A detailed answer to this question can be very involved, see the Mixer Basics Primer or the Mixer Basics Video for a detailed explanation. The short, intuitive explanation resides in the fact that the intermixing of tones takes place when the diodes are conducting, or at least partially conducting. Thus, there must be enough voltage drive to turn the diodes on to allow for the nonlinear intermixing of multiple tones. When the diode barrier is increased, the mixer will require a higher applied voltage to allow for nonlinear intermixing—hence intermodulation distortion products will be better suppressed.
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