A capacitor has lower resistance (impedance) as frequency increases. Adding an emitter capacitor effectively lowers the emitter resistance as frequency increases. Since gain in a typical common emitter amplifier is collector resitance divided by emitter resistance, this decrease in emitter resistance will increase gain as frequency increases.

The gain of a common-emitter amplifier is collector resistor divided by emitter resistor, or hFe, whichever is less. Since hFe depends on temperature, designing the amplifier to be dependent on resistance ratio makes it more stable. As such, the emitter resistance serves to stabilize the amplifier.

(Electronics) Resistor placed in the emitter lead of a transistor circuit to minimize the effects of temperature on the emitter-base junction resistance and its resistance is called swamping resistance.

The emitter bypass capacitor in a common emitter amplifier will have less resistance as the frequency increases. Since gain in this configuration is collector resistance divided by emitter resistance (within limits of hFe), the gain will thus increase for higher frequencies, making this into a high pass filter.

The gain of a class A, common emitter BJT amplifier, a fairly standard configuration, is defined as collector resistance divided by emitter resistance, or as hFe, whichever is less. Assuming that we are operating in a linear mode, and hFe is not a limiting factor, then the emitter resistance being greater than the collector resistance simply means that the gain is less than one.