Two drivers, one note: what a crossover actually does

Almost every PA box is at least two loudspeakers pretending to be one. The crossover is where the pretending happens, and a surprising amount of what goes wrong in the vocal range goes wrong right there.

It's 4:40 in the afternoon, doors at 6:30, and the system tech is doing the walk. You know the walk. Reference track on, a slow lap from the mix position to the barricade, out along the side seating, up into the balcony. Everything sounds fine at the desk, which is the point of the desk. It sounds fine in the middle of the floor. Then, about four rows up the rake on house left, the singer's voice goes thin. Not quiet. Thin. The top of the voice is still there and the chest is still there, but the part in between, the part that makes a voice sound like a person standing in front of you, has gone somewhere else. Two steps down, it's back. Two steps up, it's back. It's a stripe, maybe a meter tall, running across the seating like a watermark.

Somebody suggests EQ. Somebody always does. A 2 dB boost around 1.2 kHz makes the stripe a little less obvious and the front of the floor shouty, and the stripe is still there. Then the tech pulls up the processor, finds the high-mid box, and sees that whoever loaded the preset last week had switched the crossover from Linkwitz-Riley to Butterworth "to see what it did," and the delay on the HF output was 0.2 ms off from where the manufacturer had it. Two clicks. Walk back up the rake. Stripe gone.

That's the whole column in one scene. The crossover is the least glamorous block in the signal chain. It lives inside a processor menu or a box of coils you never open. And it's doing something physically delicate: taking one signal, splitting it into bands, sending each band through a different driver in a different place, and asking the air in front of the box to add them back together into something that looks like the original. When that addition works, you don't notice anything. When it doesn't, you get stripes, holes, phasey vocals and a lot of EQ that treats symptoms. Let's open it up.

Why the handoff exists at all

Start with the uncomfortable fact that no single driver can do the whole job at concert level. The reasons are physical, and they pull in opposite directions.

Low frequencies need volume displacement. To make a given sound pressure, a cone has to push a given volume of air, and the volume it needs goes up steeply as frequency goes down. Siegfried Linkwitz put numbers on it on his crossover page: it takes about 214 cubic centimeters of air displacement to make 90 dB SPL at 1 meter at 50 Hz. For a 6.5-inch driver that works out to roughly 14 mm of peak-to-peak excursion, which he points out is far past what that driver can actually do. At 1 kHz the same output takes (50/1000)², or 1/400th, of the excursion. That's the inverse-square-of-frequency rule for a piston: halve the frequency, quadruple the excursion. Every octave you ask a driver to go lower costs it 12 dB of excursion headroom.

That's why the bottom of the spectrum lives on big cones with long throws, and why you never want the little stuff anywhere near it. A 1-inch titanium compression driver is a wonderful thing at 3 kHz and a very expensive fuse at 300 Hz. Take B&C's DE45 as an ordinary example: 1-inch throat, titanium diaphragm, specified from 1 to 18 kHz, with a recommended crossover of 1.5 kHz and a high-pass of 12 dB per octave or steeper. A compression driver behind a horn plays by friendlier rules than a bare cone in a box, but the trend points the same way. If you cross that driver an octave low, at 750 Hz, you are asking its diaphragm for roughly four times the motion at the bottom of its band for the same output, right around where it stops being comfortable. The datasheet number isn't a suggestion. It's a warranty boundary written in hertz.

High frequencies have the opposite problem. A big cone that moves plenty of air at 80 Hz becomes directional, and then badly behaved, as the wavelength shrinks toward its own size. The usual way to talk about this is the product ka, where k is 2π divided by wavelength and a is the radius of the radiating piston. Per Dan Russell's baffled-piston animations at Penn State, below ka = 1 the piston radiates about equally in all directions, around ka = 1 it starts to beam, and as ka gets large the main lobe narrows and side lobes show up. For a 15-inch cone with an effective radius around 16.5 cm, ka = 1 lands at about 330 Hz. By 1 kHz, ka is about 3, and the idealized -6 dB beamwidth has shrunk to roughly 94 degrees. By 2 kHz it's down near 43 degrees. A 15 run full-range is a megaphone that gets narrower every time the singer goes up a third.

