Sensor Guide
Bridge Sensor and Load Cell Error Budgets: Excitation, CMRR, Drift, and Calibration
Turn a nominal bridge equation into a defensible measurement by referring electrical, thermal, mechanical, and calibration errors to one common input or output unit.
18 min · Intermediate · Updated October 12, 2026
Start with the Ideal Bridge Signal
A strain gauge changes resistance with strain. A Wheatstone bridge converts the arm imbalance into a differential voltage, and a load cell packages that bridge with a mechanical structure. Keep the ideal transfer function separate from its error terms. For a rated load cell, sensitivity in mV/V multiplied by excitation gives full-scale differential output; multiplying again by load fraction gives the ideal signal at the applied load.
Formula reference
Ideal Bridge and Load-Cell Relations
ΔR/R = GF × εVout = Vexc[R4/(R3 + R4) - R2/(R1 + R2)]VFS = S(mV/V) × VexcVsignal = VFS × (Load / Rated Load)Variable definitions
- GF
- gauge factor
- ε
- dimensionless strain
- Vexc
- bridge excitation
- S
- rated load-cell sensitivity
- Vsignal
- ideal differential output before zero and error terms
Use the Strain Gauge Calculator, Wheatstone Bridge Sensor Calculator, and Load Cell Output Calculator for the nominal electrical relationships.
Normalize the Error Budget
Do not add volts, percent full scale, ADC codes, and microstrain in one column. Refer every contributor to bridge input, conditioned output, ADC codes, or engineering units. Input-referred voltage is often the clearest electrical basis; divide it by sensitivity in volts per engineering unit to obtain force, mass, pressure, or strain error.
Formula reference
Input-Referred Error
eCM = VCM / 10^(CMRR/20)eOUT = G × eINEngineering error = eIN / Sensor sensitivityWorst case = Σ|ei|RSS = √Σ(ei²)Variable definitions
- VCM
- amplifier common-mode voltage
- CMRR
- common-mode rejection ratio in dB
- G
- signal-chain gain
- Worst case uses guaranteed bounds
- RSS requires independent statistical contributors
| Contributor | Useful Unit | Treatment |
|---|---|---|
| Bridge zero balance | Input-referred mV/V or µV/V | Tare at known zero; retain drift and repeatability terms |
| Sensitivity/span error | % of reading or full scale | Calibrate with a traceable load near the intended range |
| Nonlinearity | %FS | Use multi-point residuals; do not hide it inside gain |
| Hysteresis and creep | %FS over stated time | Test loading direction and settling time |
| Excitation/reference | ppm or % | Use ratiometric conversion where practical |
| Amplifier offset and drift | µV and nV/°C | Refer to bridge input before converting to force |
| Finite CMRR | dB | Convert common-mode voltage to input-referred error |
| Noise and ADC quantization | µV RMS / peak-to-peak / codes | State bandwidth and noise-free resolution |
| Lead and connector resistance | Ω and temperature coefficient | Use suitable 3-, 4-, or 6-wire sensing |
| Mechanical installation | %FS or measured residual | Include mounting stress, side load, and thermal gradients |
Excitation and Ratiometric Conversion
Bridge output is proportional to excitation. If the ADC reference is independent, excitation tolerance becomes span error. A ratiometric architecture uses the same source, or a measured representation of it, for excitation and conversion reference so first-order supply change cancels.
Cancellation is not unlimited. Wiring resistance can make sensor excitation differ from the reference sense point. Reference and excitation noise may occupy different bandwidths. Bridge self-heating changes resistance and mechanical temperature. Six-wire load cells provide remote sense leads specifically to reduce cable-drop error.
Worked Error-Budget Example
A 2 mV/V, 100 kg load cell uses 5 V excitation, so ideal full-scale output is 10 mV and sensitivity is 100 µV/kg. Suppose residual zero error is 8 µV, amplifier input offset after calibration is 2 µV, combined drift over the operating temperature is 5 µV, and bandwidth-limited noise is 3 µV RMS.
Guaranteed zero, offset, and drift bounds add to 15 µV, or 0.15 kg. If the 3 µV noise is independent and RMS, combine it separately: √(15² + 3²) = 15.30 µV, approximately 0.153 kg. This number still excludes load-cell nonlinearity, hysteresis, creep, reference uncertainty, and mechanical installation.
Calibration and Verification Workflow
- Warm the sensor, excitation, amplifier, and ADC to a defined operating condition.
- Record unloaded zero repeatedly to quantify noise and short-term stability before tare.
- Apply traceable loads in increasing and decreasing order to reveal hysteresis.
- Fit offset and span with two points only when residuals support a linear model; otherwise inspect a multi-point fit.
- Repeat at relevant temperatures and after settling intervals to measure drift and creep.
- Convert residuals to the same engineering unit used in the requirement.
- Verify overload recovery, wiring, shielding, grounding, common-mode range, and amplifier output headroom.
The Sensor Calibration Calculator supports slope, intercept, and residual work. The Sensor ADC Resolution Calculator checks usable code span, but its ideal LSB is not an accuracy claim.
Common Mistakes
- Treating mV/V as an absolute voltage without multiplying by excitation.
- Using nominal excitation at the PCB while ignoring cable drop at the bridge.
- Combining guaranteed limits by RSS without statistical justification.
- Calling ADC bit depth measurement accuracy.
- Removing initial zero with tare and then omitting zero drift from the budget.
- Using amplifier CMRR without checking common-mode voltage and source imbalance.
- Calibrating only in one load direction and missing hysteresis or creep.
- Ignoring mounting stress, side load, connector resistance, and temperature gradients.
Design Boundary
This workflow estimates measurement uncertainty for resistive bridge sensors. It does not replace a load-cell datasheet, mechanical finite-element analysis, certified weighing procedures, intrinsic-safety assessment, or calibration by an accredited laboratory. Safety-critical and trade measurements require applicable standards and traceable verification.
Support reference
FAQ
What does mV/V mean for a load cell?
It is rated differential output in millivolts per volt of excitation at full-scale load. A 2 mV/V cell excited by 5 V ideally produces 10 mV at rated load before zero-offset correction.
Why use a ratiometric bridge measurement?
Using the same source as bridge excitation and ADC reference makes first-order excitation change common to numerator and denominator, reducing gain error. It does not remove reference noise, wiring drop, self-heating, or amplifier errors.
Is bridge zero balance the same as amplifier offset?
No. Bridge zero balance is sensor output at zero load; amplifier input offset is added by the signal conditioner. Measure and budget them separately even if a tare operation removes their combined initial value.
How does CMRR affect a bridge measurement?
The amplifier sees millivolts of differential signal riding on a much larger common-mode voltage. Finite CMRR converts part of that common-mode voltage into input-referred error.
Can a two-point calibration remove every load-cell error?
No. It corrects linear offset and span under calibration conditions, but not hysteresis, creep, nonlinearity, temperature drift, noise, mechanical installation error, or overload damage.
Should bridge errors be added directly or by RSS?
Guaranteed worst-case limits are normally added arithmetically. RSS is appropriate only for independent, statistical, zero-mean contributors with defensible distributions.
Why does a three-wire quarter bridge reduce lead error?
With matched lead paths and the intended bridge wiring, two lead resistances affect opposing arms and largely cancel. Mismatch and temperature gradients leave residual error.
How many ADC bits does a load cell need?
Start from required engineering resolution and usable calibrated span, then add headroom for noise, drift, overload, and digital filtering. Nominal ADC bits alone do not predict noise-free resolution.