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Introduction to Output Resistance in Amplifiers
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Today we'll explore how feedback connections affect output resistance in voltage amplifiers. Can anyone tell me why output resistance is important?
It affects how much of the signal gets to the load, right?
Exactly! The lower the output resistance, the better the amplifier can drive a load. Now, we will begin with the ideal situation where the feedback network has infinite input resistance and zero output resistance.
What happens in this ideal case?
In this case, the output resistance can be defined simply by testing with a voltage source. We denote the output resistance as R_out_f and derive it using the relation to the finite input resistance and the gain.
Can you explain the gain A and feedback factor Ξ² again?
Certainly! The voltage gain A represents how much the amplifier boosts the voltage, while Ξ² is the fraction of the output voltage that is fed back. Is that clearer?
Yes, thank you!
Great! Let's move on to non-ideal conditions.
Non-Ideal Output Resistance Analysis
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When we consider non-ideal scenarios, what do you think the effects on output resistance might be?
I guess incorporating resistances like R_s would change the output resistance?
Exactly! A source resistance R_s introduces a voltage drop, which modifies the input voltage seen by the amplifier. Therefore, the output resistance R_out_f would also change.
How do we account for this mathematically?
We can derive an expression for R_out_f in terms of R_s, R_out_Ξ², and other factors. It involves using the concept of voltage division and feedback.
Does that mean if we have more resistance in the system, the output resistance increases?
That's right! More resistance typically leads to greater output resistance, which can affect performance. Let's apply this knowledge to a practical example.
Feedback Network Considerations
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Now let's discuss the feedback network itself. What do you all remember about its role?
It helps stabilize the amplifier and can reduce distortion, right?
Absolutely! A properly designed feedback loop can reduce non-linearities. However, if the feedback network has its own resistance, this also affects our output resistance.
What are the specific changes we should anticipate?
Great question! Introducing R_out_Ξ² into our calculations requires adjusting Ξ² to account for these losses, often termed as Ξ²' and Ξ²''. It can seem complex, but we'll solve it through step-by-step analysis.
What if we switch to another configuration like trans-conductance?
That's an excellent point! Each configuration has its own unique characteristics and requires specific formulas. We're entering the part where those variations come into play.
Analyzing Different Amplifier Configurations
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Finally, letβs examine various configurationsβlike current amplifiers and trans-conductance amplifiers. How do you think their output resistance analysis differs from voltage amplifiers?
Do current amplifiers have different parameters we need to consider?
Exactly! While the foundational concepts remain the same, current amplifiers shift the focus towards current gain, which bears implications on output resistance as well.
I'm curious about how we test the output resistance there.
We'll generally use a similar approach, but the output current and voltage have to be reexamined due to the feedback and sampling choices. Each amplifier introduces nuances worth noting!
So we apply our previous knowledge while adapting to these new configurations?
Exactly! Understanding these adaptations is key to mastering amplifier design and function. Let's wrap up by summarizing our sessions.
We have learned how feedback influences output resistance, the distinctions across amplifier configurations, and the underlying math associated with analyzing these systems.
Introduction & Overview
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Quick Overview
Standard
The section explains the change in output resistance of voltage amplifiers when feedback is applied, illustrating both ideal and non-ideal scenarios. It provides derivations for output resistance under different conditions, including finite input and output resistances.
Detailed
Output Resistance Change in Voltage Amplifiers
In the analysis of voltage amplifiers, the incorporation of feedback can significantly alter the output resistance of the system. Understanding this change is critical for designing effective amplifiers. This section begins by defining the setup for examining output resistance in a voltage amplifier subjected to feedback, particularly using a shunt series feedback configuration.
Initially, we consider an ideal feedback network where the input resistance is infinite, and the output resistance is zero. Under these conditions, the output resistance can be calculated by applying a voltage source at the output and measuring the current, leading to an equation that relates output resistance to the intrinsic parameters of the amplifier: finite input resistance, finite output resistance, voltage gain (A), and feedback factor (Ξ²).
As we delve deeper into the analysis, we introduce non-ideal situations, progressively factoring in additional resistances like a source resistance (R_s) and output resistance from the feedback network (R_out_Ξ²). Each added element influences the overall output resistance, demanding careful calculations and considerations in the modeling of real-world amplifiers. The section culminates by outlining the equivalent circuitry for varying configurations, such as current and trans-conductance amplifiers, emphasizing how disturbances caused by these factors can be systematically analyzed. This prepares us for subsequent exercises and applications in amplifier design.
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Introduction to Output Resistance in Feedback Connections
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So, yeah dear students, so welcome back after the short break and before the break we are talking about the change of input resistance of the different configuration. And whereas, we are going to talk about change in output resistance to start with let we consider it is a voltage amplifier and we want to see the change due to feedback connection.
Detailed Explanation
In this chunk, we are being reintroduced to the topic of output resistance specifically in the context of feedback connections in voltage amplifiers. The section emphasizes that we are interested in how the output resistance changes when feedback is applied to a voltage amplifier. Essentially, we want to explore the effects of feedback on the performance of the amplifier, which is a crucial concept in analog electronics.
Examples & Analogies
Think of a water faucet being regulated by a feedback valve. When you turn the faucet on, you want to maintain a steady stream of water. The feedback valve monitors the flow and adjusts if the pressure changes, similar to how feedback in amplifiers stabilizes output despite changes in input.
