What a crossover does
A two-way loudspeaker splits the music between a woofer, which handles the bass and midrange, and a tweeter, which handles the treble. The passive crossover is the small network of inductors and capacitors between the amplifier and the drivers that makes the split. An inductor in series passes low frequencies and blocks high ones; a capacitor in series does the opposite.
The formulas
For a crossover frequency f in hertz and a driver impedance R in ohms, the component values are a constant times R ÷ f for inductors, or a constant ÷ (R × f) for capacitors:
| Filter type | Series inductor (woofer) | Series capacitor (tweeter) | Parallel parts |
|---|---|---|---|
| 1st order, 6 dB/octave | 0.1592 × R ÷ f | 0.1592 ÷ (R × f) | none |
| 2nd order Linkwitz-Riley | 0.3183 × R ÷ f | 0.0796 ÷ (R × f) | same constants, swapped |
| 2nd order Butterworth | 0.2251 × R ÷ f | 0.1125 ÷ (R × f) | same constants, swapped |
The calculator converts the results to millihenries and microfarads. In a second-order filter, the woofer also gets a capacitor across it and the tweeter an inductor across it.
Example
At 2,500 Hz with two 8 Ω drivers and a Linkwitz-Riley filter, the woofer needs a 1.02 mH series inductor and a 3.98 µF parallel capacitor; the tweeter gets a 3.98 µF series capacitor and a 1.02 mH parallel inductor. A Linkwitz-Riley filter is −6 dB at the crossover on each side, so the two outputs add up to a flat response, provided the tweeter is wired in reverse polarity.
Choosing parts
- Use the nearest standard value; a few percent off moves the crossover point only slightly.
- Prefer air-core inductors for the woofer side if the budget allows, and film capacitors rather than electrolytics on the tweeter.
- A tweeter should be crossed at least an octave above its resonance frequency (Fs) to protect it.
Limits of the textbook formulas
Real drivers are not resistors: their impedance rises with frequency because of the voice-coil inductance, and peaks at resonance. Builders often add a Zobel network across the woofer to flatten its impedance, and an L-pad to lower a tweeter that is more sensitive than the woofer. The values from this calculator are an excellent starting point, but a measured response with a microphone is what tells you whether the crossover sums correctly in your cabinet.