Measuring by balancing
Measuring a resistance directly means trusting a meter’s accuracy. The Wheatstone bridge avoids that problem by comparing the unknown resistor with known ones and looking for a null, a zero reading. Samuel Hunter Christie described the circuit in 1833 and Charles Wheatstone made it famous ten years later. Today the same circuit sits inside scales, pressure sensors and almost every strain gauge amplifier.
The circuit
Two voltage dividers are fed by the same supply Vs:
- One side has R1 on top and R2 at the bottom, so its midpoint sits at Vs × R2 ÷ (R1 + R2).
- The other side has R3 on top and Rx at the bottom, so its midpoint sits at Vs × Rx ÷ (R3 + Rx).
The output is the difference between the two midpoints:
Vout = Vs × (Rx ÷ (R3 + Rx) − R2 ÷ (R1 + R2))
The bridge is balanced, with Vout = 0, when R1 ÷ R2 = R3 ÷ Rx, that is Rx = R2 × R3 ÷ R1.
Worked example
A 350 Ω strain gauge sits in the Rx position next to a 350 Ω reference resistor R3, with 1,000 Ω resistors for R1 and R2 and a 5 V supply. Under load the gauge rises to 351 Ω:
- Reference midpoint: 5 × 1,000 ÷ 2,000 = 2.5000 V.
- Gauge midpoint: 5 × 351 ÷ 701 = 2.5036 V.
- Output: about 3.566 mV.
- Balanced value of Rx: 1,000 × 350 ÷ 1,000 = 350 Ω, so the gauge is 0.286% above balance.
- Supply current: about 9.63 mA.
Why a bridge?
- Sensitivity: the output starts at zero, so an amplifier can magnify a change of a fraction of a percent without saturating on a large offset.
- Accuracy: at balance, the result depends only on the resistor ratios, not on the supply voltage or the meter.
- Temperature compensation: if a second, identical gauge sits in the R3 position but is not strained, temperature changes affect both sides equally and cancel.
Quarter, half and full bridges
With one active gauge, the circuit is a quarter bridge and its output is slightly nonlinear. A half bridge uses two active gauges, one in tension and one in compression, doubling the output. A full bridge, with four active gauges as in most load cells, quadruples it and is linear. Load cells are usually rated in mV/V: a 2 mV/V cell fed with 10 V gives 20 mV at full load.
Practical notes
Keep the supply voltage low enough that the gauges do not heat up, typically 2 to 10 V. Use twisted, shielded wiring, because the signals are only a few millivolts and pick up noise easily.