Model response time from bandwidth, cycles, or cutoff. Review settling limits and noise tradeoffs instantly. Build better measurements with confident parameter choices every time.
| Case | Order | τ (s) | fc (Hz) | ENBW (Hz) | 1% Settling Time (s) |
|---|---|---|---|---|---|
| Fast tracking | 1 | 0.1000 | 1.5915 | 2.5000 | 0.4605 |
| Balanced filtering | 2 | 0.2500 | 0.6366 | 0.5000 | 1.6596 |
| Lower noise mode | 3 | 0.5000 | 0.3183 | 0.1875 | 4.2030 |
| Deep averaging | 4 | 1.0000 | 0.1592 | 0.0781 | 10.0451 |
The calculator treats the output filter as a cascade of identical low-pass sections. That model matches common lock-in amplifier settings well.
fc = 1 / (2π × τ)Nτ = fref × τENBW = cn / τc1 = 0.25, c2 = 0.125, c3 = 0.09375, c4 = 0.078125e-x Σ(xk / k!) = ε, for k = 0 to n - 1tsettle = x × τHere, τ is time constant, fc is corner frequency, fref is reference frequency, ε is the allowed remaining error, and n is filter order.
A lock-in amplifier isolates weak signals at a known reference frequency. The time constant controls the output filter. That filter removes rapid fluctuations after demodulation. A short time constant reacts quickly. A long time constant suppresses more noise. The correct value depends on scan speed, signal stability, and the filter order.
This calculator converts between time constant, corner frequency, equivalent noise bandwidth, and averaging cycles. It also estimates settling time for one-pole, two-pole, three-pole, and four-pole responses. Those outputs help you predict how long the instrument needs after a step change. They also show how much bandwidth remains at the output. Lower bandwidth usually improves noise rejection, but it slows measurement updates.
Filter order matters because identical time constants do not settle equally. A higher-order low-pass filter reduces noise bandwidth more strongly. It also delays the final output longer after a change in signal amplitude, phase, or input conditions. That tradeoff is important in spectroscopy, scanning probe work, chopped optical measurements, and any experiment that moves between points quickly.
Use the corner frequency when you think in hertz. Use equivalent noise bandwidth when you care about noise power. Use cycles per time constant when you compare averaging against the reference. Use settling time when you need to know how long to wait before logging a stable number. For stepped experiments, the settling result is often the most practical limit.
Choose a shorter time constant when you need faster tracking or higher scan speed. Choose a longer one when the signal is noisy and the source changes slowly. Increase filter order when you need stronger smoothing, but remember that the displayed value will respond more slowly. Matching time constant, order, and tolerance can improve both confidence and throughput.
It is the low-pass filter time scale at the output of a lock-in amplifier. It sets how quickly the displayed signal responds after demodulation.
No. Corner frequency is a response marker. Equivalent noise bandwidth measures the bandwidth that passes the same total noise power.
More poles smooth the output more strongly. That improves noise rejection, but it also lengthens the time required to reach a chosen accuracy after a step.
Use it when your reference frequency is central to the experiment. It shows how many modulation cycles are averaged inside one filter time constant.
Common choices are 1% or 0.1%. Use tighter tolerance when final value accuracy matters more than update speed.
No. ENBW comes from time constant and filter order. Reference frequency only changes how many carrier cycles fit inside that averaging window.
Yes. Compare settling time with your dwell time per point. If dwell time is shorter, readings may lag the true value.
No. Very long values reduce noise, but they can hide real changes and make measurements unnecessarily slow.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.