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Interactive Audio Lesson
Listen to a student-teacher conversation explaining the topic in a relatable way.
Feedback System Basics
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Let's start by discussing what a feedback system is. Could someone tell me how we define it?
I think a feedback system is one where the output is fed back into the input to control its behavior.
Exactly, Student_1! Feedback systems help regulate the output. Now, can anyone tell me about the types of feedback?
There are two types: positive feedback, which amplifies changes, and negative feedback, which stabilizes the system.
Great insights! Remember, negative feedback generally improves stability and reduces gain. Let's move on to what we will calculate today.
Ideal Feedback System
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Now, let's examine an ideal feedback system. Who can remind us of its characteristics?
In an ideal feedback system, the input resistance is infinite, and the output resistance is zero.
Correct, Student_3! These characteristics will affect how we compute the voltage gain. Let's calculate the voltage gain using the formula: A' = A / (1 + Ξ²A). What values do we have for A and Ξ²?
We have A = 200 and Ξ² = 0.095.
Right! Plugging those in, what do we get for the voltage gain?
It looks like the voltage gain A' becomes 10.
Exactly. Excellent work, everyone! This shows how negative feedback can stabilize the system. Let's explore how this impacts other metrics!
Calculating Input and Output Resistance
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Next, let's calculate the input resistance, R_in of the feedback system. Can someone tell me how we do that?
We multiply the original input resistance by the desensitization factor, right?
Yes! If R_in is 1k⦠for the forward amplifier, and we have a desensitization factor of 20, what's the new input resistance?
That would be 20kβ¦!
Well done! Now, who can tell me about calculating the output resistance R_out?
For output resistance in a feedback system, we reduce the output resistance due to the feedback.
That's right! So, if our output resistance is 200β¦ in the feedback system, how does it change?
It remains at 200β¦ due to the influence of shunt configurations!
Exactly! Great work! Let's summarize what we've learned.
Output Voltage Calculation
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Letβs wrap up by calculating the output voltage based on our previous findings. We have an input voltage, V_in of 100mV. What's the output voltage with our voltage gain A'?
Since the gain is 10, the output voltage would be 10 times the input voltage, which makes it 1V.
Excellent! This is how we find the output voltage in the feedback system! What does this say about our feedback systemβs ability to amplify signals?
It indicates that we can enhance weak signals significantly using feedback!
Spot on! And that concludes our session on feedback systems. Any questions?
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
The section illustrates how to determine the voltage gain, input resistance, and output resistance of feedback systems through a detailed numerical example. It covers both ideal and non-ideal feedback scenarios, highlighting the importance of various parameters in the amplification process.
Detailed
Numerical Example
In this section, we focus on calculating key parameters of a feedback system, including voltage gain, input resistance, output resistance, and output voltage based on given amplifier and feedback characteristics. We examine two cases: an ideal feedback network characterized by infinite input resistance and zero output resistance, and a non-ideal feedback network featuring finite input and output resistances. The numerical example begins with specified values such as the forward amplifier gain, feedback factor, and input/output resistances, guiding the reader through the detailed computations necessary to derive significant metrics of the system. We learn that the feedback mechanism can considerably influence the overall characteristics of the system, positively impacting input resistance while typically reducing output resistance. Through careful calculations and re-evaluation of different scenarios, we develop a comprehensive understanding of how feedback applies in electronic circuits.
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Objective of the Numerical Example
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So here we do have numerical example and what is our objective here? It is that we need to find the voltage gain of the feedback system, input resistance, output resistance of the feedback system and the output voltage for an input voltage or the signal voltage of 100 mV.
Detailed Explanation
In this section, the primary goal is introduced as finding various parameters of a feedback system. Specifically, we want to determine:
1. Voltage Gain: This tells us how much the input signal is amplified.
2. Input Resistance: This is important in understanding how the system interacts with the connected input source.
3. Output Resistance: This relates to how the system behaves with the load connected to its output.
4. Output Voltage: Finally, we are interested in knowing what the output voltage will be when a specific input voltage (100 mV) is applied.
Examples & Analogies
Think of this as trying to understand how a sound amplifier works. If you are inputting sound through a microphone (the 100 mV signal), you want to know how much louder the sound will be after it passes through the amplifier, how easily you can connect your microphone (input resistance), how it behaves with speakers (output resistance), and finally, what volume (output voltage) you will get from it.
