Sensor Acquisition Calculation Audit
Sensor Acquisition Calculation Audit
Ada checks range fit, code step, and physical resolution behind the acquisition example
ADA · CALCULATION AUDIT
Sensor Acquisition Calculation Audit
The useful question is not how many bits the converter advertises. It is whether the physical signal uses the input range, whether the voltage step is small enough for the requirement, and whether the sensor physics can justify the extra codes.
A sensor produces 0 to 100 mV feeding a 0 to 3.3 V ADC, so the chapter proposes a gain near 33 to stretch that span across the converter’s full range rather than crowding into a handful of codes near zero. The same page notes that a 12-bit, 3.3 V ADC has a step of about 0.806 mV, and separately maps a 0 to 100 degrees C requirement across that same 0 to 3.3 V range. This audit asks the question those numbers invite: does a gain of 33 really use the ADC’s full span, and is the resulting code step small enough to matter against the sensor’s own accuracy?
Companion to the chapter Turning Signals Into Readings — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is front-end gain. The middle card applies this page's rule. The green card is conditioned sensor span. 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 front-end gain, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 33 times.
- 2
Name the relationship. conditioned span = 0.100 V x gain
- 3
Substitute with units. 0.100 V x 33 = 3.30 V
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change front-end gain
Try Predict the direction of conditioned span = 0.100 V x gain. Test another front-end gain, then compare conditioned sensor span.
Observe Gain stretches the 100 millivolt sensor span across more converter range. Reset front-end gain to 33 and compare conditioned sensor span.
Explain Gain stretches the 100 millivolt sensor span across more converter range.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Treat 0.100 V sensor span, 3.3 V ADC range, and 12-bit resolution as the fixed case; predict the code use, then select Check audit.
Gain reports 33 and converter step 0.806 mV; the physical mapping becomes 0.024414 C/code against roughly 0.5 C sensor accuracy.
Gain 33 fills the converter range so quantisation is finer, but extra ADC codes cannot recover information beyond the sensor's own accuracy.
1. Fit the small signal to the ADC
The chapter's example has a 0 to 100 mV sensor and a 0 to 3.3 V ADC. The full-scale gain is:
Without gain, the sensor would use only 0.100 / 3.3 = 0.0303, or about 3.0%, of the converter span. On a 12-bit converter that is about 0.0303 x 4095 = 124 codes instead of the available 4096 levels.
2. Check the voltage step
For the same 12-bit, 3.3 V ADC:
That voltage step is a quantization grain. It does not remove analog noise, a drifting reference, poor placement, self-heating, or a missing anti-alias filter.
3. Compare code step with physical requirement
The page maps 0 to 100 degrees C across the converter range:
12-bit: 100 / 4096 = 0.024414 degrees C/code
16-bit: 100 / 65536 = 0.001526 degrees C/code
If the sensor is only reliable to about 0.5 degrees C, the 12-bit code step is already much smaller than the sensor limit. A 16-bit reading can record more digits, but the physics and calibration decide whether those digits mean anything.
Every number above is taken from this chapter's own worked example and re-derived step by step.
Technical boundaries: The ideal gain and code-step model omits amplifier noise and saturation, ADC INL/DNL, reference tolerance, sensor nonlinearity, bandwidth, source impedance, clipping margin, and calibration error.