Build smarter filters with clear coefficients and insight. Review cutoff behavior, damping, and transfer terms. Create reliable engineering estimates with graphs, tables, and exports.
This calculator supports common analog and digital engineering filters. It reports raw coefficients, normalized coefficients, cutoff metrics, gain, phase, and a response plot.
| Filter | Transfer Function | Important Coefficient Relations |
|---|---|---|
| RC Low-Pass | H(s) = 1 / (RCs + 1) | τ = RC, ωc = 1/RC, fc = 1/(2πRC) |
| RC High-Pass | H(s) = RCs / (RCs + 1) | τ = RC, normalized form: s / (s + ωc) |
| RL Low-Pass | H(s) = R / (Ls + R) | τ = L/R, ωc = R/L, fc = R/(2πL) |
| RL High-Pass | H(s) = Ls / (Ls + R) | τ = L/R, normalized form: s / (s + ωc) |
| RLC Band-Pass | H(s) = ((R/L)s) / (s² + (R/L)s + 1/(LC)) | ω0 = 1/√(LC), Q = ω0L/R, BW = (R/L)/(2π) |
| RLC Notch | H(s) = (s² + 1/(LC)) / (s² + (R/L)s + 1/(LC)) | ω0 = 1/√(LC), Q = ω0L/R |
| EMA Digital | H(z) = α / (1 - (1-α)z⁻¹) | α = 1 - e^(-2πfc/fs), y[n] = αx[n] + (1-α)y[n-1] |
Magnitude is computed from the complex response at each frequency. Gain is converted using 20log10(|H|), and phase is measured in degrees.
| Example | Inputs | Key Output |
|---|---|---|
| RC Low-Pass | R = 1 kΩ, C = 0.1 µF | fc ≈ 1591.549431 Hz, τ = 1.000000e-4 s |
| RC High-Pass | R = 2.2 kΩ, C = 47 nF | fc ≈ 1539.216084 Hz, τ ≈ 1.034000e-4 s |
| RL Low-Pass | R = 100 Ω, L = 10 mH | fc ≈ 1591.549431 Hz, τ = 1.000000e-4 s |
| RLC Band-Pass | R = 50 Ω, L = 10 mH, C = 1 µF | f0 ≈ 1591.549431 Hz, Q = 2.000000 |
| RLC Notch | R = 50 Ω, L = 10 mH, C = 1 µF | Notch ≈ 1591.549431 Hz, BW ≈ 795.774715 Hz |
| EMA Digital | fs = 1000 Hz, fc = 25 Hz | α ≈ 0.145364, feedback ≈ 0.854636 |
A filter coefficient is a numerical value inside the transfer function or difference equation. It controls cutoff, damping, resonance, smoothing, or gain behavior in analog and digital filters.
Raw coefficients reflect the exact equation from component values. Normalized coefficients make comparison easier, simplify design review, and help when implementing transfer functions in software or simulation tools.
Use RC filters in many voltage-signal applications because they are simple and compact. Use RL filters when inductive behavior is required or when the circuit environment already includes coils.
Q is the quality factor. It measures selectivity and damping. Higher Q means a narrower passband or notch region, stronger resonance, and greater sensitivity around the center frequency.
The EMA filter is discrete-time. Its coefficient α depends on how often new samples arrive. Without the sample rate, the same cutoff frequency would produce different smoothing behavior.
It shows the computed magnitude, gain in decibels, and phase at one chosen frequency. This is useful when checking attenuation or phase shift at a critical operating point.
Filters often span several decades of frequency. A logarithmic axis reveals low-frequency and high-frequency behavior clearly, making cutoff transitions and resonance effects easier to inspect.
Yes, usually. The analog forms are suitable for transfer-function review, while the EMA form maps directly to code. Always confirm sign conventions and coefficient ordering in your target tool.
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.