The Bridge Whisper and Its Hidden Curve

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

The Bridge Whisper and Its Hidden Curve

A strain-gauge Wheatstone bridge balanced with four 350ohm resistors is loaded until one gauge shifts to 350.35ohm — a 0.1% change — and with 5 V excitation the chapter’s own knowledge check expects about 1.25 mV of differential bridge output. This audit asks the question that expectation invites: how close is that 1.25 mV approximation to the exact bridge equation, and is the resulting signal even large enough to register against a 12-bit, 3.3 V ADC’s single count?

Companion to the chapter Signal Conditioning for Sensors — every number here comes from that chapter.

Ada: The knowledge check says a 0.1% strain on a 350 ohm bridge with 5 V excitation gives about 1.25 mV. That is the small-signal approximation. Let me run both the approximate and the exact bridge output and see what the shortcut costs.

• Resistance change: 350 ohm x 0.1% = 0.35 ohm.
• Approximate output: V_out = 5 x 0.35 / (4 x 350) = 5 x 0.35 / 1400 = 1.25000 mV – the chapter’s figure.
• Exact quarter-bridge output: 5 x (350.35 / 700.35 - 0.5) = 1.24938 mV.
• The approximation runs high by (1.25000 - 1.24938) / 1.24938 = 0.050%, which is exactly dR / (2R) = 0.35 / 700.

So the linear formula is trustworthy to about 0.05% at 0.1% strain, but its error grows as dR/(2R) – at 1% strain it is ten times larger, which is why full-scale load cells need the exact expression or a linearizing circuit. And the whisper is real: 1.25 mV against a 12-bit, 3.3 V ADC step of 3.3 / 4096 = 0.806 mV is only 1.25 / 0.806 = 1.5 counts. The bridge does not shrink the signal by accident – it cancels common-mode drift by design – but that same design is why the amplifier is not optional polish: without gain the measurement barely clears a single ADC count.

Every number above is taken from the chapter’s own material and re-derived step by step.