Calculate the gain, input, and output impedances of a voltage-series feedback amplifier having \(A=-300, R_{i}=1.5 \mathrm{k} \Omega, R_{o}=50 \mathrm{k} \Omega\), and \(\beta=-1 / 15\)

Understanding the behavior of a feedback amplifier is fundamental in electronics, as feedback can either enhance or deteriorate the performance of amplifiers. A feedback amplifier routes a portion of its output signal back to its input, intended to control its gain, stability, bandwidth, or impedance characteristics. When discussing the voltage-series feedback amplifier, we encounter one where feedback is applied by mixing a portion of the output voltage with the input signal.

In the example given, the negative sign of the amplifier gain (\( A \) = -300) and feedback factor (\( \beta \) = -1/15) indicates that the feedback is negative, which provides stability and lowers the gain. The rule of thumb in feedback analysis is that negative feedback tends to make amplifiers more linear and less sensitive to component variations. This specific configuration decreases the amplifier’s gain, but at the same time improves its bandwidth and reduces its distortion, making the system more reliable overall.

The closed-loop gain of a feedback amplifier is the total gain when feedback is applied and is crucial for understanding the amplifier's behavior in a practical scenario. To calculate this, we use the formula \( A_{f} = \frac{A}{1 + A \cdot \beta} \). The parameters in the formula represent the open-loop gain (\( A \) = -300) and the feedback factor (\( \beta \) = -1/15). Applying these values leads to a simplified process, resulting in a closed-loop gain of \( A_{f} = -20 \).

This computation signifies that the gain of the amplifier is considerably reduced from its original open-loop value due to the influence of feedback. The magnitude reduction by a factor of 15, in this case, reflects closed-loop stabilization, a desirable attribute where the emphasis is on consistent operation across a variety of conditions.

Impedance plays a vital role in amplifiers by determining how much they resist the flow of electrical current. In feedback amplifiers, input and output impedances can be significantly affected by the feedback network. For the input impedance, the formula used is \( R_{if} = R_{i} \cdot (1 + A \cdot \beta) \) which, when utilizing the given parameters, gives us an adjusted input impedance. It is important to note, however, that the negative sign in our exercise is indicative of a misunderstanding, as impedances are inherently positive quantities.

Similarly, the output impedance is found using the formula \( R_{of} = \frac{R_{o}}{1 + A \cdot \beta} \) and typically, negative feedback results in a lowered output impedance. This is advantageous as it makes the amplifier less susceptible to variations in load, thus increasing its utility in different electrical networks. The negative value calculated in the solution suggests an oversight, as the output impedance should also be a positive value. Recognizing these factors and adhering to the principle that impedance must be positive is crucial to correctly analyze and understand the behavior of feedback amplifiers.