Active Filter Calculator
Filter Type
Response
2
Hz
Topology
V/V
Stage Count1
Deviation at Cutoff0.00 dB
Bode Plot (Magnitude)
Component Values per Stage
| Stage | R1 (exact) | R1 (E96) | R2 (exact) | R2 (E96) | C1 | C2 |
|---|---|---|---|---|---|---|
| 1 | 2.25 kΩ | 2.26 kΩ | 1.13 kΩ | 1.13 kΩ | 100 nF | 100 nF |
Active filters use op-amps with resistors and capacitors to shape a frequency response without bulky inductors. This designer takes a target response (Butterworth, Chebyshev, or Bessel), an order, and a cutoff frequency, computes the pole locations, and synthesizes each second-order stage as a Sallen-Key or multiple-feedback (MFB) circuit, snapping the resistor values to E96 and E24 standard parts.
Formula
R2 = Q / (2π·f·C), R1 = 1 / (2π·f·C·Q·K) (Sallen-Key, C1 = C2 = C)
- f
- Stage natural frequency = normalized pole frequency × cutoff
- Q
- Stage quality factor from the pole location
- C
- Chosen stage capacitor (1 nF to 1 µF depending on cutoff)
- K
- Passband gain of the stage
- R1, R2
- Computed resistors, then snapped to E96/E24 standard values
How it works
- Choose the response type, filter order, cutoff frequency, topology (Sallen-Key or MFB), passband gain, and—for Chebyshev—the allowable ripple in dB.
- The engine places the normalized poles (evenly spaced on the unit circle for Butterworth, on an ellipse for Chebyshev, from a lookup table for Bessel) and groups them into one stage per conjugate pole pair, each with its own natural frequency and quality factor Q.
- For each stage it picks a convenient capacitor for the frequency band, solves for R1 and R2 from the Q and stage frequency, snaps them to the nearest E96 and E24 values, and generates Bode magnitude/phase data across four decades around the cutoff.
Worked example
A 2nd-order Butterworth low-pass filter at 1 kHz, Sallen-Key topology, unity gain.
- A 2nd-order filter has one conjugate pole pair, so it is realized in a single stage with Q ≈ 0.707.
- For a 1 kHz cutoff the engine selects C = 100 nF (the 100 Hz–1 kHz band).
- R2 = Q / (2π·f·C) = 0.707 / (2π·1000·100e-9) ≈ 1125 Ω; R1 = R2 / Q² relation gives ≈ 2251 Ω.
- Snapping to E96: R1 ≈ 2.26 kΩ, R2 ≈ 1.13 kΩ.
One stage: R1 ≈ 2251 Ω (E96 2.26 kΩ), R2 ≈ 1125 Ω (E96 1.13 kΩ), C1 = C2 = 100 nF, gain 1, with a flat Butterworth −3 dB point at 1 kHz.
Frequently asked questions
- What is the difference between Butterworth, Chebyshev, and Bessel responses?
- Butterworth gives the flattest passband with no ripple. Chebyshev trades passband ripple for a steeper roll-off near cutoff. Bessel sacrifices roll-off sharpness to preserve a linear phase (constant group delay), which best maintains the shape of pulse and audio waveforms.
- When should I use Sallen-Key versus MFB topology?
- Sallen-Key is a non-inverting stage that is simple and stable for low to moderate Q and unity or modest gain. MFB (multiple feedback) inverts the signal and generally offers better high-Q performance and lower sensitivity to component tolerances, at the cost of an inverted output.
- Why are component values snapped to E96 and E24?
- Resistors are sold in standardized decade series. E24 (5% parts, 24 values per decade) and E96 (1% parts, 96 values per decade) are the most common, so the tool rounds the ideal calculated resistors to the nearest stock value you can actually buy.
- Why does a higher-order filter use multiple stages?
- Each Sallen-Key or MFB stage realizes one second-order (or first-order) section. An order-4 filter therefore needs two cascaded stages, an order-6 needs three, and so on, with each stage tuned to its own pole-pair frequency and Q.