Let's solve each part step by step, as you requested: --- ### **Step 1: Introduction to the Concept** **Common Mode Rejection Ratio (CMRR)** is a key parameter for differential amplifiers, such as operational amplifiers (op-amps). It measures the ability of the amplifier to reject input signals that are common to both input leads (common mode signals), while amplifying the difference between them (differential signals). CMRR is typically expressed in decibels (dB). --- ### **Step 2: Answer to Q5.1** **Question:** The common mode rejection ratio (CMRR) is the ratio of: Let's examine the options: - (a) the difference mode gain to the common mode gain - (b) the common mode gain to the difference mode gain - (c) noninverting gain - (d) inverting gain **Explanation:** CMRR is defined as the ratio of the differential gain (\(A_{vd}\)) to the common-mode gain (\(A_{cm}\)): \[ \text{CMRR} = \frac{A_{vd}}{A_{cm}} \] **Answer:** (a) the difference mode gain to the common mode gain --- ### **Step 3: Answer to Q5.2** **Question:** An inverting amplifier and a noninverting amplifier are built using the same values of \(R_f\) and \(R_i\), and the op-amps have identical common-mode gain values. Which has higher CMRR? - (a) the inverting amplifier has higher CMRR - (b) the noninverting amplifier has higher CMRR - (c) the CMRR is the same for the inverting and noninverting amplifiers - (d) none of the above **Explanation:** With identical op-amps and resistor values, both amplifiers have the same differential and common-mode gains. Thus, **CMRR is the same for both**. **Answer:** (c) the CMRR is the same for the inverting and noninverting amplifiers --- ### **Step 4: Answer to Q5.3** **Question:** Calculate the CMRR if \(A_{cm} = 0.5\) for the circuit, using \( \text{CMRR} = 20 \log_{10} \left(\frac{A_{vd}}{A_{cm}}\right) \) dB. **Explanation:** First, calculate \(A_{vd}\) for the given op-amp circuit (inverting amplifier): \[ A_{vd} = -\frac{R1}{R2} \] Given: \(R1 = 100k\Omega\), \(R2 = 100\Omega\) \[ A_{vd} = -\frac{100,000}{100} = -1000 \] (We use the magnitude for CMRR calculation.) Now, plug values into the formula: \[ \text{CMRR} = 20 \log_{10} \left(\frac{1000}{0.5}\right) = 20 \log_{10} (2000) \] \[ \log_{10} (2000) = \log_{10} (2 \times 10^3) = \log_{10} (2) + \log_{10} (1000) = 0.3010 + 3 = 3.3010 \] \[ \text{CMRR} = 20 \times 3.3010 = 66.02~\text{dB} \] **Answer:** 66 dB (rounded to two significant digits) --- ### **Step 5: Final Short Summary Answer** **Final Answers:** - (5.1) (a) the difference mode gain to the common mode gain - (5.2) (c) the CMRR is the same for the inverting and noninverting amplifiers - (5.3) CMRR = **66 dB** --- ### **Step 6: What We Did in Each Step** 1. **Introduced** the concept of CMRR. 2. **Answered** what CMRR is the ratio of. 3. **Compared** CMRR in inverting and noninverting amplifiers. 4. **Calculated** the CMRR in decibels using given values. 5. **Summarized** all answers briefly. 6. **Explained** the purpose of each step for clarity and completeness.