96.2. Effect of Feedback on Frequency Response (Part-B)

So if I consider say, p it is even beyond this point, something like this and then if it is having p ok. So, if I consider this is the p then the corresponding phase it could have been like this. For a and then p′ on the other hand, it is instead of here, this is p′ and which is same as p then this blue line, the phase here for A we could we can say that the phase it is having very clean step like this one.

In feedback systems, the position of poles is crucial because they determine how the system responds to changes in input. The term 'pole' refers to specific frequencies where the output of the system becomes infinite, and it influences how fast a signal can rise or fall. Here, 'p' denotes a pole position which significantly influences the properties of the feedback system. If this pole is shifted (to p′, beyond its original location), the phase response also alters, resulting in a cleaner or sharper response. In essence, moving the pole affects the system's responsiveness and stability.

Imagine an orchestra where the conductor (the feedback system) guides musicians (the poles) on how quickly to play their instruments. If the conductor starts waving the baton faster (shifting the pole), the music changes tempo, becoming more dynamic. A cleaner phase response is like playing in harmony, where everyone follows the tempo perfectly, resulting in pleasant and coherent music.

So 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.

In feedback systems, dominant poles play a vital role. In this case, the forward amplifier has two poles (p1 and p2), with the first pole (p1) being the dominant one because it affects the system's behavior at low frequencies. The feedback factor (β) remains constant across frequencies. Understanding how these poles interact with each other is essential, especially under negative feedback configurations, as it can lead to different responses in stability and transient behavior.

Think of a car with two gears (the poles). The first gear is dominant because it determines how fast you can go at low speeds. If you constantly shift to higher gears without considering the first gear, the car may become unstable. Similarly, in systems with feedback, ensuring the dominant pole's role is understood allows you to maintain a stable and effective operation.

But the anticipated shifted version of this p namely p′, if it is comparable with p, then what happens?

When the shifted pole p′ becomes comparable to the original pole p, the system undergoes significant changes. The interaction between these poles can lead to complex behavior in the system's response, potentially resulting in poles being complex conjugates instead of being real numbers. This has implications for stability and responsiveness, as complex poles indicate oscillatory behavior in the system’s output.

Consider two friends training together for a race. If both are at a similar speed (comparable), their pace can vary significantly, leading to unpredictable results. One might push the other forward, causing them to work together dynamically. This teamwork can produce better performance, but if not managed well, it could lead to confusion or miscommunication – similar to how the system might respond unexpectedly when poles shift in proximity.

The location of the pole p′ and p′ may not be real numbers. In fact, if you consider the second-order equation and write the corresponding routes, the location of the pole p′ and p′ will be complex.

In certain conditions, the resulting poles from feedback systems can become complex rather than purely real numbers. This means that the system exhibits oscillations or a resonance effect as indicated by complex conjugate pairs. The real part influences the steady-state value of the response, while the imaginary part defines the oscillatory behavior. Thus, when analyzing system behavior, these complex poles must be accounted for as they affect system stability and transients.

Think of a swing at a playground. When pushed gently, the swing goes back and forth smoothly (real poles). But if you give it a big push, it starts to oscillate wildly (complex poles), going in and out of control. Understanding this behavior helps in tuning the push appropriately.

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

A Bode plot is a graphical representation of a system's frequency response (gain and phase shift). In this discussion, the Bode plot can be used to visualize how different poles and their interactions affect the overall system behavior in terms of gain and phase shifts. Understanding the Bode plot behavior helps in assessing stability and performance metrics related to frequency responses of feedback systems.

Imagine you're tuning a radio to your favorite station. The clearer the frequency signal (the Bode plot shows gain), the better you hear the music without distortion. If the frequency is misaligned (like being off-pole), the music can get muddled with static or poor quality, similar to how feedback systems behave under varying conditions.

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