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Voltage Gain Calculation
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Today we'll calculate the voltage gain of our feedback system using the formula for voltage gain, A = Af / (1 + Ξ²Af), where Af is the forward amplifier gain and Ξ² is the feedback factor.
So, for our example with Af being 200 and Ξ² being 0.095, what will our gain be?
Good question! First, we can substitute these values into the formula. Let's compute it together.
Isn't the desensitization factor also involved in this calculation?
Correct! The desensitization factor is important as it affects our gain and input/output resistances. Remember: the higher the gain of the forward amplifier, the more influence it has on the feedback system.
Can we summarize the steps involved in calculating the voltage gain?
Absolutely! Step one: identify your Af and Ξ². Step two: plug into the formula. Step three: calculate and interpret the result. Remember to keep track of the units!
Input and Output Resistance
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Now let's move on to input resistance. We know from our earlier calculation of feedback that input resistance can be affected by feedback. Can anyone tell me how?
The input resistance increases due to the desensitization factor!
Exactly! The formula is Rin = Rn * (1 + Ξ²Af). Why do you think this is useful in circuit design?
It allows us to tailor the input resistance to align with specific circuit needs!
Exactly right! And the same concept applies when calculating output resistance, which often decreases due to feedback. Let's calculate it!
So if we have output resistance R0 and we apply feedback, what does the formula look like?
The output resistance when feedback is applied becomes R0'/ (1 + Ξ²Af). Remember, feedback can increase our input resistance while reducing our output resistance.
Output Voltage Calculation
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Now that we understand voltage gain and how it affects input and output resistances, letβs move to output voltage calculation. Who can tell me how to derive the output voltage?
Based on the input voltage multiplied by the gain!
Exactly! If our input voltage is 100 mV and our gain from earlier was calculated at 10, what would that make our output voltage?
That would be 10 times 100 mV, which is 1 V!
Good job. It's all about understanding how each component works in relation to one another. Keep these formulas handy as they'll help you in circuit analysis!
Can you recap the key points we need to remember for output voltage?
Sure! Remember: identify input voltage, compute voltage gain, and multiply. Always check back with our formulas!
Non-ideal Feedback Considerations
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Now letβs consider non-ideal feedback. How do we need to adjust our calculations from the ideal case?
We have to account for finite input and output resistances and possibly apply additional equations.
Right! Can anyone remember what the loading effect does in our calculations?
It changes the effective gain by factoring in the load connected to the circuit!
Correct! And for our next example, we will compute both loading factors and their effects on our voltage output and other parameters.
Can you show us how the formulas will change in this case?
Certainly! Weβll adapt our previous formulas to include these new parameters, so be ready to recalculate everything!
Introduction & Overview
Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.
Quick Overview
Standard
In this section, numerical examples are presented to illustrate how to determine the voltage gain, input resistance, output resistance, and output voltage of a feedback system. It highlights both ideal and non-ideal conditions, showcasing the impact of different parameters on the feedback system's performance.
Detailed
Feedback System (Part- E)
This section delves into the analysis of a feedback system for analog electronic circuits, focusing on calculating important performance metrics such as voltage gain, input resistance, output resistance, and output voltage in response to a given input signal. The analysis is guided by specific parameters including input and output resistances of the forward amplifier, its gain, and the feedback factor.
Key Concepts Covered:
- Numerical Examples: Presents the importance of calculating performance metrics in the context of a feedback system.
- Ideal vs Non-Ideal Feedback Networks: Discusses the scenario with an ideal feedback network vs one with finite resistances, emphasizing how these conditions affect system parameters.
- Formulas: Derivations and explanations of the associated mathematical formulas to compute values such as input and output resistances and voltage gains.
- Desensitization Factor: Explains how feedback impacts input and output resistances and how they can be adjusted through feedback configurations.
Each calculation illustrates essential principles within electronic circuits, offering insights into design considerations for effective feedback amplifiers.
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Objective of the 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 main goal is to calculate several parameters of a feedback system. Specifically, it aims to find the voltage gain, input resistance, output resistance, and output voltage when a signal of 100 mV is applied. These calculations are part of understanding how feedback affects the behavior of electronic circuits.
Examples & Analogies
Think of the feedback system like a thermostat in your home. When the temperature dips below a certain point, the thermostat kicks in and starts the heater. Similarly, in an electronic feedback system, the output is adjusted based on the input (in this case, the 100 mV signal) to produce a stable and desired output.
Feedback System Parameters
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And 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
This chunk outlines the essential parameters needed for the calculations: the gain of the forward amplifier is 200, indicating how much the amplifier increases the input signal; the feedback factor, which is 0.095, relates to how much of the output gets fed back into the system. The input and output resistances are crucial because they affect how the amplifier interacts with other components in the circuit.
Examples & Analogies
Imagine a factory assembly line where 200 products are made but only 9.5 of those products are checked for quality before they're sent back into the line. The gain of 200 is like the production rate, and the feedback factor is the quality control check that influences the entire process.
Case 1: Ideal Feedback Network
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So to start with, 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 first case, we consider an ideal feedback network which simplifies our calculations. An infinite input resistance means that it won't draw any current from the signal source, making the circuit more predictable. On the other hand, a zero output resistance means the system can provide high voltage without dropping voltage across itself.
Examples & Analogies
Picture a perfect sponge that can absorb unlimited water without changing the water flow. The sponge represents our infinite input resistance; it absorbs information without affecting the source. Meanwhile, think of a hose with no restrictions - it allows water to flow freely, akin to the zero output resistance that delivers maximum voltage to the output.
Calculating Voltage Gain
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So the gain of the feedback system it is 10. Now, to find the value of the input resistance R .
