Effect on Bandwidth
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Impact of Negative Feedback on Bandwidth
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Today, we're going to learn about how negative feedback affects the bandwidth of amplifiers. Can anyone tell me what we mean by 'bandwidth'?
Is it the range of frequencies that an amplifier can handle?
Exactly! Bandwidth is the frequency range over which the amplifier performs effectively. Now, when we add negative feedback to an amplifier, what do you think happens to this bandwidth?
Does it increase?
Correct! Negative feedback can help to widen the bandwidth. This is part of what we refer to as the gain-bandwidth product. The key formula to remember is BWf = BW(1 + AΞ²F), where BWf is the closed-loop bandwidth.
So, if we reduce the gain, we get better bandwidth?
That's right! It's a balancing actβlowering the gain increases the bandwidth, which can be critical in design applications.
Can you give us an example?
Certainly! For example, an amplifier with an open-loop gain of 5000 and a bandwidth of 20 kHz, when configured with a feedback factor of 0.02, will have a closed-loop bandwidth of 2.02 MHz.
To summarize, negative feedback enhances bandwidth but reduces gain, reflecting the trade-offs in amplifier design.
Understanding Gain-Bandwidth Product
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Let's dive deeper into the concept of the gain-bandwidth product. Who can explain what it means?
Is it the product of the gain and the bandwidth of the amplifier?
Yes, that's right! The gain-bandwidth product remains approximately constant for many amplifiers. This means when gain decreases, bandwidth must increase proportionally to keep the product stable.
Does this apply to every amplifier?
Good question! It's particularly true for amplifiers with a dominant pole in their frequency response, like op-amps.
So we can design them to have high bandwidth by lowering the gain?
Exactly! And understanding this relationship assists in making informed design decisions.
Thanks! I see the importance now.
To wrap up, the gain-bandwidth product illustrates how gain and bandwidth trade off against one another.
Introduction & Overview
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Quick Overview
Standard
The impact of negative feedback on bandwidth is crucial, as it allows for wider frequency response at the cost of lower gain. This trade-off is encapsulated in the gain-bandwidth product, which remains approximately constant for many amplifiers. Understanding this relationship helps engineers optimize amplifier performance.
Detailed
Effect on Bandwidth
Negative feedback profoundly influences the performance characteristics of amplifiers, particularly their bandwidth. By applying the concept of feedback, we can derive key formulas and understand the mechanisms through which feedback modifies amplifier behavior.
Gain-Bandwidth Product and Feedback
For many amplifiers, especially those characterized by a dominant pole in their frequency response, the gain-bandwidth product (GBP) is approximately constant. This means that when the gain is reduced, the bandwidth must increase proportionally to maintain a constant product.
Key Formula:
The closed-loop bandwidth of an amplifier can be expressed as:
- BWf = BW (1 + AΞ²F)
where BWf is the closed-loop bandwidth, BW is the open-loop bandwidth, A is the open-loop gain, and Ξ²F is the feedback factor. This relationship highlights that the bandwidth is extended by the desensitivity factor that reduces the gain.
Practical Example
For instance, an open-loop amplifier with a gain of 5000 and a bandwidth of 20 kHz, when configured with negative feedback (Ξ²F = 0.02), results in a closed-loop bandwidth of:
- BWf = 20 kHz Γ (1 + 100) = 2020 kHz or 2.02 MHz.
Thus, negative feedback improves frequency response significantly, enabling amplifiers to operate effectively over a broader range of frequencies.
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Mechanism of Bandwidth Increase
Chapter 1 of 3
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Chapter Content
Negative feedback has the beneficial effect of increasing the bandwidth of an amplifier.
- Mechanism (Gain-Bandwidth Product): For many amplifiers, especially those dominated by a single pole in their frequency response (like op-amps compensated for unity gain stability), the gain-bandwidth product (GBP) is approximately constant. This means that if you reduce the gain, the bandwidth must increase proportionally to maintain a constant product.
Detailed Explanation
Negative feedback increases amplifier bandwidth because of the gain-bandwidth product, which states that as you reduce the gain of an amplifier, the bandwidth increases to keep the product constant. For instance, if an amplifier has a specific gain, it can only handle certain frequencies effectively. By decreasing that gain through negative feedback, you allow it to handle more frequencies without distortion, thus increasing the bandwidth.
