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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.
In transistor circuits, for example, you bias the transistors since the input signal may not be enough to guarantee operation in the correct region of operation (eg forward active in BJT amps).
This forward biases the BE junction and the transistor can operate as desired. You reverse bias the BC junction for forward active.
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