Passive speakers work in the analogue world and have no power supply. The central element of a passive loudspeaker with multiple ways is the crossover. It assigns the frequencies to the individual ways. This is done using a more or less complex circuit consisting of inductors (inductance), capacitors (capacitance) and resistors (ohmic resistance). An inductor blocks high frequencies, i.e. it works as a low-pass filter, and a capacitor blocks low frequencies, i.e. it works as a high-pass filter. A resistor reduces the sound pressure level of a single loudspeaker driver but works equally well at all frequencies.

If an analogue, passive low-pass filter has a cut-off frequency of 200 Hz, this does not mean that it completely cuts off all frequencies above 200 Hz. Rather, it starts to suppress frequencies above 200 Hz more and more. For example, a 1st-order low-pass filter attenuates at 6 dB/octave. If you consider that a reduction of 10 dB still means half the perceived volume, you realise that such a woofer still plays far into the midrange and high-frequency range.

Higher-order filters, which attenuate 6 dB/octave more steeply with each order, help to counteract this. A 3rd-order low-pass filter attenuates at 18 dB/octave but also requires three components.

What are the advantages of high-slope filters?

1.     With flat filters, several drivers play simultaneously in each frequency range. Since the individual drivers are built completely differently, often have different cone materials and completely different sizes, this leads to:

a. Frequency-response errors, i.e. inaccurate tonal reproduction
b. Directivity effects and shifted dispersion characteristics
c. Phase errors, which manifest themselves as undefined spatial imaging
d. Impulse errors that make the music sound bland, un-dynamic and insignificant
e. Severe distortion at higher volumes, which sounds very unpleasant
f. In addition, the power-handling capacity of the individual drivers is electrically and mechanically lower, as they have to reproduce frequencies for which they were not designed

2.     Since the individual drivers are exposed to much higher electrical and mechanical loads, they must be designed and constructed accordingly. However, since a midrange driver has to fulfil fundamentally different requirements than a woofer, only a compromise driver that is neither a true woofer nor a true midrange driver can be used with flat filters. Perfect music reproduction is therefore more or less impossible, or at least severely limited.

All these disadvantages can be avoided by using high-slope filters. What are the disadvantages of high-slope filters?

a. They require more components and are therefore considerably more expensive.
b. Their calculation is much more complicated and requires sophisticated mathematical knowledge and advanced calculation methods.
c. The group delay, i.e. the time it takes for a signal to pass through the filter, is somewhat longer. The designer must take this into account as far as possible, but the delays are generally at the threshold of audibility and are therefore not significant.

A sophisticated theory of loudspeakers and multi-way systems must therefore be developed. This is exactly what we at Gauder Akustik have been doing for the last 30 years. Find out more in our videos on our YouTube channel, in which Dr. Gauder explains the basic ideas and calculations behind our loudspeaker mathematics:

https://www.youtube.com/watch?v=jz2sIYqfIVg&t=1s

https://www.youtube.com/watch?v=74x4JAAXAVQ

https://www.youtube.com/watch?v=2hFYsImgHS4&t=133s

as well as:
https://www.youtube.com/watch?v=y-JfgHVKzdk

https://www.youtube.com/watch?v=RAKnjraHIz8&t=2s

Our speakers all work with slopes of 50 dB/octave and more. This avoids all the disadvantages of flat filters described above and allows us to build truly specialised drivers. This is an immense advantage. And that is why our speakers sound so open, clear and spacious, with a wide listening area that provides a great, balanced sound image throughout the room.