Formula
A passive crossover sits between the amplifier and the drivers and splits the band with inductors and capacitors. This audio crossover calculator assumes zero source impedance and a purely resistive load equal to each driver’s nominal impedance. Real amplifiers are close to that. Real drivers are not. The numbers are a starting point to verify by measurement or simulation.
L (H) = norm × R / (2πf)
C (F) = norm / (2πf R)
Slopes: 6, 12, 18, and 24 dB per octave
Order is the slope. 1st order is 6 dB/octave, one series part. 2nd order is 12 dB/octave: a series part and a shunt part. 3rd order is 18 dB/octave, three parts, with the last series part next to the driver. 4th order is 24 dB/octave, two series parts and two shunt parts. A steeper slope keeps each driver in a narrower band and uses more parts. A shallow slope is simple and makes the drivers share a wide overlap. Component order in the drawing is from the amplifier toward the driver.
Butterworth, Linkwitz-Riley, and Bessel
The shapes come from normalized singly-terminated ladder prototypes. A 1st-order Butterworth section uses a norm of 1, so L = R / (2πf) and C = 1 / (2πf R), about 0.1592 R/f and 0.1592 / (R f). Both drivers stay in normal polarity.
2nd-order Butterworth uses L = √2 and C = 1/√2, about 0.2251 R/f and 0.1125 / (R f). Q is 0.707. Each section is about −3 dB at the crossover, and the sum has a bump of about +3 dB. Linkwitz-Riley 2nd order, the default here, uses L = 2 and C = 0.5, about 0.3183 R/f and 0.0796 / (R f). Q is 0.5. Each section is about −6 dB at the crossover, and the sum is flat when the tweeter is reversed. Bessel 2nd order uses L = √3 and C = 1/√3, about 0.2757 R/f and 0.0919 / (R f). Some tables print 0.0912 for the capacitor. This page uses the exact prototype. The passband delay is flatter than Butterworth. All three 2nd-order 2-way networks reverse the tweeter: connect tweeter + to amp −.
The low-pass is series L1, then shunt C1. The high-pass is the dual: series C1, then shunt L1. The inductor and the capacitor have the same values on both sides when the impedances match.
3rd-order Butterworth uses 3/2, 4/3, and 1/2 on the low-pass: series L1, shunt C1, series L2. The high-pass is the dual: series C1, shunt L1, series C2, and C2 sits next to the tweeter. The summed magnitude is flat. Polarity can go either way, and the phase is not the same if you flip a driver.
4th-order Linkwitz-Riley is two cascaded Butterworth 2nd-order sections. The low-pass prototype, amplifier toward the driver, is L 1.8856, C 1.5910, L 0.9428, C 0.35355. The high-pass uses the reciprocals, so the first series capacitor is the reciprocal of 1.8856. Both drivers stay in normal polarity. The sections are about −6 dB at the crossover and the sum is flat.
Choosing a frequency, and 2-way versus 3-way
Start from the tweeter. Its maker prints a minimum crossover, and a safe floor is at least an octave above the tweeter’s free-air resonance Fs. A woofer wants to be crossed before it beams, which narrows the coverage as the wavelength gets short compared with the cone, and before breakup peaks show up. A 2-way speaker hands the band over once. A 3-way speaker adds a midrange: low-pass the woofer at the low frequency, high-pass and low-pass the mid, and high-pass the tweeter at the high frequency. When the high frequency is less than three octaves above the low one, those two midrange sections interact and the real response moves away from this textbook ladder. A 4-way crossover is the same ladder at one more frequency. This page stops at 3-way, because the mid band is where the sections interact.
Drivers are not resistors
Nominal impedance is a name, often 4, 6, or 8 ohms. The voice coil’s inductance makes the impedance rise with frequency, so a network designed for a resistor ends up at a different frequency on a real driver. A Zobel across the terminals, Rz = 1.25 × Re in series with Cz = Le / Rz², flattens that rise so the crossover sees something closer to a resistor. It does not remove breakup. Measure, or simulate with the driver’s impedance curve, before you buy the parts. An L-pad on a tweeter is a series resistor Rs = R (1 − a) and a parallel resistor Rp = R a / (1 − a), with a = 10^(−A/20). It cuts level without changing the impedance the crossover sees, as long as the pad is designed for that impedance. Rate those resistors for the power they dissipate. 10 W or more is typical guidance for a home tweeter. Follow the driver and amplifier ratings.
