Instrumentation Amplifier Gain

Formula

Description

The three-op-amp instrumentation amplifier (INA) is the standard topology for precision differential measurement. The first stage (two op-amps) provides adjustable gain set by a single resistor Rg, with the formula G₁ = 1 + 2R₁/Rg. The second stage (difference amplifier) provides fixed gain G₂ = R₃/R₂, typically set to unity. The total gain is G₁ × G₂. The key advantage is that the gain is set by a single resistor (Rg) while maintaining excellent CMRR, high input impedance, and low drift. Dedicated INA ICs (INA128, AD620, AD8421) integrate all three op-amps with laser-trimmed resistors.

Variables

• G — Total voltage gain (V/V)
• R₁ — Input stage resistors (Ω, both equal)
• Rg — Gain-setting resistor (Ω)
• R₃ — Difference stage feedback resistor (Ω)
• R₂ — Difference stage input resistor (Ω)

Practical Notes

For INA ICs with R₃/R₂ = 1 (unity second stage), G = 1 + 2R₁/Rg. Common IC gain formulas: INA128/INA129: G = 1 + 50kΩ/Rg, AD620: G = 1 + 49.4kΩ/Rg. CMRR improves with higher gain and better resistor matching. For Rg = ∞ (open), G = 1 (unity gain). For maximum CMRR, the R₃/R₂ ratio must be precisely matched between the two sides of the difference amplifier — even 0.1% mismatch limits CMRR to about 66 dB.