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When you say it is wrong, are the frequencies missing, wrong or the wrong level?
Harmonic balance should work just fine. Be sure to tell it where to look for the solution frequencies. HB is not smart enough to find the output frequencies itself. As a very minimum, you should specify the RFin, LO and the sum and difference output products (ie the upper and lower sideband frequencies). Also tell it you want to look out at least to the third harmonic of each frequency.