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Some confusion comes from that any DC power to a circuit is named "DC bias". DC bias in vacuum tubes and transistors refers rather to the control voltage (grid) or current (base) to define an operation point.
Some mixers can be DC biased to allow their operation with a lower LO input power. This DC bias in fact "opens" mixer diode(s) so they do not need to rectify LO power to get into a good operation point. Also DC biased diode detectors offer a better sensitivity at low signal levels.