Design Goals

Design Description

This design amplifiers the difference between V_i1 and V_i2 and outputs a single ended signal while rejecting the common–mode voltage. Linear operation of an instrumentation amplifier depends upon the linear operation of its primary building block: op amps. An op amp operates linearly when the input and output signals are within the device’s input common–mode and output–swing ranges, respectively. The supply voltages used to power the op amps define these ranges.

Design Notes

1. R_g sets the gain of the circuit.
2. High–value resistors can degrade the phase margin of the circuit and introduce additional noise in the circuit.
3. The ratio of R₄ and R₃ set the minimum gain when R_g is removed.
4. Ratios of R₂/R₁ and R₄/R₃ must be matched to avoid degrading the instrumentation amplifier’s DC CMRR and ensuring the V_ref gain is 1V/V.
5. Linear operation is contingent upon the input common–mode and the output swing ranges of the discrete op amps used. The linear output swing ranges are specified under the A_ol test conditions in the op amps data sheets.

Design Steps

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

Design Simulations

DC Simulation Results

Transient Simulation Results

References:

1. Analog Engineer's Circuit Cookbooks
2. SPICE Simulation File SBOMAU7
3. TI Precision Labs
4. V_CM vs. V_OUT plots for instrumentation amplifiers with two op amps
5. Common-mode Range Calculator for Instrumentation Amplifiers

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