What is the difference between Butterworth, Bessel, and Chebyshev filters?

Butterworth (Q = 0.707) delivers the flattest possible passband with no amplitude ripple. Bessel (Q = 0.577) optimizes linear phase response with minimal group delay distortion and zero transient ringing. Chebyshev (Q > 1.0) achieves the sharpest initial cutoff rolloff at the expense of ripple in the passband.

Why does my real filter stop attenuating at very high frequencies?

At high frequencies (e.g. >1 MHz), real op-amps have nonzero output impedance and finite GBW. Signals can couple directly across capacitor C1 to the output without being attenuated. Placing a small passive RC pole after the op-amp suppresses high-frequency stopband leakage.

What type of capacitors should I use in active audio filters?

Always use Film capacitors (Polypropylene or Polyester) or C0G/NP0 ceramic capacitors. Avoid high-dielectric ceramics (X7R, X5R, Y5V) because their capacitance changes drastically with applied voltage, generating noticeable total harmonic distortion (THD).

Free Sallen-Key Active Low-Pass Filter Calculator

🎛️ Filter Parameters & Alignment

Filter Alignment / Polynomial Type

Target Cutoff Freq (-3dB fc in Hz) e.g. 1000 Hz = 1.0 kHz

Passband DC Gain (V/V)

Capacitor C1 (Base Value in nF) Standard film/ceramic (10 nF = 0.01 µF)

Op-Amp GBW (MHz) TL072 ~3MHz, OPA1612 ~40MHz, NE5532 ~10MHz

📊 Synthesized Component Values

Resistor R1 & R2 11.25 kΩ Equal-R topology

Capacitor C2 Value 5.00 nF C2 = C1 / (4 · Q²)

Actual Cutoff Frequency: 1,000 Hz

Rolloff Attenuation Slope: -40 dB/decade (-12 dB/octave)

Quality Factor (Q): 0.707 (Butterworth)

Min Recommended Op-Amp GBW: ≥ 0.1 MHz (100x margin)

✅ Op-Amp Margin: Selected 10 MHz GBW provides 100x headroom above cutoff. No phase distortion.

Recommended Tools & Equipment

Tested hardware and components for high reliability

100% Free Tool Zero Sign-Up

Principles of Sallen-Key 2nd-Order Active Filters

A second-order active low-pass filter provides a steep -40 dB/decade (-12 dB/octave) attenuation slope above the cutoff frequency (f_c). The classic Sallen-Key architecture uses an operational amplifier configured as a non-inverting buffer or gain stage with positive feedback through capacitor (C_1).

Equal-Resistor Filter Synthesis Formulas

In the popular equal-resistor design ((R_1 = R_2 = R)) with unity gain ((K = 1)), the natural resonant angular frequency (omega_0) and Quality Factor (Q) are defined by:

ω0 = 2 × π × fc = 1 / (R × √(C1 × C2))
Q = 0.5 × √(C1 / C2) → C2 = C1 / (4 × Q²)

This allows selecting a convenient off-the-shelf value for (C_1), calculating (C_2) to satisfy the desired (Q), and then calculating (R = rac{1}{2pi f_c sqrt{C_1 C_2}}).

Why Op-Amp Gain-Bandwidth Product (GBW) Matters

An ideal op-amp has infinite bandwidth. In real hardware, finite Gain-Bandwidth Product (GBW) causes open-loop gain to collapse at high frequencies, degrading filter attenuation and causing stopband feedthrough. As a rule of thumb, select an op-amp with GBW ≥ 50 to 100 × (Gain × fc × Q).