It's often recommended to improve the AC gain of a common emitter amplifier by putting a bypass capacitor paralell to Re, thus effectively decreasing the Ze for the signal and increasing the gain.
My question is: Won't this also lower the Z input (AC) for the amplifier? If Ze(AC) is only 100Ω or so, won't that lower Zin(AC) to around 10k (assuming a β of 100)?

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