... please don't phase me in ...
Small SubWoofers
Small subwoofers try to squeeze 10 pounds of performance into a 1 pound box. Thus, they need to 'adjust' the amp response to provide reasonable performance from a driver and volume smaller than could be considered optimum. The Force Sub uses a 250W OEM amp to power a custom 10' driver and claimed remarkably good performance of 20-250Hz ±3db. The Force is no longer manufactured, but its principles apply to small sealed subs.
Force measured near field performance. 20-200Hz ±3db which is more in keeping with two 2nd order filters of 232Hz. Top trace is level. Input level for nominal 85db listening position. Registered 120db is due to microphone proximity. Bottom trace is Phase, output inverted, and is remarkably good considering the Input Equalizer phase shift. All in, a well designed product. Sadly, no longer made.
The Force Amp
The amp has a large 15db @10hz low end gain starting @ 40Hz to linearize the driver and box. Whenever an equalization is applied, Phase is affected. It's important to remember this when adjusting filters as every filter adjustment may require a phase adjustment as well.
The Force uses an All-Pass filter to adjust phase. Input Eq Gain phase shift negates the phase control markings in absolute terms and they should be used as reference only. All-Pass phase controls operate at only a single frequency with varying degrees of shift across the passband. The horizontal bars on the 22.5° to 135° lines cross at about the frequency at which the marked phase occurs for the All-Pass filter alone. The 0° 90° frequency is 2341Hz and the 180° 90° frequency is 4.67Hz. Note that the phase is not constant across the sub's range. Input Eq Gain phase is added to these values. Filter phase is subsequently added. And finally, the actual driver response. In other words, one might as well adjust the control blindfolded.
The filter section consists of two 2nd order nominal 35-250Hz filters, 39-232Hz for installed component values. 2nd Order filter phase is about 90° at the corner frequency. Both Level and Phase are cumulative, thus by careful adjustment of the two filters one can approximate a desired level and phase. The graph shows the combined level and phase response of A 130Hz and B 180Hz.
The graph shows the cumulative input, phase and filter for the overall amp response. As can be seen, the phase, and hence time, response @ 180° is much worse than at 0°. The dotted lines show tΦ in milliseconds. Spica's Servo subwoofer used a nominal 18db/oct filter and was inverted polarity. The advantage of this arrangement is, with the Spicas rolled off an additional 6db/oct, the sub can be placed in the same plane as the mains, summing will be in phase and the total phase error will be the minimum possible. At John Bau's suggestion, I added a hardware Phase Invert for an absolute 180° flip to use in concert with the Force phase, low pass filters and passive XO1.
Small loudspeakers are not known for their stellar low end performance. The Spicas have an approximately 2nd order attenuation below 65Hz. Other small speakers will have variation on this theme dependent on the designer's chosen parameters. The combination of the
XO1 and Spica response makes for a quite complex filter slope. Integrating the Force, or any 3rd party small sub, is a tedious process. One would do well to ignore the pot legends and simply think of them as More & Less. The graph shows the
predicted response of the Force / Spica combo
after adjusting the controls by ear.
Better than ±1db! Phasor Vector sum is also within ±1db. Not too shabby.
The Importance of Phase
Phasors
This graph shows the effect phase settings of 0°, 90° and 180°. Sub polarity is inverted. The graphs are vector sums of the amplifier level and phase. Since the level does not change with an All-Pass filter, the level sum is the same for all phase settings. However, when the signal phases are included in the vector sum, the level changes dramatically.
This graph shows the optimum phase setting of 34° and its 4 inch offset from the mains. Additionally, the effect of moving the sub forward and backward 3 feet. Note how very little effect this has, as would be expected with wavelengths of several feet.
In an actual room, boundary effects will modify the response curves, affecting sub and main frequencies to varying degrees based on the sub and main boundary distance deltas.
Sub setup is definitely not plug and play.
Connection
Taking a high level input to a sub from a Tube Amp is a Very Bad Idea.
The speaker impedance controls the LEVEL INPUT TO THE SUB.
The input to the sub is ≈7.7db lower at 20Hz than 60Hz. Blecchh !! Many speakers are many times worse.
SS amps will exhibit considerably less change, but are NOT immune to LS impedance.
Current drives the LS and is not in phase with the voltage driving the sub. The sub introduces its own phase errors which is why ALL subs need Continuous Phase and Polarity controls. Without them, unless the sub was engineered for the system, it’s a crap shoot. Mostly crap!
ROLL THE LOW END FROM THE MAINS AND USE THE SUB LOW LEVEL INPUT !!!
A simple passive XO @ ½ to 1 octave above the main LS anechoic -3db point is a good starting point.
Setup
Finally