Let's solve the problem step-by-step: --- ### **Given:** - **Differential Gain (\( A_{DM} \)) = 1000** - **Common Mode Gain (\( A_{CM} \)) = 0.2** --- ## **Step 1: Common Mode Rejection Ratio (CMRR) Formula** The **Common Mode Rejection Ratio (CMRR)** is defined as: \[ \text{CMRR} = \frac{A_{DM}}{A_{CM}} \] It is often expressed in decibels (dB): \[ \text{CMRR (dB)} = 20 \log_{10} \left( \frac{A_{DM}}{A_{CM}} \right) \] --- ## **Step 2: Substitute Values** \[ A_{DM} = 1000 \] \[ A_{CM} = 0.2 \] \[ \text{CMRR} = \frac{1000}{0.2} \] --- ## **Step 3: Calculate CMRR (unitless)** \[ \frac{1000}{0.2} = 5000 \] So, \[ \text{CMRR} = 5000 \] --- ## **Step 4: Calculate CMRR in decibels (dB)** \[ \text{CMRR (dB)} = 20 \log_{10}(5000) \] First, find \( \log_{10}(5000) \): \[ \log_{10}(5000) = \log_{10}(5 \times 10^3) = \log_{10}(5) + \log_{10}(10^3) \] \[ \log_{10}(5) \approx 0.6990 \] \[ \log_{10}(10^3) = 3 \] \[ \log_{10}(5000) \approx 0.6990 + 3 = 3.6990 \] Now, \[ \text{CMRR (dB)} = 20 \times 3.6990 = 73.98 \] --- ## **Final Answers** ### **CMRR** (unitless): \[ \boxed{5000} \] ### **CMRR (dB)}: \[ \boxed{73.98~\text{dB}} \] --- ## **Importance of CMRR in Bioamplifier Design** - **CMRR** indicates how well the amplifier can reject **common-mode signals** (e.g., noise, interference) while amplifying the **differential (biopotential) signal** of interest. - In biopotential recordings (e.g., ECG, EEG), much of the unwanted noise (like mains power interference) appears equally on both electrodes (common mode). - A **high CMRR** means the amplifier effectively suppresses this noise, allowing accurate measurement of the much smaller differential biopotential signals. - **Low CMRR** would result in significant noise contaminating the output, reducing the reliability and diagnostic value of the recordings. --- ## **Summary Table** | Parameter | Value | |-------------------------|-----------| | Differential Gain | 1000 | | Common Mode Gain | 0.2 | | CMRR (unitless) | 5000 | | CMRR (dB) | 73.98 dB | --- **In conclusion:** - The amplifier has a CMRR of **5000** (unitless) or **73.98 dB**. - A high CMRR is crucial in bioamplifier design to ensure accurate and noise-free recording of biopotentials.