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Technology / Technical guide
Ratiometric Sensing: Common Reference & Residual Errors
A ratio can remove a changing factor only when the numerator and denominator share that factor in the required way. Ratiometric sensing uses this principle for a defined excitation and reference relationship. It is a conditional representation, rather than a statement that supply variation or every measurement error disappears.
A common factor cancels; other contributions remain.
Keep the sensor response, reference scale and time relationship explicit before attributing stability to a ratio.
01 / Ratio boundary
An ideal converter map uses signal relative to reference.
For a declared ideal conversion relationship, a reported code fraction can depend on r = Vsensor/Vref.
For a declared ideal conversion relationship, a reported code fraction can depend on r = Vsensor/Vref. Both are voltages, making the ratio dimensionless. Sensor excitation, ADC reference and the measured engineering quantity still have different physical roles.
TI explains a ratiometric reference using shared excitation. That example establishes the cancellation mechanism, not a supported MARSTON interface or a universal claim about every ADC. Connector appearance does not identify the internal reference relationship.
02 / Shared factor
Proportional terms can cancel algebraically.
Let Vsensor = k(x)Ve and Vref = bVe, with nonzero excitation Ve and a fixed reference factor b.
Let Vsensor = k(x)Ve and Vref = bVe, with nonzero excitation Ve and a fixed reference factor b. Then r = k(x)/b. The common Ve cancels when both quantities satisfy those relationships at the relevant time and within their valid ranges.
If k changes with temperature or another condition, that change remains. The cancellation removes the shared excitation factor only; it does not prove that the sensor’s engineering transfer function is perfectly linear, stable or accurately calibrated.
03 / Illustration
A changing supply can leave the ideal ratio unchanged.
Hypothetical factors: k = 0.2 and b = 1.
Hypothetical factors: k = 0.2 and b = 1. With Ve = 4 V, the signal is 0.8 V and the ratio 0.2. With Ve = 5 V, the signal is 1 V and the same ratio remains.
The voltages and scale are invented. This arithmetic does not specify permissible input ranges, excitation levels or a circuit connection. A constant ratio represents the declared proportional model, not a measured guarantee over a product’s operating conditions.
04 / Offset term
An additive contribution is not a common multiplier.
If instead Vsensor = kVe+o, the ratio becomes k/b+o/(bVe).
If instead Vsensor = kVe+o, the ratio becomes k/b+o/(bVe). A fixed offset o therefore remains, and its ratio contribution changes with excitation. Similar-looking voltage variation can have a different algebraic role.
With invented o = 0.01 V and the preceding factors, the ratios are 0.2025 at 4 V and 0.202 at 5 V. They are not identical. These numbers illustrate why cancellation must follow the actual terms rather than the shared-source label.
05 / Dynamic matching
Equal DC factors need not have equal time response.
Different filtering or delay in signal and reference paths can mean they do not contain the same instantaneous changing factor.
Different filtering or delay in signal and reference paths can mean they do not contain the same instantaneous changing factor. Common origin alone then does not establish transient cancellation. The time-shift guide explains one distinct timing mechanism.
Independent noise, gain variation and non-proportional sensor effects can also survive. The ADC guide separates reference relationships from code-step and dynamic-performance quantities; none can substitute for every other error description.
06 / Scope
Ratio interpretation differs from an absolute voltage result.
A sensor whose output is independent of excitation presents a different relationship: varying the denominator can change its reported ratio without a matching numerator factor.
A sensor whose output is independent of excitation presents a different relationship: varying the denominator can change its reported ratio without a matching numerator factor. Thus ratiometric and absolute representations need their own physical quantity definitions.
No MARSTON ratiometric sensor, reference source or accuracy improvement is claimed. The explanation supplies no excitation choice, wiring, recalibration or reference modification; it identifies which mathematical factors can cancel and which remain.
Related technical guides: ADC Quantisation, Bit Count & Effective Number of Bits · Sampling Jitter: Timing Error, Signal Slope & SNR · Kalman Estimation: Prediction, Innovation & Covariance.
General background: Texas Instruments: Shared-excitation ratiometric reference principles. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Vsensor | Signal voltage in the declared map | Its dependence on excitation must be explicit. |
| Vref | Reference voltage | Not automatically identical to sensor excitation. |
| Ve | Shared excitation factor | Cancellation requires the same proportional contribution. |
| o | Additive offset | Does not cancel as a common multiplier. |
| r | Vsensor/Vref, dimensionless | Valid ranges, timing and remaining factors matter. |
Engineering questions.
Does one common supply cancel every error?
No. Only the shared proportional factor cancels under its assumptions.
Does a sensor offset disappear from a ratio?
Not generally; it leaves an additive ratio contribution.
Does identical DC scaling prove transient cancellation?
No. The paths can have different time responses.
Is reference voltage the measured engineering quantity?
No. Their physical roles differ.
Are the invented voltages recommended excitation values?
No. They serve only the algebraic example.
Is a ratiometric interface confirmed for MARSTON?
No actual sensor or reference implementation is assigned.
Technical enquiry
Discuss the technical question.
A ratio can remove a changing factor only when the numerator and denominator share that factor in the required way. Share the model and applicable operating or design information for an engineering discussion.