The Divider and ADC Numbers
The Divider and ADC Numbers
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
The Divider and ADC Numbers
Voltage, code, settling, and current, ~4 minutes
A divider reading is trustworthy only when the ratio, ADC code, source impedance, and battery current all tell the same story.
A divider built from two 220 kΩ legs looks like 110 kΩ at the ADC pin, and against a 5 pF sample capacitor that gives a 0.55 us time constant — needing roughly 5 us to settle, yet the chapter warns that an ADC sampling for only about 1 us leaves the capacitor short of the true divider voltage. Swapping to 10 kΩ legs shrinks that same settling need to 225 ns. This audit asks the question that trade-off invites: exactly how much power does the low-impedance divider cost against the high-impedance one, once the settling and current numbers are both carried through?
Companion to the chapter Resistive Dividers and ADC Loading — every number here comes from that chapter.
See the relationship before changing it
The figure reads from left to right. The blue card is divider source resistance. The middle card applies this page's rule. The green card is rc time constant. 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 divider source resistance, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 110 kOhm.
- 2
Name the relationship. time constant = resistance x 5 pF
- 3
Substitute with units. 110 kOhm x 5 pF = 0.55 us
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change divider source resistance
Try Predict the direction of time constant = resistance x 5 pF. Test another divider source resistance, then compare rc time constant.
Observe Higher divider resistance slows charging of the same ADC sample capacitor. Reset divider source resistance to 110 and compare rc time constant.
Explain Higher divider resistance slows charging of the same ADC sample capacitor.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Build the divider first with 10 kOhm + 10 kOhm at 3.3 V, then compare 220 kOhm + 220 kOhm and press Check audit.
Both pairs hold Vout at 1.65 V and code near 2048, but divider current falls from 165 uA to 7.5 uA as source impedance rises 22x.
Equal 1:1 resistor ratios preserve voltage, whereas scaling both resistors upward saves current at the cost of slower ADC sample-capacitor settling.
1. The 10 kΩ thermistor example is a ratio before it is a voltage
With a 10 kΩ fixed top resistor, a 10 kΩ bottom thermistor, and a 3.3 V rail, the midpoint sits halfway up the supply:
When the bottom thermistor is 4.0 kΩ, the same equation gives the lower warm reading used above:
2. The first warm-threshold example keeps its decision margin visible
For the 5 kΩ warm point and a threshold near 1500 counts:
| Check | Arithmetic shown | Audit result |
| Warm voltage | 3.3 × 5k / (10k + 5k) | 1.10 V |
| Warm code | 1.10 / 3.3 × 4095 | About 1365 counts |
| Cool-side margin | 2048 − 1500 | 548 counts |
| Warm-side margin | 1500 − 1365 | 135 counts |
3. The ADC loading example is a time-constant audit
The high-value divider saves current but gives the ADC a high source resistance:
The battery trade-off is the other side of the same choice: 3.3 V / (10k + 10k) = 165 uA, while 3.3 V / (220k + 220k) = 7.5 uA. The 220 kΩ pair draws about 165 / 7.5 = 22 times less current, but it needs a longer sample window, a buffer capacitor, or a buffer amplifier.
Every number above is taken from the chapter’s own divider and ADC examples and re-derived step by step.
Technical boundaries: The ideal divider comparison omits resistor tolerance and temperature coefficient, ADC input leakage, sample-capacitor dynamics, reference error, quantisation noise, and any buffer's bias current.