Hong Life CalculatorsUnderstanding the passive speaker crossover calculator — concept and principle
A two-way loudspeaker sends low frequencies to the woofer and high frequencies to the tweeter. A passive crossover does this with capacitors and inductors placed between the amplifier and the drivers. This calculator gives starting component values for first-order (6 dB/octave) and second-order Butterworth (12 dB/octave) filters, from the crossover frequency and the driver's nominal impedance.
How it is calculated
With crossover frequency f_c in Hz and load impedance Z in ohms:
- 1st order: C = 1 / (2π f_c Z) for the tweeter (series capacitor), L = Z / (2π f_c) for the woofer (series inductor).
- 2nd order Butterworth: C = 1 / (2√2 π f_c Z) and L = √2 Z / (2π f_c). Each driver gets one series and one shunt element.
Capacitance is shown in microfarads (µF) and inductance in millihenries (mH).
The principle
A capacitor's reactance, 1/(2πfC), falls as frequency rises, so in series it blocks bass; an inductor's reactance, 2πfL, rises with frequency, so it blocks treble. The crossover frequency is where the reactance equals the load resistance, giving −3 dB. Two reactive parts make a second-order filter whose slope is 12 dB per octave; the √2 factors set its damping to the Butterworth value (Q ≈ 0.707), the flattest passband without a peak. The formulas treat the driver as a pure resistor equal to Z.
Worked example
- Inputs: f_c = 2,500 Hz, Z = 8 Ω.
- 1st-order C: 1 / (2π × 2,500 × 8) = 7.958 × 10⁻⁶ F = 7.958 µF.
- 1st-order L: 8 / (2π × 2,500) = 0.000509 H = 0.5093 mH.
- 2nd-order C: 1 / (2√2 π × 2,500 × 8) = 5.627 µF.
- 2nd-order L: √2 × 8 / (2π × 2,500) = 0.7203 mH.
| Crossover frequency (Hz) | 1st order: capacitor (µF) |
|---|---|
| 625 | 31.83098862 |
| 1,250 | 15.91549431 |
| 1,875 | 10.61032954 |
| 2,500 | 7.957747155 |
| 3,125 | 6.366197724 |
| 3,750 | 5.30516477 |
| 5,000 | 3.978873577 |
How to read the result
Lower crossover frequencies or lower impedances need larger parts: halving Z from 8 Ω to 4 Ω doubles C and halves L. Choose the nearest standard value (for example 8.2 µF, 0.5 mH) and check by measurement. First-order networks are simple and sum flat in amplitude, but tweeters receive more low-frequency energy. Second-order Butterworth sections protect drivers better; they are usually wired with the tweeter in reversed polarity, and the summed response then shows a mild rise of about 3 dB around f_c.
Common mistakes
- Using the nominal impedance when the driver's real impedance at f_c is quite different, especially near a woofer's voice-coil rise.
- Swapping roles: the series capacitor feeds the tweeter, the series inductor feeds the woofer.
- Using polarised electrolytic capacitors in the signal path.
Frequently asked questions
Should I use 1st or 2nd order?
Second order is the common starting point for two-way systems because it limits tweeter excursion; first order suits drivers with wide, smooth overlapping ranges.
What is a Linkwitz–Riley crossover?
A second-order Linkwitz–Riley crossover uses Q = 0.5 so each output is −6 dB at f_c and the sum is flat; its component values differ from Butterworth.
Sources: R. Small, "Constant-Voltage Crossover Network Design," Journal of the Audio Engineering Society, 1971 · V. Dickason, The Loudspeaker Design Cookbook