So the crossover isn't just a frequency splitter. It's a referee between two drivers who each fail in different directions: one runs out of excursion going down, the other runs out of dispersion going up. Somewhere in the middle there's a region where both can do the job, and the crossover's work is to hand the signal across inside that region without the audience noticing the seam.

Two filters walk into a sum

The part that trips people up is that the crossover isn't judged by what each output looks like. It's judged by what the outputs add up to, in the air, at a listener. A high-pass and a low-pass that each look perfect on their own can sum into something ugly, because when two signals add, phase matters as much as level.

The obvious first attempt is a Butterworth filter, the maximally flat one you learned in school. A 2nd-order Butterworth low-pass is 3 dB down at its corner, and so is the matching high-pass. Two outputs at -3 dB, each carrying half the power. Sounds like it should sum to flat. It doesn't. At the crossover frequency the 2nd-order low-pass has shifted phase by -90 degrees and the high-pass by +90 degrees. They're 180 degrees apart, and two equal signals 180 degrees apart sum to nothing. Rane's application note on Linkwitz-Riley crossovers describes the vector addition as producing "a zero length vector." That's a null at the crossover frequency, on axis, with perfectly good drivers.

Flip the polarity of one driver and the null becomes a peak. Now the two -3 dB outputs arrive in phase, their voltages add, and the sum is +3 dB at crossover. The 4th-order Butterworth gets you to the same place by a different road: it also sums to a 3 dB bump. A broad +3 dB hump at 1 kHz in a PA is exactly the honk you'd spend all afternoon trying to EQ out.

The fix came from Hewlett-Packard, of all places. In 1976 Siegfried Linkwitz published "Active Crossover Networks for Noncoincident Drivers" in the Journal of the Audio Engineering Society, and credited his HP colleague Russ Riley with the observation that cascading two Butterworth filters gave him what he needed. A Linkwitz-Riley filter is a Butterworth squared. Each Butterworth section is -3 dB at the corner, so two in series are -6 dB. A -6 dB voltage is half the voltage. Two half-voltage signals that arrive in phase add to one full voltage. Flat.

And they do arrive in phase. For a 4th-order Linkwitz-Riley (LR4, 24 dB per octave), each output is built from two 2nd-order Butterworth sections, so the phase shifts double. The low-pass ends up at -180 degrees at crossover and the high-pass at +180, which is 360 degrees apart, which is the same place. Linkwitz's own phrasing is the cleanest: the high-pass and low-pass are "4 x 90 degrees out of phase at all frequencies, i.e. they are in-phase." Not just at the crossover. At every frequency. That's why Rane calls LR4 the professional standard, and it matters more off axis than on, which we'll get to.

The 2nd-order version, LR2, is 12 dB per octave with each output -6 dB at crossover, but its outputs are 180 degrees apart. So you invert one driver. Linkwitz again: "the polarity of one driver must be reversed to obtain allpass behavior." If a box has an LR2 network and someone wires the tweeter in "correct" polarity, you get the null back. If you've ever opened a passive cabinet and found the HF driver wired red-to-black and assumed the factory made a mistake, now you know why it might not have.

Odd orders are their own animal. A 3rd-order Butterworth crossover (18 dB per octave) actually sums to flat magnitude, but its two outputs sit 90 degrees apart at all frequencies. Flat on axis, in quadrature everywhere. That sounds harmless until you move off axis, and then it isn't. Hold that thought too.

One more thing Linkwitz-Riley does not fix, and Rane's note is upfront about it: the power response. At crossover each driver is putting out half the voltage, so a quarter of the power, and two quarters make a half. A two-way LR system has a 3 dB dip in total radiated power at the crossover frequency even though it's flat on axis. In a reflective room, where the reverberant field is built out of power response, that can make the crossover region sound a touch recessed.

The phase you pay for flat

People sometimes describe LR4 as "phase coherent," which is true in the narrow sense that the two outputs agree with each other. It is not true in the sense that the summed output agrees with the input. The sum of an LR4 crossover is an all-pass: flat magnitude, but with phase that rotates a full 360 degrees from low frequencies to high. Rane's note puts it plainly: the outputs are in phase with each other but out of phase with the input.

