Brief Summary
This lecture introduces the concept of feedback in analog electronics, distinguishing between negative and positive feedback. It explains how negative feedback, while reducing gain, enhances the stability and reduces sensitivity to parameter variations, making it crucial for amplifier design. The lecture also touches upon positive feedback, its applications, and the conditions leading to instability.
- Introduction to feedback theory, negative and positive feedback.
- Explanation of negative feedback and its advantages in circuit design.
- Discussion of positive feedback, its limitations, and specific applications.
Introduction to Feedback
The lecture transitions from discussing feed-forward amplifiers to introducing feedback, a critical aspect of circuit design. It aims to cover negative and positive feedback, including their advantages, disadvantages, and applications. The discussion begins with a linear block model where an input signal, v i, is multiplied by a transfer function, G, to produce an output, Gv i, establishing a feed-forward structure.
Basic Feedback System
The lecture introduces a feedback loop where a portion of the output, X naught, is sampled and fed back to the input through a block with a transfer factor H, resulting in HX naught. This setup includes an "error detector" that calculates the difference between the input, X i, and the feedback signal, HX naught, producing an error signal, epsilon. The error signal is then fed into the feed-forward block with gain G, leading to the equation (X i - H*X naught) * G = X naught, which is fundamental in control systems engineering.
Negative vs. Positive Feedback
The lecture distinguishes between negative and positive feedback, defining negative feedback as a system where the error is the difference between the input and the feedback signal. Conversely, positive feedback involves adding the input and feedback signal, eliminating the error detection process. The discussion emphasizes the importance of negative feedback, highlighting its origins in the work of a person named Black, who sought to reduce distortion in amplifiers.
Real-World Examples of Feedback
The lecture explores real-world examples of negative feedback, including its presence in nature, such as the meditative states achieved by yogis. Scientists discovered that yogis in meditation predominantly generate Alpha waves. Biofeedback, an electronic method, can assist ordinary individuals in achieving a meditative state by providing feedback on their Alpha wave activity, demonstrating the practical application of negative feedback to improve individual performance.
Advantages of Negative Feedback
The lecture addresses the benefits of negative feedback, particularly its ability to make the system's gain independent of the forward transfer parameter (G) of the open-loop amplifier. By ensuring that G is very high and the product of G and H (the feedback factor) is much greater than 1, the overall gain becomes approximately 1/H. This makes the amplifier insensitive to variations in G caused by temperature or time, a crucial advantage in amplifier design.
Voltage, Current, and Phase Feedback Structures
The lecture extends the discussion to different types of feedback structures, including voltage, current, and phase feedback, noting that the core theory remains valid across these variations. Voltage differencing is achieved using a differential amplifier, while current differencing is done through a node. The lecture also touches on phase lock loops, which are negative feedback systems where the ratio of phase changes is described by G / (1 + G*H).
Follower Circuits
The lecture introduces the concept of follower circuits, including voltage, current, and phase followers, where the output closely follows the input. In a voltage follower, the output voltage is the same as the input voltage (V naught / V i ≈ 1/H), achieved when H equals 1, meaning the entire output voltage is fed back without attenuation. Similarly, current and phase followers maintain the output current or phase equal to the input.
Sensitivity Improvement with Negative Feedback
The lecture discusses the trade-offs of negative feedback, acknowledging the reduction in the forward transfer parameter as a disadvantage but emphasizing the significant advantage of improved sensitivity. This improvement is quantified by the sensitivity factor, defined as the percentage variation in G f (gain with feedback) compared to the percentage variation in G (original gain). The sensitivity factor is equal to 1 / (1 + GH), where GH is the loop gain.
Loop Gain and Feedback Type
The lecture defines loop gain as the product of G and H, crucial for determining the sensitivity of the feedback system. A high loop gain results in a sensitivity factor approaching zero, indicating that the system is insensitive to variations in the active parameter. The lecture also clarifies that negative feedback occurs when the loop gain has a negative sign, achieved when the input and output oppose each other.
Positive Feedback Analysis
The lecture transitions to analyzing positive feedback, where the output is added to the input, resulting in a gain of G / (1 - GH). Unlike negative feedback, positive feedback can increase the gain beyond G, but it also increases the sensitivity factor to 1 / (1 - GH). When G*H equals 1, the gain becomes infinite, leading the amplifier to saturation.
Positive Feedback and Instability
The lecture explains that positive feedback with G*H greater than or equal to 1 leads to instability, where the output is no longer linearly related to the input. This condition results in the amplifier operating in saturation, making it unsuitable for amplification purposes due to high sensitivity to active parameter variations. However, positive feedback is intentionally used in comparators, where the output indicates whether a voltage has crossed a certain threshold.
Summary of Feedback Concepts
The lecture concludes by summarizing the key distinctions between negative and positive feedback, noting that positive feedback with a loop gain greater than 1 results in instability. The focus shifts to negative feedback with a loop gain much greater than 1 for future applications, highlighting its practical use in amplifier designs due to its stability and reduced sensitivity to parameter variations.
