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What's the difference between a Butterworth and Linkwitz-Reilly?

Truely an interesting situation.

The inductance/impedience of the 2241H woofer is creating a second order filter for the 2251J mid. When the 2241 woofer is disconnected, the slope on the mid appears as a 1st order (on the 61-band RTA) letting the speaker play to <100 Hz petering as it goes down, with some peaks, from ~1kHz. But there is a suck-out/drop-out at ~350 Hz.

When the 2241H is connected, the mid goes to a second (or more) order filter falling like a stone at ~350Hz. But the entire band above this is pushed up flattening it out up to the ~1kHz peak. If the 2241 is replaced by an 8-ohm non-inductive resistor, the mid does not fall like a stone at ~350Hz and largely resembles the curve without the 2241 connected, just falling a bit more at toward bottom end of <100 Hz.

The arrangement seems to have little measureable effects on the 2241H and its spectrum looks pretty much the same with or without the additional connection to the 6.8 mfd cap. Perhaps there is a bit more roll-off above the 350 Hz crossover frequency (notable at ~500Hz and up) which is a welcome trait. The 6.8 cap also controls the upper range of the 2251J up to its crossover point and a larger value increases the rolloff while a smaller value decreases the rolloff increasing brightness. The 6.8 looks to be about the flattest using common values.

Recognize that unlike the 2241H, the 2251J has no inductance (differential drive with a neodynium magnet) and any loss to the upper frequencies of the 2241 is from the combination of the 6.8 mfd through the 16 ohm load (of the 2251J) to ground which is very minor when compared to the 47 mfd dumping to ground directly.
 
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