96.5.1. Gain Plot of A

So, if I consider say, p it is even beyond this point, something like this and then if it is having p ok.

In this introduction to the gain plot of the system A, we are trying to visualize the location of the poles in the feedback system. The poles, represented as points on a graph, determine the behavior and stability of the system. The position of these poles can be critical as it impacts the overall gain and frequency response of the system. By defining 'p', the speaker suggests that if 'p' is located further away from a reference point, it may exhibit different characteristics compared to when it's closer.

Think of the poles as anchors of a boat. If the anchors (poles) are further away from the boat (system), the boat can sway more with the waves (frequency changes). However, if the anchors are closer, the boat remains stable and balanced.

First of all, forward amplifier it is having 2 poles; p1 and p2; β is independent of frequency and the system of course, it is ‒ve feedback system.

The forward amplifier in the feedback system features two distinct poles, p1 and p2. The mention of β (beta) implies that this feedback configuration does not vary with frequency, meaning it stays constant as the frequency changes. Understanding the stability that emerges from a negative feedback system is crucial here, as it can often lead to improved performance and damping of unwanted oscillations in a circuit.

Imagine you are riding a bike on a windy day. The bike represents the forward amplifier and the wind pushes against you representing external changes (frequency). If you have a friend (negative feedback) who stabilizes you from wobbling, you can ride much smoother despite the wind.

if I again if I come back to the feedback system gain A which is having an expression of and then we obtain this expression.

In this chunk, we discuss how the feedback system gain A can be affected by the positions of the dominant pole p1 compared to p2. By assuming that p1 is the dominant pole due to its lower frequency, we can simplify our analysis by considering only the most significant pole while ignoring the less significant effects from the other pole. This approximation allows us to focus on the poles that have the most influence on the system's behavior.

Think of a room with two noisy people arguing (p1 and p2). If you are trying to concentrate on one person's argument, you might ignore the other as it doesn’t significantly affect your understanding. This helps clarify your focus.

So depending on the coefficient of s square, here and s and their relative value, we may get expression of the poles it will be complex.

As we analyze the behavior of the feedback system, we note that if the coefficients of the polynomial in the denominator change relative to each other, it might provide complex pole locations. These complex poles can significantly alter the system's response, potentially introducing oscillations or instabilities that are not present when all poles are real. Understanding this helps in designing more stable feedback systems.

Imagine a pendulum swinging. If we introduce some forces that aren’t aligned (like wind from different directions), the pendulum might start swinging erratically instead of smoothly, akin to how complex poles can lead to unexpected behavior in a circuit system.

So let me try to sketch the Bode plot of A, A and maybe the loop gain also.

The Bode plot is a graphical representation of the gain and phase across frequencies. When sketching the Bode plot for gain A, we observe two poles at p1 and p2. These poles help shape the responses in both the magnitude (gain) and phase components of the feedback system, showcasing the stability and transient response due to the feedback gains.

Think of a chef adjusting spices in a dish. The gain plot is like a recipe showing how flavorful a dish is at different amounts of spices (frequencies). Poles on this plot represent optimal spice levels that bring out the best flavors without making it too spicy or bland.

--