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Crossover and price
It has long been known that a slight change in the crossover frequencies of the bass and midrange bands in a three-way system can have a noticeable effect on the sound. In different parts of the range of audible frequencies, the human ear uses different ways to determine the direction to the sound source. In the mid-frequency range of interest to us, the phase mechanism of perception predominates, based on the difference in distances between the sound source and the ears. The boundaries of this range (from 350 to 1700 Hz) are determined by the size of the human head (or rather, the distance between the auricles). However, what is important for us now is that both the frequencies of the section of the LF and MF bands in a three-band system, and their "vicinities" fall into this critical range. Since the crossover cannot provide perfect separation of the bands, there is a zone of joint action in which both speakers sound at the same time. Phase shifts between the signals reproduced by them have a significant impact on the formation of the scene. The sum of signals arising in this range can improve the focus of the stereo image, or it can also blur the scene. The phase distortions of a high-quality system should be minimal, but this is only one side of the problem, giving food for reasoning about the musicality of filters of various types. Not only the absolute phase shift introduced by the filter is important, but the relative shift between the frequency bands at the output of the filters is much more important. But more on that later. The phase shift and roll-off slope of the frequency response (AFC) outside the passband of the filter is determined by its order and is 90 degrees and 6 dB/octave per order. That is, the first order filter provides 6 dB/octave attenuation with a full phase shift of 90 degrees, the second order filter provides 180 degrees and 12 dB/octave, and so on. At the cutoff frequency, the filter attenuation is 3 dB, and the phase shift is half of the full value (i.e. 45 degrees for the 1st order filter and 90 for the XNUMXnd order). Only the smoothness of the bending of the frequency response in the region of the cutoff frequency and the total frequency response of the system, as well as the phase characteristics, depend on the type of filter. In industrial designs of active crossovers, Butterworth, Bessel and Sallen-Key filters built on repeaters are most widely used. As a rule, second-order filters are used. Each of these types has its own advantages and disadvantages. Bessel filters have the smoothest phase response (like a single RC circuit), but the overall frequency response has a 3 dB dip at the crossover frequency. Butterworth filters provide a flat overall frequency response, but their phase response is steeper. Finally, Sallen-Key filters (equicomponent filters) are very convenient in mass production because (as the name implies) they require parts of the same rating and with a large tolerance, which is not the case with Butterworth and Bessel filters, which require precise parts. However, the phase and frequency characteristics of equal component filters are the worst, so they are used only in budget models.
The most interesting thing (as promised) is not in the frequency and not in the phase characteristics, but in the relative phase shift of the signals between the outputs of the HPF and LPF. For second-order filters, it is close to 180 degrees over the entire frequency band, but it remains constant only for the Butterworth filter. For Bessel and Sallen-Key filters, the phase shift decreases near the crossover frequency. The simulation result of "ideal" second-order filters with a crossover frequency of 400 Hz is shown in Figure 2.
The resulting "hump" on the phase characteristic indicates that the phase difference in the region of the crossover frequency changes quite sharply, and the localization of the apparent sound source can also change accordingly. The same picture will be observed when changing the cutoff frequency of one of the filters, which is sometimes used when adjusting the total frequency response of the system. The phase of the signal emitted by the dynamic head has little in common with the phase of the voltage applied to it (it is individual for each type of head), but it is desirable to minimize distortions of this kind in the crossover. Any filter (both active and passive) uses reactive elements - capacitances and inductances, therefore it introduces phase and time distortions into the signal. LF filters (Low Pass) introduce delay and phase lag into the signal, which can be corrected to a certain extent by the phase shifter. By using a second-order Bessel filter in combination with such a phase equalizer, a filter with a perfectly linear phase response can be obtained. As for the HPF (High Pass), they form a phase advance, which is fundamentally impossible to match with the existing LPF. However, in this case, it is possible to use an additional function filter (AFF) to form the high-band signal. The output signal of such a filter is obtained by subtracting from the input signal its part that has passed through the low-pass filter. Obviously, in this case, phase distortions are compensated and the phase difference of the signals at the output of the LPF and FDF remains constant over the entire frequency band. However, the filters of the additional function have a significant drawback - the steepness of the falloff of the frequency response is only 6 dB / octave, which can sometimes be insufficient. By the way, according to this scheme, crossovers are performed with synchronous adjustment of the crossover frequency of adjacent bands. Only the low-pass cutoff frequency is adjusted, and the high-frequency band is synchronously changed by using the auxiliary function filter. To tune the cutoff frequency in the active filter, it is necessary to synchronously change the values of the frequency-setting links. Potentiometers are used to smoothly adjust the cutoff frequency. It is easy to calculate that a four-section potentiometer (for two channels) is required to tune the second-order filter. In order to reduce the cost in recent years, budget amplifier models are increasingly using simplified second-order filters, in which only one link is tuned in frequency. Such filters cannot be attributed to any specific type, because an "ideologically consistent" filter is obtained only in one of the extreme positions of the regulator.
Finally, in the bass section of the built-in crossovers of some amplifiers, a variable Q high-pass filter is used, which makes it possible to obtain an increase in the frequency response in the region of the cutoff frequency up to 10 dB. This solution eliminates a separate bass booster stage, but at the same time introduces significant phase distortions. In this case, this is quite acceptable, because at a frequency of 30 ... 40 Hz, the phase shift is not perceived by ear. However, in the mid-frequency range, where the phase mechanism of signal source localization works, it is desirable to use phase-linear filters to better construct the frontal scene. This will eliminate the "blurring" of the scene and increase the accuracy of localization of apparent signal sources, especially with spatially separated bass and midrange emitters. Publication: www.bluesmobil.com/shikhman
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