4 Design Steps

Similar to Design Notes, the steps for designing the external circuitry of the two op amp INA is not different from the discrete method. The following list describes the steps in the document covering the discrete design:

1. Calculate the transfer function of the circuit.
   Equation 1. $$\begin{gathered} {\mathrm{V}}_{\mathrm{o}}={\mathrm{V}}_{\mathrm{iDiff}}\times \mathrm{G}+{\mathrm{V}}_{\mathrm{ref}}=({\mathrm{V}}_{\mathrm{i}2}-{\mathrm{V}}_{\mathrm{i}1})\times \mathrm{G}+{\mathrm{V}}_{\mathrm{ref}} \\ \mathrm{when} {\mathrm{V}}_{\mathrm{ref}}=0, \mathrm{the} \mathrm{transfer} \mathrm{function} \mathrm{simplifies} \mathrm{to} \mathrm{the} \mathrm{following} \mathrm{equation}: \\ {\mathrm{V}}_{\mathrm{o}}=({\mathrm{V}}_{\mathrm{i}2}-{\mathrm{V}}_{\mathrm{i}1})\times \mathrm{G} \\ \mathrm{where} \mathrm{G} \mathrm{is} \mathrm{the} \mathrm{gain} \mathrm{of} \mathrm{the} \mathrm{instrumentation} \mathrm{amplifier} \mathrm{and} \mathrm{G}=1+\frac{{\mathrm{R}}_4}{{\mathrm{R}}_3}+\frac{2{\mathrm{R}}_2}{{\mathrm{R}}_{\mathrm{g}}} \end{gathered}$$
2. Select R₄ and R₃ to set the minimum gain.
   Equation 2. $$\begin{gathered} {\mathrm{G}}_{\min }=1+\frac{{\mathrm{R}}_4}{{\mathrm{R}}_3}=5\frac{\mathrm{V}}{\mathrm{V}} \\ \mathrm{Choose} {\mathrm{R}}_4=20\mathrm{k\Omega } \\ {\mathrm{G}}_{\min }=1+\frac{20\mathrm{k\Omega }}{{\mathrm{R}}_3}=5\frac{\mathrm{V}}{\mathrm{V}} \\ {\mathrm{R}}_3=\frac{{\mathrm{R}}_4}{5-1}=\frac{20\mathrm{k\Omega }}{4}=5\mathrm{k\Omega }\to {\mathrm{R}}_3=5.1\mathrm{k\Omega } (\mathrm{Standard} \mathrm{Value}) \end{gathered}$$
3. Select R₁ and R₂. Make sure that R₁ / R₂ and R₃ / R₄ ratios are matched to set the gain applied to the reference voltage at 1V/V.
   Equation 3. $$\begin{gathered} \frac{{\mathrm{V}}_{\mathrm{o}\_\mathrm{ref}}}{\mathrm{Vref}}=\left(-\frac{{\mathrm{R}}_3}{{\mathrm{R}}_4}\right)\times \left(-\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}\right)=\frac{{\mathrm{R}}_3\times {\mathrm{R}}_2}{{\mathrm{R}}_4\times {\mathrm{R}}_1}=1\frac{\mathrm{V}}{\mathrm{V}} \\ \frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}=\frac{{\mathrm{R}}_4}{{\mathrm{R}}_3}\to {\mathrm{R}}_1={\mathrm{R}}_3=5.1\mathrm{k\Omega }\mathrm{ }\mathrm{and}\mathrm{ }{\mathrm{R}}_2={\mathrm{R}}_4=20\mathrm{k\Omega } (\mathrm{Standad} \mathrm{Value}) \end{gathered}$$
4. Select R_g to meet the desired maximum gain G = 10V/V.