Detailed Explanation
The gain of 10 indicates that the output voltage is ten times greater than the input voltage. For instance, if we input 100 mV, we would expect 1 V as output (100 mV multiplied by the gain of 10). We then focus on calculating the input resistance, showing how feedback can modify the amplifier's characteristics.
Examples & Analogies
Consider a magnifying glass: it doesn't just make things look bigger; it also has its own characteristics, like how much light it can gather. Similarly, feedback in a circuit changes how the original input signal is amplified while also affecting other properties like resistance.
Input Resistance Calculation
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So note that just by this feedback network the input resistance it is getting increased by a factor of 20 which means that if the main amplifier input resistance it was 1 k, the feedback system input resistance it is becoming 20 k.
Detailed Explanation
This portion emphasizes the effect of feedback on input resistance. The input resistance increases significantly due to feedback, going from 1 kβ¦ to 20 kβ¦. This increase means the feedback network makes it easier to connect other components to the amplifier without affecting the signal.
Examples & Analogies
Think of this as a crowd at a concert. When more people join in and support the music, the noise or input resistance becomes larger, allowing more sounds to be amplified without drowning out the main performance.
Output Resistance Calculation
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So the shunt connection it is reducing the resistance which means that the output resistance it will be = = 200 β¦.
Detailed Explanation
In this part, it is shown that the output resistance decreases to 200 β¦ because of the shunt configuration used in the feedback network. This is beneficial for the system, as lower output resistance can improve power transfer to the load.
Examples & Analogies
Imagine youβre at a concert trying to push through a crowd, but instead of everyone blocking you, some move aside to let you pass. The less resistance allows you to get through easily, just as a lower output resistance makes it easier for the circuit to deliver power to the connected component.
Output Voltage Calculation
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So the output voltage v it is 10v . So that is giving us 10 Γ 100 mV = 1 V.
Detailed Explanation
Here, we calculate the output voltage based on the previously determined gain. If we input 100 mV and the gain is 10, the output will be 1 V. This simple calculation encapsulates the essence of how feedback systems increase signal strength.
Examples & Analogies
Imagine a party where one personβs excitement gets everyone else enthusiastic β the energy grows exponentially. Just as that excitement reflects back in an amplified way, our feedback system causes the output voltage to amplify based on the input.
Transition to Case 2: Non-Ideal Feedback
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Now if I consider the 2nd case, I should not say it is ideal. So this part may be ideal, but with finite resistance.
Detailed Explanation
In this chunk, the transition is made to a second case where feedback is non-ideal. Differences from the first case include finite input and output resistances, which introduce complexities in calculations and expected outputs.
Examples & Analogies
Think about ordering food online versus directly at a restaurant. Online, you are limited by the selections offered; you might have to deal with delays. Similarly, non-ideal conditions introduce limits that we have to account for in calculations.
Load Affected Parameters
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So we need to be careful that A it is giving us 200, but Aβ² it is different.
Detailed Explanation
This emphasizes the careful distinction between the ideal and actual gain calculations. The presence of load changes the gain we expect from what the forward amplifier states, necessitating a correction using load factors.
Examples & Analogies
Think of an athlete like a runner who can sprint at full speed in a race alone but slows down considerably when carrying extra weight. Similarly, in an electronic circuit, adding load impacts the performance of the system, changing expected behavior.
The Calculated Results
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So here we do have here it is . In fact, again I have done this calculation.
Detailed Explanation
This segment encapsulates the calculations to deduce the changes in parameters based on new conditions and how feedback alters not just performance but also the internal characteristics like gain and resistance. Detailed calculations are performed to derive new values.
Examples & Analogies
Think of recalibrating the settings on a machine after switching it to a different task. Just as those recalibrations affect the output, so too do the calculations for electronic systems when conditions change.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
-
Numerical Examples: Presents the importance of calculating performance metrics in the context of a feedback system.
-
Ideal vs Non-Ideal Feedback Networks: Discusses the scenario with an ideal feedback network vs one with finite resistances, emphasizing how these conditions affect system parameters.
-
Formulas: Derivations and explanations of the associated mathematical formulas to compute values such as input and output resistances and voltage gains.
-
Desensitization Factor: Explains how feedback impacts input and output resistances and how they can be adjusted through feedback configurations.
-
Each calculation illustrates essential principles within electronic circuits, offering insights into design considerations for effective feedback amplifiers.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
-
In Case 1, the voltage gain of the feedback system was calculated to be 10 using the given forward amplifier gain of 200 and the feedback factor of 0.095.
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In Case 2, the introduction of finite input and output resistances reduced the voltage gain and adjusted the input and output resistances accordingly.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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Gain of voltage is your game, feedback factor holds the fame!
π Fascinating Stories
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Imagine a party where everyone is invited (feedback) ensuring no one arrives late (input/output conditions) improving the overall experience (performance).
π§ Other Memory Gems
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FOR VGiN - Forward for Output, Resistances, Voltage Gain & Input Needs.
π― Super Acronyms
RIG - Remember Input Gain for feedback analysis.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
-
Term: Voltage Gain
Definition:
The ratio of output voltage to input voltage, typically expressed in decibels (dB).
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Term: Feedback Factor (Ξ²)
Definition:
A measure of how much of the output is fed back into the system input.
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Term: Desensitization Factor
Definition:
The factor that quantifies the extent to which feedback affects the input and output resistances of a feedback system.
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Term: Input Resistance (Rin)
Definition:
The resistance seen by the input signal when applied to the amplifier, which can change due to feedback.
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Term: Output Resistance (Rout)
Definition:
The resistance seen at the output of the amplifier, often decreased by feedback.