Capacitors, inductors, and the active alternative
Film capacitors are the usual choice in a speaker crossover. A non-polar electrolytic works and costs less. It is larger for the value, and it is the part people replace first. Inductors are air-core or iron-core. Air-core coils do not saturate. They get big, and the wire’s DCR is in series with the driver. Iron-core coils are smaller for the same millihenries and they can saturate on a peak. Keep DCR in the design: it pads the driver and, on a subwoofer, it changes the alignment. Stock capacitors follow the E12 series, 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, and 8.2 times a decade. Paralleling two capacitors gets closer than one of those values. Inductors here round to the nearest 0.05 mH. Values under 0.1 mH are also shown in microhenries.
An active or DSP crossover does this split before the amplifiers, so each driver has its own amp and the passive parts disappear. Car-audio head units often include a high-pass and a low-pass for the same reason. A passive low-pass in front of a subwoofer is still this page’s low-pass mode. Coils above about 4 mH get large and lossy, which is why that job is usually active. The box those coils would feed is the subwoofer box calculator. The seat and the screen in the room are the TV viewing distance calculator and the projector throw distance calculator.
Nothing here is an electrical code, a power-system design, or a life-safety instruction. Speaker wiring is low voltage. The component values assume a resistive load at the nominal impedance. Resistors and capacitors still have to be rated for the amplifier’s power and voltage.
Worked examples
1st order, 8 Ω, 2,500 Hz. Low-pass series L1: 0.51 mH · stock 0.50 mH. High-pass series C1: 7.96 µF · nearest E12 8.2 µF.
1st order, 4 Ω, 3,000 Hz. Low-pass series L1: 0.21 mH · stock 0.20 mH. High-pass series C1: 13.26 µF · nearest E12 12 µF.
2nd order Butterworth, 8 Ω, 2,500 Hz. Low-pass series L1: 0.72 mH · stock 0.70 mH; shunt C1: 5.63 µF · nearest E12 5.6 µF. High-pass series C1: 5.63 µF · nearest E12 5.6 µF; shunt L1: 0.72 mH · stock 0.70 mH.
2nd order Linkwitz-Riley, 8 Ω, 2,500 Hz. Low-pass series L1: 1.02 mH · stock 1.00 mH; shunt C1: 3.98 µF · nearest E12 3.9 µF. High-pass series C1: 3.98 µF · nearest E12 3.9 µF; shunt L1: 1.02 mH · stock 1.00 mH. Tweeter reversed.
2nd order Bessel, 8 Ω, 2,500 Hz. Low-pass series L1: 0.88 mH · stock 0.90 mH; shunt C1: 4.59 µF · nearest E12 4.7 µF. High-pass series C1: 4.59 µF · nearest E12 4.7 µF; shunt L1: 0.88 mH · stock 0.90 mH.
2nd order Linkwitz-Riley, 4 Ω, 3,000 Hz. Low-pass series L1: 0.42 mH · stock 0.40 mH; shunt C1: 6.63 µF · nearest E12 6.8 µF. High-pass series C1: 6.63 µF · nearest E12 6.8 µF; shunt L1: 0.42 mH · stock 0.40 mH.
3rd order Butterworth, 8 Ω, 2,500 Hz. Low-pass series L1: 0.76 mH · stock 0.75 mH; shunt C1: 10.61 µF · nearest E12 10 µF; series L2: 0.25 mH · stock 0.25 mH. High-pass series C1: 5.31 µF · nearest E12 5.6 µF; shunt L1: 0.38 mH · stock 0.40 mH; series C2: 15.92 µF · nearest E12 15 µF.
4th order Linkwitz-Riley, 8 Ω, 2,500 Hz. Low-pass series L1: 0.96 mH · stock 0.95 mH; shunt C1: 12.66 µF · nearest E12 12 µF; series L2: 0.48 mH · stock 0.50 mH; shunt C2: 2.81 µF · nearest E12 2.7 µF. High-pass series C1: 4.22 µF · nearest E12 3.9 µF; shunt L1: 0.32 mH · stock 0.30 mH; series C2: 8.44 µF · nearest E12 8.2 µF; shunt L2: 1.44 mH · stock 1.45 mH.
