Common Mode Rejection Ratio (CMRR) - 4.1.5 | EXPERIMENT NO. 7: DIFFERENTIAL AMPLIFIER AND BASIC OP-AMP GAIN STAGES | Analog Circuit Lab
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4.1.5 - Common Mode Rejection Ratio (CMRR)

Practice

Interactive Audio Lesson

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Introduction to CMRR

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0:00
Teacher
Teacher

Today, we will explore the Common Mode Rejection Ratio, or CMRR. Can anyone explain what CMRR stands for?

Student 1
Student 1

Is it how well an amplifier can reject common signals?

Teacher
Teacher

Exactly! CMRR measures how effectively a differential amplifier can reject signals that are common to both inputs while amplifying the differential signal. Now, why do you think this is important?

Student 2
Student 2

It’s probably important to minimize noise in the output, right?

Teacher
Teacher

Correct! A higher CMRR indicates better noise rejection, which is crucial in sensitive applications. Let's look at how we can calculate CMRR.

CMRR Calculation

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0:00
Teacher
Teacher

The CMRR is calculated using the formula CMRR = |A_d| / |A_cm|. Can someone tell me what A_d and A_cm represent?

Student 3
Student 3

A_d is the differential gain, and A_cm is the common-mode gain, right?

Teacher
Teacher

Good! So, if we say our differential gain, A_d, is -45.19 and our common-mode gain, A_cm, is -0.0235, how do we find the CMRR?

Student 4
Student 4

We plug them into the formula to get CMRR = |-45.19| / |-0.0235|.

Teacher
Teacher

Exactly! This gives us a very high CMRR value! Can someone convert that to decibels?

Student 1
Student 1

I remember we can do that with 20 * log10 of the CMRR.

Teacher
Teacher

Great memory! Using that approach, we would find that the CMRR in dB is about 65.6 dB.

Importance and Application of CMRR

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0:00
Teacher
Teacher

Now, let’s delve into why having a high CMRR is so crucial in practical scenarios. What could be some applications requiring high CMRR?

Student 2
Student 2

Maybe in audio applications where we need to eliminate background noise?

Teacher
Teacher

Exactly! Audio systems benefit greatly from high CMRR to ensure that only the desired sound is amplified. Can you think of any other applications?

Student 3
Student 3

Medical instruments like ECG or EEG would need it.

Teacher
Teacher

Right again! In those cases, rejecting common-mode noise ensures accurate readings from sensitive medical equipment.

Introduction & Overview

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Quick Overview

CMRR measures a differential amplifier's effectiveness in rejecting common-mode signals while amplifying differential ones.

Standard

The Common Mode Rejection Ratio (CMRR) quantifies how well a differential amplifier can reject signals common to both inputs. A high CMRR indicates superior performance, essential for minimizing noise in applications. The section details the formula for calculating CMRR and provides examples illustrating its significance.

Detailed

Common Mode Rejection Ratio (CMRR) in Differential Amplifiers

The Common Mode Rejection Ratio (CMRR) is a critical parameter in assessing the performance of differential amplifiers. It defines the ratio of the differential gain to the common-mode gain, effectively highlighting an amplifier's ability to differentiate between desired input signals and noise that affects both inputs equally.

Key Points:

  • Definition: CMRR is defined as the ratio of the absolute value of the differential gain (A_d) to the absolute value of the common-mode gain (A_cm).
  • Formula:
  • CMRR = |A_d| / |A_cm|
  • Decibel Representation: It can also be expressed in decibels (dB) as:
  • CMRR_dB = 20 * log10(CMRR)
  • Performance Benchmark: Generally, a good differential amplifier will have a CMRR greater than 60 dB, indicating excellent noise rejection capabilities.
  • Example Calculation: In practical scenarios, measurements of A_d and A_cm can be used to compute the CMRR, illustrating the effectiveness of the amplifier in real-world applications. For instance, if A_d = -45.19 and A_cm = -0.0235, the CMRR would calculate to approximately 1923, yielding a CMRR_dB of about 65.6 dB.
    This section underlines the significance of CMRR in maintaining high integrity of amplified signals while minimizing interference from common noise sources.

Audio Book

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Definition of CMRR

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● CMRR is a measure of a differential amplifier's ability to reject common-mode signals while amplifying differential signals. A higher CMRR indicates better rejection of common-mode noise.

Detailed Explanation

The Common Mode Rejection Ratio (CMRR) quantifies how effectively a differential amplifier can filter out noise signals that affect both inputs equally. It essentially indicates the amplifier's ability to differentiate between the signal we want (the difference between the two inputs) and the signal we don't want (the common signals that appear in both inputs). If CMRR is high, the amplifier can ignore unwanted signals, making it more effective in noisy environments.

Examples & Analogies

Imagine you're trying to listen to your favorite music in a crowded café. The music you want to hear is like the differential input signal, and the chit-chat and clanking dishes around you represent the common-mode signals (noise). A good pair of noise-cancellation headphones is similar to a high CMRR; they block out the chatter while allowing you to enjoy the music clearly.

