Design Goals

Design Description

A strain gauge is a sensor whose resistance varies with applied force. The change in resistance is directly proportional to how much strain the sensor is experiencing due to the force applied. To measure the variation in resistance, the strain gauge is placed in a bridge configuration. This design uses a two op amp instrumentation circuit to amplify a differential signal created by the change in resistance of a strain gauge. By varying R₁₀, a small differential voltage is created at the output of the Wheatstone bridge which is fed to the two op amp instrumentation amplifier input. Linear operation of an instrumentation amplifier depends upon the linear operation of the primary building block: op amps. An op amp operates linearly when the input and output signals are within the input common-mode and output-swing ranges of the device, respectively. The supply voltages used to power the op amps define these ranges.

Design Notes

1. Resistors R₅, R₆, and R₇ of the Wheatstone bridge must match the stain gauge nominal resistance and must be equal to avoid creating a bridge offset voltage.
2. Low tolerance resistors must be used to minimize the offset and gain errors due to the bridge resistors.
3. V_ex sets the excitation voltage of the bridge and the common-mode voltage V_cm.
4. V_ref biases the output voltage of the instrumentation amplifier to mid-supply to allow differential measurements in the positive and negative directions.
5. R₁₁ sets the gain of the instrumentation amplifier circuit.
6. R₈ and R₉ set the common-mode voltage of the instrumentation amplifier and limits the current through the bridge. This current determines the differential signal produced by the bridge. However, there are limitations on the current through the bridge due to self-heating effects of the bridge resistors and strain gauge.
7. Make sure that R₁ = R₃ and R₂ = R₄ and that ratios of R₂/R₁ and R₄/R₃ are matched to set the V_ref gain to 1 V/V and maintain high DC CMRR of the instrumentation amplifier.
8. Linear operation is contingent upon the input common-mode and the output swing ranges of the op amps used. The linear output swing ranges are specified under the A_ol test conditions in the op amps data sheets.
9. Using high-value resistors can degrade the phase margin of the circuit and introduce additional noise in the circuit.

Design Steps

1. Select R₅, R₆ and R₇ to match the stain gauge nominal resistance
   ${\mathrm{R}}_{\mathrm{gauge}}={\mathrm{R}}_5={\mathrm{R}}_6={\mathrm{R}}_7=120\mathrm{\Omega }$
2. Choose R₉ to set the common mode voltage of the instrumentation amplifier at 2.39 V
   ${\mathrm{V}}_{\mathrm{cm}}=\frac{\frac{{\mathrm{R}}_{\mathrm{bridge}}}{2}+{\mathrm{R}}_9}{{\mathrm{R}}_{\mathrm{bridge}}+{\mathrm{R}}_9}\times {\mathrm{V}}_{\mathrm{ex}}$
   ${\mathrm{V}}_{\mathrm{c}\mathrm{m}}=\frac{\frac{120\mathrm{ }\mathrm{\Omega }}{2}+{\mathrm{R}}_9}{120\mathrm{ }\mathrm{\Omega }+{\mathrm{R}}_9}\times 2.5\mathrm{ }\mathrm{V}=2.39\mathrm{ }\mathrm{V}$
   $\frac{\frac{120\mathrm{ }\mathrm{\Omega }}{2}+{\mathrm{R}}_9}{120\mathrm{ }\mathrm{\Omega }+{\mathrm{R}}_9}=\frac{2.39\mathrm{ }\mathrm{V}}{2.5\mathrm{ }\mathrm{V}}=0.96$
   $0.04 {\mathrm{R}}_9={49.7\to \mathrm{R}}_9=\frac{49.7}{0.04}=1.24\mathrm{ }\mathrm{k}\mathrm{\Omega }=1.27\mathrm{ }\mathrm{k}\mathrm{\Omega }\mathrm{ }\left(\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{ }\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}\right)$
3. Calculate the gain required to produce the desired output voltage swing
   $\mathrm{G}=\frac{{\mathrm{V}}_{\mathrm{oMax}}-{\mathrm{V}}_{\mathrm{oMin}}}{{\mathrm{V}}_{\mathrm{iDiff}\_\mathrm{Min}}-{\mathrm{V}}_{\mathrm{iDiff}\_\mathrm{Min}}}=\frac{\mathrm{4.72}\mathrm{V}-\mathrm{0.225}\mathrm{V}}{\mathrm{0.00222}\mathrm{V}-(-\mathrm{0.00227}\mathrm{V})}=1001\frac{\mathrm{V}}{\mathrm{V}}$
4. Select R₁, R₂, R₃, and R₄. To set the V_ref gain at 1 V/V and avoid degrading the instrumentation amplifier’s CMRR, R₁ must equal R₃ and R₂ must equal R₄.
   $\mathrm{Choose}{\mathrm{R}}_1={\mathrm{R}}_3=5.1\mathrm{k\Omega }\mathrm{and}{\mathrm{R}}_3={\mathrm{R}}_4=\text{20}\mathrm{k\Omega }\mathrm{(Standard\; value)}$
5. Calculate R₁₁ to meet the required gain
   $$\begin{gathered} \mathrm{G}=1+\frac{{\mathrm{R}}_4}{{\mathrm{R}}_3}+\frac{2\times {\mathrm{R}}_2}{{\mathrm{R}}_{11}}=1001\frac{\mathrm{V}}{\mathrm{V}} \\ \mathrm{G}=1+\frac{20\mathrm{k\Omega }}{\text{5.1}\mathrm{k\Omega }}+\frac{2\times {\mathrm{R}}_2}{{\mathrm{R}}_{11}}=1001\frac{\mathrm{V}}{\mathrm{V}}\to 4.92+\frac{40\mathrm{k\Omega }}{{\mathrm{R}}_{11}}=1001\frac{\mathrm{V}}{\mathrm{V}}\to \frac{40\mathrm{k\Omega }}{{\mathrm{R}}_{11}}=996.1\to {\mathrm{R}}_{11}=\frac{40\mathrm{k\Omega }}{996.1} \\ =40.15\mathrm{\Omega }\to {\mathrm{R}}_{11}=40.2\mathrm{\Omega }\mathrm{(Standard\; value)} \end{gathered}$$
6. Calculate the current through the bridge
   $$\begin{gathered} {\mathrm{I}}_{\mathrm{bridge}}=\frac{{\mathrm{V}}_{\mathrm{ex}}}{{\mathrm{R}}_8+{\mathrm{R}}_9+{\mathrm{R}}_{\mathrm{bridge}}}=\frac{2.5\mathrm{V}}{0\mathrm{\Omega }+1.27\mathrm{k\Omega }+120\mathrm{\Omega }} \\ {\mathrm{I}}_{\mathrm{bridge}}=\frac{2.5\mathrm{V}}{1.27\mathrm{k\Omega }+120\mathrm{\Omega }}\to {\mathrm{I}}_{\mathrm{bridge}}=1.80\mathrm{mA} \end{gathered}$$

Design Simulations

DC Simulation Results

References

1. Analog Engineer's Circuit Cookbooks
2. SPICE Simulation File SBOMAU4
3. TI Precision Designs TIPD170
4. TI Precision Labs
5. V_CM vs. V_OUT plots for instrumentation amplifiers with two op amps

Design Alternate Op Amp