System Parameters
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The parameters of the feedback systems are given here input resistance and output resistance of the forward amplifier and the gain of the forward amplifier it is 200 feedback network, the feedback factor it is 0.095.
Detailed Explanation
In this chunk, the parameters necessary for calculations are listed, including:
- Input Resistance of the Forward Amplifier: This is the resistance seen by the input signal, which influences how much of the signal is actually accepted by the amplifier.
- Output Resistance of the Forward Amplifier: This is how the amplifier behaves in relation to the load.
- Gain of the Forward Amplifier: This is stated as 200, indicating how many times the input signal is amplified.
- Feedback Factor: This value (0.095) shows the part of the output that is fed back into the input, which is crucial for determining the overall behavior of the feedback system.
Examples & Analogies
Imagine you have a music speaker system. The input resistance is like how much power the speaker can take from the source. The output resistance is how much the speaker can resist the flow of electricity when playing music. The gain represents how much louder the sound will be amplified, just like raising the volume knob on your stereo.
Case 1: Ideal Feedback Network
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Let me consider this relatively simpler case, case-1 where we consider ideal feedback network having the input resistance it is infinite and its output resistance on the other hand it is 0 as we are generating voltage.
Detailed Explanation
In this ideal scenario (Case 1):
- Input Resistance is considered infinite, meaning the amplifier does not draw any current from the input signal, leading to perfect signal handling.
- Output Resistance is considered zero, meaning that the system can supply any amount of current without affecting the output voltage, which is ideal for power transfer. This simplification allows us to make basic calculations without complex interactions.
Examples & Analogies
This is like having an internet connection where there is no slow-down for the connecting device (infinite input resistance), and it can download as much data as it wants without any limit (zero output resistance). You experience fast and responsive internet.
Calculating Voltage Gain
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So to start with, let we have the derivation of this A rather Aβ² or rather A of v_f. As we know that this A it is the forward amplifier gain. So the A it is given 200 v_f and on the other hand, feedback factor it is 0.095.
Detailed Explanation
Here, the voltage gain (A) is calculated using the provided parameters:
- The forward amplifier gain (A) is set at 200.
- The feedback factor (Ξ²) is 0.095.
The gain of the feedback system can be calculated as:
\[ A_{feedback} = \frac{A}{1 + \beta A} \]
This formula combines the effects of the forward gain and the feedback to give the effective gain of the feedback system, simplifying calculations for real circuits.
Examples & Analogies
Imagine a water pump (the amplifier) that pumps water at a high rate (gain of 200), but using a feedback pipe (feedback factor) that allows some water to flow back to the source. The effective water flow seen downstream (output gain) will be less than just the pump's capacity because of that return flow.
Finding Input Resistance
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To find the value of the input resistance R_in_f, it is getting amplified by the desensitization factor. So that should be R_in_f (1 + Ξ²A). And R_in is 1 k Γ 20 and that gives us 20 kβ¦.
Detailed Explanation
The input resistance is calculated using the original input resistance of the forward amplifier and the desensitization factor:
\[ R_{input} = R_{in}(1 + \beta A) \]
Substituting the known values:
- Original input resistance is 1kΞ©, multiplied by the factor of 20 (due to feedback), leads us to an increased total input resistance of 20kΞ©. This shows how feedback can substantially increase the input resistance in a circuit.
Examples & Analogies
Think of input resistance like a filter in a water system. By using feedback, the system can handle more water flow without clogging up. Originally the filter could handle a small amount of water (1kΞ©); with improvements (the feedback factor), it can handle significantly more without being overwhelmed (20kΞ©).
Calculating Output Resistance
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Now we need to calculate the output resistance R_out_f. Here we do have shunt connection, so the output resistance it will be equal to = 200 β¦.
Detailed Explanation
For the output resistance, the shunt connection reduces the overall resistance. Thus, the output resistance is calculated and results in 200Ξ©. This shows how feedback connections can lower the output resistance, allowing the feedback system to effectively drive the load connected to it.
Examples & Analogies
Imagine two roads merging into one lane. If they both can handle lots of traffic individually (high resistance), when they merge, they may allow less traffic (lower output resistance) to pass through one lane effectively without slowing down.
