Negative Feedback Amplifier Calculations (for Voltage-Series Feedback)
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Introduction to Negative Feedback
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Welcome class! Today, we will delve into the concept of negative feedback in amplifiers. Can anyone explain what negative feedback means?
Isn't it when part of the output is fed back to the input to reduce the overall gain?
Exactly! Negative feedback helps stabilize the amplifier's performance. It can decrease distortion and make the gain more predictable. Why do you think reducing gain might be beneficial?
It could help prevent clipping distortion when the amplifier is overdriven?
Right! Now letβs mention a mnemonic to remember the benefits of negative feedback: 'ADS' - it Amplifies stability, Decreases distortion, and Stabilizes gain. Thatβs a good starting point!
Can you give an example of where negative feedback is notably used?
Certainly! Operational amplifiers (Op-Amps) commonly utilize negative feedback in various applications, including audio amplifiers and filters.
To wrap up this session, negative feedback not only reduces gain but can enhance many performance characteristics of amplifiers.
Calculating Closed-Loop Gain
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Now that we understand negative feedback, letβs look at our first calculation: the closed-loop gain. Can someone share the formula?
Is it A_f = A / (1 + AΞ²)?
Correct! Where $A$ is the open-loop gain and $Ξ²$ is the feedback factor. If we have an open-loop gain of 100 and a feedback factor of 0.1, what would the closed-loop gain be?
Using the formula, A_f = 100 / (1 + 100 * 0.1) = 100 / 11 = 9.09.
Great job! This shows how impactful feedback can be and how it dramatically reduces gain. Can anyone think of a trade-off involved with this?
Maybe it impacts the output voltage level?
Exactly! Thereβs always a trade-off: you gain stability and linearity but at the cost of lower gain.
In summary, mastering this calculation is essential for designing effective amplifiers!
Feedback Effects on Input and Output Resistance
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Moving forward, let's explore how negative feedback affects input and output resistance. Who knows the correlation?
I think negative feedback increases input resistance and decreases output resistance?
"Spot on! For voltage-series feedback, the formulas are:
Bandwidth and Distortion Reduction
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Let's discuss bandwidth. How does negative feedback influence it?
Doesn't it increase the bandwidth of the amplifier?
Yes! The formula is $BW_f = BW(1 + AΞ²)$. So if our initial bandwidth without feedback is 10 kHz and we use feedback with a loop gain of 50, what is our new bandwidth?
It would be 10 kHz * 51 = 510 kHz.
Correct, fantastic! This shows how negative feedback can extend the frequency response of an amplifier.
And it helps with distortion, right?
Yes! Negative feedback can also significantly reduce distortion. Why might this occur?
It reduces non-linearities by keeping the amplifier operating within its linear range?
Excellent point! So as we conclude, remember how feedback extends bandwidth while minimizing distortion, making amplifiers more effective for high-fidelity applications.
Introduction & Overview
Read summaries of the section's main ideas at different levels of detail.
Quick Overview
Standard
This section elaborates on voltage-series negative feedback mechanisms, detailing how such feedback can lower gain while increasing input resistance and bandwidth, thereby mitigating distortion in amplifiers. Key formulas for calculating closed-loop gain, input and output resistances, and bandwidth are presented to facilitate understanding.
Detailed
Negative Feedback Amplifier Calculations (for Voltage-Series Feedback)
Negative feedback is a fundamental concept in amplifier design that plays a crucial role in enhancing performance. This section focuses specifically on voltage-series feedback amplifiers, which utilize feedback that is in series with the input signal.
Key Concepts Covered:
- Feedback Mechanism: In voltage-series feedback, a portion of the output voltage is fed back to the input, effectively reducing the overall gain of the amplifier while improving stability and linearity.
- Calculations: The section provides essential formulas:
- Closed-Loop Gain (A_f):
$$ A_f = \frac{A}{1 + A\beta} $$
where $A$ is the open-loop gain and $eta$ is the feedback factor, indicating the fraction of the output that is fed back. - Input Resistance with Feedback:
For voltage-series feedback:
$$ R_{in(f)} = R_{in}(1 + A\beta) $$ - Output Resistance with Feedback:
$$ R_{out(f)} = \frac{R_{out}}{1 + A\beta} $$ - Bandwidth Extension: Negative feedback extends the bandwidth according to:
$$ BW_f = BW(1 + A\beta) $$ - Distortion and Stability: Feedback significantly reduces distortion and enhances stability, making amplifiers less sensitive to variations in component parameters.
