# Electronic – LM324 op-amp wheatstone bridge amplifier formula

operational-amplifierstrain-gagetheveninwheatstone-bridge

I'm planning to use an LM324 opamp as a signal amplifier for a cell load (strain gauge in a Wheatstone bridge). This particular application is shown in the datasheet (see image). It shows the Wheatstone brige (bottom-left resistor is the strain gauge) and the opamp in a differential amplifier circuit. My problem is I can't quite figure out how the formula is calculated.

I get I have to use Thevenin on both sides of the bridge. This gives me:

$$R_{t-}=\frac{R}{2}$$

$$V_{t-} =\frac{ V_{REF}}{2}$$ for the right side of the bridge and
$$R_{t+}\approx{\frac{R}{2}}$$

$$V_{t+} \approx{\frac{ V_{REF}+\delta V_{REF}}{2}}$$
for the left side. Now the circuit becomes: and the differential amplifier circuit formula gives me:

$$v_o = \frac{R_f}{R/2}(v_{t+}-v_{t-})=\frac{R_f}{R/2} \frac{\delta V_{REF}}{2}$$

which differs from the datasheet formula for a 1/2 factor.

So, what's wrong with my calculation?

Your problem resides in the oversimplification of $$V_{t+}$$
If you take directly the tension divider between the R and R(1+delta) resistors you get instead $$V_{t+} = V_{REF}\frac{1+\delta}{2+\delta}$$
$$v_o = \frac{R_f}{R/2}\frac{\delta V_{REF}}{2(2+\delta)} \approx \frac{R_f}{R}\frac{\delta V_{REF}}{2}$$