Detailed analysis of frequency response, frequency characteristics and frequency distortion

Understanding the frequency response of a common-emitter amplifier is essential for analyzing how it behaves across different frequencies. This involves examining both the amplitude and phase characteristics, as well as identifying key parameters such as the lower cutoff frequency (f_L), upper cutoff frequency (f_H), and bandwidth (BW). These concepts help explain the phenomenon of frequency distortion in amplifiers.

3.1.1 Representation of Frequency Response

The frequency response of an amplifier can be expressed as:

Āu(f) = Au(f)∠φ(f)

Where:

• A_u(f) represents the amplitude-frequency characteristic, showing how the gain changes with frequency.
• φ(f) represents the phase-frequency characteristic, indicating the phase shift introduced by the circuit at different frequencies.

Figure 3.1 shows the typical amplitude and phase responses of a single-transistor common-emitter amplifier. From the amplitude curve, we observe that the gain decreases at both low and high frequencies. At low frequencies, the coupling capacitor's reactance increases, reducing the signal voltage applied to the input. At high frequencies, the internal capacitance of the transistor becomes more significant, causing shunting effects that reduce the current gain.

The phase response also reveals important information. In the low-frequency region, an additional phase shift of up to 90° occurs compared to the mid-frequency range. In the high-frequency region, the phase shift may drop by up to -90°, leading to a lagging output signal.

3.1.2 Lower Limit Frequency, Upper Limit Frequency, and Bandwidth

f_L is the lower limit frequency, beyond which the amplifier’s gain starts to decrease. f_H is the upper limit frequency, where the gain begins to roll off at higher frequencies. The bandwidth (BW) is defined as the difference between f_H and f_L, i.e., BW = f_H − f_L.

The bandwidth reflects the ability of the amplifier to respond to signals across a wide range of frequencies. A larger bandwidth means better performance in handling multi-frequency inputs, making it a critical specification in amplifier design.

3.1.3 Frequency Distortion

Frequency distortion occurs when the amplifier cannot maintain a flat gain and constant phase shift across its entire bandwidth. This results in different frequency components of the input signal being amplified or delayed differently, leading to waveform distortion.

There are two main types of frequency distortion:

• Amplitude-frequency distortion: This happens when different frequency components are amplified to different extents. For example, if a signal contains two frequencies, f₁ and f₂, and the amplifier boosts f₁ more than f₂, the output waveform will be distorted.
• Phase-frequency distortion: This occurs when different frequencies experience varying phase shifts. If one frequency is delayed more than another, the output signal can become misaligned, causing distortion.

As shown in Figure 3.2, when both amplitude and phase distortions are present, the output signal becomes significantly altered. Understanding these effects is crucial for designing stable and accurate amplification systems.