CMRR Calculation Formula

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● CMRR=frac∣A_d∣∣A_cm∣

Detailed Explanation

To calculate the CMRR, we take the absolute values of the differential gain (A_d) and the common-mode gain (A_cm). The formula shows that CMRR is the ratio of how much the amplifier amplifies the desired differential signal compared to the noise signal that is common in both inputs. A larger differential gain relative to the common-mode gain results in a higher CMRR, indicating better performance.

Examples & Analogies

Think of CMRR as a coffee-to-water ratio when making coffee. If you want a rich cup of coffee (desired differential gain), but you pour in too much water (common-mode gain), the coffee will be weak. A high ratio of coffee to water means a better brew—just like a high CMRR means better differential amplification over common-mode noise.

CMRR in Decibels

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● In decibels: CMRR_dB=20log_10left(frac∣A_d∣∣A_cm∣right)

Detailed Explanation

CMRR can also be expressed in decibels (dB), which is a logarithmic way to represent ratios. The formula states that we take the logarithm (base 10) of the ratio of the absolute values of the differential gain and the common-mode gain, then multiply by 20. This conversion to dB makes it easier to compare levels of CMRR because dB scales are more intuitive and manageable for large ranges of values.

Examples & Analogies

Using dB is like measuring sound intensity. If one sound is 10 times louder than another, we express this difference in decibels. Similarly, saying a CMRR of 60 dB means that the differential gain is 1000 times greater than the common-mode gain is easier for engineers to comprehend than dealing with raw numbers.

Desired CMRR Levels

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● A good differential amplifier will have a very high CMRR (e.g., > 60 dB).

Detailed Explanation

In practice, a CMRR greater than 60 dB is considered good for differential amplifiers. This level indicates that the amplifier largely ignores common-mode signals, making it suitable for applications where clarity and integrity of the differential signal are paramount. A high CMRR ensures that the amplifier maintains accurate performance in real-world, noisy environments.

Examples & Analogies

Consider a high-quality microphone used for recording sound. A well-designed microphone with high sensitivity to the voice and low sensitivity to background noise will produce clear recordings. This is similar to a differential amplifier with a high CMRR, effectively highlighting the desired signal while filtering out unwelcome background noise.

Numerical Example of CMRR Calculation

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● Numerical Example (CMRR): Using the previous examples, A_d=−45.19 and A_cm=−0.0235. CMRR=frac∣−45.19∣∣−0.0235∣approx1923 CMRR_dB=20log_10(1923)approx20times3.28approx65.6textdB

Detailed Explanation

In this example, we see that by substituting the values of A_d and A_cm into the CMRR formula, we find an approximate value of 1923. When converting to decibels, we find an approximate CMRR of 65.6 dB. This high value indicates that the differential amplifier performs well in rejecting common-mode signals relative to the signals it needs to amplify.

Examples & Analogies

This numerical illustration can be likened to a filtering process in photography. Imagine you are editing a photo to enhance the colors while minimizing the background distortion. The higher the quality of filter (analogous to a high CMRR), the clearer and more vibrant the colors appear against a muted background, just as a high CMRR ensures the desired signal shines through a noisy environment.

Definitions & Key Concepts

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Key Concepts

  • Common Mode Rejection Ratio (CMRR): Measures an amplifier's ability to reject common-mode signals.

  • Differential Gain (A_d): Output signal ratio to differential input signal.

  • Common-Mode Gain (A_cm): Output signal ratio to common-mode input signal.

  • Decibel (dB): Logarithmic scale for measuring ratios, often used for gains.

Examples & Real-Life Applications

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Examples

  • If a differential amplifier has a differential gain of -40 dB and a common-mode gain of -2 dB, the CMRR would be calculated to demonstrate that the amplifier effectively rejects the noise.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • CMRR is a number that's rather grand, / It helps reject noise, just as we planned.

📖 Fascinating Stories

  • Imagine you're at a concert; the music (differential signal) is loud, but the chatter (common-mode signal) is all around. A high CMRR helps amplify the music while muting the chatter.

🧠 Other Memory Gems

  • C = Common, M = Mode, R = Rejection, R = Ratio. Just remember ‘Common and Rejection’ together!

🎯 Super Acronyms

CMRR

  • Common Mode Rejection Ratio
  • where Common Mode is what we want to reject.

Flash Cards

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Glossary of Terms

Review the Definitions for terms.

  • Term: Common Mode Rejection Ratio (CMRR)

    Definition:

    Ratio that quantifies a differential amplifier's ability to reject common-mode signals while amplifying differential signals.

  • Term: Differential Gain (A_d)

    Definition:

    The ratio of the output voltage to the differential input voltage.

  • Term: CommonMode Gain (A_cm)

    Definition:

    The ratio of the output voltage to the common-mode input voltage.

  • Term: Decibel (dB)

    Definition:

    A logarithmic unit used to express the ratio of two values, commonly used to measure gain.