99.4.2 - Upper and Lower Limits of R
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Introduction to Feedback Configurations
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Today, we will dive into feedback configurations in amplifiers. Can anyone explain why feedback is important?
Feedback helps improve the stability and bandwidth of the amplifier.
Exactly! Now, resistor R plays a vital role in these configurations. We need to determine its upper and lower limits for effective feedback. Why do you think this is necessary?
It’s probably about ensuring the amplifier operates correctly!
Great point! Let’s explore how the limits on R can affect circuit stability and operation.
Determining Upper and Lower Limits
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To set our limits for R, we must examine several conditions, like the loop gain needing to be greater than one. What is loop gain?
Loop gain is the product of gains around the feedback loop, right?
Correct! Setting conditions for R ensures we maintain effective feedback. Can anyone suggest what happens if the resistance values are not appropriately set?
Unstable behavior and possibly oscillations could occur in the circuit.
Exactly! Stability is paramount. Now let's work through how to calculate R based on conditions we set.
Impact of Resistor R on Circuit Parameters
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As we set limits on R, various circuit parameters, like input and output resistance, are also influenced. Can you think of how these parameters interact?
If R impacts input resistance, changing it might also alter how much of the input signal is processed.
Exactly! It's all interconnected. The desensitization factor will also heighten input resistance with feedback. Can anyone recall the formula for this?
It’s something like input resistance equals original input resistance multiplied by the desensitization factor.
Perfect! Let’s detail how to apply this practically in feedback configurations.
Practical Application: Numerical Example
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Now, let's transition into a numerical example. Understanding practical numbers is key. What values do we need to plug into our equations?
We would need values like collector current, bias resistor values, and beta.
Excellent! By substituting our values, we’ll derive R limits. It's important to perform these calculations accurately to ensure our feedback circuit operates effectively.
So, we can set R based on these calculations to fit within our derived limits!
That's right! This process helps us apply theoretical knowledge in real-world applications.
Introduction & Overview
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Quick Overview
Standard
This section focuses on finding the upper and lower limits for resistor R in feedback circuits. It outlines the criteria necessary for effective feedback, explaining how these limits affect circuit parameters like gain, resistance, and performance in analog electronic applications.
Detailed
Upper and Lower Limits of R
In feedback configurations within analog electronic circuits, understanding the upper and lower limits of resistor R is crucial for achieving desired performance. This section describes how to determine the suitable range of resistor R based on feedback conditions, emphasizing the necessity of evaluating both circuit gains and feedback effects. The criteria established help in ensuring that the loop gain is maintained at a level significantly beyond unity, consequently minimizing loading effects on the input and output resistances. The relationship between resistor values affects parameters like input resistance, output resistance, and overall gain, allowing circuits to function efficiently with optimal performance.
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Introduction to Feedback Limits
Chapter 1 of 3
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Chapter Content
So, quickly we can say that this G it was g of the transistor. In fact, G′ also we said it is well approximated by g of the transistor and R it is r , R it is r . And of course, β it is R . Now to find the suitable range of R , we need to consider this three conditions which gives us that the magnitude of the loop gain it is much higher than 1 and then here the loading effect of the input resistance of the feedback network, output resistance of the feedback network we can compare with input resistance of the circuit and on the to avoid the loading effect of the input resistance on the feedback network.
Detailed Explanation
In this chunk, we discuss the relationships between G, R, and the feedback network's conditions. G represents the transconductance, which is a key parameter in amplifiers. In this case, G is approximated to the characteristics of the transistor (g). To establish effective feedback, we need to define the range for R which is the resistor's feedback factor. We have three important conditions to ensure effective feedback: 1) The loop gain should be greater than 1 for stability, 2) The loading effect must be considered to compare input and output resistances appropriately, and 3) Avoid feedback network resistance impacts.