- Implications: By applying the appropriate feedback, amplifiers can achieve more predictable and manageable performance, essential for precise applications like audio and instrumentation.
Importance
Understanding negative feedback in amplifiers is crucial for students of electronics as it lays the groundwork for developing efficient, stable circuits with minimized distortion, a necessity in modern electronic devices.
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Feedback Factor Calculation
Chapter 1 of 6
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Calculated Feedback Factor ($\beta$): \[ \beta = \frac{R_2}{R_1 + R_2} \] = [Your Calculation]
Detailed Explanation
The feedback factor, denoted by \( \beta \), represents the portion of the output voltage that is fed back to the input to control the amplifier's gain. It is calculated using the resistors \( R_1 \) and \( R_2 \) in the feedback network. Specifically, \( R_2 \) is the resistor connected across the feedback path, while \( R_1 \) is connected in series with the input. The formula indicates that \( \beta \) is the proportion of the output signal that influences the amplifier's behavior, thus affecting its overall performance.
Examples & Analogies
Imagine you are adjusting the volume on a speaker. The feedback factor is like the small knob that you adjust to control how much sound is played back to the input, helping you maintain a consistent volume level without feedback causing distortion.
Open-Loop Gain Assumption
Chapter 2 of 6
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Assume/State Open-Loop Gain ($A$): (If using Op-Amp, state typical $A$ like $10^5$. If discrete, use measured $A$ from 7.3). \[ A = [Value] \]
Detailed Explanation
The open-loop gain, denoted as \( A \), is the gain of an amplifier when no feedback is applied. For operational amplifiers (Op-Amps), this gain can be extremely high, often on the order of \( 10^5 \) or more. This high gain ensures that even small input signals are amplified significantly. If a discrete amplifier circuit is used, the open-loop gain should be measured separately and reported. Understanding this gain is crucial because it forms the basis for calculating the closed-loop gain when feedback is introduced.
Examples & Analogies
Think of open-loop gain as the maximum capacity of a public speaker without any sound control. When someone shouts into the microphone, they'll amplify the sound significantly, but without feedback management, the volume can become overwhelming and distorted, just like an unregulated amplifier.
Closed-Loop Gain Calculation
Chapter 3 of 6
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Calculated Closed-Loop Gain ($A_f$): \[ A_f = \frac{A}{1 + A\beta} \] = [Your Calculation]
Detailed Explanation
The closed-loop gain \( A_f \) is the gain of the amplifier when negative feedback is applied. This formula shows that as feedback is introduced (controlled by \( \beta \)), the overall gain is reduced. This gain reduction happens because the feedback counteracts some of the input signal, stabilizing the amplifier. A larger \( A \) or \( \beta \) will result in less closed-loop gain, making the amplifier's output more predictable and stable.
Examples & Analogies
Imagine a car with a powerful engine (analogous to the open-loop gain). When you apply brakes (feedback), the car slows down (reduced gain). The feedback allows precise control over the speed, preventing the car from speeding out of control, much like how feedback stabilizes the output of an amplifier.
Input Resistance with Feedback
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Calculated Input Resistance with Feedback ($R_{in(f)}$): \[ R_{in(f)} = R_{in(\text{without feedback})} (1 + A\beta) \] = [Your Calculation] \text{ Ξ©}
Detailed Explanation
The input resistance with feedback, represented as \( R_{in(f)} \), reflects how the application of feedback influences the input impedance of the amplifier. When voltage-series feedback is utilized, this resistance increases, providing the amplifier with a more stable input. The formula indicates that applying feedback effectively increases the resistance seen by the input signal, which can lead to improved performance and better interfacing with other circuit elements.
Examples & Analogies
Consider input resistance like a wide entry gate to a garden. When you add some feedback (like a filter or buffer), the entrance becomes more inviting, allowing for better access (improved impedance), thereby enhancing the overall flow of people (signals) into the garden (the amplifier).
