[DIY] Passive Crossover in the DSP Era

And so, dear reader: after assembling one or more speaker kits - probably ending up disappointed - you have decided to take your audiophile destiny into your own hands and make the big step: building your first speaker from scratch, choosing the cabinet and components according to your own taste. Well, well... you have no idea of the thicket you are about to step into! But if this statement of mine hasn't discouraged you (I hope not, because building speakers is, at least for me, the most enjoyable aspect of DIY), continue reading this article, because I wrote it with you specifically in mind.

I would like to start by making it clear that I do not belong to the “passive components party.” One of the few systems I truly appreciated at Milano Hi-End 2024 Show actually used a DSP crossover (from now on, DSP). I also dislike the habit - now almost a rule - of polarizing every topic into opposing factions: it only impoverishes the debate and the quality of opinions. That said, I believe passive crossovers can still offer concrete advantages, which I will try to summarize:

Simplicity and cost-effectiveness: no additional amplifiers, cables, or, of course, DSP are needed. Not all DIYers use budget amplifiers, and given the investment already made in them, they may not want to buy equally expensive units or add cheaper ones alongside them.

Signal quality: if the DSP is of poor quality - as in any field, some components are better than others - it can introduce noise and distortion. Moreover, not all audiophiles are comfortable, and in the case of low-quality DSP, rightly so with the idea of converting an analog signal to digital and then back to analogue again; in such cases, they prefer to rely on passive components.

Reduction of load dependency: even though a DSP can correct the final acoustic response, it cannot intervene on electrical load dependency, which is particularly pronounced in many OTLs (i.e. a tube amplifier without an output transformer), some minimalist amplifiers, and even in certain Class D amplifiers. In these situations, the use of passive components - such as a properly designed network - can help make the load more consistent electrically at high frequencies, improving stability and coupling with amplifiers sensitive to impedance variations.

Finally, the frequent claim “I use DSP, so I can do whatever I want” is not entirely accurate. Without delving into technical considerations that go beyond the scope of this series of articles, not even the best DSP in the world can fully compensate for the shortcomings of our listening environments or of our speakers and drivers. Undoubtedly, we can achieve a more linear frequency response, but we will still hear bloated or sluggish bass in the case of poor speaker placement, the resonances of our speakers and drivers, and, in some cases, additional colouration.

Since reality is never black and white, a passive crossover is not incompatible with either an active crossover or digital signal processing; on the contrary, this approach allows the advantages of both worlds to be combined. In a three way (or more) loudspeaker, it can be a good idea to cross the low frequency band actively, leaving the “dirty work” to the woofer or subwoofer, driven by a powerful but not necessarily high end amplifier, because low frequencies benefit the most from digital correction and at the same time are those to which we are least sensitive in terms of distortion. Moreover, as our old scribe teaches us, the mid and high bands require lower current reserves than the bass, allowing us to focus more on refinement. Finally, nothing prevents the use of a digital processor upstream of passive loudspeakers to perform room correction: all that is needed is a computer with CamillaDSP installed and a good audio output - but that might be material for another article.

One last consideration before venturing into the forest of passive crossover design, armed with a machete and a backpack full of first aid kits, K rations, resistors, capacitors, and inductors: this series of articles is intended to guide anyone who wants to start designing passive crossovers from scratch or to improve their skills, doing so with little or no expenditure on equipment (assuming you already have a PC). If, on the other hand, you are already a renowned designer or have microphones that are linear up to a million hertz and an anechoic chamber... write to me! I want to become your new best friend. This series of articles also makes no claim to be exhaustive on such a vast and complex subject; rather, it aims to be a concise guide, to be complemented with further reading (such as Vance Dickason's Loudspeaker Design Cookbook) and, if needed, video tutorials related to the software I will discuss - even though these tools are generally intuitive and often accompanied by well made documentation.

The crossover

Let's start by establishing a fundamental point: the crossover is a central part of a loudspeaker's design, almost as important as the cabinet construction and the choice of drivers. A good crossover, in addition to splitting the audio signal into different frequency bands (low, mid, and high) and assigning them to the drivers best suited to reproduce them, must ensure that the drivers work together as if they were a single sound source. Easier said than done.

In high fidelity, despite the ongoing lobotomization conspiracy against the audiophile, carried out for years by dealers and manufacturers of esoteric components, the design dominates. By this, I mean that a speaker built following a sound design, with decent components, will undoubtedly sound better than one built according to standard formulas but using esoteric components. Therefore, it is worth focusing - at least in the initial phase - on the design itself.

In the previous paragraph, I introduced the topic closest to my heart: the petition to abolish fixed formulas for crossovers, which TNT‑Audio will soon launch to bring it to the European Parliament, hoping that even non EU countries will follow this good example. Talking with DIYers, both in person and virtually, I realized that this '80s and '90s approach is still very popular. The various formulas (Bessel, Butterworth, Linkwitz‑Riley) are theoretical models and should be considered as such: valid for ideal drivers - flat frequency response, perfectly linear impedance - conditions that no real driver meets, no matter how fat your wallet. For this reason, using the famous “standard” crossover values, or worse, pre assembled crossovers found online, cannot lead to satisfactory results.

So, dear reader, join the fight against this anachronistic problem that still affects many DIYers today: sign the petition, and let's start together from the real data of the drivers.

