Math Bridge: Constants that move with a prototyping kit

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Math BridgePrototypingStruggle-friendly runway

Which constants must be retested when a kit changes form?

Use one cold-room RTD reading and one enclosure antenna loss to see why a familiar formula still needs fresh evidence.

Voltage Vera, the prototyping guideVoltage Vera guides
The one targetSeparate a stable equation from constants that changed.
The chapter caseA −20 °C PT100 and a 4 dB antenna loss.
What it buys youA migration review that knows what to retest.

A field team faces an unresolved physical question: Which constants must be retested when a kit changes form? They must answer it before changing pt100 resistance on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is pt100 resistance. The middle card applies this page's relationship. The green card is ratiometric code. 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

PT100 resistance changes ratiometric code An input card leads through the page relationship to the ratiometric code result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. One review can hold two independent ledgers, provided it does not pretend that changing one constant changed the other subsystem.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for pt100 resistance is 4.

  2. 2

    Name the relationship. R(-20)=100(1+0.00385x-20)=92.3 ohm code=(92.3/430)x32,768≈7,034 ΔT=(430/32,768)/(100x0.00385)=0.0341 °C EIRP: 2 dBm-4 dB=-2 dBm power cut=10 4/10 =2.51x

  3. 3

    Substitute the chapter fixture. Set pt100 resistance to 4. The page ledger gives ratiometric code as 7034 counts.

  4. 4

    Read the result. Keep counts beside the value. Use it only inside the technical boundary on this page.

Predict, then change pt100 resistance

Try Predict the direction of ratiometric code. Move one control, calculate, then check your prediction.

4
Chapter baseline
Ratiometric code

Observe One review can hold two independent ledgers, provided it does not pretend that changing one constant changed the other subsystem. Reset the control to 4 and compare ratiometric code.

Explain Only pt100 resistance moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only pt100 resistance moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only pt100 resistance. It replays the chapter fixture; it is not a field prediction.

1. Start with the sensor's real measurement

A PT100 does not output temperature as a number. Its resistance changes with temperature. The front end compares that resistance with a known reference, and firmware turns the ratio into an ADC code. The equation can stay the same after migration while lead resistance, heating, reference value, or antenna gain changes.

Voltage Vera: A reused formula is not reused evidence. Check the constants that the new board, lead, enclosure, and ground plane actually provide.

2. Name every algebra move

1

Scale the RTD resistanceR(T)=R0(1+αT).

2

Form the measurement ratioDivide R(T) by the reference resistance.

3

Turn the ratio into countsMultiply by 2N.

4

Add antenna power in dBEIRP=Pt+G.

5

Undo a dB lossA loss L cuts power by 10L/10.

3. Reproduce the chapter case

R(−20)=100(1+0.00385×−20)=92.3 Ω
code=(92.3/430)×32,768≈7,034
ΔT=(430/32,768)/(100×0.00385)=0.0341 °C
EIRP: 2 dBm−4 dB=−2 dBm
power cut=104/10=2.51×

The RTD equation and EIRP equation are unchanged. The migration question is whether the new lead path and antenna layout still deserve the old constants.

4. Try the enclosure loss

TryMove the antenna gain loss while the cold-room RTD case stays fixed.

PT100 resistance
Ratiometric code
Resistance step
Temperature step
Original EIRP
Migrated gain
Migrated EIRP
Radiated-power cut
Power retained

ObserveEach extra dB lowers migrated gain and EIRP. The RTD values do not move because this control changes the antenna path, not the sensor path.

ExplainOne review can hold two independent ledgers, provided it does not pretend that changing one constant changed the other subsystem.

Technical boundaries.

These are first-order RTD and antenna ledgers, not a certification result.

RTD curve
The linear form is a teaching approximation; precision work uses the full standard relation
Wiring
Lead resistance and self-heating depend on the real probe and excitation method
Antenna
Gain loss depends on enclosure, ground plane, cable, orientation, frequency, and surroundings

Repeat the sensor and radio evidence scripts on the migrated assembly.

5. Turn the maths into a change condition

If the lead length, excitation, reference resistor, board layout, enclosure, or ground plane changes, the old result becomes a hypothesis. Keep the equation, update the measured constants, and compare the same output fields.

6. Record the evidence state

Store the RTD class, wiring method, lead length, excitation current, reference resistor, ADC mode, temperature reference, transmit setting, antenna, enclosure, ground plane, orientation, frequency, RSSI method, and firmware revision.

7. Check yourself

Why is a PT100 about 92.3 Ω at −20 °C in this example?
Answer: R=100(1+0.00385×−20)=92.3 Ω.
Why does a 4 dB loss cut power by about 2.51×?
Answer: Power ratios use 10L/10, so 104/10=2.51.
Does an unchanged formula prove the migrated kit is equivalent?
Answer: No. The lead, reference, board, ground plane, and enclosure can change the constants feeding it.
Honesty boundary.

The arithmetic reproduces the chapter's PT100/MAX31865 and representative antenna-loss example.

92.3 Ω
The ideal linear PT100 value, not a complete wired measurement
0.0341 °C
A code step, not total temperature accuracy
2.51×
A power ratio from gain loss, not a measured range ratio

Correct, not complete: this ledger does not approve a kit migration without repeated physical evidence.

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