4th order Linkwitz-Riley, 4 Ω, 3,000 Hz. Low-pass series L1: 0.40 mH · stock 0.40 mH; shunt C1: 21.10 µF · nearest E12 22 µF; series L2: 0.20 mH · stock 0.20 mH; shunt C2: 4.69 µF · nearest E12 4.7 µF. High-pass series C1: 7.03 µF · nearest E12 6.8 µF; shunt L1: 0.13 mH · stock 0.15 mH; series C2: 14.07 µF · nearest E12 15 µF; shunt L2: 0.60 mH · stock 0.60 mH.
3-way Linkwitz-Riley, 500 Hz and 4,000 Hz. Woofer low-pass at 500 Hz, 8 Ω. series L1: 5.09 mH · stock 5.10 mH. shunt C1: 19.89 µF · nearest E12 18 µF. Midrange high-pass at 500 Hz, 8 Ω. series C1: 19.89 µF · nearest E12 18 µF. shunt L1: 5.09 mH · stock 5.10 mH. Midrange low-pass at 4,000 Hz, 8 Ω. series L1: 0.64 mH · stock 0.65 mH. shunt C1: 2.49 µF · nearest E12 2.7 µF. Tweeter high-pass at 4,000 Hz, 6 Ω. series C1: 3.32 µF · nearest E12 3.3 µF. shunt L1: 0.48 mH · stock 0.50 mH. Ratio 8, so there is no spacing warning. The 5.09 mH coil is past 4 mH.
Zobel, Re 6.4 Ω, Le 0.5 mH. Rz 8.0 Ω, Cz 7.81 µF.
L-pad, 8 Ω at 4 dB. Rs 2.95 Ω, Rp 13.68 Ω. 6 Ω at 3 dB. Rs 1.75 Ω, Rp 14.54 Ω.
Nearest E12. 5.63 µF is 5.6 µF. 7.96 µF is 8.2 µF.
Reference
The checks for this page. Inductors are millihenries. Capacitors are microfarads. Low-pass is listed before high-pass.
| Case | Result |
|---|---|
| 1st, 8 Ω, 2,500 Hz | L 0.51 · C 7.96 |
| 1st, 4 Ω, 3,000 Hz | L 0.21 · C 13.26 |
| Butterworth 2, 8 Ω, 2,500 Hz | L 0.72 · C 5.63 |
| LR2, 8 Ω, 2,500 Hz | L 1.02 · C 3.98 |
| Bessel 2, 8 Ω, 2,500 Hz | L 0.88 · C 4.59 |
| LR2, 4 Ω, 3,000 Hz | L 0.42 · C 6.63 |
| Butterworth 3, 8 Ω, 2,500 Hz | LP 0.76, 10.61, 0.25 · HP 5.31, 0.38, 15.92 |
| LR4, 8 Ω, 2,500 Hz | LP 0.96, 12.66, 0.48, 2.81 · HP 4.22, 0.32, 8.44, 1.44 |
| LR4, 4 Ω, 3,000 Hz | LP 0.40, 21.10, 0.20, 4.69 · HP 7.03, 0.13, 14.07, 0.60 |
| 3-way LR2, 500 / 4,000 Hz | Woofer 5.09, 19.89 · mid HP 19.89, 5.09 · mid LP 0.64, 2.49 · tweeter 6 Ω 3.32, 0.48 |
| Zobel, Re 6.4, Le 0.5 mH | Rz 8.0 Ω · Cz 7.81 µF |
| L-pad | 8 Ω, 4 dB: 2.95 and 13.68 · 6 Ω, 3 dB: 1.75 and 14.54 |
Questions
What crossover frequency should I use for a 2-way speaker?
The drivers set it. A 2-way crossover often lands somewhere from about 1.5 kHz to 3.5 kHz. Keep the tweeter at least an octave above its resonance Fs, and at or above the minimum the maker prints. Cross the woofer before it beams or breaks up. The default on this page, Linkwitz-Riley at 2,500 Hz and 8 ohms, is a series 1.02 mH and a shunt 3.98 µF on the woofer, and the same parts swapped on the tweeter. That is a starting point for a crossover calculator, not a recommendation for a particular driver.
