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It is shown that the attainment of LSA oscillations in epitaxial layers of GaAs does not rely on operation of the layers in small primary resonant circuits. Restrictions on circuit dimensions have thus been relaxed and LSA oscillations obtained in large scale microwave cavities. Layers of thickness 9-12.5 microns have been operated at frequencies from 26.5-40 GHz, the oscillations being tuned over this band by a conventional short-circuit plunger. The frequency of LSA oscillation is shown to be determined entirely by the natural circuit frequency. The tuning characteristics of the oscillations in various waveguide circuits are described and some general circuit features emerge which are of importance for a tunable LSA source. In particular it is noted that in some circuits a localized and therefore fixed frequency resonance occurs. It is also noted that LSA oscillations cannot occur if circuit Q is insufficiently high. The work has been carried out on a pulse basis to avoid thermal effects, and most of the experiments described have been carried out using unencapsulated devices. The maximum efficiency observed in these experiments was 4 percent.