Theory of Multi-Way Loudspeakers

By Gauder Akustik

Why do we build multi-way loudspeakers?

Human hearing ranges from 16 Hz to around 16,000 Hz (at a young age), i.e. over 10 octaves, an enormous range when you consider that the eye can only see one octave. Accordingly, it is difficult for a single loudspeaker to reproduce this wide range of frequencies.

In the bass range, we need large, heavy cones with small magnets; in the midrange, we need light, much smaller cones with a strong drive; and in the treble range, we need very small, extremely light cones with the strongest possible drive. All of this follows from the laws of mechanics, strength of materials and, last but not least, acoustics.

As you can see, it is impossible to reconcile all these requirements. It is essential to make compromises here. A first compromise is to divide the 10 octaves between two loudspeaker drive units. Such designs are correspondingly diverse, as the proportions of the individual drivers can vary greatly. In the classic three-way speaker, three specialists share the 10 octaves, which can bring a significant improvement. The same applies to four-way loudspeakers. Five-way loudspeakers are extremely rare and hardly offer any further advantages.

The crossover

How do we build these multi-way loudspeaker systems?

A crossover is required so that the individual specialists are assigned their respective frequencies correctly. A crossover is a circuit consisting of inductors (inductance), capacitors (capacitance) and ohmic resistors, which are connected together according to certain rules to form so-called low-pass filters (only low frequencies are allowed through), high-pass filters (only high frequencies are allowed through) and band-pass filters (only midrange frequencies are allowed through).

Unfortunately, these low-pass, high-pass and band-pass filters, also known as analogue electrical filters, are not infinitely steep, so lower and higher frequencies can still pass through, although they are increasingly attenuated in the process. In the simplest filter circuits, they work with a slope of 6 dB/octave: every time the frequency is doubled or halved, the sound pressure level is reduced by 6 dB. A reduction of 10 dB corresponds to a halving of the volume. However, studies have shown that sounds at -40 dB can still be perceived clearly. So, if you cross over a woofer at 400 Hz with a 1st-order filter, this means that the woofer is 3 dB quieter at 400 Hz and then rolls off at 6 dB/octave above that frequency. At 3,200 Hz (three octaves higher), it is only 18 dB quieter, which corresponds to about a quarter of the volume. It therefore still contributes significantly and overlaps with the signal from the midrange driver. At 400 Hz, both are equally loud.

The same happens at 3,200 Hz, where the tweeter generally takes over sound reproduction. At 3,200 Hz, the midrange driver and tweeter are equally loud, and the midrange driver rolls off at 6 dB/octave. At 12,800 Hz, the midrange driver is therefore about 12 dB quieter, which corresponds to slightly more than half the volume. As midrange cones are heavier and larger than tweeter cones, many midrange drivers gradually stop producing sound at 7,000-8,000 Hz on their own. But one thing is clear: especially above 3,400 Hz, the wavelengths become shorter than 10 cm, and if two loudspeaker drivers emit the same signal, both signals interfere strongly with one another and thus distort the original signal. This cannot be beneficial. You lose the spatial information as well as the temporal impulse information. Because the attacks of individual instruments are now blurred, the music loses its drive and crispness. And that is what music is all about!

What is the solution? Either you use a full-range driver (which is really not a good solution), accept the shortcomings (6 dB/octave crossovers), or use crossovers that separate much more steeply, for example with 12 dB/octave or 18 dB/octave.

We at Gauder Akustik take this a big step further. We have developed a process in which the slope of our crossover filters exceeds 50 dB/octave. After less than an octave, our individual drivers are no longer audible at all. The overlap is therefore very small, meaning that each drive unit reproduces only the frequencies it is truly capable of handling. Interference effects are minimised. The impulse response is optimal (as confirmed by the trade press in every test), and the spatial imaging remains stable and expansive. So, when using our loudspeakers, you do not necessarily have to sit exactly in the middle. Of course, the electrical power-handling capacity is also higher, which dramatically increases the service life of the individual drivers. This is one of the reasons why we provide a 10-year full warranty upon registration.

However, due to the complex circuitry, our crossovers contain significantly more components than competitor products (for example, 64 components in our DARC 200 three-way speaker), making them larger and considerably more expensive. We also use selected, high-quality components to ensure that the circuits function precisely. All of this results in a significant cost factor, but we accept this even for the Arcona 40 in order to set a sound milestone in every class.

What are the disadvantages of higher-order crossovers?

The group delay, i.e. the time it takes for an electrical signal to pass through the crossover, increases slightly. However, this effect is much smaller than the settling time of musical instruments, and we also compensate for this disadvantage with our TDC technology.

As you can see, a sophisticated crossover is the most important component of a multi-way loudspeaker. That is why we devote so much time and effort to it!