The Bridge Whisper and Its Hidden Curve
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.
See the relationship before changing it
The figure reads from left to right. The blue card is bridge resistance shift. The middle card applies this page's rule. The green card is linear bridge output. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only bridge resistance shift, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 0.1 %.
- 2
Name the relationship. output = 5 V x fractional resistance shift / 4
- 3
Substitute with units. 5 x 0.001 / 4 x 1,000 = 1.25000 mV
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change bridge resistance shift
Try Predict the direction of output = 5 V x fractional resistance shift / 4. Test another bridge resistance shift, then compare linear bridge output.
Observe The bridge output grows with strain but remains tiny beside a raw ADC count. Reset bridge resistance shift to 0.1 and compare linear bridge output.
Explain The bridge output grows with strain but remains tiny beside a raw ADC count.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Treat the displayed 0.1% shift in a 350 ohm bridge arm with 5 V excitation as the fixed case; predict the output, then invoke Check audit.
The linear estimate displays 1.25000 mV, the exact bridge gives about 1.24938 mV, and the raw 12-bit ADC sees only 1.5 counts.
Bridge symmetry rejects common changes but leaves only 1.25 mV differential output, making amplification essential despite accurate small-strain linearisation.
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 exactlydR / (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.
Technical boundaries: The quarter-bridge approximation leaves out gauge-factor tolerance, transverse sensitivity, lead resistance, temperature compensation, excitation drift, amplifier noise, ADC reference error, and large-strain curvature.