96.3. Location of Poles in Feedback Systems

Analog Electronic Circuits Prof. Pradip Mandal Department of Electronics and Electrical Communication Engineering Indian Institute of Technology, Kharagpur Lecture – 96 Effect of Feedback on Frequency Response (Part-B)

In this section, we are introduced to the concept of poles in a feedback system. Poles are critical for understanding the behavior of a feedback system's frequency response. The discussion focuses on how the location of these poles influences system performance, particularly how they can be shifted with feedback.

Think of poles as anchors in a boat. If the anchors (poles) are smoothly placed, the boat (system) will sail smoothly. If you start pulling one anchor closer to the other, the boat may start to tilt or behave erratically, depending on how close they get—this mimics how poles interact in a feedback system.

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. And we consider p1; it is lower frequency than p2 which means that p1 is referred as dominant pole.

Here, we see that in a feedback system with two poles, p1 and p2, the pole p1 is regarded as the dominant pole because it operates at a lower frequency than p2. Typically, the dominant pole has the most significant effect on the system’s response because it affects the lower frequency behavior more than the higher frequency one.

Imagine a meeting where one person, the dominant speaker (p1), is talking slowly and clearly (lower frequency), while another person (p2) tries to add information quickly. The audience (system) is likely to focus more on the slower speaker, as they are easier to understand. This demonstrates how the dominant pole impacts the feedback system more than the other.

But the anticipated shifted version of this p namely p′, if it is comparable will with p2, then what happens? ... a factorization of this p equation may or may not be having a meaningful factorization.

This chunk discusses the outcomes when the location of the shifted pole p′ becomes comparable to the second pole p2. If they are close enough, it can lead to complex pole behavior, which makes analyzing the system's output more complicated because the new poles may not be real numbers and could become complex. This affects stability and frequency response.

Consider two friends who often talk loudly at the same time (p1 and p2). If one friend starts to shout louder (shifting poles), but gets too close to the other (comparable location), it may create confusion, making it hard for others around them to understand what's being said. Similarly, in a feedback system, poles that are too close create complex interactions.

However, this p′ and p′, they need not be real numbers. ... depending on the relative value of this p2 and specific conditions, they may create real poles or complex conjugate poles.

In feedback systems, when determining the location of poles, it’s revealed that p′ and p′ may not be real. The nature of these poles—whether real or complex—changes based on other factors in the system. This dependency introduces variability in system response, particularly concerning stability. Understanding how to compute these locations leads to better design of feedback systems.

Think of trying to balance a pencil on the tip of your finger. If you make a small change in the angle, the pencil might fall (instability). The stability of the pencil (system) relies heavily on your fingers (pole locations) getting the balance right. The same principles apply to feedback systems where slight adjustments can lead to very different outcomes.

So depending on this value, ... whether these 2 poles they are really real poles remaining as real pole or they are becoming complex conjugate.

This section elaborates on how the interaction between poles determines their nature, whether they remain as distinct real poles or transform into complex conjugate pairs. The transition of poles like this often signifies critical changes in the system's frequency response characteristics, influencing oscillation and peak behaviors.

Imagine a teeter-totter. If both sides are balanced (real poles), it moves up and down smoothly. But if one side gets heavier (complex poles), it starts to wobble more erratically. In electronics, this represents how feedback can change the behavior of a system depending on the locations of poles.

We have discussed about the location of poles of a feedback system. ... This gives you fair idea that how the poles locations are getting changed.

The section concludes by summarizing how the location of poles in feedback systems can significantly influence the system's overall behavior. The course outlines different scenarios examining how feedback and pole locations impact stability and performance across various cases, particularly focusing on the importance of dominant poles.

Reflecting back on our earlier analogies, think of orchestra musicians. If all musicians (poles) play harmoniously together (pole location optimized), the music sounds beautiful. However, if one musician starts playing off-key or out of sync with the others (poorly placed poles), the overall performance is compromised. Understanding and managing pole locations ensures systems perform optimally.

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