Note that an ideal multiplier would output only the sum and difference frequencies, not the originals. But it is much simpler to simply build a non-linear amplifier that has strong distortion components (quadratic distortion) at the sum and difference frequencies, and it is OK since everything but the diference is filtered out by the IF stage.
Best regards,
Bob Masta dqatechATdaqartaDOTcom D A Q A R T A Data AcQuisition And Real-Time Analysis