Every home/office/etc that I have measured (or friends) using SMAART needs extra delay (compared to just distance) on the mains to get the best phase relationship (in the MLP) between the subs and mains. This isn't models, this is actual measurements in a room. Every video online that I have watched on how to get proper phase integration (from people measuring phase directly) has had the same thing, some of these are huge concert halls to big meeting rooms, etc.
I fully recognise that analog filters have group delay associated with their responses. Maybe you could have expanded on the important features to make things clearer.
When trying to achieve smooth integration between a subwoofer and the main speakers, there is a need for complementary filter responses in order to get good results. That's a basic tenet of loudspeaker crossover design. Any group delay in the LPF and HPF sections needs to be complementary in nature in for smooth blending between the responses to occur. Keep in mind that my models have included the natural responses of the subwoofers and the main speakers to some level of fidelity, with the phase responses being embodied in those models.
The same principles apply to the blending between woofers and midranges, or bass-mids and tweeters, or midranges and tweeters. There is nothing special about the response of a subwoofer. It is just like a bandpass filtered midrange unit, albeit with the frequency response of the midrange being suitably scaled. The subwoofer-to-woofer integration behaves substantially like that of a midrange-to-tweeter integration problem, albeit the subwoofer often has a natural bandwidth measured in octaves that is likely to be less than that of a typical midrange unit.
Have you measured phase in a room directly using software like Smaart or Open sound meter? If not try it and then we can continue these discussions.
I've measured magnitude and phase responses of loudspeakers when designing and building crossover networks for two way loudspeaker systems using CLIO and IMP. I am aware of concepts such as phase cancellation, polarity reversal, group delay, and time delay. VituixCAD has many features for including all of those effects in the simulations, and I have made use of them over and over again. In any measurements, just like in models, it is important to identify the contributing factors. So, please, continue the discussion if you would care to do so.
The following is a simple model created in VituixCAD. It has a subwoofer with a 4th-order Butterworth HP response that is –3dB at 20 Hz. The subwoofer's natural response at high frequencies is assumed to be a 2nd-order Butterworth LP response with a –3dB point at 180Hz. These seem quite typical behaviour of a good subwoofer.
In this particular example, the main speaker is assumed to have a 4th-order HP response that is –6dB at 80Hz, with the response shape being that of a 4th-order HP Linkwitz-Riley filter. It should be possible to build a speaker such as this. After all, it's just another filter shape, and the Thiele-Small vented box theory spent a lot of effort analysing maximally-flat vented systems as these are usually desirable.
From the plot below, it is evident that,
even without any delay on the main speakers, we get almost textbook-quality smooth integration between the subwoofer and the main speaker. Why might that be? There doesn't appear to be any "inherent delay" in the subwoofer's response that causes grief for the correct and smooth integration of the two response functions. Or am I missing something here? Of course, the implementation of the Linkwitz-Riley filters needs to be in the analog domain, so that there is no DSP processing delay added to our system. Or if there is DSP filtering at work, then the processing delays on the subwoofer and main speaker should be
identical for this simulation to be accurate. That much we can understand from this simple model, let alone accurate measurements. Furthermore, the slight dip around 200Hz is caused by a mismatch in the phase response between the acoustic filtered outputs of the subwoofer and the main speaker. This is caused by two factors: 1) the natural LP response of the main speakers and 2) the natural bandpass response of the subwoofer, in the frequency range of interest.
Now, if the output of the subwoofer is delayed by 5.5ms relative to that of the main speaker, then we get the following response. The response has a pronounced dip just above the crossover frequency. Note that this time delay is not inherent in the subwoofer, but could be due to some DSP-associated processing delay. The 5.5ms was chosen as it seems to be representative of DSP-assisted subwoofers, so might be often encountered in practice.
Why is the dip centred on a frequency a little higher in value than the crossover frequency? It's not due to any inherent delay in the subwoofer, but simply due to the fact that the LP and HP responses are not exactly complementary in the strict Linkwitz-Riley sense. They are close, but not perfectly matched in this particular case.
How do we fix this problem that has been introduced by delaying the output of the subwoofer relative to the output from the main speaker? The deep null suggests, to those who may have simulated and/or measured such behaviour, that a polarity inversion could help. The following plot shows the result obtained when the polarity of the subwoofer is inverted (many subwoofers have this ability). However, although we have inverted the polarity of the subwoofer, the summed response is nowhere near as flat as that which was shown on the first plot. The reason for this is that the time delay added to the subwoofer has a linear phase response.
As the phase response of acoustic outputs of both the subwoofer and woofer is nonlinear, trying to correct the large dip via a simple polarity inversion is not quite sophisticated enough, as the results above clearly show. In this instance, the best approach would be to add a delay of 5.5ms to the main speakers, and we then would get the good integration shown in the very first plot. As is seen above, this is another example of the Linkwitz-Riley filter topology's remarkable tolerance to phase errors in the acoustic HP and LP responses, which was pointed out by Linkwitz in his journal paper all those years ago, and hence the popularity of Linkwitz-Riley filters.
This example hopefully helps to illustrate that the subwoofer has no inherent delay, and it can be treated just like any other filter response function. If there are delays that show up in the measurements, then they are coming from other sources.