We have analyzed vertical miniband transport in GaAs-based superlattices subject to a d.c. field Eo which drifts the system into the regime of negative differential mobility jointly with a perturbing single-frequency electric field E,, sin(2ogt). Our balance equation formulation takes account of strong electron-electron interactions which tend to thermalize the system rapidly about the center-of-mass motion. In this, we consider E,o >~ Eo, so that the perturbing a.c. field is strong, and the responding steady periodic miniband current (evolving after transients relax) exhibits harmonic content beyond the impressed single frequency, characteristic of non-linear time harmonic generation. The scattering mechanisms are bulk phonons and random impurities. The superlattice treated here is a one-dimensional line of periodically spaced quantum dots of period d= 15 nm, lateral diameter dr = 10 nm, quantum well width a = 8 nm, carrier line density Nld= 0.314 and miniband width xl = 220 K. The impressed period of oscillation is taken as 2n/co = 4 ps, and, using material parameters appropriate to GaAs, we determine the harmonic composition of the periodic miniband current as a function of the high frequency amplitude E,o.