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Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier
For the circuit shown in Figure 1(a), the equivalent circuit for C1 is a high-pass filter, C3 and $(RC + RL)$ form another high-pass filter. With FETs, the input coupling capacitor is usually smaller because of the high input resistance. The output capacitor may be smaller or larger
Effect of Bypass Capacitors
A bypass capacitor causes reduced gain at low-frequencies and has a high-pass filter response. The resistors “seen” by the bypass capacitor include RE, re ́, and the bias resistors. For example, when the frequency is sufficiently high $XC ≅ 0\Omega$ and the voltage gain of the CE amplifier is Av = Rc/re ́. At lower frequencies, $XC\gt\gt 0\Omega$ and the voltage gain Av = Rc/(re ́ + Ze).
Internal Capacitance's
The high-frequency response of an amplifier is determined by internal junction capacitances. These capacitance's form low-pass filters with the external resistors. Sometimes a designer will add an external parallel capacitor to deliberately reduce the high frequency response.