Electronic – LM324 op-amp wheatstone bridge amplifier formula


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.

bridge amplifier from datasheet

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:


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

V_{t+} \approx{\frac{ V_{REF}+\delta V_{REF}}{2}}
for the left side. Now the circuit becomes:

wheatstone to thevenin

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?

Best Answer

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 $$V_{t+} = V_{REF}\frac{1+\delta}{2+\delta}$$

Which is approximately the same as what you used, but yields the good formula.

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