Subwoofer frequency response equalization
The subwoofer is intended for the frequency range below 40 Hz, where the response of the driver in the small box rolls off considerably. An investigation of power requirements had shown that it is feasible to obtain maximum excursion Xmax with a reasonable size amplifier. Therefore, equalization can make the unit into a useful subwoofer. The amount of equalization can be estimated from the [EQ] tab of closed-box1.xls , after the target response has been defined in block 5 under [Spec's].
The effect of the poles
at 30 Hz and 46 Hz will be canceled by zeros at the same frequencies, in order to
bring up the frequency response. The circuit for this is shown below. It uses
the layout of the WM1 printed circuit board .
Alternatively, the Linkwitz
Transform circuit topology could have been used, since even for this case of real
axis poles the realizability criterion k > 0 in block
6 under [Spec's] is satisfied with Fp = 20 Hz and
Qp = 0.5, for example. This circuit can also be accommodated on the WM1 board.
The above asymptotic match of the measured frequency response curve indicates
poles at 30 Hz and 46 Hz, which corresponds
to F0 = sqrt(30 x 46) = 37.2 Hz and Q0 = 37.2/(30 + 46) = 0.49.
The necessary boost in gain cannot be carried too far, or the equalizer circuit runs into voltage clipping at the power supply rails. Since it is likely that there will be some room gain at the very low frequency end, the response is not equalized to be flat, which helps with the clipping concern. A subsonic rumble highpass filter would defeat the purpose of the subwoofer. I have not found that rumble is an issue, if the subwoofer system is designed for large voltage swings and volume displacements.
The actual low frequency response curve was arrived at interactively, by observing the acoustic response, while modifying the two low frequency corners of the boost. The ultimate roll-off is governed by these new poles at 15 Hz and 6.4 Hz. The 450 Hz pole compensates for the rise in response as the woofer becomes directional. This removes associated phase shift from consideration when crossing over around 100 Hz.
Before the subwoofer can be used in a sound system, it must be matched up with the existing woofer. The necessary crossover circuitry can be constructed on the MT1 circuit board . The low frequency roll-off of the existing woofer may require additional equalization in order to obtain the desired acoustic highpass response. This can be accomplished with the biquad circuitry on the WM1 circuit board.
In my case, I have used at one time the LFE output of the Lexicon DC-2 processor, which has a 40 Hz lowpass function with 24 dB/oct roll-off slope and I relied on this unit to handle the integration with the left and right speakers in my system. Now I use dedicated circuitry to divide the preamplifier output signal between THOR and ORION in order to obtain an exact 40 Hz LR4 acoustic crossover between each main speaker and its subwoofer. The two THOR units are placed together on the floor in the left front corner of my living room which is still acoustically close at 40 Hz to the radial distances from my listening positions to the main speakers.
THOR can be used as a subwoofer for the ORION to increase its low frequency output volume. It can, of course, also serve as a regular woofer, when crossed over around 100 Hz to a midrange. In that application it may not be necessary to equalize it at all, since the frequency response roll-off is gradual and only 6 dB down at 30 Hz. But an active crossover is needed. The design procedure for the crossover is as follows: