Bridges

Bridge circuits measure small changes in impedance with great precision. Learn the Wheatstone bridge balance and output equations, quarter/half/full strain bridges, the Kelvin bridge for low resistance, and AC bridges for L and C.

A bridge is two voltage dividers side by side, with a detector between their midpoints. When the dividers have equal ratios, the midpoints are at the same voltage and the detector reads zero — the bridge is balanced. Any small change in one arm unbalances it, producing a small differential voltage centred on zero instead of a tiny change on top of a large one.

That makes bridges the standard way to measure strain, weight, pressure, temperature and component values with high sensitivity.

An analogy

A bridge is like a balanced see-saw: when both sides match it sits level; add a single grain to one side and it tips — you detect the tiny difference rather than weighing each side separately.

Balanced (null) measurement

In a classic laboratory Wheatstone bridge, you adjust a calibrated resistor until the galvanometer reads zero, then compute R_x from the known ratio. Because the detector only has to find zero, its own accuracy doesn't matter — only the reference resistors do.

Deflection bridges and strain gauges

In sensors the bridge isn't rebalanced; the output voltage is measured. Using more active gauges increases output and compensates temperature.

Kelvin double bridge

Below ~1 Ω, lead and contact resistance swamp the measurement. The Kelvin double bridge adds a second set of ratio arms so connection resistances cancel, measuring micro-ohms — busbar joints, shunts, motor windings.

AC bridges

With AC excitation and impedances, balance requires both magnitude and phase to match: Z₁Z_x = Z₂Z₃. Maxwell and Hay bridges measure inductance and Q; the Schering bridge measures capacitance and dielectric loss (tan δ) of high-voltage insulation; the Wien bridge measures frequency and is the basis of the Wien oscillator.

Ratiometric measurement

The bridge output is proportional to excitation, so modern designs use the same excitation as the ADC reference (ratiometric). Excitation drift then cancels exactly, and 24-bit sigma-delta ADCs with built-in PGAs read load cells directly.

Formulas

Worked example: Balanced Wheatstone bridge

Given: R₁ = 100 Ω, R₂ = 1000 Ω; R₃ = 470 Ω at balance

Find: R_x.

Answer: 4.7 kΩ

Worked example: Quarter-bridge strain output

Given: V_s = 5 V; R = 350 Ω, ΔR = 0.35 Ω (500 µε, GF 2)

Find: Output voltage.

Answer: ≈ 1.25 mV

Common mistakes

Applications

Key takeaways

Going further