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Why and when I must multiple/divide the resistors connected to a transistor by hfe or beta? I want to know all cases and all the reasons please. Sorry I have no reference book to look at for the reason.
You don't. What are you talking about? Be specific. When you are calculating impeadances, you sometimes use products and quotents involving gain. But that's only in certain circumstances. For example, a transistor in a common emitter configuration, operating in the active region, the current in the emitter resistor (no load) is equal to the base current times (1 + β). So, the total impeadance see at the base is:
R = E(in)/I = E(in)/(1 + β)I(in)
rearranging:
R(1 + β) = E(in)/I(in),
So the resistance at the base is multiplied as a result of the controlled current source of the transistor.
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