Speaker Box Alignments from Numerical Optimization - The Quasi-Chebyshev Alignment

After seeing many speaker designers returning to trial-and-error approaches that seem to forget the historical work and analytical approach, Lars Risbo decided to explore numerical optimization to synthesize attractive alignments both for reflex and passive radiator box types. This reference article basically expands on Claus Futtrup's "Loudspeaker Bass Reflex Alignments" article series published in audioXpress, and expanded with dedicated articles in Voice Coil.

Speakerbench, the web-based application for loudspeaker design with an emphasis on an advanced transducer model, has been officially available since March 2020. Created by Claus Futtrup and Jeff Candy, the online tool celebrates its fifth anniversary with a significant update that introduces new valuable features, plus comprehensive documentation. Originally intended to support the loudspeaker DIY community, Speakerbench is increasingly recognized by global speaker designers at all levels.

After discussing computation of discrete alignments such as B4, BL4, LR4, IB4, and CD4, this new article in the "Computation of Bass Reflex Alignments" article series explores the real-world situation where it becomes impossible to have a system design that exactly matches a certain driver Qt, normally described as an alignment error (or misalignment). The technique presented allows designers to modify tuning towards a desired target response function.

The first issue of Voice Coil for 2025 is now available and includes a new article by Claus Futtrup about computation of alignments, Dave Morrison discussing Spikes & Isolation for Speaker Decoupling and another valuable directory of Earphone and Headphone Manufacturers and parts. On his Test Bench, Vance Dickason characterizes the new Scan-Speak D3004/666000 metamodal TPCD dome tweeter and the Dayton Audio UMII10-22 Ultimax II 10" Subwoofer.

The fifth article by Claus Futtrup in his series about loudspeaker bass reflex alignments explores the concept of transitional alignments, which is helpful in bridging between filter types. The example details a transitional alignment between Butterworth B4 and Linkwitz-Riley LR4. This article series started in May 2024 with “Computation of Bass Reflex Alignments," the series expanded with classical alignments such as the B4, the LR4, the IB4, and most recently, the CD4 vented alignment, in the August 2024 issue.

In this December 2024 issue there's a new DSP product review of the Marani Pro Audio MIR260A outboard processor, and Lars Risbo shares his expertise in Numerical Optimization applied to Speaker Box Alignments. Essential resources are the updated directories of Test and Measurement and of Simulation and CAD Software vendors. On Test Bench, Vance Dickason characterizes the Faital Pro HF110 1" Neodymium Motor Compression Driver and the SB Acoustics Satori MR16TX-8 6.5" TPCD Midrange.

In the fourth article from Claus Futtrup in his series about the invention, concept, and historical perspective of loudspeaker bass reflex alignments, he explores the Critically Damped Fourth-Order (CD4) bass reflex alignment. This alignment remains one of the least known and hasn't been discussed in literature related to loudspeaker design, even though it allows for interesting output properties. This article was originally published in Voice Coil, August 2024.

Before computers were broadly available for loudspeaker bass reflex box simulations, engineers relied on "Alignments" for their designs. Such box alignments are typically named after equivalent filter functions that the high-pass response of the box was aligned after — for example, Butterworth (B4) and Bessel (BL4) — to name a few. This article, the third in this series, explores the rarely talked about Inter-Order Butterworth (IB4) alignment, mentioned originally by Richard Small and Neville Thiele.

In Voice Coil October 2024, Claus Futtrup writes about Compliance Alteration, and Mike Klasco and Nora Wong prepared an updated directory of Integrated Electronics for Loudspeakers. James Croft returns with a "Loudspeaker" patent review, granted to industry veteran Michael Levy, and Vance Dickason focuses solely on the eagerly awaited Purifi Audio PTT10.0X04-NAB-01 10" Midbass Woofer.

Before computers were broadly available for loudspeaker bass reflex box simulations, engineers relied on "Alignments" for their designs - typically named after equivalent filter functions that the high-pass response of the box was aligned after — for example, Butterworth (B4) and Bessel (BL4) — to name a few. In this article, Claus Futtrup now focuses on the Linkwitz-Riley (LR4) Bass Reflex Alignment.