What is the difference between Butterworth and Linkwitz-Riley?
A 2nd-order Butterworth section (Q 0.707) is about −3 dB at the crossover and the two drivers sum about +3 dB where they overlap. Linkwitz-Riley 2nd order (Q 0.5) is two cascaded 1st-order sections, about −6 dB at the crossover, and the sum is flat when the tweeter is reversed. LR4 is two cascaded Butterworth 2nd-order sections, 24 dB per octave, and it sums flat with normal polarity. Bessel trades some of that shape for flatter delay. At 8 ohms and 2,500 Hz, Butterworth is 0.72 mH and 5.63 µF, Linkwitz-Riley is 1.02 mH and 3.98 µF, and Bessel is 0.88 mH and 4.59 µF.
Why reverse tweeter polarity?
A 2nd-order low-pass and high-pass each move through 180° across the crossover, so the drivers oppose each other where they overlap. Connect tweeter + to amp − and they add again. That reversal is the usual choice for Butterworth, Linkwitz-Riley, and Bessel 2nd-order networks. On a 2nd-order 3-way, reverse the midrange instead: the woofer and the tweeter each have one 2nd-order section, and the mid has two. 1st order leaves both drivers normal. So does a 4th-order Linkwitz-Riley. 3rd-order Butterworth can go either way, and the two choices do not have the same phase.
How do I calculate a 3-way crossover?
Set a low frequency for the woofer-to-mid handoff and a high frequency for the mid-to-tweeter handoff. The woofer is a low-pass at the low frequency. The midrange is a high-pass at the low frequency cascaded with a low-pass at the high frequency. The tweeter is a high-pass at the high frequency. Each section uses that driver’s impedance. A Linkwitz-Riley 3-way with an 8 ohm woofer and mid, a 6 ohm tweeter, 500 Hz and 4,000 Hz: woofer 5.09 mH and 19.89 µF; mid high-pass the same parts swapped; mid low-pass 0.64 mH and 2.49 µF; tweeter 3.32 µF and 0.48 mH. Keep the high frequency at least three octaves above the low one, or the mid’s two sections interact.
What capacitor blocks bass from a tweeter?
A single series capacitor is a 1st-order high-pass, 6 dB per octave. Capacitance is 1 / (2π f R). At 8 ohms and 2,500 Hz that is 7.96 µF, and the nearest E12 value is 8.2 µF. At 4 ohms and 3,000 Hz it is 13.26 µF. Use high-pass only on this page for that one part. The slope is shallow, so the tweeter still sees energy below the corner. Film capacitors are the usual choice. A non-polar electrolytic is a budget substitute. The capacitor has to be rated for the amplifier voltage.
Do I need a Zobel network?
Only if the driver’s impedance rise is moving the crossover. Voice-coil inductance makes the impedance climb with frequency, so the network stops seeing the nominal ohms. A Zobel across the driver is Rz = 1.25 × Re in series with Cz = Le / Rz², with Le in henries. Re 6.4 ohms and Le 0.5 mH give Rz 8.0 ohms and Cz 7.81 µF. It flattens that rise. It does not fix cone breakup. Use Re and Le from the datasheet, then check the result with a measurement.
Can I use a passive crossover for a subwoofer?
Yes. Low-pass only on this page is the coil and capacitor in front of the sub. The parts get large. A coil above about 4 mH is bulky and lossy, and its DCR changes the box alignment. An active or DSP low-pass, including the filters in a lot of car head units, is usually the better tool. The enclosure itself is the subwoofer box calculator.
Sources
- Siegfried H. Linkwitz and Riley, “Active Crossover Networks for Noncoincident Drivers,” Journal of the Audio Engineering Society, 1976. Linkwitz-Riley targets a flat summed magnitude, with each section at −6 dB at the crossover.
- Butterworth and Bessel ladder prototypes, as tabulated for singly-terminated filters. Anatol I. Zverev, Handbook of Filter Synthesis, is the usual reference for those normalized values.
- Vance Dickason, Loudspeaker Design Cookbook. Crossover slopes, Zobel compensation, and L-pad attenuation in the form used by speaker builders. The result still depends on the drivers.