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If I wanted to amplify an ac signal with no dc offset by a BJT, does ac signal required an external dc source on it, so that the bjt won't recitfiy the signal as the BE part of the Bjt just behaves like a diode?
If you want to amplify a AC signal with no dc offset then you need to use a bjt amplifier with bipolar supply. If you are talking about common emittor configuration then voltage output will be a collector pin. You can refer any basic text book.
Yes, you must need an external DC source to avoid rectification. You know, all biasing circuits used for BJT provides DC offset for the incoming AC signal. Hence you must need to offset the AC signal before amplifying by a transistor. You can eliminate the output DC signal by using of coupling capacitor called blocking capacitor.