Feedback System Input Resistance
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Understanding Input Resistance
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Today, we’re going to explore the concept of input resistance in feedback systems. Can anyone tell me what they think input resistance is?
Is it how much resistance the system has at the input?
Exactly! Input resistance refers to the resistance seen at the input terminals of our feedback system, which can affect the performance of our circuits. Let’s dive deeper into how this is calculated with load-affected transimpedance.
What does load-affected transimpedance mean?
Good question! Load-affected transimpedance, denoted as Z', takes into account how the load impacts the output voltage. Think of it like a reduction factor. Remember the acronym Z' = Z * T, where T represents this attenuation factor.
Resistance in Parallel
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To find the input resistance of our feedback system, we need to know how to deal with resistances in parallel. Why do you think resistances are combined this way?
I think it’s because more paths for current can lower the total resistance?
Right again! When resistances are in parallel, they reduce total resistance which influences the voltage across the input terminals. The resulting voltage can ultimately define how efficiently our feedback system operates.
How do we actually calculate it then?
Let’s say we have R1 and R2 in parallel; the formula is 1/R_total = 1/R1 + 1/R2. This can be linked back to our input resistance calculation!
Correcting Common Mistakes
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A common pitfall when discussing input resistance is mistakenly adjusting the feedback factor β. Remember, once we establish β, it shouldn’t change during our calculations. Can anyone remind me why this is crucial?
Is it because we need to keep our feedback consistent?
Exactly! Consistency in β is key for accurate results. If we change it mid-calculation, we may end up with incorrect values for resistance.
Deriving Input and Output Resistance
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Now that we’ve covered input resistance, how do you think it affects the output resistance?
Maybe they’re linked, since they both relate to circuit performance?
Absolutely! The characteristics of the input resistance can directly impact the output. We’ll explore this relationship in detail after a short break.
Introduction & Overview
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Quick Overview
Standard
The section explores the calculation of input resistance in feedback systems, highlighting how load-affected transimpedance and finite resistances together influence this measurement. By analyzing how these resistances combine in parallel, the derivation highlights critical aspects of system performance.
Detailed
Feedback System Input Resistance
In this section, we delve into the concept of input resistance in feedback systems, focusing on the importance of load-affected transimpedance, represented as Z′, and the impact of finite resistances, R, in parallel configurations. The input resistance of the feedback system includes components such as the attenuation factor and the original load, Zm. The parallel nature of these resistances significantly influences the voltage development and ultimately the system's performance. The section also touches on a common mistake regarding the feedback factor (β), clarifying that it should remain constant while analyzing resistance configurations. This thorough understanding sets the stage for further exploration of output resistance in feedback systems.
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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
Input resistance in a feedback system is a key factor that affects how efficiently a circuit operates. When we talk about input resistance, we denote it with a variable (let's call it R). In this context, we need to understand that R is considered 'finite', meaning it isn't zero but has a measurable value. We also talk about Z′, which refers to the load-affected transimpedance. This means that the input resistance is affected by how much the component 'loads' the system, which can impact the overall circuit behavior. The attenuation factor is a measure of how much the original signal is reduced due to the load and must be accounted for when analyzing the input resistance.
Examples & Analogies
Think of a water pipe system where your tap water is the electrical signal. If you place a garden hose (representing a load) at the end of the pipe, the flow of water is reduced because of the added resistance. When you measure the pressure in the pipe, you're measuring the input resistance, which helps you understand how much the hose is affecting the tap water flow.
Calculating Load-Affected Impedance
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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 and its expression it is Z ×.
Detailed Explanation
When we calculate the load-affected transimpedance Z′, we multiply the original impedance Z by a certain factor (which might be the attenuation factor or any other relevant factor). This adjustment reflects how the load modifies the resistance experienced by the signal. It is crucial to replace the original impedance in our calculations with this adjusted impedance Z′ to accurately analyze the circuit behavior under load conditions.
Examples & Analogies
Imagine a highway that can handle 100 cars per minute without any issues. If a construction zone reduces this capacity to 80 cars per minute, the highway now has a new effective 'impedance.' This adjustment must be acknowledged, just like adjusting calculations for Z in a feedback system to reflect the real situation with load due to certain conditions.