Phase rotation over frequency is group delay. It means some frequencies come out later than others. For LR4 the summed response is a 2nd-order all-pass, and its group delay at and below the crossover works out to about 2√2 divided by 2π times the crossover frequency. At a 1 kHz crossover that's about 0.45 ms. That's nothing. At a 100 Hz sub-to-top crossover it's about 4.5 ms, and it peaks a little higher, around 5.4 ms, near 64 Hz. Your kick drum's fundamental is leaving the system a few milliseconds behind its click.

Go steeper and the bill goes up. An LR8 (48 dB per octave) crossover at 100 Hz has roughly 11.8 ms of group delay at the crossover frequency, with a peak above 12 ms just below it. Rane gives the trade-off in useful terms: at a 1 kHz crossover, the LR4's -1 dB points sit at 591 Hz and 1,691 Hz, about 1.5 octaves of overlap, while LR8 squeezes that to 769 Hz and 1,301 Hz, about three-quarters of an octave. Steeper is tighter. But the LR8's step response overshoots about 30 percent versus about 15 percent for LR4, and takes roughly twice as long to settle. Wikipedia's entry makes the same point: above 4th order, the growing group-delay peak near crossover makes things less practical.

Is any of this audible? Less than the forums want it to be. Rane's position is that LR4's group delay is, in their view, not audible in real music systems. Linkwitz reported that smoothing the group delay with a different filter shape gave "no audible benefits" in his own experiments. At sub crossovers the numbers get to a few milliseconds, and that's where reasonable people disagree.

What I'll say with more confidence is that group delay matters a lot more for alignment than for perception. The 4.5 ms that an LR4 at 100 Hz adds to the sub band is 4.5 ms you have to account for when you time-align subs to tops. If you set a crossover in one processor and the sub delay in another, and somebody changes the crossover from LR4 to LR8 "for tighter subs," they have just moved the sub's arrival by several milliseconds at the frequencies where the subs and tops overlap. Your alignment, which was right, is now wrong, and the console didn't change. We spent a whole column on alignment in "Late on purpose." The crossover is one of the places alignment goes to die quietly.

Electrical slope is not acoustic slope

There's a distinction that separates people who've read the processor manual from people who've measured a box: the filter you dial in is not the filter the audience hears. The audience hears the filter multiplied by the driver.

Every driver has its own natural roll-off. A woofer in a vented box falls off at the bottom on its own. A compression driver on a horn falls off below the horn's cutoff and its own resonance. A cone rolls off at the top because of voice coil inductance and breakup. So the acoustic output of each band is the electrical filter stacked on top of the driver's native response. Linkwitz gives the classic example on his crossover page: a single capacitor in series with a tweeter will "not necessarily create a phase-linear 6 dB/octave crossover," because the tweeter's own high-pass behavior adds to it, and the real acoustic slope can end up closer to 18 dB per octave.

This is why the target in serious loudspeaker design is the acoustic response. Linkwitz states the goal as an electrical filter that makes the acoustic sum behave as an all-pass: "The sum of acoustic lowpass and highpass outputs must have allpass behavior without high Q peaks in the group delay." The manufacturer measures the driver, then designs whatever electrical shape is needed to make the driver's acoustic output land on an LR4 curve (or whatever they chose). The processor might say "LR4 at 1.1 kHz" on the HF output, but there's probably also a shelf, a few parametric filters and a delay value sitting next to it that turn the driver's real response into that target. This is the main reason I get nervous when someone overrides a factory preset's crossover "because I like Butterworth." You're not changing the crossover. You're changing one ingredient in a recipe that was balanced around the others.

Passive crossovers make this worse, because now the filter's components are interacting directly with the driver's impedance, which is not a resistor. Rod Elliott's write-up on passive Linkwitz-Riley networks at Elliott Sound Products is blunt about it: design for the measured impedance at the crossover frequency, because "the nominal impedance is just that - nominal." Voice coil inductance makes impedance rise with frequency, typically 3 to 5 dB per octave by his figures, which moves the corner and bends the filter shape.

