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Interactive Audio Lesson
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Understanding Common-Mode Gain (A_cm)
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Today, we are going to explore the concept of common-mode gain, denoted as A_cm. Can anyone tell me what common-mode signals are?
Are they the signals that are identical at both inputs?
Exactly! Now, why do you think we want to measure A_cm?
To see how well the amplifier rejects those common signals?
Right again! So, A_cm indicates how much common-mode voltage is amplified. Ideally, we want A_cm to be as low as possible to ensure high performance.
Remember the acronym 'REJECT' for performance: R is for Rejection of unwanted signals. This will help you recall the importance of A_cm.
Calculating Common-Mode Gain (A_cm)
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Now let's look at how we calculate A_cm. The formula is A_cm = V_out / V_ic. Can someone explain what each variable represents?
V_out is the output voltage when common-mode input is applied, and V_ic is the common-mode input voltage?
Exactly! For our BJT differential amplifier, we can also express A_cm as A_cm = - (R_C / (2R_E')). Why do you think we need to consider R_E'?
Because it affects how the current flows through the transistors in the common emitter configuration?
Yes! Good observation. Understanding these relationships helps us see how circuit design influences A_cm.
Here's a mnemonic to help you remember: 'RE-C' for Resistor - Emission - Calculation!
Implications of Common-Mode Gain Measurement
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Now that we understand how to measure A_cm, why is having a low A_cm significant in practical applications?
It means the amplifier can effectively reject unwanted noise or signals that are the same on both inputs?
Exactly! A low A_cm translates to a higher Common Mode Rejection Ratio, or CMRR, which is crucial for high-fidelity applications.
So, a high CMRR indicates that the amplifier is good at differentiating the input signals?
Yes! Remember: 'C.M.R.R. is the King for Rejection Rates.' This will help you remember its importance.
To sum up our session, a good A_cm performance means lower error and interference in the output.
Introduction & Overview
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Quick Overview
Standard
The common-mode gain (A_cm) is a critical parameter in evaluating the performance of a differential amplifier, as it reflects the amplifier's ability to reject common signals. This section details how to measure A_cm and the factors influencing its value, ultimately contributing to understanding the Common Mode Rejection Ratio (CMRR).
Detailed
- Common-Mode Gain (A_cm): A_cm is defined as the output voltage resulting from a common-mode input, where both inputs are supplied with the same voltage. Ideally, this output should be zero, indicating perfect common-mode rejection.
- Calculation of A_cm: The formula for calculating A_cm involves the output voltage divided by the common-mode input voltage:
\[ A_{cm} = \frac{V_{out}}{V_{ic}} = -\frac{R_C}{2R_E'} \]
Here, R_E' is the effective resistance at the common emitter node, which varies based on whether a simple resistor or a more complex current source is employed. - Practical Considerations: In practice, A_cm is non-zero, indicating that some level of common-mode signals is amplified. A low A_cm value is desirable and implies high performance, particularly in applications requiring effective noise suppression.
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Introduction to Common-Mode Gain
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● When a pure common-mode input signal (V_in1=V_in2=V_ic) is applied, the amplifier ideally produces no output. In a real amplifier, there is a small output due to imperfections.
Detailed Explanation
The common-mode gain (A_cm) refers to the output produced by the amplifier when both input signals (V_in1 and V_in2) are identical (or common). In an ideal case, a differential amplifier is designed to reject such common signals, hence the output would be zero. However, due to practical imperfections in the circuit, a small output may still occur.
Examples & Analogies
Think of a noise-cancelling headphone. When someone is listening to music, the headphone is designed to ignore 'common' sounds like a hum from an air conditioner. Ideally, it doesn't pick up this humming noise, but sometimes, due to technical limitations, a faint noise may still come through.
