95.3.2. Feedback Influence on Two Poles

Now, let us come to the first case before we go into the first case again we like to recapitulate what we have discussed. In fact, we have discussed this kind of situation where this is the forward amplifier, this is the feedback network and then, we do have signal mixture and then we do have signal sampler.

In this introductory chunk, the speaker is recapping previous discussions about feedback systems. It sets up the context for the current examination of how feedback impacts the frequency response of amplifiers. The forward amplifier, feedback network, and signal analysis are the core elements being discussed, establishing a foundational understanding for students.

Consider a feedback system in a car’s cruise control. The car’s speed sensor provides feedback to adjust the throttle. Just like in analog circuits, the feedback influences the system's response, maintaining a steady speed.

So, to start with let you consider case I, what we have in this situation it is yeah. So, when you say case I we assume that β it is independent of frequency. So we can say that β is remaining constant and in the system, it is −ve feedback system in DC condition and let you consider that forward amplifier it is having a transfer function which is having only one pole.

In this segment, the situation is narrowed down to Case I where the feedback factor β is treated as constant, allowing for a simpler analysis. The forward amplifier is defined to have only one pole, which simplifies the calculations and predictions about how feedback affects amplifier performance. Understanding this setup is crucial for recognizing more complex scenarios later.

Imagine a single pulley system where strings guide a load; the load only moves in response to the force applied—in this case, the constant feedback. Just like pulley systems, the feedback will influence how the amplifier behaves in response to input signals, determining gain stability.

Now, if you recall that the feedback system transfer function assuming it is having a minus sign here it is and A(s) it is given here and β is independent of frequency.

This chunk focuses on the mathematical representation of the feedback system through the transfer function, emphasizing the role of negative feedback in the analysis. The key takeaway is the understanding that the system can be described mathematically, which is essential for predicting behavior when feedback is applied.

Think of the transfer function as a recipe where the ingredients (A and β) must be combined just right to produce the desired dish (the amplifier’s output). The negative feedback is like adjusting a recipe based on taste—balancing flavors to achieve a perfect meal.

So, as I say that in this case this is and this is independent of frequency, this is also independent of frequency which means that the location of the p′ it is clearly it is a shifted version of this p.

In this section, the effect of feedback on the pole location (shifting from p to p′) is discussed. This shift is significant as it indicates how feedback alters the response characteristics of an amplifier, affecting stability and bandwidth. Understanding this shift is key to mastering feedback principles in circuit design.

Consider a car racing on a curvy track—the pole p represents the original track layout, while the pole p′ is the modified route after making adjustments based on feedback from the car's performance. Adjustments can improve speed and control, illustrating how feedback shapes outcomes.

So, we can say from this point onwards A it is following A in other words we can say that it is having a bend and this bend it is imposing a pole incidentally that is what this p′ and this p′ it is p(1 + βA).

The concluding statements clarify that, post-bend in the gain plot, the feedback system's behavior aligns with the original amplifier's characteristics along with the shifted pole. This concept is vital for understanding how feedback modifies frequency response and introduces the critical insight that gain and bandwidth products remain consistent.

Imagine learning to ride a bike—initially, you might encounter bumps that cause wobbles (the bend), but as you adjust and maintain balance, you start gliding smoothly (following the original track). Feedback and practice reshape your biking experience, similar to how circuits adapt through feedback.

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