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Understanding Feedback System Basics
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Welcome back, everyone! Today, let's dive into feedback systems. Can anyone explain why feedback is important in amplifier circuits?
Feedback helps to stabilize the gain and improve linearity.
It also reduces sensitivity to component variations, right?
Correct! Feedback systems help us control gain and input/output resistance. There are different feedback configurations, such as negative feedback. Who can tell me what negative feedback does?
Negative feedback reduces the gain but increases the input resistance.
Exactly! This process is what we call desensitization. Remember, it's crucial for stability and precision in circuit design.
In summary, feedback plays a vital role in enhancing performance. Let's now move on to deriving the input resistance of feedback systems.
Derivation of Input Resistance
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Let's derive the input resistance in our feedback system. We'll start from the basic relationship. When we apply an input voltage, what happens?
The voltage gets divided between the input port and the feedback voltage. The input voltage is larger due to feedback.
Correct! Now, letβs express this mathematically. If we denote the input resistance as R_in_f, how do we represent it in terms of the input resistance without feedback?
R_in_f = R_in Γ (1 + Ξ²A) where A is the forward gain and Ξ² is the feedback factor.
Perfect! So, this expression shows how feedback increases the input resistance significantly. Everyone following so far?
Yes! It's clear how the feedback factor amplifies the resistance.
Great! This understanding is fundamental as we move towards practical scenarios. Let's explore how finite loads affect this equation.
Practical Implications of Load
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Now that weβve derived the input resistance under ideal conditions, letβs discuss practical implications. What changes when we introduce finite load resistance?
The output voltage might drop, affecting both input and output resistance.
That's right! When the load resistance is finite, we need to reconsider our equations. Say we have a load resistance, what would be the new input resistance expression?
It would be R_in_f = R_in (1 + Ξ²Aβ²), where Aβ² is the load-affected gain.
Exactly! Great attention to detail. We learn that real-world scenarios always need us to check feedback performance against actual load and resistance values.
In summary, we see how load greatly influences feedback, reminding us to always analyze circuits in practical contexts.
Introduction & Overview
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Quick Overview
Standard
The section details the derivation of input resistance in feedback systems, starting from ideal conditions and extending to practical scenarios where finite loads and resistances influence the system behavior. It covers voltage amplification configurations and their implications on input and output resistances.
Detailed
Deriving Input Resistance of Feedback System
In this section, we delve into understanding the input resistance of a feedback system, particularly in analog electronic circuits. A feedback system can significantly alter the input resistance of an amplifier, an effect derived from the configuration of the feedback employedβspecifically, shunt and series feedback.
The discussion begins by considering an ideal feedback network, where input resistance is infinite (ideal voltage source) and output resistance is zero. Under these assumptions, the derived expression links the input resistance of the amplifier to the feedback parameters, using key formulas to clarify the relationship:
- The feedback network increases the input resistance by the desensitization factor, typically expressed as R_in_f = R_in (1 + Ξ²A), where Ξ² is the feedback factor and A is the forward voltage gain.
As the discourse progresses, we adapt this model to reflect non-ideal conditions where practical resistances and loads come into play. Here, we analyze the effects of loading on input resistance and note how different configurationsβlike transconductance amplifiersβimpact the feedback characteristics. By covering specific cases of finite loading and resistances, we derive relevant equations maintaining an emphasis on the system's behavior under real-world constraints.
Overall, this section emphasizes how feedback significantly impacts amplifier performance through changes in input and output resistance, equipping students with the understanding needed to analyze and design feedback systems effectively.
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Introduction to Input and Output Resistance
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In this segment, we discuss the effect of the feedback system on input resistance and output resistance, which are crucial in analyzing amplifiers.
Detailed Explanation
When analyzing feedback systems, it's important to understand how they affect both input and output resistance. The feedback can modify the resistances observed by an external circuit. Typically, feedback systems aim to improve performance metrics such as stability and bandwidth by altering these resistances. The discussion begins with the assumption of an ideal feedback configuration, where input resistance is infinite and output resistance is zero.
Examples & Analogies
Think of a meeting room where the sound system is set up. Ideally, you want the microphones (input) to capture every sound (infinite resistance to sound interference) while the speakers (output) push sound with no obstruction (zero output resistance). However, in practice, there will be some level of resistance affecting performance.
Voltage Amplifier and Feedback Connection
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We consider a voltage amplifier and its feedback connection, which is shunt-series or voltage-series feedback. The input port is connected in series with the feedback port, necessitating considerations of actual finite resistances.
