A strain gauge is a serpentine foil pattern bonded to a surface. When the surface stretches or compresses, the foil deforms with it, changing its resistance by a tiny fraction. The gauge factor (GF) relates this: ΔR/R = GF × ε, where ε is strain (dimensionless, often in µε — microstrain). Typical metal foil gauges have GF ≈ 2.0, and typical strains in loaded structures are 100–1000 µε. That means resistance changes of just 0.02%–0.2%. You cannot measure this directly with an ohmmeter — you need a bridge.

Bridge configurations:

• Quarter bridge — one active gauge, three fixed resistors. Simplest, but sensitive to lead resistance and temperature.
• Half bridge — two active gauges on opposite faces of a bending beam (one stretched, one compressed). Doubles output and cancels temperature drift.
• Full bridge — four active gauges. Quadruples output, cancels temperature, and eliminates lead-wire effects. Standard in load cells.

The output math: For a full bridge with excitation Vex and all four gauges seeing strain magnitude ε, the differential output is:

Vout = Vex × GF × ε

Example: A 350 Ω full-bridge load cell with 5 V excitation measuring 500 µε produces Vout = 5 × 2.0 × 500×10⁻⁶ = 5 mV. That's a full-scale signal on the order of millivolts — right in the noise floor of most ADCs without amplification.

The signal chain:

• Excitation source — a low-noise, stable voltage (or current) reference. Use ratiometric measurement: feed the same reference to your ADC so gain and offset drift cancel.
• Instrumentation amplifier — high CMRR (>100 dB) is critical because the bridge output sits at Vex/2 as common-mode. A single-resistor-gain INA (INA333, AD8422) with G = 100–1000 lifts the millivolt signal into the volt range.
• Low-pass filter — cutoff around 10–100 Hz for mechanical measurements (bandwidth of strain is slow). Kills 60 Hz hum and EMI picked up by long gauge leads.
• ADC — 24-bit delta-sigma (ADS1232, HX711) is standard because it integrates INA + reference + ADC and delivers 20+ noise-free bits.

Practical gotchas: Self-heating from excitation current changes the gauge resistance directly — keep excitation power under about 2–5 mW per gauge for stable measurements. Shield the leads and route them as twisted pairs. If your gauges are more than a meter away, use 6-wire Kelvin connection so the ADC senses the excitation voltage right at the bridge, not at the amplifier board — otherwise lead resistance drift shows up as gain drift.

Rule of thumb: Expect 1–3 mV/V full-scale output from commercial load cells. To get 1 count of noise per gram on a 10 kg scale, you need roughly 24-bit resolution — which is why HX711-class chips exist.