If the gain of an amplifier changes from a value of \(-1000\) by \(10 \%\), calculate the gain change if the amplifier is used in a feedback circuit having \(\beta=-1 / 20\).

Whenever we deal with electronic amplifiers, understanding the 'feedback circuit' is paramount. Essentially, a feedback circuit is a system that is designed to control its own operation or output by feeding back a portion of its output signal to the input. This has a major impact on the overall performance of the amplifier, including its stability, bandwidth, and gain.

In a negative feedback circuit, which is our focus here, the feedback signal is out of phase with the input, resulting in a decrease of the amplifier’s overall gain - but with the tradeoff of improvements in bandwidth and distortion characteristics. The amount of feedback in a circuit can be quantified by the feedback factor, symbolized as \(\beta\), which in our exercise is given as \(\beta=-1/20\). This means that a small portion of the output signal is inverted and fed back to the input.

Feedback influences an amplifier’s behavior significantly. When implemented correctly, it can reduce noise, make the gain more predictable, and enhance linearity. For students aiming to master electronics, grasping the function of a feedback circuit is a foundational skill.

The gain of an amplifier is a measure of how much it amplifies the input signal. It's usually defined as the ratio of output voltage to the input voltage and is a critical factor in the functionality of electronic circuits. When presented with an amplifier gain problem, it's important to follow the formula for calculating gain changes.

For calculating new gain when there's a percentage change, the formula is: \( G' = G + \frac{G \times \text{gain change}}{100} \). This formula takes into account both the original gain (G) and the percentage increase or decrease. In the exercise provided, the original gain, \(G\), is \( -1000 \), and we have a \( 10\% \) increase in gain. By applying the formula, the amplifier's gain changes to \(G' = -900\).

It is always beneficial to understand how to manipulate and apply this formula in various scenarios, making it easier to calculate the performance of amplifiers under different conditions.

Understanding 'percentage gain change' is vital when working with electronic amplifiers. It describes how much the amplifier’s gain has increased or decreased in terms of percentage. In a typical scenario, a percentage gain change means that the amplifier’s ability to increase the signal’s amplitude is either enhanced or reduced by that percentage.

In the context of our exercise, the amplifier originally had a gain of \( -1000 \). When we say there's a \( 10\% \) gain change, this is not adding \( 10 \) to the gain but rather increasing the gain by \( 10\% \) of its original value. The negative sign indicates that the gain is inverting the signal. After calculating the percentage change, you can observe a change in the original gain from \( -1000 \) to \( -900 \), which represents that \( 10\% \) incremental change.

Students should note that the percentage gain change is an essential step to mirror real-world adjustments to amplifier systems, and being proficient at calculating it means being able to predict how those changes will affect the overall system performance.