Detailed Explanation
In this configuration, the feedback is connected in such a way that it samples the output voltage and feeds it back to the input. This configuration is crucial as it helps in determining how the input voltage is modified by the feedback, which in turn alters the input resistance. We're focusing on a voltage amplifier where changes brought by feedback need to be analyzed with real values instead of ideal assumptions.
Examples & Analogies
Imagine a speaker system where the sound output (speaker) feeds back into a monitoring microphone. If the microphone picks up too much sound from the speakers, it can create a feedback loop, impacting the sound quality. Here, the shunt-series connection helps in understanding how this setup can alter sound input and output signals.
Deriving Input Resistance
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To derive the input resistance of the feedback system, we stimulate the circuit with a signal source v and observe the current entering the port, defining the input resistance as v/i.
Detailed Explanation
The input resistance (R_in_f) is defined as the ratio of the input voltage (v_s) to the input current (i_s). By establishing this ratio, we can derive an expression that incorporates the feedback factor (Ξ²) and the gain (A) of the amplifier. As we apply voltage (v), it combines with the feedback voltage (Ξ²v), resulting in a comprehensive ratio that highlights how feedback modifies input resistance.
Examples & Analogies
Consider a water tank system. The voltage is like the water level (v), while the current is the rate of flow (i). If the tankβs overflow (feedback) is constantly returning water to the tank, it modifies how quickly the water rises. Similarly, in circuits, the feedback can change how we see the effective resistance.
Effects of Finite Load Resistance
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In practical scenarios, if the load resistance is finite, this will affect the voltage available at the port, which diverges from the internally developed voltage.
Detailed Explanation
When a load resistance (R_L) is integrated into the circuit, it impacts the voltage seen at the input port. This is because some voltage drop occurs across the load, resulting in a modified input resistance formula that accounts for loading effects. The relationship becomes more complex since now we need to introduce a load-affected gain (Aβ²) into our calculations.
Examples & Analogies
Think of it as a restaurant where customers (the load) occupy tables (resistance). If every table is filled (load being finite), the service speed (input resistance) decreases because the waiters (input signals) can't serve effectively. Thus, a finite load changes how efficiently the restaurant operates, just like load resistance modifies electrical circuits.
Considering Practical Feedback Network Resistance
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If the feedback network also has a finite resistance, it influences the input resistance expression through the feedback voltage interactions.
Detailed Explanation
In a real-world scenario, not only does the load resistance matter, but the feedback network's resistance also plays a significant role. By incorporating this into the overall feedback mechanism, it creates additional variables that affect how input voltage is divided across different circuit parts. This necessitates a careful balance in analyzing how the feedback impacts performance.
Examples & Analogies
Imagine a team project where not only the main contributors (the load) are involved, but also multiple other facilitators (feedback network resistance). Their influence can either support or hinder the project flow, indicating how crucial it is to understand all partiesβ impact on the final outcome. Similarly, feedback network resistance alters the input resistance in meaningful ways.
Definitions & Key Concepts
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Key Concepts
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Negative Feedback: Using feedback reduces sensitivity and stabilizes gain.
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Input Resistance: Resistance seen by the input signal that affects performance.
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Desensitization Factor: Factor determining how much feedback affects input or output resistance.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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In an operational amplifier with feedback, the input resistance increases significantly compared to a standalone amplifier due to feedback.
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When introducing a load in a feedback circuit, the gain reduces as part of the current flows through the load instead of the feedback network.
Memory Aids
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π΅ Rhymes Time
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Feedback aids the gain and yields, input resistance grows like fields.
π Fascinating Stories
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Once upon a time, in a land of circuits, feedback whispered to amplifiers, stabilizing their power and growing their resistance like magic plants in a garden.
π§ Other Memory Gems
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Remember 'FIRS': Feedback increases resistance significantly.
π― Super Acronyms
DRIVE - Desensitize Resistance In Voltage Equations.
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Feedback System
Definition:
A configuration in electronic circuits where a portion of the output is fed back to the input to control the circuit's behavior.
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Term: Input Resistance (R_in)
Definition:
The resistance encountered by the input signal at the input port of an amplifier, affecting the signalβs behavior.
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Term: Desensitization Factor
Definition:
The multiplication factor by which feedback increases the input or output resistance, typically expressed as (1 + Ξ²A).
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Term: Forward Gain (A)
Definition:
The amplification factor of an amplifier without feedback, quantified as the ratio of output voltage to input voltage.
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Term: Load Resistance (R_L)
Definition:
The resistance presented by the load connected to the output of the amplifier, which affects the behavior of the entire circuit.