**Introduction:**

Common-mode rejection ratio (CMRR) is an important parameter that measures the ability of an amplifier to reject unwanted signals that are present on both inputs, known as common-mode signals. A high CMRR indicates that the amplifier is effective at rejecting these signals, while a low CMRR indicates that the amplifier is less effective. In this article, we will discuss how to calculate CMRR and explore its importance in amplifier design.

## What is CMRR?

CMRR is a measure of an amplifier’s ability to reject unwanted signals that are present on both inputs. These unwanted signals are known as common-mode signals because they are common to both inputs. CMRR is defined as the ratio of the differential gain (the gain between the two inputs) to the common-mode gain (the gain of the amplifier for common-mode signals). In other words, it measures how much the differential gain is larger than the common-mode gain.

A high CMRR indicates that the amplifier is effective at rejecting common-mode signals. For example, if an amplifier has a CMRR of 80 dB, it means that the differential gain is 80 dB larger than the common-mode gain. This means that the amplifier can reject common-mode signals that are up to 80 dB larger than the differential signal.

### How to calculate CMRR?

There are different methods to calculate CMRR depending on the type of amplifier and the measurement setup. The most common method is to measure the differential gain and the common-mode gain separately and then calculate the ratio.

To measure the differential gain, a differential input signal is applied to the amplifier, and the output voltage is measured. The differential gain is then calculated as the ratio of the output voltage to the input voltage. This is usually expressed in decibels (dB), which is a logarithmic scale. For example, if the output voltage is 5 volts and the input voltage is 0.1 volts, the differential gain is 20 log (5/0.1) = 46 dB.

To measure the common-mode gain, a common-mode input signal is applied to both inputs of the amplifier, and the output voltage is measured. The common-mode gain is then calculated as the ratio of the output voltage to the input voltage. Again, this is usually expressed in decibels. For example, if the output voltage is 2 volts and the input voltage is 0.1 volts, the common-mode gain is 20 log (2/0.1) = 34 dB.

Once the differential gain and the common-mode gain are measured, CMRR can be calculated as the difference between the differential gain and the common-mode gain. This is also expressed in decibels. For example, if the differential gain is 46 dB and the common-mode gain is 34 dB, the CMRR is 46 dB – 34 dB = 12 dB.

### What is the formula for CMRR?

The formula for CMRR is the ratio of the differential gain (Ad) to the common-mode gain (Ac) and is expressed in decibels (dB). The formula can be written as CMRR = 20 log (Ad / Ac).

### How do you calculate CMRR by ADM and ACM?

To calculate CMRR by ADM (differential mode gain) and ACM (common-mode gain), we first need to measure the output voltage of the amplifier in response to a differential input signal and a common-mode input signal. The differential gain is calculated as the ratio of the output voltage to the differential input voltage, while the common-mode gain is calculated as the ratio of the output voltage to the common-mode input voltage. The CMRR can then be calculated using the formula CMRR = 20 log (Ad / Ac).

### How do you calculate common mode gain?

The common-mode gain is the gain of an amplifier for signals that are present on both inputs (common-mode signals). To calculate the common-mode gain, a common-mode input signal is applied to both inputs of the amplifier, and the output voltage is measured. The common-mode gain is then calculated as the ratio of the output voltage to the common-mode input voltage, expressed in dB.

### What is the value of CMRR?

The value of CMRR varies depending on the amplifier and its design. A high-quality amplifier typically has a CMRR of 60 dB or higher, while a low-quality amplifier may have a CMRR of less than 30 dB.

**CMRR formula in dB**

The formula for CMRR in dB is CMRR = 20 log (Ad / Ac), where Ad is the differential gain and Ac is the common-mode gain.

**Common mode gain formula**

The formula for common-mode gain is the ratio of the output voltage to the common-mode input voltage, expressed in dB.

**CMRR stands for**

CMRR stands for Common-Mode Rejection Ratio.

### What is CMRR in op-amp?

In an op-amp (operational amplifier), CMRR refers to the ability of the amplifier to reject common-mode signals. It is a measure of how well the op-amp can amplify the difference between two input signals while rejecting any noise or interference that is present on both inputs.

**CMRR unit**

The unit of CMRR is decibels (dB), which is a logarithmic unit used to express the ratio of two values.

**CMRR of differential amplifier**

The CMRR of a differential amplifier is the ratio of the differential gain to the common-mode gain, expressed in dB. A high-quality differential amplifier typically has a CMRR of 80 dB or higher.

**How to calculate CMRR of instrumentation amplifier**

To calculate the CMRR of an instrumentation amplifier, we first need to measure the differential gain and the common-mode gain separately. The differential gain is the gain between the two inputs, while the common-mode gain is the gain for signals that are present on both inputs. The CMRR can then be calculated using the formula CMRR = 20 log (Ad / Ac).

**Common mode rejection**

Common mode rejection refers to the ability of an amplifier to reject common-mode signals, which are signals that are present on both inputs. It is a measure of how well the amplifier can amplify the difference between two input signals while rejecting any noise or interference that is present on both inputs. CMRR is a commonly used parameter to express common mode rejection.

### What is CMRR and why is it important?

CMRR stands for Common-Mode Rejection Ratio and it is a measure of an amplifier’s ability to reject common-mode signals, which are signals that are present on both inputs. CMRR is important because it indicates how well an amplifier can amplify the difference between two input signals while rejecting any noise or interference that is present on both inputs.

### What is the formula for calculating CMRR?

The formula for calculating CMRR is CMRR = 20 log (Ad / Ac), where Ad is the differential gain and Ac is the common-mode gain.

### How do you calculate differential gain and common-mode gain?

Differential gain is calculated as the ratio of the output voltage to the differential input voltage, while common-mode gain is calculated as the ratio of the output voltage to the common-mode input voltage.

### What is the unit of CMRR?

The unit of CMRR is decibels (dB), which is a logarithmic unit used to express the ratio of two values.

### What is a good CMRR value?

A high-quality amplifier typically has a CMRR of 60 dB or higher, while a low-quality amplifier may have a CMRR of less than 30 dB. A high-quality differential amplifier typically has a CMRR of 80 dB or higher.

### How can I improve the CMRR of my amplifier?

The CMRR of an amplifier can be improved by using a balanced circuit design, minimizing the effects of component mismatch, using a differential input signal, and increasing the differential gain.

### Can I calculate CMRR for different types of amplifiers?

Yes, CMRR can be calculated for different types of amplifiers, such as operational amplifiers (op-amps), instrumentation amplifiers, and differential amplifiers.

### What is the difference between CMRR and PSRR?

CMRR measures an amplifier’s ability to reject common-mode signals, while PSRR (Power Supply Rejection Ratio) measures an amplifier’s ability to reject noise that is present on the power supply. Both parameters are important for high-quality amplifier performance.

### Is CMRR the only parameter that determines an amplifier’s performance?

No, there are other parameters that are important for amplifier performance, such as input impedance, output impedance, bandwidth, and distortion. However, CMRR is an important parameter that can significantly affect an amplifier’s performance in certain applications.

## Conclusion:

CMRR is an important parameter that measures the ability of an amplifier to reject unwanted signals that are present on both inputs. It is defined as the ratio of the differential gain to the common-mode gain. A high CMRR indicates that the amplifier is effective at rejecting common-mode signals. To calculate CMRR, the differential gain and the common-mode gain need to be measured separately, and the ratio needs to be calculated. CMRR is an important parameter in amplifier design, and designers need to ensure that it meets the required specifications for their application.