Examples & Analogies
Think of a water pipe that can only carry water at a certain speed. If you lower the pressure (like reducing the gain), the pipe can handle more water flow without bursting (this would be like increasing the bandwidth). If you tried to push more water through at a high pressure, it might burst, which relates to distortion in electronic amplifiers.
Formula for Closed-Loop Bandwidth
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Chapter Content
The closed-loop bandwidth (BWf) is related to the open-loop bandwidth (BW) by:
BWf = BW(1 + AΞ²F)
Detailed Explanation
The formula BWf = BW(1 + AΞ²F) shows how bandwidth is directly influenced by the feedback factor. The term (1 + AΞ²F) describes how feedback increases the bandwidth as gain is lowered. Essentially, for any feedback applied, the bandwidth increases because the feedback allows the amplifier to operate at a wider range of frequencies while still maintaining stability.
Examples & Analogies
Imagine a bus route (the amplifier's bandwidth) that can only cover a specific area (certain frequencies). If you lower the number of passengers (feedback), the bus can take more detours to cover more area (expanded bandwidth), meaning it can serve a wider region without running into traffic jams (signal distortion).
Numerical Example: Bandwidth Extension
Chapter 3 of 3
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Chapter Content
An open-loop amplifier has a low-frequency gain A=5000 and a 3dB bandwidth BW=20 kHz. It is configured with negative feedback where the feedback factor Ξ²F =0.02.
- Calculate the loop gain (AΞ²F): AΞ²F = 5000 Γ 0.02 = 100.
- Calculate the closed-loop bandwidth (BWf): BWf = BW(1 + AΞ²F) = 20 kHz Γ (1 + 100) = 20 kHz Γ 101 = 2020 kHz = 2.02 MHz. The bandwidth has significantly increased from 20 kHz to 2.02 MHz, demonstrating the dramatic improvement in frequency response offered by negative feedback.
Detailed Explanation
In this example, by applying negative feedback, the bandwidth of an amplifier increased dramatically from 20 kHz to 2.02 MHz. This shows how negative feedback can drastically expand the range of frequencies an amplifier can handle effectively. The loop gain (AΞ²F) helps quantify this effect, letting us see exactly how feedback impacts the overall performance of the amplifier.
Examples & Analogies
Consider a sprinting athlete (the amplifier) who can only run at a certain speed (20 kHz). When given the right training (negative feedback), they can extend their running capabilities dramatically (up to 2.02 MHz). This showcases how proper techniques can enhance performance capabilities, similar to how feedback enhances the bandwidth of an amplifier.
Key Concepts
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Bandwidth: The effective frequency range of an amplifier.
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Gain-Bandwidth Product: A constant that shows the trade-off between gain and bandwidth.
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Closed-loop Bandwidth: The frequency range of an amplifier when feedback is applied.
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Feedback Factor: The ratio of feedback to output indicating feedback strength.
Examples & Applications
An amplifier configured with a feedback factor of 0.02 having an open-loop gain of 5000 and a closed-loop bandwidth calculated as 2.02 MHz.
If an amplifier has an open-loop bandwidth of 50 kHz and is set to a feedback factor of 0.01, the closed-loop bandwidth improves proportionally.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
To keep signals bright and clear, negative feedback is near. It widens the range, makes gains strange.
Stories
Imagine a dance hall where each dancer must stay in sync. If one dancer (the feedback) pulls back (negative feedback), the dance floor opens up, allowing more couples (frequencies) to join without stepping on toes.
Memory Tools
Remember 'G-BP' for Gain-Bandwidth Product: Gains down, bandwidth up!
Acronyms
Use 'G-BW' as a reminder
Gain and Bandwidth trade-offs are key!
Flash Cards
Glossary
- Bandwidth
The range of frequencies over which an amplifier operates effectively.
- GainBandwidth Product (GBP)
The constant product of the amplifier's gain and bandwidth, which illustrates the trade-off between the two.
- Closedloop Bandwidth (BWf)
The bandwidth of an amplifier when feedback is applied.
- Feedback Factor (Ξ²F)
The ratio of the feedback signal to the output signal, indicating how much of the output is fed back into the input.
Reference links
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