  We theoretically investigated the scheme allowing to avoid destructive
space-charge instabilities and to obtain a strong gain at microwave and THz
frequencies in semiconductor superlattice devices. Superlattice is subjected to
a microwave field and a generation is achieved at some odd harmonics of the
pump frequency. Gain arises because of parametric amplification seeded by
harmonic generation. Negative differential conductance (NDC) is not a necessary
condition for the generation. For the mode of operation with NDC, a limited
space-charge accumulation does not sufficiently reduce the gain.