Calculating Output Voltage
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So the output voltage v_o is very straight forward. From here to here, the gain we obtain it is A'. So, here to here the gain it is 10. So it is giving us very simple situation. So the output voltage v_o it is 10v .
Detailed Explanation
To find the output voltage, we multiply the input voltage by the newly calculated gain of the feedback system (which was found to be 10). So with an input voltage of 100 mV:
\[ v_o = A_{feedback} \times v_{in} = 10 \times 0.1 V = 1 V. \]
This output voltage indicates how much the input signal has been amplified after processing through the feedback system.
Examples & Analogies
Consider a small speaker producing a sound (input voltage). When you increase the volume (gain), the sound becomes louder. If your speaker amplifies that sound output to 1 V when starting from a very small notice, it shows how effectively it amplified the sound for you to hear much better.
Case 2: Non-Ideal Feedback
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Now let me consider the 2nd case, I should not say it is ideal. So this part may be ideal, but with finite resistance. In fact, we are considering relatively low input resistance.
Detailed Explanation
In Case 2, we analyze a non-ideal situation, meaning the input and output resistances are finite rather than infinite or zero. We have lower input resistance and different output characteristics, which means calculations have to take the new values into account. This reflects more accurately how real-world circuits operate.
Examples & Analogies
It's like saying a car has a certain gas mileage (input resistance) on the highway, but when you're in city traffic with many stops (output resistance), that mileage reduces. In real-life scenarios, equipment does not perform perfectly as in ideal conditions.
Load Affected Gain and Resistance Adjustments
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So how do we find this Aβ²? So the way we define this Aβ² is A multiplied by whatever the load we do have here, it may be external or it may be internal part of the feedback network.
Detailed Explanation
To find the adjusted gain (Aβ²), we consider the load that affects performance. This includes both the load connected to the output and internal network effects that arise due to circuit interactions that reduce gain. This calculation alters the understanding of how input and output values relate under feedback.
Examples & Analogies
Think of this as a team project where one person is responsible for a large part of the workload. If they get overwhelmed (the load), their productivity (the effective gain) decreases. By understanding their limitations, you can adjust your expectations of how much the team can achieve.
Final Calculations and Conclusions
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So we may say that this is also some form of the R without considering R. In fact, I was telling that A, A it is having two approaches.
Detailed Explanation
At the end of the examples, we can summarize that adjustment in both input and output resistances can drastically affect the overall performance. Different approaches provide a way to calculate where the feedback dramatically alters how we can expect the system to perform.
Examples & Analogies
This is similar to testing different battery types in a flashlight. Each battery may provide power differently based on how they're connected. Adjusting for feedback allows us to calculate how effective our flashlight will be with a particular type of battery and compare advantages in real-time.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Voltage Gain: The relationship of input voltage to output voltage, indicating amplification.
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Input Resistance: Resistance encountered by the input signal, influencing system performance.
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Output Resistance: Resistance presented at output, impacting the efficiency of signal transfer.
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Desensitization Factor: The influence feedback has on the amplifying characteristics, affecting both gain and resistance.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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With a forward amplifier gain (A) of 200 and a feedback factor (Ξ²) of 0.095, the voltage gain (A') calculates to 10, while the increased input resistance reaches 20kβ¦.
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Using ideal and non-ideal feedback characteristics, the output close to expectations reveals how calculations vary with altered parameters.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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To get the gain, just multiply, input wattage to output, let it fly!
π Fascinating Stories
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Imagine a classroom where every student's voice (the input) is amplified by a microphone (the feedback system); the louder the input, the more everyone hears (the output).
π§ Other Memory Gems
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Gains Increase β G for Gain, I for Input β remember both together to find output functions.
π― Super Acronyms
GIRL
- Gain
- Input
- Resistance
- Load β remember it to understand the interplay of circuit configurations!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Feedback System
Definition:
A system where output is routed back to input to influence behavior.
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Term: Voltage Gain (A')
Definition:
The ratio of output voltage to input voltage in a feedback system.
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Term: Input Resistance (R_in)
Definition:
Resistance faced by the input signal in a feedback system.
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Term: Output Resistance (R_out)
Definition:
Resistance seen at the output of a feedback system.
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Term: Desensitization Factor
Definition:
A factor showing how feedback changes characteristics of the system.