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Emitter Bypass Capacitors and Gain.
The Emitter resistance generates feedback and thus reduces the gain of a transistor amplifier. The capacitors reduce the impedance of the emitter circuit, which reduces feedback and increases amplifier gain at higher frequencies.
Below we see a partial view of the circuit above showing the 1kHz signal levels at the Base, Emitter and Collector of the transistor. Note the effect of the capacitors being switched in and out with the relays. The capacitors bypass the 1kHz signal to ground; this maintains the emitter voltage at a steady DC level. This increases the AC signal seen across the Base/Emitter junction (VB- VE), which increases the AC signal gain of the circuit.
The effect of the bypass capacitors is frequency dependent as shown below.