Characteristics of an Ideal Feedback Network
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And since it is voltage amplifier as we have discussed, the circuit is given here. The configuration here it is referred as shunt series feedback or voltage series Feedback circuit. And to start with let we consider the feedback network it is ideal namely its input resistance, it is infinite and the output resistance as it is producing voltage, output resistance it is 0.
Detailed Explanation
This chunk discusses the characteristics of an ideal feedback network within a voltage amplifier setup. In ideal scenarios, the input resistance should be infinite, meaning the circuit does not draw any current from the input source. Meanwhile, the output resistance being zero means that the amplifier can deliver maximum voltage output without any loss due to resistance. This sets the foundation for understanding how practical systems deviate from these ideal conditions.
Examples & Analogies
Imagine a perfect spigot (like a sink faucet) that never leaks and can deliver a perfect stream of water when turned on. Its βinfinite input resistanceβ means no loss of water from the hose it connects to, and a βzero output resistanceβ means all the water gets delivered to where you point it, allowing maximum flow without waste.
Determining Output Resistance
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However, for the forward amplifier we are considering finite input resistance and finite output resistance. We do have the voltage dependent voltage source A v, v it is appearing at the input of v in in the forward amplifier. Now, to know the output resistance what we can do? We can stimulate this output port by say voltage source v and then we observe the corresponding current say i and the then port impedance or port resistance it is defined by R out_f.
Detailed Explanation
This chunk shifts focus from ideal to practical situations by introducing the concept of finite resistances in the amplifier. We define a real-world scenario where the forward amplifier has both finite input and output resistances. To determine the output resistance, we apply a voltage source to the output port and measure the resulting current. This setup allows us to calculate the port's impedance, which is crucial for understanding the actual performance of the amplifier under feedback conditions.
Examples & Analogies
Imagine that the faucet we previously discussed now has some restrictions in the pipe, which represents the finite resistances. When you try to turn it on, some water flows out, but you need to measure how much comes out compared to how much youβve put in to understand how resistant the system is to flow under these conditions.
Deriving Output Resistance Expression
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So, while we are doing this exercise we have to keep the input port appropriate. So, that it will support the feedback connection, namely we in this case the signal here it is voltage and so, we do have the ideal signal voltage source connected. However, we have to keep its magnitude, signal magnitude should be 0. Which means that we are essentially shorting this input port while we are doing this exercise to find the output resistance. Now, that is the condition and let we derive the expression of this R out_f in terms of R and probably A and Ξ².
Detailed Explanation
In order to derive the expression for the output resistance again, it's crucial to maintain certain conditions. Specifically, we must ensure that the input signal is zero, essentially creating a short circuit at the input. This allows us to accurately measure the output resistance without interference from input signals. The derivation involves expressing the output resistance R_out_f in terms of the forward amplifier's parameters, including its resistances and feedback factors (denoted as Ξ²).
Examples & Analogies
This is similar to taking measurements in a controlled environment where you've blocked all other variables. If you're trying to measure water pressure at a point in a pipe, you ensure other valves are closed (akin to shorting inputs) to get the clearest reading of pressure solely from the source you want to measure.
Non-Ideal Resistance Considerations
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So, let us consider that we do have a source resistance called R_s. So, to get the output resistance R_out_f in presence of a series resistance called source series resistance called R_s and of course, we have to keep the signal here it is 0, so; that means, it is getting shorted like this. Now, in this condition; v_in, the input voltage at this port can be written in terms of Ξ²v.
Detailed Explanation
As we introduce non-ideal conditions by adding a source resistance (R_s), the calculations become more complex. The input voltage can still be related to the output by the feedback factor Ξ². This chunk illustrates how real-world components interact within the amplifier circuit, impacting the output resistance calculation. Specifically, we observe how the output resistance changes due to the series resistance, which influences the voltage distribution across components.
Examples & Analogies
Consider a hose with a small leak (the source resistance) affecting water flow. If you measure how much water comes out when the faucet is running, you must account for the leak, as it reduces the effective flow (voltage) reaching the end. You'll need to adjust how much you expected to flow based on the leakage.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Feedback: A crucial mechanism in amplifiers to stabilize and adjust performance through returning part of the output signal.
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Output Resistance: Important for understanding how much signal reaches the load and how feedback can influence this characteristic.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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In a voltage amplifier with a finite output resistance, feedback will change this resistance value, influencing the load's performance.
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A trans-conductance amplifier connects currents with voltages, resulting in a distinct analysis for output resistance.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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In amplifiers where feedback flows, lower output resistance shows, driving loads, that's how it grows!
π Fascinating Stories
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Imagine a gardener watering plants - the feedback helps maintain just the right amount of water, similar to how feedback keeps amplifier performance optimal.
π§ Other Memory Gems
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Fabulous Amplifiers Reap Output Success (F.A.R.O.S) - Feedback, Amplifier, Resistance, Output, Stability.
π― Super Acronyms
R.A.N. - Resistance Adjusted with Feedback Network.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Feedback
Definition:
A process where a portion of the output signal is returned to the input of a system to enhance or reduce its performance.
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Term: Output Resistance (R_out)
Definition:
The resistance seen by the load connected to the output of an amplifier, which can vary due to feedback.
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Term: Voltage Gain (A)
Definition:
The ratio of the output voltage to the input voltage in an amplifier.
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Term: Feedback Factor (Ξ²)
Definition:
The fraction of the output voltage that is fed back to the input.