Design three op-amp IA with gain 50

An instrumentation amplifier (IA) is a precision difference amplifier with buffered inputs. It has very high input impedance, high CMRR and a gain set by one resistor. It is used to amplify small transducer signals in noisy, high common-mode environments.

Features of an instrumentation amplifier

• Very high input impedance on both inputs
• High CMRR (100 dB or more), which rejects common-mode noise
• Gain set by a single external resistor RG, accurate and stable
• Low offset voltage and drift, low noise
• Low output impedance

Three op-amp IA and gain

 V1 --->(+)\
           A1>---+--Vo1--[R2]--+--[R3]--+
       +->(-)/   |             |        |
       |         R1          (-)\       |
       +---------+              A3>-----+--> Vo
       RG                    (+)/
       +---------+             |
       +->(-)\   R1   Vo2--[R2]+--[R3]--GND
       |   A2>---+--Vo2
 V2 --->(+)/

The current through RG is (V1 − V2)/RG. The same current flows through both R1 resistors, so:

Vo2 − Vo1 = (V2 − V1)(1 + 2R1/RG)
Vo = (R3/R2)(Vo2 − Vo1) = (R3/R2)(1 + 2R1/RG)(V2 − V1)

Design for gain A = 50

Option 1, all gain in the first stage:

1. R2 = R3 = 10 kΩ, so the difference stage gain = 1.
2. 1 + 2R1/RG = 50, so 2R1/RG = 49.
3. Choose RG = 1 kΩ:

R1 = 49 × 1 kΩ / 2 = 24.5 kΩ

(Or fix R1 = 10 kΩ, then RG = 2R1/(A − 1) = 20k/49 = 408 Ω; use a 390 Ω resistor plus a 50 Ω trimmer.)

Option 2, split the gain (10 × 5):

• First stage: 1 + 2R1/RG = 10, with RG = 2 kΩ and R1 = 9 kΩ
• Difference stage: R3/R2 = 5, with R2 = 10 kΩ and R3 = 50 kΩ

A = 5 × (1 + 2 × 9k/2k) = 5 × 10 = 50

Check (option 1): A = 1 × (1 + 2 × 24.5k/1k) = 1 + 49 = 50.

Design values (option 1): R1 = 24.5 kΩ (×2, matched), RG = 1 kΩ, R2 = R3 = 10 kΩ (×4, 0.1 % matched), op-amps such as OP07 or LM324.

Gain can be changed by adjusting RG only, without disturbing CMRR.