Eddie guidesA technician must decide whether reference code width is safe before changing reference adc resolution on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is reference adc resolution. The middle card applies this page's rule. The green card is reference code width. 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 reference adc resolution, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 12 bits.
- 2
Name the relationship. reference code width = 3,300 mV / 2^bits
- 3
Substitute with units. 3,300 / 2^12 = 0.8057 mV
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change reference adc resolution
Try Predict the direction of reference code width = 3,300 mV / 2^bits. Test another reference adc resolution, then compare reference code width.
Observe More reference bits split the same 3.3 volt span into smaller ideal bins. Reset reference adc resolution to 12 and compare reference code width.
Explain More reference bits split the same 3.3 volt span into smaller ideal bins.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Start with the physical story
An ADC replaces a smooth voltage with code bins. One reading can miss by half a bin, while many uniformly placed errors have a smaller RMS size.
2. Name every algebra move
Count codeslevels=2^N.
Find one stepq=Vref/levels.
Bound one readingpeak=q/2.
Average squared errorRMS=q/sqrt(12).
Map into temperatureDivide millivolts by sensor sensitivity.
3. Reproduce the chapter case
q=3300/4096=0.8057 mV
peak=q/2=0.4028 mV
RMS=q/sqrt(12)=0.2326 mV
LM35 RMS floor=0.0233 °C
ideal SNR=74.0 dB
A fine quantisation floor does not erase the LM35 accuracy band of about ±0.5 °C.
4. Try one real input
TryMove the control, predict the direction, then compare every output.
ObserveEach extra bit halves step, peak error, and RMS noise while adding about 6.02 dB of ideal SNR.
ExplainBit depth controls quantisation only; reference noise, analogue noise, nonlinearity, calibration, and sensor accuracy remain.
This is a transparent first-order teaching ledger tied to the chapter constants.
- Ideal ADC
- The model assumes uniform rounding and no missing codes or nonlinearity.
- Reference
- Reference and front-end noise can dominate the ideal quantisation floor.
- Sensor
- A smaller code step does not improve the physical sensor itself.
Correct, not complete: this ledger does not qualify an ADC, reference, analogue front end, or sensor.
5. Use the result in the design
Choose bits only after mapping the required physical change into volts and comparing every larger uncertainty source.
6. Record the evidence state
Record Vref, effective number of bits, code histogram, sensitivity, span, noise, accuracy, calibration residual, and sampling rate.
7. Check yourself
Why is RMS smaller than half an LSB?
Does 16-bit guarantee better accuracy?
Does bit depth set Nyquist rate?
The arithmetic reproduces the named chapter case; it is an inspectable model, not a component approval.
- Ideal ADC
- The model assumes uniform rounding and no missing codes or nonlinearity.
- Reference
- Reference and front-end noise can dominate the ideal quantisation floor.
- Sensor
- A smaller code step does not improve the physical sensor itself.
Correct, not complete: this ledger does not qualify an ADC, reference, analogue front end, or sensor.