Output Resistance with Feedback
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Calculated Output Resistance with Feedback ($R_{out(f)}$): \[ R_{out(f)} = \frac{R_{out(\text{without feedback})}}{1 + A\beta} \] = [Your Calculation] \text{ Ξ©}
Detailed Explanation
The output resistance with feedback, denoted as \( R_{out(f)} \), tells us how the amplifier's output impedance is influenced by the feedback applied. Typically, voltage-series feedback reduces the output resistance, allowing the amplifier to drive loads more effectively. When the output resistance is lowered, the amplifier can maintain better control over the voltage delivered to the load (speaker, for instance), thus ensuring enhanced performance.
Examples & Analogies
Think of output resistance as a faucet's nozzle. When you apply a restriction (similar to introducing feedback), the water flows more efficiently and steadily, providing a better delivery to the plants you are watering (the load). If you remove the restriction, water might sputter and deliver inconsistent flow, just like a high output resistance can lead to poor performance in an amplifier.
Bandwidth with Feedback
Chapter 6 of 6
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Calculated Bandwidth with Feedback ($BW_f$): \[ BW_f = BW_{(\text{without feedback})} (1 + A\beta) \] = [Your Calculation] \text{ Hz}
Detailed Explanation
The bandwidth with feedback, represented as \( BW_f \), indicates the frequency range over which the amplifier operates effectively after applying feedback. Introducing feedback typically extends the bandwidth of the amplifier, allowing it to maintain its gain across a wider range of frequencies. This extension enhances signal fidelity and performance, ensuring that the amplifier can faithfully reproduce signals without significant distortion across its operational spectrum.
Examples & Analogies
Imagine a radio tuner. Without feedback, the tuner has a limited range of stations it can pick up well (narrow bandwidth). When you improve the receiver (akin to adding feedback), it can catch more stations clearly across a broader range of frequencies, making it versatile and reliable for listening.
Key Concepts
-
Feedback Mechanism: In voltage-series feedback, a portion of the output voltage is fed back to the input, effectively reducing the overall gain of the amplifier while improving stability and linearity.
-
Calculations: The section provides essential formulas:
-
Closed-Loop Gain (A_f):
-
$$ A_f = \frac{A}{1 + A\beta} $$
-
where $A$ is the open-loop gain and $eta$ is the feedback factor, indicating the fraction of the output that is fed back.
-
Input Resistance with Feedback:
-
For voltage-series feedback:
-
$$ R_{in(f)} = R_{in}(1 + A\beta) $$
-
Output Resistance with Feedback:
-
$$ R_{out(f)} = \frac{R_{out}}{1 + A\beta} $$
-
Bandwidth Extension: Negative feedback extends the bandwidth according to:
-
$$ BW_f = BW(1 + A\beta) $$
-
Distortion and Stability: Feedback significantly reduces distortion and enhances stability, making amplifiers less sensitive to variations in component parameters.
-
Implications: By applying the appropriate feedback, amplifiers can achieve more predictable and manageable performance, essential for precise applications like audio and instrumentation.
-
Importance
-
Understanding negative feedback in amplifiers is crucial for students of electronics as it lays the groundwork for developing efficient, stable circuits with minimized distortion, a necessity in modern electronic devices.
Examples & Applications
In audio amplifiers, negative feedback is used to reduce distortion, leading to clearer sound quality.
In operational amplifiers, feedback is crucial to configure gains and control bandwidth effectively.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
Feedback's the key, as clear as can be, helps us avoid distortion, keeps linearity free.
Stories
Imagine youβre tuning a guitar amp. Each time it distorts, you adjust the volume with a feedback mechanism until the sound is clear. That's negative feedback in play!
Memory Tools
R.G.B - Remember Gain goes Down; Bandwidth goes Up with feedback.
Acronyms
ADS
Amplifies stability
Decreases distortion
Stabilizes gain.
Flash Cards
Glossary
- Negative Feedback
A process where a portion of the output signal is routed back to the input, reducing the overall gain and improving stability and linearity.
- ClosedLoop Gain (A_f)
The gain of an amplifier when negative feedback is applied, calculated using the formula A_f = A / (1 + AΞ²).
- Feedback Factor (Ξ²)
The fraction of the output signal that is fed back to the input of the amplifier.
- Input Resistance (R_in)
The resistance presented by the amplifier at its input terminals.
- Output Resistance (R_out)
The resistance the amplifier presents to its load at the output terminals.
- Bandwidth (BW)
The range of frequencies over which an amplifier operates effectively.
Reference links
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