What this Linkwitz-Riley calculator does
This page calculates practical values for a Linkwitz-Riley crossover, one of the most widely used crossover alignments in speaker design and DSP audio processing. It gives you:
- Digital biquad coefficients (
b0, b1, b2, a1, a2) for low-pass and high-pass filters - Support for LR2 (12 dB/oct) and LR4 (24 dB/oct)
- Analog component estimates for equal-component Sallen-Key stages
- Quick sanity checks like attenuation near crossover
Why Linkwitz-Riley filters are popular
A Linkwitz-Riley crossover is designed so the low-pass and high-pass sections sum flat at the crossover region when drivers are in phase and properly time-aligned. In practical speaker systems, this makes it easier to get smooth handoff between woofer and tweeter or between subwoofer and mains.
The key behavior is that each branch is about -6 dB at crossover, so the two outputs combine to about 0 dB overall (in ideal conditions).
LR2 vs LR4
- LR2: 2nd order overall, 12 dB/oct slope, gentler rolloff
- LR4: 4th order overall, 24 dB/oct slope, steeper rolloff and common in active crossovers
Core formulas
For analog equal-component sections, the natural frequency relation is:
fc = 1 / (2πRC)
So if you choose capacitor value C, resistor value is:
R = 1 / (2πfcC)
For the equal-component Sallen-Key approximation used here:
- LR2 section target uses approximately Q = 0.5 (gain near unity)
- LR4 uses two Butterworth-like stages with Q ≈ 0.707 each (non-inverting gain K ≈ 1.586)
How to use this calculator
- Select LR2 or LR4.
- Enter your target crossover frequency (for example, 1800 Hz or 2500 Hz).
- Enter DSP sample rate (44.1 kHz, 48 kHz, 96 kHz, etc.).
- Optionally enter a capacitor value in nF for analog stage estimates.
- Click Calculate and copy the coefficients into your DSP or plugin code.
Practical engineering notes
1) Real drivers are not ideal
Even perfect filter math will not guarantee perfect acoustic summation. Driver response, offset, baffle diffraction, and phase behavior all matter.
2) Measure after designing
Use REW, ARTA, or your preferred measurement platform to verify acoustic phase and final crossover behavior.
3) Keep enough headroom in DSP
When cascading sections (especially LR4 or higher), internal signal peaks can increase. Manage gain staging to avoid clipping.
4) Passive vs active
This tool is primarily aimed at active analog/DSP workflows. Passive speaker crossovers need full impedance-aware design, not just ideal textbook formulas.
Quick example
For an LR4 crossover at 2000 Hz and 48 kHz sample rate, this calculator will produce one low-pass biquad and one high-pass biquad section, each intended to be cascaded twice. If you choose 10 nF capacitors for an analog build, it also estimates the corresponding resistor value per stage.