Examples & Analogies
Think of G as the speed limit on a highway. If the speed limit is too low (I.e., loop gain less than 1), cars (signals) won't flow well. If the on- and off-ramps (input/output resistances) are not balanced, traffic (signal feedback) can bottleneck. Hence, we have to ensure proper limits for the road layout (R), so traffic keeps moving smoothly.
Conditions for Effective Feedback
Chapter 2 of 3
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Chapter Content
On the other hand if I consider this condition it is it is suggesting that if you follow this one then loading effect of R of the feedback network, R it can be ignored. So, and of course, this is R and if you look into say this network and it is very simple network. So, it is easy to see that R it is nothing but R . In fact, R = R . In fact, so, whenever we look into the output port of the feedback network it works as a voltage source and this voltage source it is having a Thevenin equivalent resistance and this resistance it is R and that is what the output resistance of the feedback network.
Detailed Explanation
This chunk emphasizes another important condition where the loading effect of feedback resistance R can be negligible. This means the feedback network can operate as a simple voltage source, where resistance is constant. By equating the feedback network's R with its output resistance, we simplify the analysis. We are essentially stating that under these conditions, our model can be simplified, making calculation and understanding of feedback much straightforward.
Examples & Analogies
Picture a garden hose with water flowing through it. The feedback network (hose) can be thought of as a water source. If the hose is blocked (much like a high loading effect), the flow will be reduced. However, if the hose has no obstruction (resistance negligible), the water flows freely, making it easy to manage the watering of the plants (feedback effects).
Determining the Range for R
Chapter 3 of 3
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Chapter Content
So, in summary we can say that G′ it is also it can be well approximated by g . Input resistance of the circuit it is of course, r of the transistor and then R of the circuit main amplifier it is r . And then, what is the feedback factor? It converts the signal the current signal into voltage it is it is equal to R , the unbypassed part of the R . So, with this information now we can go for finding appropriate value or range of this R .
Detailed Explanation
In this section, we summarize earlier points and derive a way to determine the appropriate value for R based on transconductance and circuit characteristics. We see how G prime (G′) simplifies to g, allowing us to use the transistor's input resistance in our calculations. The feedback factor as R helps convert signals, emphasizing the importance of utilizing the unbypassed portion of R for effective feedback. This understanding is crucial in selecting an appropriate R range, aiding us to design better feedback circuits.
Examples & Analogies
Imagine tuning a musical instrument, where G is the tuning key. Understanding how tight or loose the string (the resistance and other components) behaves as you turn the key allows you to find the correct pitch (feedback effects). Similarly, effectively setting R will ensure the right notes (feedback currents and voltages) harmonize in an electrical circuit.
Key Concepts
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Feedback Significance: Key in amplifiers for stability and performance.
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Loop Gain: Essential for stability, needs significant values for effective feedback.
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Desensitization Factor: Influences input and output resistances, improving performance.
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Upper and Lower Limits of R: Critical for achieving the desired amplifier behavior.
Examples & Applications
The relationship between resistor R and input/output resistances in feedback systems.
Calculating limits for R based on established criteria for amplifier stability.
Memory Aids
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Rhymes
In circuits where feedback is the key, R must be right, you see!
Stories
Imagine a lake with water flowing. If too much comes in, it overflows (instability); too little and the plants dry up (ineffective feedback). Just like R!
Memory Tools
FLIR - Feedback Limits Input Resistance.
Acronyms
R - Really needed for right amplifier functioning!
Flash Cards
Glossary
- Feedback
A process in which a portion of the output signal is fed back to the input to enhance the performance or stability of a system.
- Loop Gain
The product of the gains of all elements in a feedback loop, used to evaluate the stability of the feedback system.
- Resistance
A measure of the opposition to current flow in an electrical circuit, typically measured in Ohms (Ω).
- Desensitization Factor
A term describing how feedback affects the input and output resistances in feedback circuits.
- Input Resistance
The resistance faced by the input signal in a circuit; crucial for determining how much signal is processed.
- Output Resistance
The resistance a circuit presents to its output, impacting how much load can be driven effectively.
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