FRD and ZMA: the Fundamental Data

To design a crossover, two types of files are required, here referred to by their extensions:

.FRD (Frequency Response Data): is the data that describes the variation of a driver's output as a function of frequency: the well-known frequency response. Below is an example of the on-axis frequency response of a compression tweeter with a SEOS12 horn.

.ZMA (Impedance Magnitude & Angle): it contains the variation of the driver's impedance - both magnitude and phase - as a function of frequency. Same driver and same horn.

Only by having these two files is it possible to reliably reconstruct the real behaviour of the drivers and simulate the effect of the crossover even before building it. Today, this allows a level of prediction that, until not many years ago, was beyond the reach of the DIYer. In my experience, when the measurements are carried out correctly and refer to the real system, the discrepancy between simulation and final result can remain within about 1 dB, reaching 2 dB in the worst cases.

So, where can you find these miraculous FRD and ZMA files? Essentially, there are three paths, dear fellow DIYer:

1) On the web, many enthusiasts have already measured a large number of loudspeaker drivers and made these files freely available. Very good resources are loudspeakerdatabase.com (Loudspeaker Database does not provide FRD or ZMA files in the strict sense. Instead, it provides data files that are functionally equivalent to FRD and ZMA for use in VituixCAD and in a few other compatible loudspeaker design programs. These files contain frequency response, phase, impedance and geometry data, but are stored in a different, software-specific format and cannot be directly exchanged as standard FRD/ZMA files.) and DIYaudio. Until a few years ago, an excellent free resource was the Italian site Dibirama. Today, downloading the loudspeaker files from their database requires an annual subscription of about 25 euros. Their catalogue is continuously expanding, and their measurement methodology is carried out very meticulously (which is not always the case with measurements made by hobbyists).

2) The second method is to use a simple program such as FPGraphTracer or the SPL Tracer function (probably the more accurate of the two) in VituixCad 2. By using these tools, it is sufficient to obtain the images of the frequency response and impedance of the drivers (all serious loudspeaker manufacturers provide these data, more or less “beautified”) and quickly convert them into FRD and ZMA files. We cannot rely on a very high level of precision, but for early projects they are perfectly adequate. In the image below, the main operations to be performed are highlighted in yellow. In this case they are applied to the frequency response image of a Ciare HW210, a driver that has the right characteristics to be used as the bass section in a not very efficient but fascinating and inexpensive dipole. The manufacturer only provides the on-axis response; in this case this is not a critical limitation because, in the intended application, the driver will be used only in the part of the bandwidth where its directivity is practically omnidirectional.

The same procedure shown also applies to off-axis measurements (when available) and to impedance. In this example I used FPGraphTracer , but the operation of SPL Tracer is identical. Follow these steps:

Drag the limit bars to the X and Y axis boundaries: These purple bars define the minimum and maximum values of the measurement. The horizontal axis corresponds to frequency and the vertical axis to dB or impedance in ohms.

Set the limits and select the scale type: Set the minimum and maximum values for both axes so that the entire curve is properly covered. Typically, the frequency axis is set to logarithmic (in this case 20 Hz–20 kHz) and the decibel axis to linear (for example 60–110 dB).

Trace the curve: Left-click directly on the curve: the program will automatically record the points and display them in fuchsia, as shown in the image below. Check that the traced curve matches the original frequency-response image; several attempts may be needed to obtain an accurate result.

Export the file: Save the file in .FRD format when tracing the frequency response and in .ZMA format when tracing the impedance. Go to File → Save data, name the file, and select the correct format.

3) The third method, finally, is to measure the drivers yourself. This is what we do when we want to work with the highest possible accuracy, by measuring the drivers directly mounted in the cabinet that we have so lovingly built for them. This allows us to observe the effects of the front baffle, the interactions caused by box mounting, the response in our listening room, the real crossover slopes, and many other aspects that we will leave aside for now.

Measurements require some basic equipment, but they provide a significant advantage both in design and especially in final tuning. This is clearly the best approach, but if this is your first build and you do not want to put too much on your plate, you can avoid the expense for the time being (even though it is not particularly high). Nothing prevents you from taking measurements later and refining or further developing the crossover at a later stage. Those who prefer to proceed step by step can skip the next article or postpone reading it. That is, of course, unless you want to build a baffleless loudspeaker: in that case, a microphone is mandatory... together with a healthy spirit of adventure!

How to go from simulation to physical construction and, if desired, to instrumental verification

The goal is to provide a clear and repeatable method that allows anyone to design passive crossovers without relying on generic formulas or random trial and error.

In the next article we will dive into a very delicate topic: how to correctly perform the necessary measurements. Get your microphones ready!

DISCLAIMER. TNT-Audio is neither a shop, nor a HiFi company or a repair laboratory for HiFi components. We don't sell anything. It is a 100% independent magazine that neither accepts advertising from companies nor requires readers to register or pay for subscriptions. If you wish, you can support our independent reviews via a PayPal donation. After publication of reviews, the authors do not retain samples other than on long-term loan for further evaluation or comparison with later-received gear. Hence, all contents are written free of any “editorial” or “advertising” influence, and all reviews in this publication, positive or negative, reflect the independent opinions of their respective authors. TNT-Audio will publish all manufacturer responses, subject to the reviewer's right to reply in turn.

Passive Crossover in the DSP Era

A Mini-Guide for DIYers and a Call Against the Unthinking Use of Fixed Formulas in Crossovers

Introduction

The crossover

FRD and ZMA: the Fundamental Data