Equation 1 and Equation 2 are used to calculate V_OUT.

Equation 1.

Equation 2.

In an ideal case, Equation 3 then calculates R₁ = R and R₂ = R_g, and V_OUT:

Equation 3.

However, the resistors have tolerances; therefore, the resistors cannot be perfectly matched.

R₁ = R ± ΔR₁

R₂ = R₂ ± ΔR₂

R = R ± ΔR

R_g = R_g ± ΔR_g

Equation 4.

Equation 5 shows that by developing the equations and neglecting the second order, the worst case is when the tolerances add up:

Equation 5.

where

• Tol = 0.01 for 1%
• Tol = 0.001 for 0.1%

If the resistors are perfectly matched, then Tol = 0 and Equation 6 calculates V_OUT:

Equation 6.

The highest error is from the common mode:

Equation 7.

Gain of 10, R_g / R = 10, and Tol = 1%:

Common mode error = ((4 × 0.01) / 1.1) × 12 V = 0.436 V

Gain of 10 and Tol = 0.1%:

Common mode error = 43.6 mV

The resistors were chosen from 2% batches.

R₁ and R 12 kΩ

R₂ and R_g 120 kΩ

Ideal Gain = 120 / 12 = 10

The measured value of the resistors:

R₁ = 11.835 kΩ

R = 11.85 kΩ

R₂ = 117.92 kΩ

R_g = 118.07 kΩ