Detailed analysis of frequency response, frequency characteristics and frequency distortion

Understanding the frequency response of an amplifier is essential for analyzing its performance across different frequencies. This section explores the frequency characteristics of a common-emitter circuit, provides a qualitative analysis of its behavior, and introduces key concepts such as f_L (lower limit frequency), f_H (upper limit frequency), and BW (bandwidth). It also discusses frequency distortion and how it affects signal integrity.

3.1.1 Representation of Frequency Response

The frequency response of an amplifier can be represented as:

Ȧ_u(f) = A_u(f) ∠ φ(f)

Where:

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

Figure 3.1 illustrates the amplitude and phase frequency characteristics of a typical single-transistor common-emitter amplifier. From the amplitude curve, we observe that the gain decreases in both the low-frequency and high-frequency regions. This is due to the influence of coupling capacitors at lower frequencies and inter-electrode capacitances at higher frequencies.

Causes of Gain Reduction:

In the low-frequency range, as the frequency decreases, the capacitive reactance of the coupling capacitor increases, leading to a greater voltage division effect. This results in less voltage being applied to the input of the amplifier, causing the output voltage to drop and the overall gain to decrease.

In the high-frequency range, the capacitive reactance of the transistor's internal capacitances decreases, increasing their shunting effect. This reduces the actual current being amplified, thereby lowering the gain.

From the phase-frequency characteristics, we can see that in the low-frequency band, an additional phase shift of Δφ from 0° to 90° occurs compared to the mid-frequency range. In the high-frequency band, an additional phase lag of Δφ from 0° to -90° is observed.

3.1.2 Lower Limit Frequency, Upper Limit Frequency, and Bandwidth

f_L is the lower limit frequency, marking the point where the gain begins to drop significantly at lower frequencies.

f_H is the upper limit frequency, where the gain starts to decline at higher frequencies.

BW stands for bandwidth, calculated as BW = f_H - f_L.

The bandwidth indicates how well the amplifier can respond to signals of various frequencies. A wider bandwidth means better frequency response and is a crucial parameter for evaluating the performance of an amplifier.

3.1.3 Frequency Distortion

Frequency distortion occurs when the amplification circuit cannot maintain a flat gain and consistent phase shift across the entire frequency range. This leads to differences in amplification and phase shifts for different frequency components of the input signal, resulting in waveform distortion.

There are two types of frequency distortion:

• Amplitude-Frequency Distortion: This happens when different frequency components of the input signal are amplified to different degrees.
• Phase-Frequency Distortion: This occurs when different frequency components experience different phase shifts, altering the shape of the output waveform.

For example, consider an input signal containing two sinusoidal components at frequencies f₁ and f₂. If the amplifier treats both frequencies equally in terms of gain and phase shift, the output remains undistorted, as shown in Figure 3.2(a). However, if the gain for f₂ is reduced, the output becomes distorted, as seen in Figure 3.2(b)—this is amplitude-frequency distortion. Similarly, if the phase shift differs between f₁ and f₂, the output waveform will also distort, as shown in Figure 3.2(c)—this is phase-frequency distortion.