What is the formula for Settling Time to N-Bit Accuracy?

The Settling Time to N-Bit Accuracy formula is ts = (N + 1) × ln(2) × τ, where ts—Settling time to ½ LSB (s); N—Resolution in bits; τ—Dominant time constant of the response (s).

What does ts mean in the Settling Time to N-Bit Accuracy formula?

ts is Settling time to ½ LSB (s).

Settling Time to N-Bit Accuracy

Q: How do you calculate Settling Time to N-Bit Accuracy?

Use the formula ts = (N + 1) × ln(2) × τ. To settle a single-pole exponential response to within half an LSB of an N-bit converter takes a fixed number of time constants—about 0.69 × (N + 1). Enter the values you know in the calculator above and it solves for the remaining variable.

ts = (N + 1) · ln2 · τ

Calculator

Settling Time

Resolution (bits)

Time Constant

Result

—

Formula

ts = (N + 1) × ln(2) × τ

Description

To settle a single-pole exponential response to within half an LSB of an N-bit converter takes a fixed number of time constants—about 0.69 × (N + 1). This determines how quickly an ADC driver or multiplexed signal can be sampled at full accuracy. Higher resolution demands more settling time, trading throughput against precision.

Variables

ts — Settling time to ½ LSB (s)
N — Resolution in bits
τ — Dominant time constant of the response (s)

Practical Notes

Settling to 12 bits needs ~9 time constants; to 16 bits ~12. Real amplifiers add slew-rate and higher-order terms, so allow margin beyond this single-pole estimate.

Related Concepts

All Op-Amps formulas →

Non-Inverting Amplifier Inverting Amplifier Summing Amplifier Difference Amplifier Gain-Bandwidth Product Common-Mode Rejection Ratio Op-Amp Integrator Gain Op-Amp Differentiator Gain

Need more features?

Save calculations, import telemetry data, simulate battery discharge, and collaborate with your team.

Try the App