Chris Collins

Tools · electronics

Speaker crossover designer

Design a passive 2-way or 3-way loudspeaker crossover — Butterworth, Linkwitz–Riley, Bessel or Chebychev, 1st to 4th order — for the nominal or the real driver impedance, with Zobel, resonance notch, L-pad and baffle-step networks, a circuit simulation of the summed SPL, phase, impedance and reverse null (FRD and ZMA files welcome), standard part values, a parts list with ratings, a schematic and a CSV.

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How to use it

Pick the drivers and the crossover points, and the designer works out every inductor, capacitor and resistor, simulates the finished circuit with the drivers' real impedance, and shows how the drivers add up in front of the speaker. Presets start from a typical 6.5″ woofer and 1″ dome tweeter at 2.5 kHz LR4, a textbook check (2nd-order Butterworth, 8 Ω, 3 kHz), an LR2 with the tweeter reversed, a 3rd-order Butterworth, a 3-way and a simple 1st-order design.

How to use it

  1. Crossover. Choose 2-way or 3-way, then for each crossover point the frequency, the alignment and the order (Linkwitz–Riley comes in 2nd and 4th order). Design the filters for the nominal impedance (the textbook tables) or for the real load — |Z| of the driver, with its Zobel or notch, at the crossover frequency. The parts table shows the values both ways.

  2. Drivers. Enter Re, Le, Fs, Qes and Qms from the data sheet (they give the impedance curve), the nominal impedance, the sensitivity at 2.83 V / 1 m, and the acoustic offset — how far the driver’s acoustic centre sits behind the closest one. The low corner defaults to Fs with Q = Qts; for a woofer in its box use the box’s fc and Qtc from the speaker box designer. The top roll-off stands in for cone break-up or a dome’s own limit. Import FRD (frequency, dB, phase) and Import ZMA (frequency, ohms, phase) to replace the models with measurements; an FRD without phase gets a minimum phase computed from its magnitude.

  3. Impedance correction. Zobel puts Rz = Re in series with Cz = Le/Re² across the driver, cancelling the rise from the voice-coil inductance so a low-pass sees a resistor. Resonance notch is a series R–L–C across the driver tuned to Fs: C = 1/(2π·Fs·Re·Qes), L = Qes·Re/(2π·Fs), R = Re·(1 + Qes/Qms) — mostly for tweeters crossed not far above their resonance.

  4. Level. The tweeter (and midrange) is padded down to the reference level — the woofer’s sensitivity less the baffle-step compensation — with an L-pad (Rs = R·(1 − 10−A/20), Rp = R·10−A/20/(1 − 10−A/20), so the filter still sees R) or a single series resistor (the filter is then designed for R
    Rs). Leave the pad on auto or type the dB.

  5. Polarity. Textbook follows the ideal electrical sum: 2nd-order and LR2 filters are 180° apart, so the upper driver is reversed; LR4 is in phase; odd orders are 90° or 270° apart and sum flat in magnitude either way round. Best simulated tries both and keeps the flatter acoustic sum, offsets and driver roll-offs included.

  6. Baffle step. Below about f₃ = 115 / baffle width (m) the woofer radiates into the whole room rather than in front of the baffle and loses up to 6 dB. The model applies that step as a first-order shelf; the compensation network is an inductor in parallel with a resistor, in series with the woofer: R = Rw·(10A/20 − 1), L = R/(2π·f₃·√G). 3–4 dB suits a speaker near a wall, 6 dB a free-standing one.

  7. Simulation. Each driver’s ladder is solved as a complex-impedance circuit — the amplifier as an ideal voltage source, every coil with its DC resistance, every capacitor with its ESR, the compensation networks and the driver’s impedance as the load. The SPL tab shows each driver (sensitivity × simplified response or FRD × the voltage the crossover leaves it × the baffle step, delayed by its offset), the sum, and the reverse null — the sum with one driver reversed, which should show a deep, narrow notch at the crossover when the two are in phase. Phase and Impedance show the rest, including the minimum impedance the amplifier sees.

  8. Parts. Values snap to E12 or E24 capacitors, E24 resistors and stocked inductor values, with the error shown (and a pair of capacitors in parallel when one alone is more than 3% off); the simulation uses the snapped values. Each part gets a suggested type, the estimated coil DCR for the wire gauge you choose, and a rating from the amplifier’s power: resistors at a quarter of the worst full-power sine, capacitors at 1.5 × the peak voltage. Schematic draws the circuit (download as SVG); Parts CSV exports the list.

Method and assumptions

  • The filters are the classic all-pole polynomials, normalised so the low-pass and high-pass of a pair meet at the crossover frequency (Butterworth −3 dB, Linkwitz–Riley −6 dB; Bessel and Chebychev phase-matched in the same way, so Dickason’s 2nd-order Bessel and Q = 1 "Chebychev" come out). The passive ladder is synthesised by a continued-fraction (Cauer) expansion of the polynomial for a zero-impedance source and a resistive load — the method behind the textbook tables, so the 2nd-order Butterworth at 8 Ω and 3 kHz gives 0.600 mH and 4.69 µF, and LR4 gives the familiar 0.3000·R/f, 0.2533/(R·f), 0.1500·R/f, 0.0563/(R·f).

  • A filter only behaves as designed into a resistance. Real drivers rise with Le and peak at Fs, which is why the Zobel and notch exist and why the simulation, not the formula, is the answer. In a 3-way the midrange’s high- and low-pass sections load each other when the band is narrow (under about three octaves); the plot shows the real result.

  • Driver models are simple: free-air impedance, a second-order high-pass corner and low-pass roll-off, no directivity, no diffraction beyond the baffle step. For a real design measure the drivers in the box (FRD and ZMA files) and treat the result here as a start for listening and measurement.

  • Coil DCR is estimated for a Brooks-proportioned air-core winding (L = 2.549·10⁻⁶·c·N² H, after Grover) — 1 mH of 18 AWG comes out near 0.46 Ω, in line with suppliers' figures; iron and ferrite cores are taken as a quarter of that.

Sources: Vance Dickason, Loudspeaker Design Cookbook; Siegfried Linkwitz, "Active crossover networks for noncoincident drivers" (JAES, 1976); Harry F. Olson, Acoustical Engineering, for the baffle step; Frederick Grover, Inductance Calculations. The example drivers are generic, not any maker’s.

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