Crossover Summation

Canonical Definition

Crossover summation is the vector addition of the acoustic outputs of adjacent drivers through their overlap region. The result depends on each driver's magnitude and phase at the observation point, not on the electrical filter labels alone.

Vector Addition In One Table

For two equal-magnitude coherent signals, relative phase controls the sum:

The general equal-amplitude relationship is:

Result amplitude = 2A × cos(Δφ / 2)

Real drivers are rarely equal in magnitude across the whole band, so the measured result is a frequency-by-frequency vector sum.

Electrical Filters Versus Acoustic Slopes

An electrical crossover label describes the transfer function being applied to the signal. The acoustic slope also includes:

• the driver's natural response and breakup behavior
• enclosure, baffle, horn, or waveguide loading
• off-axis response at the microphone or listener
• path length and acoustic-center offset
• other filters, EQ, protection networks, and amplifier response

A DSP set to 3 kHz Linkwitz-Riley fourth order does not guarantee that the measured acoustic responses form a 3 kHz LR4 pair.

What Common Alignments Expect

These are target relationships, not guarantees. Measure the drivers and the sum.

Normal Sum And Reverse-Polarity Null

A strong verification sequence is:

1. Measure the lower-frequency driver alone.
2. Measure the higher-frequency driver alone from the same position and timing reference.
3. Measure both drivers in the intended polarity.
4. Invert one driver and measure again.

For an intended in-phase crossover, the normal sum should be smooth and the reverse-polarity measurement should produce a repeatable null near the crossover region. The depth and symmetry of that null depend on level match, phase match, distortion, noise, position, and directivity.

Delay And Acoustic Center

A path-length or effective acoustic-center offset creates frequency-dependent relative phase. Adding delay to the earlier driver can improve the intended overlap relationship, but the correct value is the one that produces the useful acoustic sum—not necessarily the value that makes two impulse peaks coincide.

Horn-loaded drivers, waveguides, subwoofer systems, and steeply filtered drivers can have effective timing behavior that differs substantially from tape-measured front surfaces.

Directivity And The Crossover Lobe

Two separated drivers create a directional interference pattern through their shared band. Relative delay, vertical or horizontal spacing, and crossover slope control where the main lobe points and where off-axis cancellations occur.

• A flat response at one microphone position can hide a tilted lobe.
• Moving the microphone may reveal a rapid crossover change.
• Vehicle glass, dash, seats, and door placement make the real pattern asymmetric.
• Multi-seat tuning is a coverage compromise, not one universal delay value.

Measurement Workflow

1. Protect every driver with a safe initial crossover.
2. Fix the microphone at the chosen reference position.
3. Use one timing reference for all measurements.
4. Measure each driver individually at the same level and settings.
5. Inspect magnitude and relative phase through the overlap region.
6. Adjust level, polarity, crossover frequency, slope, EQ, and delay deliberately.
7. Measure the normal sum and reverse-polarity null.
8. Repeat at nearby positions or seats when coverage matters.
9. Listen with representative content after the measurement goal is met.

Common Failure Patterns

Related Resources

• Time Alignment And Acoustic Integration
• Phase
• Polarity
• Acoustic Center
• Phase Shift Reference
• Crossover Design And Implementation