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27.6.1. Output Resistance in Presence of Emitter Resistor
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Today we'll explore the importance of the emitter resistor in a common emitter amplifier. Can anyone explain what an emitter resistor is used for?
It helps stabilize the operating point of the circuit.
Exactly! It stabilizes against variations in beta, but what’s the trade-off?
It can decrease the gain of the amplifier.
That's correct! The gain is reduced and can be described by the formula A = -g_m R_C / (1 + g_m R_E). Can someone explain what g_m represents?
g_m is the transconductance of the transistor.
Great! Remember that the presence of R_E impacts the gain, especially when it is large. To help with memory, think of 'REducing Gain' due to R_E.
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Now, how do we express the output voltage with respect to the emitter resistor?
v_out = -g_m R_C * v_in / (1 + g_m R_E).
Right! As R_E increases, what happens to the gain?
The gain decreases. The overall voltage gain becomes smaller.
Exactly, and this loss in gain may hinder circuit performance. To combat this, we sometimes use coupling capacitors to disconnect R_E from AC signals.
So, the capacitor allows AC signals to pass while keeping DC bias intact?
Spot on! Think of it as 'Coupling for Clarity'—we couple AC while keeping DC stable.
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Let's look at how to calculate output resistance in the presence of R_E. What do we know about it?
It's lower when R_E is present because it affects the parallel resistance.
Good point! When R_C and other resistors are involved, how do we express R_out?
R_out = R_C || (R_E + r_pi) where r_pi is the base-emitter resistance.
Excellent! You can think of 'Rout Equals to Ruined Output with Emitter' to recall how R_E influences the output resistance.
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Finally, what are some practical guidelines we should follow when designing circuits using R_E?
We need to ensure R_E is not too large; otherwise, it affects gain too much.
And we must keep R_B small compared to (1 + β)R_E.
Exactly! Balance is key. It’s like having a 'Fine Tune' for both stability and performance.
What happens if we ignore this guideline?
Ignoring it can lead to poor performance. Remember this as 'Good Design = Gain and Stability.'
Overview
Short Summary
This section focuses on the impact of an emitter resistor on the output resistance of a common emitter amplifier and how it modifies the circuit's voltage gain and stability.
Medium Summary
In this section, we analyze how the presence of an emitter resistor affects the output resistance in a common emitter amplifier configuration. The section explains the balance between gain degradation and operating point stabilization due to β variations, and how to recover gain without compromising circuit stability by employing coupling techniques.
Detailed Summary
The inclusion of an emitter resistor (R_E) in a common emitter amplifier plays a crucial role in stabilizing the operating point against variations in the transistor's current gain (β). However, this stabilization often leads to a degradation in voltage gain. The voltage gain is expressed as A = -g_m R_C / (1 + g_m R_E), where g_m is transconductance and R_C is the load resistance. The introduction of R_E impedes the gain, particularly when its value is significant, whereby the output voltage and the gain of the circuit are decreased.
To combat this issue, a coupling capacitor can be used to ground the emitter for AC signals, thus effectively removing R_E from the gain equation for small signals while retaining it for DC conditions to maintain bias stability. This ensures both signal integrity and operational stability. The understanding of output resistance and the formulation of input and output parameters, including R_in and R_out in this context, is vital for practical circuit design and analysis.
Reference YouTube Videos
Audio Book
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Create a free accountWhile we will be doing this similar kind of exercise, we need to find as I said that we need to find what will be the output resistance R of this voltage amplifier, while we are mapping this small signal equivalent circuit into a voltage amplifier. What you have to do? Again we will be stimulating this circuit from this port by say a signal source called v or say v and then we can observe the corresponding current let we mark it as say i. And while we are doing this exercise we have to keep this signal 0 since it is voltage signal so, we are making this is ground.
Detailed Explanation
To determine the output resistance of the voltage amplifier, we apply a voltage signal from the output port and monitor the resulting current. During this analysis, we set other input signals to zero (ground) to isolate the output circuit behavior. By measuring how the output voltage changes in relation to the injected current, we can calculate the output resistance.
