Lock-In Time Constant Calculator

Case	Input Type	Given Values	Calculated τ	Cutoff Frequency	95% Settling Time
Example 1	R and C	10 kΩ, 10 µF	0.100000 s	1.591549 Hz	0.299573 s
Example 2	Cutoff	25 Hz	0.006366 s	25.000000 Hz	0.019099 s
Example 3	Approx. ENBW	5 Hz	0.050000 s	3.183099 Hz	0.149787 s

Formula Used

1) RC Time Constant

τ = R × C

Use this when you know the effective resistance and capacitance of the low-pass stage.

2) From Cutoff Frequency

τ = 1 / (2πf_c)

This links the first-order low-pass cutoff frequency to the time constant.

3) Approximate Equivalent Noise Bandwidth

ENBW ≈ 1 / (4τ)

This approximation is useful for quick first-order filter estimates in lock-in style measurements.

4) Step Response

V(t) = V_final(1 - e^-t/τ)

This predicts how quickly the filtered output approaches its final value after a step change.

5) Attenuation Magnitude

|H(f)| = 1 / √(1 + (2πfτ)²)

This shows how strongly the first-order low-pass stage reduces signal components at a chosen frequency.

Important note: some instruments use higher-order filters or vendor-specific definitions. The ENBW relation here is a practical first-order approximation.

How to Use This Calculator

Select the calculation mode that matches your known measurement data.
Enter the values with the correct units for resistance, capacitance, cutoff, ENBW, or settling target.
Set an observation time to estimate how close the output gets to its final value.
Enter a reference frequency to inspect attenuation at that frequency.
Press Calculate to show the result above the form.
Review the summary table, settling times, and Plotly response graph.
Use the CSV or PDF buttons to export the displayed results.

FAQs

1) What does the lock-in time constant represent?

It describes how fast the low-pass output responds after a change. A larger time constant smooths noise more strongly, but it also slows the output and increases settling time.

2) Why does a larger time constant reduce noise?

A larger time constant narrows the effective low-pass bandwidth. Narrower bandwidth rejects more rapid fluctuations, so random noise is reduced, though response speed becomes slower.

3) How is cutoff frequency related to time constant?

For a first-order low-pass response, cutoff frequency and time constant are linked by τ = 1 / (2πf_c). Increasing cutoff makes the system faster and decreases τ.

4) What is settling time in this calculator?

Settling time is the time needed for the response to reach a chosen percentage of the final value. Common checkpoints are 90%, 95%, and 99%.

5) Why is ENBW shown as approximate?

The exact relationship depends on filter order and instrument design. This page uses a first-order approximation, which is good for quick estimates and teaching purposes.

6) What does the attenuation value mean?

It shows how much a sinusoidal component at the chosen reference frequency is reduced by the low-pass stage. Lower magnitude or more negative dB means stronger attenuation.

7) Can I use this for general RC filters?

Yes. The underlying equations are standard first-order low-pass relations, so the calculator also works for ordinary RC timing and filtering estimates.

8) What graph is displayed after calculation?

The graph plots the step response from zero to five time constants. It helps you see how fast the output approaches the final amplitude you entered.