The Beta Conversion and the RTD Comparison
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
The Beta Conversion and the RTD Comparison
The firmware result is only credible if the units survive the trip from resistance physics to kelvin arithmetic and back to Celsius.
A 10 kΩ NTC thermistor with Beta constant 3950 is the chapter’s worked example: it reads 10 kΩ at 25°C but only 4.0 kΩ once warmed, and the chapter’s Beta equation is supposed to convert that resistance back into a temperature. Elsewhere the same chapter contrasts this exponential curve with a PT100 RTD, whose resistance is expected to rise almost linearly with temperature. This audit asks the question that contrast invites: does the Beta equation actually recover a sensible temperature from the 4.0 kΩ reading, and does the RTD’s response really stay as linear as the chapter claims?
Companion to the chapter Thermistor Linearization — every number here comes from that chapter.
Thermistor check
Use the chapter’s values: R0 = 10 kΩ at T0 = 25 °C = 298.15 K, B = 3950, and measured R = 4.0 kΩ.
1/T = 1/298.15 + (-0.9163/3950) = 0.0033540 - 0.0002320 = 0.0031220
T = 1/0.0031220 = 320.3 K; Celsius = 320.3 - 273.15 = 47.2 °C
Physics check
The negative logarithm is expected: an NTC thermistor has lower resistance when warmer. A falling resistance must produce a temperature above the 25 °C reference, so 47.2 °C has the right direction before the number is trusted.
Linear sensor contrast. For the PT100 comparison in this page, R = R0(1 + αT) = 100(1 + 0.00385×100) = 100(1 + 0.385) = 138.5 Ω. That near-linear result is why the RTD calculation feels like a calibration line while the thermistor needs the exponential model.
Every number above is taken from the chapter’s own thermistor and RTD examples and re-derived step by step.