Feedback System Output Resistance
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Understanding Finite Resistance
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Today, we are going to explore input resistance in feedback systems. Can anyone tell me what we mean when we say the resistance is finite?
Is it because it has a specific measurable value, unlike an open circuit?
Exactly! It's crucial in understanding how systems behave under load. We denote this input resistance as R, and we can calculate it using the load-afflicted transimpedance, Zm.
So, how does Zm relate to the overall input resistance?
Great question! The load-afflicted transimpedance modifies the input resistance which we can represent as Z' = Zm × attenuation factor. It's this interplay that impacts the system's response.
Can we treat these resistances as parallel circuits in this scenario?
Yes, that's right! When components are in parallel, we must consider how each affects the voltage output. Let's summarize: input resistance is finite, influenced by Zm and any other parallel resistances.
Role of Feedback and Beta
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Now, let's shift our focus to feedback parameters. How many of you remember what beta represents in our equations?
Isn't it the feedback factor?
Correct! Beta is crucial to our calculations. It shouldn't change unless we explicitly modify feedback conditions. When calculating input resistance, we express it as (1 + beta) × R.
So, if we have multiple resistances involved, how do we combine them?
Good point! Those resistances will be part of a summation when calculating total input resistance. Let’s recap: we consider both external and internal resistances while ensuring beta remains constant during these calculations.
Parallel Resistance in Depth
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Let’s talk about how parallel resistances interact. Why do you think analyzing them is essential for our feedback systems?
Because it affects the output voltage we get from the system, right?
Exactly! The output voltage is derived from these interconnections. The voltage developed at the output, Vo, can be represented as Vo = Zm × I × attenuation factor. How does this representation help us understand the system?
It indicates how changes in load affect the entire system's performance!
Very well said! It’s all about how the changes in one part influence the output. It emphasizes the importance of calculating resistances accurately in feedback systems. Who can summarize our takeaways from this session?
We learned that parallel resistances affect output and input resistance calculations substantially!
Introduction & Overview
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Quick Overview
Standard
In this section, we examine the input resistance of feedback systems, focusing on the calculations of load-afflicted transimpedance and the adjustment of resistance models. The interplay of these components is crucial for a comprehensive understanding of feedback mechanisms.
Detailed
Feedback System Output Resistance
In this section, we delve into the intricacies of calculating the input resistance of feedback systems. The primary focus is on understanding how load-afflicted transimpedance affects overall resistance. Key points include:
- Finite Resistance: The input resistance is considered finite, with measurements based on original load resistance, denoted as Zm, and the attenuation factor affecting this load.
- Parallel Resistance Model: The analysis also covers the parallel configuration of resistances, leading to the development of voltage across components that are critical for system stability.
- Revisiting Input Resistance: The expression for input resistance incorporates both the effect of feedback (beta) and external resistances to yield an accurate model for system dynamics. A correction in terminology regarding beta is necessary to avoid confusion in subsequent discussions.
Overall, understanding these parameters is essential in engineering feedback control systems efficiently.
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Understanding Input Resistance
Chapter 1 of 5
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Chapter Content
Again I have to make this correction and then if I consider this R it is finite. Then the input resistance of the feedback system it will be given by this where Z′ it is load affected trans impedance and look when I say load affected it is basically whatever the attenuation factor we do have here that we need to consider along with the original Z.
Detailed Explanation
The input resistance of a feedback system depends on various components, including resistance (R) and load-affected transimpedance (Z′). When we say 'load affected,' we're acknowledging that the load's effect alters the impedance we measure. It's crucial to consider both the original impedance (Z) and how this might change due to the presence of feedback.
Examples & Analogies
Imagine you have a garden hose connected to a nozzle. The water pressure in the hose represents the transimpedance, and the nozzle represents the feedback system. If the nozzle is narrow (like a maximum load), it restricts the flow (input resistance) of water, much like how load affects our electrical circuits.
Calculating Input Resistance
Chapter 2 of 5
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So, Z′ it will be Z × ... On the other hand, if I consider this resistance also it is finite. So, if I consider that then the corresponding Z need to be replaced by ... So, why we have to consider these are in parallel that is because this resistance and this resistance they are coming in parallel.
