Effect of random manufacturing errors on slow wave circuit performance

Summary form only given, as follows. Manufactured, nominally periodic slow wave circuits inevitably have small errors in their construction, that is, every unit cell is slightly different from every other one. The usual mathematical treatment invokes Floquet´s theorem for the perfectly periodic circuit. This formulation is the basis of several computational treatments in which phase shift boundary conditions are applied to a single unit cell in order to compute the resonant frequency(ies) as a function of the phase shift per section. If, however, an actual circuit departs from perfect periodicity, the usual treatment must be modified. In the present paper, we present a method by which this can be done. We apply our formulation to the practical problem of predicting the reflection coefficient (s/sub 11/) as a function of the rms construction errors in a particular case, namely a pi-section bandpass filter circuit that is used in computer models of crossed-field vacuum tubes. The formula we obtain may therefore be used to specify manufacturing tolerances in circuit construction. Results from computer simulations of the operation of a crossed-field amplifier in which random circuit errors have been introduced will be presented, and compared to simulations using perfectly periodic circuits.