Take a 2nd-order passive LR2 low-pass into a driver you're treating as a pure 8 Ω at a 1.5 kHz crossover. For a series inductor and a shunt capacitor, the corner is set by 1/√(LC) and the Q by R√(C/L). For an LR2 you want Q = 0.5. Solve it and you get L = 2R/ω and C = 1/(2Rω), where ω = 2π × 1,500. That's about 1.70 mH and 6.63 µF. Now play the show. The voice coil heats, its resistance rises, and say the effective load climbs from 8 Ω to 10 Ω. The corner frequency doesn't move, because L and C didn't change, but the Q goes from 0.5 to 0.625. Your Linkwitz-Riley has drifted most of the way toward a Butterworth shape, and we've already seen what a Butterworth does at the seam. Elliott lists exactly this thermal shift among the reasons active crossovers win: as the coil heats, impedance rises and the crossover frequency and filter shape move with it.

The standard band-aid is a Zobel network, a resistor and capacitor in parallel with the driver that flattens the rising inductive impedance. Elliott's recipe: set the resistor roughly equal to the voice coil's DC resistance, then pick the capacitor so its reactance matches the inductor's at the frequency where the inductive reactance equals that resistance. That simplifies to C = Le/Re². For a driver with Re = 5.6 Ω and Le = 1 mH, you get about 32 µF. It works, but it's a patch: it costs amplifier power as heat and does nothing for the driver's acoustic output. Linkwitz's broader complaint about passive networks is that "they block the power amplifier from taking maximum control over the voice coil motion."

None of this means passive boxes are bad. Elliott himself says passive suits small two-way systems and the mid-to-high section of a bi-amped system. It means that a passive network is a crossover that changes with temperature and with whatever amplifier you hang on it, and you should EQ it with that in mind. His own measurements show the response picking up roughly a 1.5 dB peak when the network is driven from a 4 Ω source instead of a near-zero-impedance amplifier.

One small passive part that survives even in fully active rigs: the protection capacitor. John Burnett's ProSoundWeb piece on active crossovers recommends a series capacitor in front of the HF drivers even when the filtering is done at line level, 47 µF on the compression driver in his example, because amplifier turn-on thumps and DC offset "could easily destroy driver and tweeter." Run the numbers on that cap with an 8 Ω driver and its -3 dB point is about 1/(2π × 8 × 47 µF), or roughly 420 Hz. That's well below a 1.5 kHz crossover, so it barely touches the passband, but it adds another 6 dB per octave of roll-off below it. One more ingredient in the acoustic slope that isn't on the processor screen.

Inches and microseconds

All of the summing math above assumed both drivers are in the same place. They never are. They sit beside or above each other, and their acoustic centers (the point the sound appears to come from) are usually at different depths. A compression driver sits at the back of a horn. A cone's acoustic center is somewhere in its throat. The distance between the two is a time offset, and at the crossover frequency a small time offset is a big phase offset.

On axis first. Say the HF arrives 0.25 ms late relative to the LF at a 1 kHz crossover. At 343 m/s that's about 8.6 cm of path difference, and it's a quarter period of 1 kHz, which is 90 degrees. Two half-voltage signals 90 degrees apart sum to about 0.707 instead of 1, so the crossover region drops by 3 dB. Make it 0.5 ms (17 cm, half a period) and the two outputs cancel completely at 1 kHz. Even an eighth of a millisecond, about 4.3 cm, takes 0.7 dB out of the seam. That's the same order as the depth difference between a horn throat and a woofer cone.

That's what the per-output delay in your processor is for, and why factory presets carry numbers like 0.18 ms that look suspiciously precise. They were measured. If you ever rebuild a box's tuning, look at the phase traces of the two bands through the crossover region in Smaart or whatever you use, and adjust the delay until the traces overlay in the region where both bands are contributing. The magnitude will follow.