Calculating Common-Mode Gain (A_cm)
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● For a differential amplifier with a current source approximated by a large emitter resistor R_E:
A_cm=fracV_out1V_ic=−fracR_C2R_E′
Where R_E′ is the effective resistance seen at the common emitter point. If a BJT current source is used, R_E′ represents the output resistance of the current source (which is typically very high). If a simple large resistor R_E is used, then R_E′=R_E.
Detailed Explanation
To quantify how much output the amplifier produces due to common-mode signals, we can calculate A_cm. The formula indicates that A_cm is dependent on the ratio of collector resistor (R_C) and the effective resistance at the emitter point (R_E'). The smaller the A_cm, the better the amplifier is at rejecting common signals. R_E' can be considered either as a high value if using an ideal current source or the nominal resistor value in simpler designs.
Examples & Analogies
Imagine a filter designed to separate coffee from grounds. A high-quality filter (similar to a high R_E') would let the coffee pass through but trap most grounds. This is akin to how a well-designed differential amplifier lets differential signals through while holding back common-mode inputs.
Ideal versus Real-World Common-Mode Gain
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● Ideally, for a perfect common-mode rejection, A_cm should be zero.
Detailed Explanation
In theory, the best differential amplifier has a common-mode gain of exactly zero. This means it doesn’t output any voltage when both inputs are the same. Practically, achieving this is challenging due to mismatches in transistor characteristics, resistances, and other non-ideal effects that introduce some level of common-mode gain into the output.
Examples & Analogies
Consider a music director who can perfectly tune out the sound of the traffic outside (ideal A_cm = 0). In reality, there might be some faint sound of traffic that still manages to interrupt the music, similar to how real amplifiers can still produce slight outputs for common-mode inputs.
Numerical Example for Common-Mode Gain
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● Numerical Example (Common-Mode Gain): Assume the same differential amplifier with R_C=4.7kOmega. The common current source is approximated by a resistor R_E=100kOmega to a negative supply.
A_cm=−frac4.7kOmega2times100kOmega=−frac4.7200=−0.0235 (very small, as desired).
Detailed Explanation
In this example, we apply the values given to calculate the common-mode gain. Here, we take the collector resistor and the emitter resistor into account to arrive at a very small value for A_cm. The physical result shows how the amplifier behaves under common-mode conditions, indicating its efficiency in rejecting unwanted signals.
Examples & Analogies
This scenario is like making a smoothie. You're trying to make a delicious drink (the desired output), but if too many unwanted ingredients get in (common-mode inputs), then they dilute your smoothie. The example shows how eliminating these impurities should ideally be the goal.
Definitions & Key Concepts
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Key Concepts
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Common-Mode Gain (A_cm): The output signal resulting from identical input signals.
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Effective Resistance (R_E'): Impacts how the common-mode gain is calculated.
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Common Mode Rejection Ratio (CMRR): An important performance metric for amplifiers.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example of common-mode gain: If both inputs of an amplifier are supplied 1V and the measured output is 0.01V, then A_cm = 0.01V / 1V = 0.01.
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When designing a differential amplifier, if R_C = 4.7kΩ and R_E = 100kΩ, plug these into A_cm = - (R_C / (2R_E')) to find the common-mode gain.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
🎵 Rhymes Time
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For signals that blend the same, A_cm is the output's name.
📖 Fascinating Stories
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Imagine a noisy party where everyone is speaking the same phrases; the room is full, but only one voice stands out — that’s like a low A_cm helping us focus on the unique message.
🧠 Other Memory Gems
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Remember 'CARE' for Common-mode A_cm Rejection Effect.
🎯 Super Acronyms
REJECT - for performance, Rejection of common-mode signals is Key.
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: CommonMode Gain (A_cm)
Definition:
A measure of the output voltage derived from the same input signal applied to both inputs of a differential amplifier.
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Term: Effective Resistance (R_E')
Definition:
The resistance seen at the common emitter node which influences current flow within a differential amplifier circuit.
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Term: Common Mode Rejection Ratio (CMRR)
Definition:
A metric indicating how well a differential amplifier can reject common-mode signals relative to the desired differential signal.