--- title: "Design three op-amp IA with gain 20" subject: "Advanced Electronics" chapter: 4 key: "semester_4/advanced_electronics:design-3opamp-ia-gain-20" source: https://www.bctengineer.com/q/semester_4/advanced_electronics/design-3opamp-ia-gain-20 site: BCT Engineering --- # Design three op-amp IA with gain 20 Advanced Electronics · Chapter 4: Instrumentation and Isolation Amplifiers - Asked in: 2073 Shrawan, 2+5 marks; 2069 Asar, 2+5 marks (asked 2 times) - Video: [Instrumentation Amplifiers Explained (Amplifiers #7)](https://www.youtube.com/watch?v=VfJ2AHO2aHg) — Aaron Danner - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/advanced_electronics/design-3opamp-ia-gain-20 - Whole chapter: https://www.bctengineer.com/md/semester_4/advanced_electronics/chapter-4 ## Question What are the features of Instrumentation Amplifier? Hence design a three op amp Instrumentation Amplifier having gain 20. ## Short answer IA has high input Z, high CMRR, gain set by R_G. For gain 20, choose R₂=R₃=10k℧, R_G=1k℧; then R₁ = (20−1)/2 × 1k = 9.5k℧ (matched). Output: Vo = (R₃/R₂)(1+2R₁/R_G)(V₂−V₁). ## Answer An instrumentation amplifier (IA) is a precision differential amplifier with very high input impedance, high CMRR and an accurately set gain. It is used to amplify small differential signals from transducers in the presence of large common-mode noise. #### Features of an instrumentation amplifier - Very high input impedance (both inputs buffered), so it does not load the source - Very high CMRR (typically 100 dB or more) - Gain set by a single resistor RG, adjustable and stable - Low offset voltage, low drift and low noise - Low output impedance and high slew rate #### Three op-amp IA ```text V1 --->(+)\ A1>---+--Vo1--[R2]--+--[R3]--+ +->(-)/ | | | | R1 (-)\ | +---------+ A3>-----+--> Vo RG (+)/ +---------+ | +->(-)\ R1 Vo2--[R2]+--[R3]--GND | A2>---+--Vo2 V2 --->(+)/ ``` A1 and A2 form the buffered input stage. A3 is a difference amplifier. ```text Vo = (R3/R2)(1 + 2R1/RG)(V2 − V1) ``` #### Design for gain A = 20 Make the difference stage a unity-gain stage so that all the gain is in the first stage (only RG needs to be adjusted). 1. Choose R2 = R3 = 10 kΩ, so R3/R2 = 1. 2. Then 1 + 2R1/RG = 20, so 2R1/RG = 19. 3. Choose RG = 1 kΩ: ```text R1 = 19 × RG / 2 = 19 × 1 kΩ / 2 = 9.5 kΩ ``` Alternatively, fix R1 = 10 kΩ: ```text RG = 2R1/(A − 1) = 20 kΩ/19 = 1.053 kΩ ``` Use 1 kΩ fixed plus a 100 Ω trimmer. **Check:** A = (10k/10k)(1 + 2 × 9.5k/1k) = 1 × (1 + 19) = 20. **Design values:** R1 = 9.5 kΩ (two, matched), RG = 1 kΩ, R2 = R3 = 10 kΩ (four, 0.1 % matched for high CMRR), op-amps for example 741, OP07 or TL084. The four resistors of A3 must be closely matched (R3/R2 equal on both sides). Mismatch directly reduces CMRR. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the differential gain of the three op-amp IA? A. (R3/R2)(1 + R1/RG) B. (R2/R3)(1 + 2R1/RG) C. (R3/R2)(1 + 2R1/RG) D. (R3/R2)(2R1/RG) Answer: C. Vo = (R3/R2)(1 + 2R1/RG)(V2 - V1). (Key point: Gain formula) 2. Why is the difference stage made unity gain (R2 = R3) in the design? A. So all gain is in the first stage and can be set by RG alone B. To reduce input impedance C. To make CMRR zero D. To remove the need for matched resistors Answer: A. With R3/R2 = 1 the gain is 1 + 2R1/RG, adjustable with just RG. (Key point: Design approach) 3. For gain 20 with RG = 1 kOhm and R3/R2 = 1, what is R1? A. 10 kOhm B. 9.5 kOhm C. 19 kOhm D. 20 kOhm Answer: B. 2R1/RG = 19, so R1 = 19 x 1k/2 = 9.5 kOhm. (Key point: Design values) 4. Which is a key feature of an instrumentation amplifier? A. Low input impedance B. Very high input impedance and high CMRR C. Gain set by many matched resistors D. Low CMRR for noise pickup Answer: B. An IA has very high input impedance, high CMRR and gain set by one resistor. (Key point: IA features) ## Close variants set in other exams - [Design three op-amp IA with gain 50](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Adesign-3opamp-ia-gain-50) — Advanced Electronics, chapter 4, asked 3× ## Related in Advanced Electronics - [IA features; 3 op-amp IA output voltage](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aia-features-3opamp-output) — Advanced Electronics, chapter 4 - [3 op-amp IA advantages; electromagnetic isolation](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Athree-opamp-ia-electromagnetic-isolation) — Advanced Electronics, chapter 4 - [Output voltage of two op-amp IA](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Atwo-opamp-ia-output) — Advanced Electronics, chapter 4 - [3 op-amp IA output and common-mode rejection](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Athree-opamp-ia-cm-rejection) — Advanced Electronics, chapter 4 - [Single op-amp IA with mismatched resistances](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Asingle-opamp-ia-mismatched) — Advanced Electronics, chapter 4 ## Related in other subjects - [Ideal op-amp properties; non-inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 3× - [Ideal op-amp properties; inverting gain](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-inverting-gain) — Basic Electronics Engineering, chapter 4, asked 3× - [Voltage gain of non-inverting op-amp](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-noninverting-gain) — Basic Electronics Engineering, chapter 4, asked 2× - [Op-amp properties and summing amplifier](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Aopamp-props-summer-v1-2v2-3v3) — Basic Electronics Engineering, chapter 4