How to calculate CMRR of instrumentation amplifier?
2 Answers
The Common-Mode Rejection Ratio (CMRR) of an instrumentation amplifier is a measure of its ability to reject common-mode signals, which are signals that appear simultaneously and in phase on both input terminals. A high CMRR indicates that the amplifier is effective in rejecting noise and interference that is common to both inputs.
### Formula for CMRR
CMRR is defined as the ratio of the differential gain (\(A_d\)) to the common-mode gain (\(A_{cm}\)):
\[
\text{CMRR} = \frac{A_d}{A_{cm}}
\]
CMRR is often expressed in decibels (dB):
\[
\text{CMRR (dB)} = 20 \cdot \log_{10} \left(\frac{A_d}{A_{cm}}\right)
\]
### Steps to Calculate CMRR
1. **Determine the Differential Gain (\(A_d\))**:
- The differential gain is calculated based on the resistor values in the instrumentation amplifier circuit. For a typical instrumentation amplifier with resistors \(R_1\) (feedback resistors) and \(R_g\) (gain-setting resistor), the differential gain can be expressed as:
\[
A_d = 1 + \frac{2R_1}{R_g}
\]
2. **Determine the Common-Mode Gain (\(A_{cm}\))**:
- The common-mode gain is often determined through experimentation or simulation, as it can be affected by the matching of the input resistors and other factors. However, if you can assume ideal conditions, you can calculate \(A_{cm}\) based on the configuration of the instrumentation amplifier. In practice, it's often much smaller than \(A_d\).
3. **Calculate CMRR**:
- Using the values of \(A_d\) and \(A_{cm}\), plug them into the CMRR formula.
### Example Calculation
Suppose you have:
- \(R_1 = 10 \, k\Omega\)
- \(R_g = 1 \, k\Omega\)
1. Calculate \(A_d\):
\[
A_d = 1 + \frac{2 \times 10,000}{1,000} = 1 + 20 = 21
\]
2. Assume \(A_{cm} = 0.01\) (based on measurement or estimation).
3. Calculate CMRR:
\[
\text{CMRR} = \frac{21}{0.01} = 2100
\]
\[
\text{CMRR (dB)} = 20 \cdot \log_{10}(2100) \approx 20 \cdot 3.322 = 66.44 \, dB
\]
### Conclusion
CMRR is a crucial specification for instrumentation amplifiers, especially in applications where high precision is required, such as in medical devices and sensor applications. Higher CMRR values indicate better performance in rejecting unwanted common-mode signals.
### Formula for CMRR
CMRR is defined as the ratio of the differential gain (\(A_d\)) to the common-mode gain (\(A_{cm}\)):
\[
\text{CMRR} = \frac{A_d}{A_{cm}}
\]
CMRR is often expressed in decibels (dB):
\[
\text{CMRR (dB)} = 20 \cdot \log_{10} \left(\frac{A_d}{A_{cm}}\right)
\]
### Steps to Calculate CMRR
1. **Determine the Differential Gain (\(A_d\))**:
- The differential gain is calculated based on the resistor values in the instrumentation amplifier circuit. For a typical instrumentation amplifier with resistors \(R_1\) (feedback resistors) and \(R_g\) (gain-setting resistor), the differential gain can be expressed as:
\[
A_d = 1 + \frac{2R_1}{R_g}
\]
2. **Determine the Common-Mode Gain (\(A_{cm}\))**:
- The common-mode gain is often determined through experimentation or simulation, as it can be affected by the matching of the input resistors and other factors. However, if you can assume ideal conditions, you can calculate \(A_{cm}\) based on the configuration of the instrumentation amplifier. In practice, it's often much smaller than \(A_d\).
3. **Calculate CMRR**:
- Using the values of \(A_d\) and \(A_{cm}\), plug them into the CMRR formula.
### Example Calculation
Suppose you have:
- \(R_1 = 10 \, k\Omega\)
- \(R_g = 1 \, k\Omega\)
1. Calculate \(A_d\):
\[
A_d = 1 + \frac{2 \times 10,000}{1,000} = 1 + 20 = 21
\]
2. Assume \(A_{cm} = 0.01\) (based on measurement or estimation).
3. Calculate CMRR:
\[
\text{CMRR} = \frac{21}{0.01} = 2100
\]
\[
\text{CMRR (dB)} = 20 \cdot \log_{10}(2100) \approx 20 \cdot 3.322 = 66.44 \, dB
\]
### Conclusion
CMRR is a crucial specification for instrumentation amplifiers, especially in applications where high precision is required, such as in medical devices and sensor applications. Higher CMRR values indicate better performance in rejecting unwanted common-mode signals.