For an ideal MOS Gilbert cell mixer, we can see only the even order harmonics of the LO frequency at the common source. But each drain current of the switching pair actually includes the odd order harmonics of LO frequency, they just cancel out at the common source due to 180 degree out of phase. I don't know how to use the theoretical analysis to prove it. how does each switching pair current look like, and how does the two current cancel the LO freqency (or odd order harmonics) at the common source?  
Moreover, I found each drain current of switching pair increases as the LO signals increases. why it is like that, how to use theoretical analysis to prove such a phenomena? (I use sinusoidal signal as the LO source.)