Directivity And Lobing

Canonical Definition

Directivity describes how acoustic output varies with angle, while lobing is the directional pattern produced when separated radiators overlap and interfere with angle-dependent path differences.

Driver Beaming

As wavelength becomes small relative to the radiating diameter, a driver's output generally narrows. A large midbass that is wide at low frequency can become increasingly directional before its measured on-axis response falls.

This matters because crossover frequency should consider not only how high or low each driver can play, but whether their radiation patterns overlap smoothly.

Two-Source Path Difference

For two separated sources, the path difference changes with observation angle:

Approximate path difference: ΔL = d × sin(θ)
Phase difference: φ = 360° × ΔL / λ

where d is center-to-center spacing, θ is observation angle, and λ is wavelength.

When the contributions have similar magnitude and approach opposite phase, a directional cancellation lobe can form. The frequency and angle of the lobe change with spacing, delay, filter phase, acoustic centers, and mounting geometry.

Spacing And Wavelength

Keeping effective source spacing small compared with wavelength reduces severe interference. A spacing near or below one-half wavelength is a useful screening heuristic for two sources covering the same frequency region, but real crossovers also depend on unequal magnitudes, limited overlap, acoustic centers, and baffle or cabin effects.

Use the heuristic to identify risk, then measure the installed system instead of treating it as a universal pass/fail rule.

Why Steeper Filters Do Not Eliminate Lobing

A steeper crossover reduces the frequency span where both drivers contribute strongly, which can reduce some interference. It does not remove:

• the angular path difference at the crossover itself
• acoustic-center offset
• directivity mismatch between the drivers
• phase error through the remaining overlap
• seat and mounting geometry

Steeper slopes can also make the result more sensitive to the exact crossover region and phase relationship.

Common Car-Audio Geometries

Measurement Workflow

1. Record driver size, center-to-center spacing, mounting angle, and acoustic geometry.
2. Measure each driver individually through the intended crossover region.
3. Measure the normal combined response at the primary listening point.
4. Move the microphone to relevant nearby heights, angles, or seats.
5. Compare the handoff shape, not only the overall tonal curve.
6. Adjust crossover frequency, slope, delay, polarity, level, mounting angle, or driver choice as needed.
7. Recheck the final target at the intended listening positions.

Why EQ Is Limited

EQ can alter the response at one measurement point, but it cannot make an angle-dependent lobe disappear everywhere. If a filter fills a hole at the driver's ear while increasing a peak at the passenger seat, the underlying coverage problem remains.

Fix geometry, crossover region, directivity match, or source contribution before using position-specific EQ as a compromise.

Design Goal: Controlled Coverage

The best crossover is not necessarily the one with the flattest single on-axis trace. It is the one that provides:

• safe driver operation
• useful magnitude and phase integration
• acceptable coverage over the intended seating window
• predictable direct and reflected sound
• reasonable sensitivity to head movement

Related Resources

• Acoustic Crossover
• Crossover Summation
• Cancellation Null
• Acoustic Center
• Crossovers, EQ, And Acoustic Targets