Parallel Resistance Consideration
Chapter 3 of 5
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So, why we have to consider these are in parallel that is because this resistance and this resistance they are coming in parallel. So, the voltage getting developed here which is v o which is of course, reduced version of internally developed voltage. So, the v it is Z × i ×.
Detailed Explanation
In feedback systems, when determining the input resistance, it's important to consider how resistances behave when they are in parallel. When two resistances are in parallel, the total resistance is less than either of the individual resistances. This is important because it affects the voltage developed across the input. The voltage, denoted as v_o, is thus a reduced version of what would otherwise be generated if we only considered one resistance. This relationship is crucial for understanding how signals are affected as they travel through the system.
Examples & Analogies
Consider two water hoses connected side by side to a water source. While a single hose can allow a certain amount of water through, having two hoses together allows more water to flow through both, effectively lowering the overall resistance and increasing the total flow. In our system, this means more signal can be transmitted efficiently.
Revising Input Resistance Expressions
Chapter 4 of 5
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So, if we consider the previous cases probably I yeah, I can see one small mistake I have done. In this case when I explained that the we do have R here we do have this resistance and this resistance then the input resistance of the feedback system it is (1 + β ) + R this β of course, it is remain should remain unchanged it should not be β′ because the effect of this one I have already considered here.
Detailed Explanation
When we include more parameters in our calculations, it is crucial to revisit and possibly revise the input resistance expressions. The input resistance of the feedback system can be calculated using the formula (1 + β) + R, where β refers to the feedback factor. It is important to keep this value unchanged (not to switch it to β′), as this reflects earlier considerations in our calculations. Any mistakes in understanding or applying these values can lead to incorrect conclusions about the system's performance.
Examples & Analogies
Think of building a pyramid. If you incorrectly place one brick (like changing β to β′), the entire structure will be unstable. Every brick (or value) must be placed correctly to ensure the pyramid (or system) stands strong and performs correctly.
Transition to Output Resistance
Chapter 5 of 5
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On the other hand, affect of R and these R they are considered in this where it is A × . Yeah the mistake I have committed before it is that I said it is β′, but actually it is not β′. I think that is all we have to discuss, but of course then we have to consider the other feedback rather all this feedback circuit to find what will be the consequences in the output resistance.
Detailed Explanation
This portion transitions from discussing input resistance to output resistance. It highlights that while we've analyzed input resistance and feedback, we also need to consider how these factors influence the output resistance. The connection between R and the output conditions (such as the feedback loops) must be understood to fully map out how the circuit behaves in various scenarios. This continued analysis is fundamental to understanding the entire feedback system.
Examples & Analogies
Imagine that after building a bridge (the input analysis), you also need to inspect the highway (output) it leads to, ensuring that traffic flow remains smooth. The planning of the bridge won't be enough without considering how it will affect the traffic below.
Key Concepts
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Input Resistance: Effects circuit performance.
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Transimpedance: Converts current to voltage.
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Load Effect: Impacts total resistance values.
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Parallel Resistance: Reduces total system resistance.
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Feedback Factor: Maintains consistency in calculations.
Examples & Applications
Calculating the input resistance of a feedback system with given resistances.
Exploring how changing the load affects output voltage and input resistance.
Memory Aids
Interactive tools to help you remember key concepts
Rhymes
To find input resistance, use the load so wise; Z' stands tall, while in parallel they rise.
Stories
Imagine a parade where resistors are cheering together. When they stand side-by-side, they lighten the load, making the whole parade move faster, just like resistors in parallel ease overall resistance.
Memory Tools
Remember PIR: Parallel Is Reduced - hinting at total resistance in parallel.
Acronyms
Use LATER for remembering input resistance steps
Load-affected
Attenuation
Transimpedance
Equivalent Resistance.
Flash Cards
Glossary
- Input Resistance
The resistance seen at the terminals of a feedback system, affecting how signals are processed.
- Transimpedance
A measure of a system's capability to convert input current into output voltage.
- Loadaffected Transimpedance (Z′)
Transimpedance that quantifies how a load influences voltage outcomes in feedback systems.
- Attenuation Factor (T)
A factor that indicates how much a signal is reduced, affecting transimpedance.
- Resistance in Parallel
A configuration where two or more resistors share connections on both ends, leading to combined lower resistance.
- Feedback Factor (β)
The fraction of the output signal that is fed back to the input, crucial for analyzing system stability.
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