ORDER AND SLOPE OF FILTERS
Filters are grouped by orders according to the number of reactive elements that make it up. It is named first-order filter if it is made by a reactive element only: an inductor, as we have already seen, is a first-order filter. We'll have a second-order filter combining together an inductor and a capacitor, a third-order filter inserting a second inductor, and so on. Then we can attribute to a filter its order by counting the reactive elements that compose it. But beware, often instead of an only element it is preferred for various reasons to use a combination of two or more elements, connected in series or in parallel, according to rules that we'll best illustrate later on. In this case we'll refer to the combination as only a single component.
Every order is characterized by its own specific attenuation slope or rolloff. This represents in decibel per octave (dB/oct) the rate with which the filter operates the rejecting of the unwanted frequencies. Try to remember that the decibel is the unit of acoustic intensity, and that octave is generically called the space that runs between a certain frequency and its double or its half.
To better understand, try imagining
any filter. As we have already seen, it will allow the transit of a
certain portion of frequencies only. This portion takes the name of wave
band and to it is
assigned the conventional value of 0dB. At the cut frequency point
the signal will be subjected to an attenuation of
A first-order filter produces a rolloff of 6dB/oct. beyond the cut point. For example, a first-order lowpass filter with cut frequency tuned to 500hz, will let pass intact the lower frequencies, will return the 500s attenuated by 3dB, after which it will attenuate by 6dB the first octave (1Khz), by 12dB the second (2Khz), by 18dB the third (4Khz), and so on, with a constant — you'll say asymptotic to make a good impression at a cocktail-party — slope of 6dB for every next octave.
A second-order filter produces a rolloff of 12dB/oct beyond the cut point. Referring to the previous example, we'll always have the 500s attenuated by 3dB, but already the 1000s will be 12dB down while the 4000s even 36dB below. A third-order filter produces a rolloff of 18dB/oct beyond the cut point. A fourth-order filter produces a rolloff of 24dB/oct and so on, with an increase ratio in attenuation slope equal to 6dB/oct for every next order.
How do you decide a preference to any one order over another? It can be many reasons, from building easiness and musicality of lower orders, to the ability of the most daring ones to guarantee protection to overcharged transducers. But choice criteria, won't get tired to repeat it, never have to disregard the analysis of the characteristics of the speaker on which the filter must be closed. Among these one deserves to be analyzed in detail, the speaker dispersion