Crossover design for horns with curved vertical dispersion patterns
The vertical dispersion of a horn loudspeaker rarely behaves like the textbook constant directivity pattern many engineers assume. A tractrix or bi-radial horn with a curved profile produces a spreading wavefront that changes shape with frequency, which complicates the task of integrating it with a woofer through a crossover network. Getting this right matters whether the system ends up in a dedicated listening room in Sydney or a mastering suite in Berlin.
Designing a crossover for such a horn requires balancing directivity control, phase coherence, and the mechanical realities of the drivers themselves. Unlike a flat-fronted constant directivity design, the curved horn asks the engineer to account for how acoustic energy redistributes vertically as wavelength shrinks. The result is a more nuanced approach to slope, frequency, and time alignment than a simple textbook recipe.
Understanding curved vertical dispersion
A horn with a curved vertical contour, such as a spherical or exponential flare, behaves like a segment of a larger spherical source at low frequencies and gradually transitions toward a more directional pattern as the wavelength shortens. This means the vertical coverage angle narrows with rising frequency, producing what engineers describe as a beaming effect above a few kilohertz. The crossover point must therefore be chosen not just for driver capability but for where this narrowing begins to cause problems.
In practice, the vertical beamwidth of a curved horn might start at 90 degrees at the bottom of its operating range and tighten to 40 degrees or less as it approaches its upper limit. This contrasts sharply with a constant directivity horn, which maintains a more consistent vertical angle across its band. The Australian listener who places a speaker close to a side wall in a Brisbane suburb home will experience different reflections than someone with a treated room in Adelaide, and the crossover must account for both the horn's behaviour and the room.
Choosing the crossover frequency
The crossover frequency sets the boundary between the horn and the partnering woofer or midrange driver. For a curved vertical dispersion horn, this point is dictated by several primary factors, though practical considerations refine the final choice.
Key considerations when setting the crossover point:
- The compression driver's lower usable limit before distortion rises
- The horn's vertical beamwidth at the top of its operating range
- The woofer's upper limit before its own directivity becomes problematic
- The room's vertical dimensions and listener seating height
- The intended acoustic axis relative to seated ear height
A typical TAD-Pioneer compression driver paired with a well-designed wooden horn might hand over anywhere between 800 Hz and 1.2 kHz, depending on the woofer's capabilities. Engineers often set the crossover too high to chase perceived detail, but this can push the horn into a frequency region where vertical beaming becomes severe. Listeners seated off-axis vertically, perhaps on a higher sofa in a two-tier Melbourne home cinema room, will notice the upper-midrange energy dropping away. Setting the crossover a little lower, even at the expense of pushing the compression driver harder, preserves a smoother vertical response for everyone in the room.
Slope selection and phase coherence
The slope of the crossover, meaning how steeply each driver rolls off outside its passband, has a profound effect on the summed vertical response. Gentle slopes such as 6 dB per octave produce minimal phase disruption but leave drivers operating well outside their ideal range, which can colour the sound and stress the diaphragms. Steeper slopes like 24 dB per octave offer better driver protection and reduce interference, but they introduce significant phase shifts that must be carefully managed.
For a horn with curved vertical dispersion, an 18 dB per octave slope often strikes the right balance. It keeps the compression driver within its comfort zone while limiting the overlap region where vertical lobing can occur. Sunship Audio's preference for why we choose simple topologies for high-end systems is rooted in this kind of engineering pragmatism: a clean, straightforward network does the job without the unpredictability of exotic filter types. The filter's phase behaviour can then be predicted and compensated for in the time-alignment stage.
Time alignment in passive networks
Because the acoustic centres of the compression driver and the woofer rarely sit in the same physical plane, the wavefronts from each must be aligned in time at the listening position. Active DSP can handle this electronically, but a passive crossover network achieves the same result through careful component choice and physical driver placement. Zobel networks, all-pass filters built from inductors and capacitors, and even deliberate offset of the horn mouth can shift the apparent arrival time of one driver relative to the other.
The curved vertical dispersion of the horn adds another layer: as the wavefront spreads and the beam narrows, the acoustic centre effectively moves. Engineers compensate by treating the crossover as a three-dimensional problem, adjusting the physical recess of the horn and the network's group delay to keep the wavefronts coincident across the listening window. Visitors to the Berlin demonstration room often hear the result: a stable, three-dimensional image that holds together whether the listener sits, stands, or moves to the side.
Minimising vertical lobing
When two drivers operate in the same frequency range, they create an interference pattern that varies with vertical angle. This is the source of vertical lobing, the comb-filter effect that makes the sound change dramatically as you move your head up or down. With a curved vertical dispersion horn, the problem is acute because the horn's own narrowing coverage changes the relative level reaching the listener from above and below the axis.
Common pitfalls in vertical dispersion crossover design:
- Choosing a first-order slope for its simplicity and accepting severe lobing
- Ignoring driver-to-driver physical offset entirely
- Using a steep slope without correcting for phase shift
- Assuming the horn's acoustic centre sits at its mouth
- Failing to verify the result with music in a real room
The mitigation strategies fall into three categories: steep crossover slopes to reduce overlap, careful time alignment to keep the wavefronts coherent, and physical offset of the drivers to control the vertical interference pattern. A steep slope alone is not enough if the drivers are not time-aligned, and time alignment alone cannot fix a sloppy crossover region. The combination is what produces a smooth vertical power response, which translates to a stable tonal balance across a wide listening area.
| Crossover approach | Typical slope | Vertical lobing risk | Time alignment complexity | Best suited for |
|---|---|---|---|---|
| First-order (6 dB/oct) | Gentle | High | Low | Short-throw, nearfield use |
| Second-order (12 dB/oct) | Moderate | Medium | Moderate | Multi-driver floorstanders |
| Third-order (18 dB/oct) | Steep | Low | High | Horn-loaded main systems |
| Fourth-order (24 dB/oct) | Very steep | Very low | Very high | Active DSP-controlled systems |
| Linkwitz-Riley (4th order) | Very steep | Very low | Very high | Symmetric power response |
Practical implementation and tuning
Building the crossover begins with selecting high-quality components that maintain their values over time: air-core inductors, film capacitors, and precision resistors. The network is assembled on a rigid board with careful attention to grounding and lead dress, then installed in the heavily braced birch plywood cabinet. Each unit is measured in the Berlin listening room using both swept sine waves and music signals, with adjustments made to component values to compensate for driver unit variation.
The final tuning involves music. Pink noise, single instruments, and full orchestral passages help the engineer verify that the crossover transition is invisible, that voices remain natural, and that the dynamic contrasts of a well-recorded jazz album come through without strain. Photos of completed systems and their internal construction are available in the project gallery, where visitors can see the layout of components, bracing patterns, and horn integration in finished loudspeakers. For the Australian market, where listening rooms range from converted warehouses in Perth to compact apartments in Sydney's inner west, the same design principles apply but the implementation must flex. Sunship Audio works with clients to specify driver combinations, horn profiles, and crossover points that suit the room size, the listener's preferred seating height, and the acoustic treatment already in place. The curved vertical dispersion of the chosen horn becomes a tool rather than a constraint, shaping the sound to fit the space.