Using a new experimental technique the response of the auroral ionosphere to a very powerful HF wave amplitude modulated by an ELF square wave has been determined independent of the obfuscating effects of earth-ionosphere-waveguide resonances. It has been found that when resonance effects are compensated for, the odd harmonic amplitude ratios are predominantly those one would expect for a square wave, slightly modified by the non-linear relationship between generated ELF signal and HF radiated power. The even harmonic amplitude ratios are found to be much lower than those observed in earlier experiments and have been modeled by assuming unequal electron heating and cooling time constants and hence different rise and fall times for the ionospheric currents. ¿ American Geophysical Union 1993