Strain Gauges, Load Cells & Bridge Circuits

Bonded strain gauges measure deformation indirectly through resistance. The gauge factor

$$GF=\frac{\Delta R/R}{\varepsilon}$$

relates fractional resistance change to strain $\varepsilon=\Delta L/L$. For $GF=2.0$ and $500\ \mu\varepsilon$, $\Delta R/R=0.001$: a 350 Ω gauge changes by only 0.35 Ω.

Why a Wheatstone bridge #

A bridge converts tiny resistance changes into a differential voltage while allowing multiple gauges to add desired strain and cancel temperature or bending modes. For one active arm and small $\Delta R$,

$$\frac{V_o}{V_{exc}}\approx\frac{1}{4}\frac{\Delta R}{R}=\frac{GF\varepsilon}{4}.$$

The example above yields 0.5 mV/V, or 2.5 mV at 5 V excitation. A full bridge can produce four times the quarter-bridge sensitivity when the four strains have appropriate signs.

Mechanics comes first #

The gauge measures strain where it is bonded, not abstract force. Adhesive thickness, surface preparation, transverse sensitivity, creep, load introduction, temperature gradients, and structural hysteresis all precede the electronics. A high-quality amplifier cannot correct a poorly defined strain field.

Excitation and readout #

Ratiometric conversion rejects common excitation drift because both bridge output and ADC reference scale with $V_{exc}$. Remote sense compensates wire drop to a distant bridge. An instrumentation amplifier needs enough common-mode range for the bridge midpoint and enough headroom for bridge offset before applying large gain.

At 2 mV/V sensitivity and 5 V excitation, a 10 mV full-scale signal amplified by 250 becomes 2.5 V. If bridge zero imbalance is 4 mV, it consumes another 1 V after gain. Design gain from full tolerance, not nominal zero.

Temperature and lead resistance #

Quarter bridges are especially sensitive to lead resistance and its temperature coefficient. Three-wire arrangements cancel equal lead resistances only approximately; full bridges put all active elements at the measurement site and enable mechanical temperature compensation, but still have span and zero drift.

Verification #

Use shunt calibration to inject a known resistance change and verify bridge wiring, excitation, gain, and digital scaling. It does not validate the mechanical load path. Complete commissioning also needs unloaded zero, known physical loads in both directions, creep/return-to-zero, overload recovery, and temperature checks.