Now off axis, which is where the scene at the top of this column came from. Even with the acoustic centers perfectly aligned on axis, two drivers spaced vertically by a distance d have a path-length difference of d·sin(θ) to a listener at angle θ above or below. At some angle that difference reaches half a wavelength, and the two outputs cancel there. With a woofer and horn 40 cm apart, center to center, and a 1 kHz crossover (wavelength about 34.3 cm), the first nulls land where sin(θ) = 0.343 / (2 × 0.4), which is about ±25 degrees. That's a stripe in the vertical coverage at the crossover frequency, right where the vocal lives.

With LR4 the outputs are in phase at all frequencies, so that lobe is symmetric and the main beam points straight down the axis. That's the "zero lobing error" Rane talks about. With a filter whose outputs aren't in phase, the main lobe tilts. Rane's note runs the numbers for a Butterworth crossover at 1,700 Hz with drivers 7 inches apart: the response peaks at +3 dB 15 degrees below the axis and cancels 15 degrees above it. The lobe tilts toward the driver that's lagging. Figure 4 shows the same effect with a 3rd-order Butterworth at our 1 kHz example: the LR4 nulls sit symmetrically at ±25 degrees, while the quadrature outputs of the BW3 push the nulls to about -11 and +39 degrees and swing the main lobe upward.

In a big room this is the difference between a vocal that's even from the floor to the balcony and one with a hole in it at row 14. Which brings us back to the opening scene. The stripe wasn't caused by the Butterworth or the 0.2 ms alone. The time offset tilts the lobe the same way the filter phase does. Get either one wrong and the null walks off its symmetric position and into a block of seats. EQ can't fix that, because EQ changes both drivers' contribution at that frequency equally, at every angle. The geometry is still the geometry.

This is also why some loudspeaker layouts look the way they do. Linkwitz points out that with vertically stacked drivers the polar axis "will tilt" if the outputs aren't in phase at crossover, and one remedy is symmetry: a woofer-mid-tweeter-mid-woofer arrangement puts a driver on both sides of the one it's crossing to, so the lobes are forced back onto the axis. Coaxial drivers go a step further and try to put both acoustic centers on the same line.

Where to cross, and why it's usually not your call

So where should the handoff happen? The crossover should be low enough that the woofer hasn't beamed into a narrower pattern than the horn, and high enough that the HF driver isn't being asked for excursion it doesn't have.

The first constraint is directivity. A 90-degree horn throws a 90-degree pattern above its pattern-control frequency. The woofer next to it is roughly hemispherical at low frequencies and narrows as frequency rises. If you cross where the woofer is still at 140 degrees, the coverage suddenly snaps from wide to 90 degrees as the horn takes over. If you cross where the woofer has already narrowed to 60 degrees, the coverage pinches and then widens again at the handoff. Either way, off-axis seats hear a dip or bump at the crossover that on-axis seats don't. QSC frames its own design rule this way, as matching "the high-frequency horn coverage to the woofer's directivity at the crossover frequency." Linkwitz states the same requirement from the other side: "the power response of the two drivers must be similar in the crossover region."

Now look at Figure 5. Using the idealized baffled-piston model, a 15-inch cone's -6 dB beamwidth passes through about 94 degrees near 1 kHz, and through 60 degrees near 1.5 kHz. A 12-inch cone is still about 137 degrees wide at 1 kHz and hits about 102 degrees at 1.2 kHz. The model is crude (real cones aren't rigid pistons and a box isn't an infinite baffle), but there's a reason the "15 and a 90-degree horn crossed around 1 kHz" box has been a staple of the industry for decades, and why a 12-inch two-way usually crosses a bit higher. The geometry practically chooses the number for you.

The second constraint is the HF driver's bottom end, like the DE45's 1.5 kHz recommendation. The two don't always overlap. A 15-inch woofer wants to hand off by about 1 kHz to keep its pattern under control, and a small-format compression driver might want to start at 1.5 kHz to keep its diaphragm in one piece. The gap between those two numbers is where loudspeaker design actually happens: bigger-format compression drivers with 1.4-inch or larger exits, horns with lower pattern-control frequencies, three-way designs with a dedicated midrange, or careful compromises with steeper slopes so each driver spends less time outside its comfort zone.