Examples & Analogies
Think of this process like measuring the resistance of a water pipe. You close the faucet (set other signals to zero), then apply a known amount of pressure (the voltage signal), and measure how much water flows through (the current). The relationship between the pressure and the flow gives you the 'resistance' of the pipe.
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Create a free accountSo, at the output port what we have it is only R remaining. So, if I am applying v here, C y the current flow through this circuit it is mainly this is the current. Now, the current of v course, that will be v so, that is the i. So, from that we can say directly that R = R.
Detailed Explanation
In this part of the circuit analysis, we find that the output resistance primarily consists of the resistance R associated with the circuit setup. When we apply a voltage, the current through this resistance can be directly measured. This simple relationship shows how the output resistance is essentially determined by the resistor present in the circuit.
Examples & Analogies
Imagine a light bulb connected to a battery. The light bulb represents our output resistance. When you turn the battery on (apply voltage), the light bulb illuminates based on the resistance. If you take a measurement of how brightly it shines, you get a direct sense of its resistance; the brightness indicates the relationship between the voltage and the current flowing through it.
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Create a free accountWhile we will be doing this exercise, we need to find as I said that we need to find what will be the output resistance in presence of R , we will be stimulating this circuit by say v . So, this is we are stimulating and then we are observing this i and while we are doing this exercise, we have to keep in mind that we have to make this voltage input signal to be 0.
Detailed Explanation
When examining the output resistance with the emitter resistor in place, we again stimulate the circuit and observe the resulting current. We keep the input voltage at zero during this measurement. The presence of the emitter resistor influences the output resistance by creating an added path through which current can flow, impacting the overall resistance seen at the output.
Examples & Analogies
Think of this like adjusting gears on a bicycle. Adding a gear makes it easier to pedal (less resistance), but you still need to balance how hard you push on the pedals (the input signal). In our circuit, the emitter resistor alters the balance of current and voltage to determine how 'hard' it is to get the desired output.
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Create a free accountSo, what we can say that v it since it is function of i . So, we can take this v right side. So, we can say this gives us the expression and it can be shown that from this one, it can be shown that this is the resistance of the lower part then total resistance of course, this will be R in parallel with that.
Detailed Explanation
After accounting for the effects of the emitter resistor, we derive a comprehensive expression that combines the outputs of both circuit paths: the primary output resistance from R and any additional resistance influenced by the configuration of the circuit. This leads us to conclude that the overall effective output resistance can be calculated by finding the parallel combination of R and the newly calculated resistance.
Examples & Analogies
Imagine two narrow pipes draining into a larger tank; the flow speed will vary based on how both pipes are connected. If one part allows more water through (less resistance), the total flow is determined by the combination of both. Similarly, in circuits, the final resistance seen at the output involves combining the resistances from various components.
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Key concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
- Emitter Resistor (R_E):
Vital for stabilizing the operating point against variations in β but reduces voltage gain.
- Transconductance (g_m):
It shapes the voltage gain, crucial for predicting the amplifier’s behavior.
- Voltage Gain (A):
Essential metric for amplifier performance, affected directly by the presence of R_E.
- Output Resistance (R_out):
Defines how a circuit will resist current flow, its calculation changes with the emitter resistor.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
An amplifier with R_E of 1 kΩ might see a significant drop in gain compared to one without R_E, demonstrating its impact on performance.
Using a coupling capacitor can effectively eliminate R_E from the gain equation for AC signals, thus recovering the gain.
Memory aids
Imagine a seesaw where one side is the gain and R_E is a weight that keeps it stable. Too heavy, and the other side drops; too light, and it sways too much.
Remember 'Getter Emitter' to recall how R_E helps stabilize the gain but reduces its value.
Flash Cards
Glossary
Emitter Resistor (R_E)
A resistor placed in the emitter leg of a transistor circuit used to provide thermal stability.
Transconductance (g_m)
A parameter representing the relationship between the input voltage and output current in a transistor.
Voltage Gain (A)
The ratio of the output voltage to the input voltage, often expressed in decibels.
Load Resistance (R_C)
The resistance connected to the collector of the transistor affecting the output current.