I've noticed several waveguide/horns with midband ripple that was equalized using response-shaping tank circuits in the crossover.
In the past, I used to rarely see this practice used on compression horns, except as a peaking circuit for the extreme high-frequencies where compression drivers just had no output. Top-octave compensation was first-order to conjugate mass-rolloff, but sometimes manufacturers added an additional pole around 12kHz - 15kHz to counter the extra rolloff from voice-coil inductance. I don't know of anyone that tried to counter the final pole from the front chamber, which doesn't usually set in until around 18kHz or 20kHz anyway.
As for me, I simply avoided using compression drivers until they had evolved to the point where top-octave performance was good and no peaking circuits were required. My crossovers use a simple first-order slope to counter mass rolloff. It's pure and simple.
In fact, Pi Speakers have never used tank circuits for response shaping. It is nearly a philosophical choice for me, and the reasons are described in various documents. But to be brief, I tend to try and find acoustic solutions to acoustical problems rather than to equalize on-axis response, which often adversely affects off-axis response.
Only if the response is the same in all axes will "voicing" be right in all axes. If a designer uses tank circuits to mitigate ripple caused by directivity changes, then they are using electrical equalization to smooth on-axis response, but the end result is that power response is made worse.
One thing that quadratic waveguides and catenary (OS, PS or EC) waveguides have in common is that they are very nearly conical horns. These tend to be peaky if made too small. This is both because of internal quarter-wave modes and because of directivity shifts. Both are problematic, in my opinion.
If the horn is so short it is suffering from 1/4λ peaking
in its midband, then power response is varying as the horn is more efficient at modal frequencies than in between modes. So equalization can fix both on-axis and off-axis SPL, but the problem is the acoustic center is moving back and forth too. The movement of the acoustic center makes the forward lobe oscillate with the movement of the apparent sound source. Naturally, off-axis response suffers.
Alternatively, if the ripple is caused by directivity shifts
, then what is really happening is the horn is getting louder on-axis when beamwidth narrows and quieter on-axis when beamwidth widens. Conversely, it is getting quieter off-axis when beamwidth narrows and louder off-axis when it widens. These two are equal and opposite because power response is flat. So if response shaping is used to equalize on-axis response, then power response is modified and off-axis response suffers.
Likewise, I'm not sure I would want to incorporate response shaping for the ripple caused by the baffle edge
, for the same reason. It's a directivity shift, so equalizing on-axis flat makes power response non-flat. I'd rather have flat power response in a speaker designed for uniform-directivity. That is the point, after all.
For these reasons, I question the efficacy of response shaping in waveguide crossover circuits, beyond the simple first-order compensation for mass-rolloff. It may seem attractive to smooth response ripple in some devices, but I think if response ripple is excessive enough to require tank circuits, the waveguide itself is probably not worthwhile.