For a manufactured box with a factory preset, the crossover point, slope, alignment delay and the EQ around them were chosen together, after measurement, to balance excursion, directivity, power response and thermal limits. You can change them. Know what you're trading. Lowering the HF crossover to "warm up the box" moves excursion stress onto the most fragile driver in the system. Raising it to "save the compression driver" pushes the woofer into its beaming region and narrows the vocal coverage. Making the slope steeper to "reduce overlap" adds group delay and, as we saw, can disturb the alignment you already had.

The place where you do get to choose is between boxes: subs to tops, and sometimes tops to a separate mid-high cluster. That handoff usually lives in the system processor, and the same physics applies at a larger scale. The tops' low-frequency roll-off is part of the acoustic slope. The subs and the tops are rarely at the same height or depth. And the group delay of the sub-to-top crossover, 4.5 ms for LR4 at 100 Hz, sits right in the band where you are trying to get two different box types to add instead of fight. Choose the crossover, then align. Never the other way around.

FIR: buying phase with time

Every filter we've talked about so far is an IIR filter, the kind that has an analog equivalent. Linkwitz-Riley, Butterworth, the coils and caps in a passive box, the 4th-order state-variable filter Rane developed in 1983, the year Rane and Sundholm shipped the first commercial Linkwitz-Riley crossovers: all of them have a phase response tied to their magnitude response. If you want a 24 dB per octave slope, you get the phase shift that comes with it, and the summed output rotates.

Modern loudspeaker processors increasingly offer a different option: FIR filters, which can be designed for linear phase. A linear-phase FIR has a symmetric impulse response, and per Julius O. Smith's notes on filter design at Stanford's CCRMA, a symmetric FIR of length N delays every frequency by exactly (N - 1)/2 samples. Every frequency by the same amount. No rotation. No group-delay hump at crossover. A linear-phase FIR crossover sums to a clean delayed copy of the input, not an all-pass. And you can have steep slopes without paying for them in phase. The Yamaha and Lake white paper for the MY8-LAKE card makes exactly this pitch: linear-phase FIR crossovers give smoother transitions with minimal phase interference between drivers and let you narrow the overlap between bands.

The academic version of this goes back further than the marketing. Vanderkooy and Lipshitz published "A Family of Linear-Phase Crossover Networks of High Slope Derived by Time Delay" in the JAES in 1983, and Linkwitz describes the same family on his site: a high-pass defined as a pure delay minus a low-pass, HP = e^(-sT) - LP, which by construction sums back to the delay. The math has been known for decades. What changed is that DSP got cheap enough to do it in a box on a stand.

The price isn't money. Linear phase costs latency, and the lower the crossover, the more latency it costs. The MY8-LAKE paper is admirably specific about this. For its linear-phase crossovers at 48 dB per octave, an alignment delay of 1.25 ms supports a lowest crossover of about 1.03 kHz. Double the delay to 2.5 ms and you get down to about 515 Hz. Five milliseconds gets you to 258 Hz, and 10 ms gets you to 129 Hz. Notice the pattern: halving the crossover frequency doubles the latency. That's not a quirk of one product. A filter has to "see" enough cycles of a frequency to shape it, and low frequencies have long cycles. A 1,024-tap FIR at 48 kHz spans 21.3 ms of time, which is about two cycles of 100 Hz, and its linear-phase delay is (1,024 - 1)/2 samples, or about 10.7 ms.

For a mid-to-high crossover at 1 kHz or above, a millisecond or so of extra latency is nothing. For a sub-to-top crossover it can be 10 ms or more, on top of whatever the console and network already cost you. You know where that ends up if you've ever drawn up a latency budget: in the monitor world, in the IEM mix of a drummer who can hear the difference between their acoustic snare and the PA's version of it. The Yamaha paper says it outright: for low-latency live use, a classic IIR crossover for the subwoofer may be the better choice. That's a manufacturer selling FIR telling you not to use FIR everywhere. Believe them.