Detailed Explanation
When calculating input resistance, we must account for resistances in parallel. When two or more resistors are in parallel, the overall resistance decreases, which impacts the total impedance of the system. Here Z′ reflects this adjustment made to the original impedance (Z) when new resistances are considered alongside it.
Examples & Analogies
Think about two pathways to a destination. If both paths are available (like two resistors in parallel), you can either take one or the other or both, leading to an easier and quicker route (lower total resistance). This is how adding more parallel paths can reduce the overall impedance in a circuit.
Input Voltage Development
Chapter 3 of 5
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So the voltage getting developed here which is v_o which is of course, reduced version of internally developed voltage. So, the v_o is Z × i × ...
Detailed Explanation
The output voltage (v_o) in the feedback system is derived from the product of impedance (Z) and the input current (i). This relationship shows how feedback affects the output voltage by scaling it based on the system's impedance. It's essential to understand that this is a reduction of the original voltage developed within the system.
Examples & Analogies
Imagine using a magnifying glass to see a tiny object. The output you perceive is more significant than the original but still influenced by how close the glass is to the object (impedance). Similarly, the interaction between voltage and current determines the output in an electrical system.
The Role of Resistance in Feedback
Chapter 4 of 5
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Now if I consider this also which means if I consider this resistance also then that resistance also coming in parallel. So, I think that is how we can calculate the corresponding input resistance of the feedback system.
Detailed Explanation
When calculating the input resistance of a feedback system, it's necessary to recognize all parallel resistances contributing to the total resistance. Each resistance adds a pathway for current, resulting in lower effective input resistance that can improve system performance.
Examples & Analogies
Think of a fitness regimen where you can do multiple exercises at once. Each exercise represents a resistance. If you do several at the same time (parallel), it enhances your overall fitness (input resistance). More pathways lead to improved efficiency in your workout—just like how multiple resistances improve the electrical system.
Correction and Clarification
Chapter 5 of 5
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Yeah in this case when I explained that we do have R here we do have this resistance then the input resistance of the feedback system it is (1 + β) + R.
Detailed Explanation
In this segment, a correction is made regarding the input resistance calculation involving a factor β. Acknowledging how external resistances affect this formula is critical, and the term (1 + β) + R represents the overall effective resistance based on feedback and external resistances.
Examples & Analogies
It's like adjusting a recipe to feed more people. The main ingredients (resistances) multiply along with a scaling factor (β) to ensure everyone has enough to eat (effective input resistance). Understanding how each part contributes helps us maintain balance in our systems.
Key Concepts
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Finite Resistance: Input resistance is finite and measurable, crucial for system stability.
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Load-Affected Transimpedance: Modifications by loading conditions affect total resistance calculations.
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Feedback Factor (Beta): Represents the closed-loop gain affecting overall input resistance calculations.
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Parallel Resistance: The interaction between multiple resistances in a feedback configuration.
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Output Voltage: Voltage developed is a key outcome of input conditions and resistance configurations.
Examples & Applications
If R1 = 1kΩ and R2 = 2kΩ are in parallel, the total resistance can be calculated using the formula 1/R_total = 1/R1 + 1/R2.
In a feedback system with a beta factor of 0.5, the new input resistance would be calculated as (1 + 0.5) × R, indicating how feedback affects the input from the source.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
For feedback systems, resistances play, to impact voltage in a fascinating way.
Stories
Imagine a feedback loop where a wise elder (beta) whispers instructions to manage resources (resistances) effectively, ensuring stability and harmony.
Memory Tools
Remember the acronym FRL: Finite Resistance Matters, because feedback rules how we Level input.
Acronyms
RBI
Resistance
Beta
Input—three key components to remember when analyzing feedback systems.
Flash Cards
Glossary
- Input Resistance (R)
The resistance seen by the input signal in a feedback system, which influences how the signal interacts with the system.
- LoadAffected Transimpedance (Zm)
The transimpedance value that has been modified by the loading conditions, critical for determining input resistance.
- Feedback Factor (Beta)
A parameter that quantifies the proportion of output feedback fed back into the system to regulate total gain.
- Parallel Resistance
A configuration of two or more resistive components where the total resistance decreases, affecting voltage and current flow.
- Output Voltage (Vo)
The voltage available at the output after considering the effects of resistances and feedback in the system.
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