Filter implementation

Electrical filtering of the audio bandwidth is necessary. This can be done either through passive filtering or active filtering.
A passive crossovers is the traditional way to set up a filter design for speakers. Here, inductors and capacitors possibly in combination with resistors are used directly on the speaker terminals. The filter components must be calculated to handle the power requirement.

Active versus passive crossovers.

Active crossovers indicate the way in which electronic filtering before the power amplifier is applied. Usually opamps perform this task in combination with capacitors and resistors. Some differences between active filters and passive filters can be mentioned. This is just a limited list of differences and, in my opinion active filtering is actually always superior to passive filtering with the disadvantage of a more complex electronic filter/ amplifier system and thus more expensive.

  1. Less inter modulation distortion (IMD) because each power amplifier is used in a restricted bandwidth.
  2. Less low frequency overload of amplifier especially for the higher frequencies (above 100Hz).
  3. Increased dynamic range. A combination of a 60W and 30W amplifier (active) will reach comparable results on power and distortion level as one 175W amplifier with passive filtering.
  4. Improved impulse behavior for all frequencies.
  5. Prevention of high frequency resonance's that might be caused by passive filters.
  6. Better and more accurate filter results because of the constant load of the amplifier with one single speaker without passive components.
    This is also because active filtering allows easy manipulation of important quantities like amplitude, phase and group velocity.
  7. Improved subjective sound quality with active crossovers.
  8. Easy adaptation of SPL of each speaker to the room acoustics with active crossovers.
  9. Better coupling of low frequency amplifier to the woofer. Speaker wiring is very short.

Implementation of the active crossovers.

In the speaker design on this web, active filtering is the key issue in the total design. All simulations on filter matching between speakers as described below are based on the mathematics of filters given on this website. The results of these simulations are shown in the graph for the complete speaker system.

filter_calculation.gif (17188 bytes)

The full crossover uses natural (second order) filtering via closed box design, Butterworth (BW) and Linkwitz-Riley (LR) filters. The audio set is combined with speakers specificly designed to work with the electronic filters. It uses a separate subwoofer and two speakers for the left and right channel (satellites) which, by itself can cover the full audio range.

The realisation of the active filters with its physical parameters is done using an own created program which calculates the (summing) reponses of the crossover (see picture above). Simulations on the electronic implementation is done using PSPICE. The graphs are shown below for the bass section. Different filter sections are displayed.  simulation_bass_small.gif (10859 bytes)

The blue curve in the amplitude-frequency characteristic indicates the resulting gain at the output of the filter. The green and red curve are from the high and low pass sections. The other graph shows the group velocity also for the same filter section. It can be observed that, for creating the correct amplitude curves, the group velocity rapidly increases near 25Hz (the yellow curve is the filter output). Nevertheless, this is already close to the inaudible bass range and will not negatively affect the bass perception.sim_bass_vg_small.gif (10491 bytes)

The bass speaker is connected to the following three filtering parts:

  • Subsonic filtering at 19 Hz using BW filter. This is required to avoid extreme cone displacements in the subsonic region (some CDs still have information in these low frequencies). When not filtered effectively this can damage the woofer mechanically. It is chosen to use second order BW filters in order to obtain a rapid roll-off below 20 Hz without affecting the 20-30 Hz region to much in SPL.The effect of natural roll-off of the speaker in its enclosure is accounted for.
  • Adaptation of the bass response using a Linkwitz-Riley transform. This transform controls and amplifies selectively those frequencies that have poor performance when the speaker is used in a closed box. The transform is calculated to operate with a total Q=0.71 and a Fc=31Hz. The maximum gain (A) =6.5dB at 25Hz. This improves the bass response at the very low end to fully cover the normal audio bass range. The addtional gain, however, reduces the maximum electrical power to the speaker since this means that the speaker has to handle 4x more electrical power at 25 Hz. This drives the speaker quickly to its limits. Also the amplifier must be capable of delivering this low frequency power to the speaker!. Don't underestimate the buffering capacity required for this!!
  • Low pass filtering using second order BW filtering at 75Hz. Here, BW is chosen from calculations which indicates that BW gives the best match to the bass-mid speaker.
  • bass_filter.gif (5584 bytes)

    The bass-mid speaker:

  • High pass filtering is applied to match the bass speaker without having a too large boost around 100Hz. The bass-mid needs slight filtering in the low end to avoid this boost. The acoustical response from this speaker is modeled as a second order filter (closed boxed). In Combination with this natural roll-off of the speaker, a second order LR-filter is used with Fc=40Hz. This results in a good match with the bass. It is assumed that bass and bass-mid are in one line in the room (equal distance to the speaker). Although this will not always be the case, the effects of a phase difference is not too dramatic since the wavelength at 100Hz is very large.
  • Given the acoustical response of both bass-mid and tweeter, the best crossover frequency is 2kHz. A low pass fourth order LR-filter is used here to combine to a perfect flat response. To make the theoretical transfer function within electronic design, a slight deviation from 2kHz was necessary. The effect of it has been checked on the total acoustic response.
  • mid_high_filter.gif (8380 bytes)

    The high speaker:

  • High pass filtering is applied to match the bass-mid speaker. Also here a fourth order LR-filter is used. Since the crossover frequency is close to the resonance of the tweeter, the natural roll-off of the tweeter is used in the filter calculation by means of a second order filter. This model fits very well the real acoustic response as compared with the datasheet.
  • To correct for horizontal displacement (phase difference) between bass-mid and tweeter, an electronic delay is inserted of 60us. This was the maximum delay that was reasonably available from using one opamp at this crossover frequency. Further delay correction (a total of 180us is needed) is done through mechanical construction. Alternatively, additional opamps can be applied for the full correction (but in this design one opamp was left over and mechanical displacement appears to have its advantages).

  • Measurements on the electrical crossovers are indicated below. It shows a perfect match to the targeted calculations and simulations.

    filter_measured.gif (18015 bytes)


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