Control of IM3 distortion in helix TWTs by harmonic injection-an Eulerian hydrodynamical study

Helix traveling-wave tube equations were formulated under Eulerian-fluid approximations, extending the nonlinearity up to the third-order. Closed-form solutions for the nonlinear equations were obtained by the method of Laplace transforms for the circuit electric field, which was then interpreted, for RF output power. The RF fundamental output power estimated by the present Eulerian theory was validated against that done by the Lagrangian analysis and the regime of agreement of the two theories was ascertained. Then within this range of validity were found the third-order intermodulation products at the frequencies 2f₁-f₂ and 2f₂-f₁, for the case of two-balanced signal inputs, one at the frequency f₁ and the other at f₂. The multisignal output power spectrum predicted by the two theories also showed a fairly close agreement. The role of the two additional second harmonic signals injected at the input, one at the frequency 2f₁ and the other at 2f₂, in controlling the third-order intermodulation products (distortion) was next studied by the simple Eulerian hydrodynamic analysis. By harmonic injection at the signal frequency 2f₁ (2f₂) alone, the intermodulation product at 2f₁-f₂ (2f₂-f₁) could be reduced but not at 2f₂-f₁ (2f₁-f₂). For the reduction of both the intermodulation products, the harmonic inputs at the frequencies 2f₁ and 2f₂, respectively, need to be simultaneously injected. In particular, the optimum values of the RF input power levels and phases of the second harmonic inputs relative to the corresponding fundamental inputs, which would result in a minimum in the third-order intermodulation distortion in the device, were found