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Computer
ADC step size and dynamic range
Smallest voltage step an analogue-to-digital converter can resolve.
- Ref
- CMP-05
- Rev
- v1
- Field
- Computer
- Result
- ΔV [mV]
ΔV the size of one step (the LSB), Vspan the full input span and n the number of bits. An ideal uniform n-bit converter splits the span into 2ⁿ bins. The sampling rate must also satisfy fs > 2 fmax.
An n-bit converter can only report 2ⁿ different levels. The step size is the voltage span divided by that number, which sets the smallest change it can see.
Calculator
- Number of levels 2ⁿ4,096
- Ideal dynamic range 6.02n + 1.7674 dB
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Every extra bit doubles the number of levels and adds about 6 dB of ideal dynamic range.
- Real converters give fewer “effective” bits than their nominal count because of noise and distortion.
- Choose the input span to match the sensor’s output so the signal uses most of the range.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mV) | Local step | Change in result |
|---|---|---|---|---|---|---|
| n Number of bits | 8 to 24 bits | 1.967e-4 | 12.89 | 12.89 | +10% | −56.5 % |
| Vspan Input span | 0.5 to 20 V | 0.1221 | 4.883 | 4.761 | +10% | +10 % |
Sweep of Number of bits
| Number of bits (bits) | Step size (mV) |
|---|---|
| 8 | 12.89 |
| 10 | 3.223 |
| 12 | 0.8057 |
| 14 | 0.2014 |
| 16 | 0.05035 |
| 18 | 0.01259 |
| 20 | 0.003147 |
| 22 | 7.868e-4 |
| 24 | 1.967e-4 |
Sweep one variable
Variables and how each one contributes
Step size
What the equation gives you. Everything else feeds it.
Input span
Full input voltage range of the converter. Directly proportional.
Number of bits
Resolution of the converter. Each extra bit halves the step size.
Worked example with the values above
- Levels: 212 = 4,096.
- Step = 3.3 V / 4,096 = 8.057×10−4 V.
- In millivolts, 0.8057 mV per step.
Assumptions and limits
- Ideal uniform converter.
- Signal fills the input span.
- Sampling above twice the highest signal frequency, with an anti-alias filter.
Common mistakes
- Assuming noise-free bits: effective bits are lower.
- Using 2ⁿ − 1 steps in some definitions; check the datasheet.
- Undersampling and aliasing.
Statistics and uncertainty
The quantisation error is uniform within ±½ step, giving an RMS error of ΔV/√12, about 0.29 LSB. Real converters add noise, offset and gain error of a few LSB, usually specified as ENOB.
Where it is used
- Radar, sonar and sensor digitisation.
- Data acquisition and telemetry.
- Choosing a converter for a measurement system.
Maths you need
- Powers of two: 2ⁿ levels
- Sampling: Nyquist criterion