Why is LR preferred over Butterworth?

LR achieves flat summation (-6 dB per output, 0 dB combined). Butterworth produces +3 dB peak (-3 dB outputs sum to +3). LR provides matched phase between outputs, ensuring proper acoustic summation without polarity complications.

What slope for a two-way speaker?

LR4 (24 dB/oct) is the standard: flat summed response, adequate driver protection, manageable group delay. LR2 offers wider overlap. LR8 provides steep isolation but more group delay.

How to verify crossover alignment?

Measure each driver individually, then both together. Individual traces cross at -6 dB (LR) or -3 dB (Butterworth). Combined shows smooth summation. Phase converges at crossover. Coherence above 0.85.

What is acoustic offset?

Physical distance between driver acoustic centers. Tweeter typically 2-5 cm closer than woofer. Creates time difference shifting alignment. Compensate with electronic delay or tilted baffle angle.

Why is LR preferred over Butterworth?

LR achieves flat summation (-6 dB per output, 0 dB combined). Butterworth produces +3 dB peak (-3 dB outputs sum to +3). LR provides matched phase between outputs, ensuring proper acoustic summation without polarity complications.

What slope for a two-way speaker?

LR4 (24 dB/oct) is the standard: flat summed response, adequate driver protection, manageable group delay. LR2 offers wider overlap. LR8 provides steep isolation but more group delay.

How to verify crossover alignment?

Measure each driver individually, then both together. Individual traces cross at -6 dB (LR) or -3 dB (Butterworth). Combined shows smooth summation. Phase converges at crossover. Coherence above 0.85.

What is acoustic offset?

Physical distance between driver acoustic centers. Tweeter typically 2-5 cm closer than woofer. Creates time difference shifting alignment. Compensate with electronic delay or tilted baffle angle.

Crossover Design — Butterworth vs Linkwitz-Riley

Filter Fundamentals

Defined by order (slope) and topology. Second-order = 12 dB/oct. Fourth-order = 24 dB/oct. Higher orders provide steeper attenuation but more phase rotation, affecting off-axis response and power handling in the crossover region.

Butterworth

Maximally flat, -3 dB at crossover. Summed = +3 dB peak. Even-order pairs are 180 degrees apart, needing polarity reversal. Fourth-order outputs are 360 degrees apart (in phase), +3 dB without reversal.

Linkwitz-Riley

Two cascaded Butterworth filters. LR4 = -6 dB at crossover per output, 0 dB summed. Matched phase, flat summation, adequate slope. The industry standard for professional two-way and three-way loudspeaker systems.

Practical Considerations

Acoustic offset between drivers adds propagation delay shifting alignment. Transfer function measurement per AES-2id verifies actual acoustic crossover behavior. Electronic delay or baffle angle compensates offset.

FIR vs IIR

IIR: frequency-dependent group delay. FIR: linear phase, constant delay but with processing latency. IIR for live sound (negligible latency). FIR for studio monitoring (superior time domain).