Although the group delay can be obtained from the simulation, albeit indirectly, one doesn't really need to see it.
When applying the Linkwitz Ttransform filter, we are dealing with minimum-phase equalisation. Therefore, in terms of group delay, the behaviour of the subwoofer is a very well known quantity, as it corresponds to that of a 2nd-order Butterworth high-pass filter response function (Qtc = 0.71 was chosen as the target EQed response shape). Thus, there really is no need to check the group delay, as it is going to be better than that of a 3rd-order Butterworth high-pass function, which itself is better than that of a 4th-order (vented) Butterworth high-pass function, etc.
The other thing to keep in mind is that, for a second-order high-pass filter (e.g., a closed-box loudspeaker system), when the F3 is reduced by one octave, then the group delay near the cut-off frequency is doubled. The two are inextricably linked.
Hence, there's no need to look at group delay specifically, as it's just a by product of whatever the cut-off frequency is. Just keep in mind that the sealed
It is also worth noting that, for two closed box systems with cut-off frequencies F3a and F3b, where F3a < F3b, the system with F3a will have lower group delay over much of its operating range than does the system with the higher F3, F3b. This illustrates that, to some extent, having a higher peak group delay actually benefits the system's group delay response above the frequency where the peak occurs, plus we get the benefit of the additional bass output of course, which is going to be the very audible part of the overall system response.
To get the group delay, we need to specify what system we are considering. Is it the high-pass response of the sealed subwoofer, without the effect of the low-pass filter in the circuit? That's what most programs show. If so, then when the low-pass filter is removed, the F3 of the system is rises to F3 = 33.2 Hz. Below is the corresponding group delay plot of just such a system. This is the group delay curve of a standard 2nd-order Butterworth high-pass filter with F3 = 33.2 Hz, which corresponds to a sealed subwoofer with Qtc = 0.71.
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Noting that this subwoofer will be used to supplement an existing speaker system, it's worth looking at the group delay at low frequencies that occurs when the subwoofer is integrated with the main speakers. This shows that the group delay around 30 Hz is 15 ms, whereas the "perfect" subwoofer had a group delay of about 7 ms at 30 Hz. Apologies for all the other unwanted curves, but VituixCAD doesn't allow them to be turned off even though they are quite irrelevant.
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If we chose to use 2nd-order filters for the purpose of integrating the subwoofer with the main speakers, we would get the following results. This shows lower levels of group delay across the board. For example, compare the differences in group delay at 50 Hz for the two simulations. Funnily enough, the present 2nd-order filter setup has less group delay, but it also has 2 dB less output at 30 Hz. That is, its cut-off frequency has increased, reducing the group delay.
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And below is the simulation of a vented subwoofer instead of the sealed subwoofer. A bit of tweaking of the low-pass filter setting and gain has been required to get a reasonably flat integrated response. Note how the group delay has increased, but not by as much as might originally have been expected. Of course, as demonstrated before, some of that is simply due to the fact that the low-frequency F3 of this vented system is slightly higher than the F3 of the first sealed system that was analysed in this manner.
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