The other cost is subtler. Because the linear-phase impulse response is symmetric around its peak, half of it comes before the peak. A steep linear-phase crossover filter rings both after a transient and before it, at frequencies near the crossover. That pre-response is a mathematical consequence of the symmetry, not a defect in any particular product. Whether it's audible in a given system depends on the slope, the frequency, how the drivers sum it back out, and who you ask. FIR isn't bad. It just isn't free, and "linear phase" on a spec sheet is a trade, not an upgrade.

Plenty of modern presets quietly mix the two: IIR down low where latency would hurt, FIR up top. The screen just says "preset loaded."

What you can take back to the desk

Most of us aren't designing loudspeakers. We're inheriting them, flying them, aligning them and mixing on them. So this is the field version.

Trust the box preset more than your instincts about it. The crossover point, slope, polarity and alignment delay inside a factory preset were chosen together. If the box sounds wrong, check that the right preset is loaded for the right box and the right amp channel before you touch any of the crossover parameters. A preset for the 12-inch version loaded on the 15-inch version is an easy way to get a stripe in the vocal.

If you change the slope, re-check the alignment. Going from LR4 to LR8 at 100 Hz adds about 7 ms of group delay at the crossover frequency. Changing the filter type changes the arrival time of the band. Whatever your sub alignment was before, it isn't now.

Polarity at the crossover is not a matter of taste. LR2 wants one leg inverted. LR4 wants both the same. If someone has "corrected" polarity on an HF output, you'll get a cancellation or a bump at the crossover. A quick check with a measurement mic on axis, LF and HF muted and unmuted in turn, then together, should show the sum higher than either alone through the crossover region. If the sum dips below either one, something is upside down or late.

Walk the vertical, not just the horizontal. Most coverage checks are a lap across the room. Crossover lobing problems show up as you move up and down relative to the box: rows of a rake, a balcony, standing versus sitting. If a band of seats sounds thin in the 1 to 2 kHz range and the seats above and below sound fine, think geometry and alignment before you think EQ.

Keep an eye on what passive boxes do when they're hot. A passive LR2 that was Q = 0.5 at 8 Ω is closer to 0.625 when the load has climbed to 10 Ω. Long sets at high level move a passive crossover. If a passive wedge starts sounding harsh at the end of a long night, it may not be your ears.

Use FIR where latency doesn't hurt. Mid and high crossovers: great. Sub-to-top in a show with in-ears: count the milliseconds first. The MY8-LAKE paper's 10 ms for a 129 Hz linear-phase crossover is a good number to have in your head when someone tells you linear phase is free.

Don't EQ geometry. If the problem changes with position, it's interference, and EQ moves both drivers at once. Fix the timing, the polarity or the filter. Then EQ what's left.

The best crossover is the one nobody in the audience knows is there. The singer sounds like one person standing in one place, even though the sound is coming from two drivers 40 centimeters apart, handing off a vocal in the middle of a word. The math that makes that work is old, the HP engineers who got there first were solving a hi-fi problem, and the physics hasn't moved since. What has moved is how much of it is hidden behind a preset name. Worth knowing what's in there.

Above the Fader

Sauce

• Linkwitz-Riley Crossovers: A Primer (Rane Note 160, Dennis Bohn)
• Crossovers (Linkwitz Lab, Siegfried Linkwitz)
• Linkwitz-Riley filter (Wikipedia)
• Active Crossover Networks for Noncoincident Drivers, Linkwitz, JAES 1976 (AES E-Library)
• Passive Linkwitz-Riley crossovers (Elliott Sound Products)
• Understanding active loudspeaker crossovers (ProSoundWeb, John Burnett)
• MY8-LAKE white paper (Yamaha / Lake)
• Linear-phase filters and symmetric impulse responses (Julius O. Smith, CCRMA)
• Baffled piston directivity (Dan Russell, Penn State Acoustics and Vibration Animations)
• B&C DE45 compression driver datasheet
• Directivity matching (QSC Live Sound blog, Christophe Anet)
• Crossovers: an old paper, a new article (Filter Wizard), citing Vanderkooy and Lipshitz, JAES 1983

Featured photo: Tara-mae Miller on Unsplash. Diagrams: Above the Fader, computed from the filter transfer functions.