave gain of the device
IbBeam current
IcriticalCritical current for oscillation to start
ĨnModified Bessel function of first-kind of order n
ISTCritical current for a tapered circuit for oscillation to start
ISNTCritical current for a non-tapered uniform circuit for oscillation to start
K0Interaction impedance for forward space-harmonic mode
K−1Interaction impedance for backward space-harmonic mode
ЌnBessel function of second-kind of order n
LTotal interaction length
LcriticalCritical length of the circuit for oscillation to start
LdBTotal loss of the circuit in decibel
LnLength of the nth taper circuit
λeElectronic wavelength
λgGuided wavelength in the circuit
mTaper ratio L1/L
pHelix pitch
QCPierce's normalised space-charge parameter
RPlasma frequency reduction factor
ρ0Charge density of the un-modulated electron beam
u0Electronic velocity of the un-modulated electron beam
VbBeam voltage
ωOperating frequency in radians
ωpPlasma frequency in radians
ωqReduced plasma frequency in radians
Analysis of backward-wave oscillation criterion is one of the essential steps for designing a broadband travelling-wave tube (TWT) amplifier. In this paper, a methodology for the analysis of the backward-wave oscillation criterion in a helix travelling-wave tube has been proposed with emphasis on its usage as a design tool. The analysis is also extended for a slow-wave structure having distributed RF loss and a closed-form equation has been proposed for calculating the critical interaction length. The analysis is further extended for a step-tapered TWT with distributed circuit loss included in the analysis. The method is finally applied to design a typical slow-wave structure used in an X-Ku band TWT having a step-tapered output circuit.
Backward-wave oscillation, helix travelling-wave tube, slow-wave structure, step-taper circuit, TWT, amplifier design, travelling-wave tube
