Backward-wave oscillator: Difference between revisions

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According to Floquet's theorem (see [[Floquet theory]]), the RF electric field E(z,t) can be described at an [[angular frequency]] ω, by a sum of an infinity of "spatial or space harmonics" E<sub>n</sub>
 
:<math>E(z,t) =<math>\sum_{n=-\infty}^{+\infty} {E_n}e^{j({\omega}t-{k_n}z)}</math>
 
where the [[wavenumber|wave number]] or propagation constant k<sub>n</sub> of each harmonic is expressed as:
 
:k<sub>n</sub> = (Φ + 2nπ) / p (-π < Φ < +пπ)
 
z being the direction of propagation, p the pitch of the circuit and n an integer.