No, it's a "Moog like" structure of four single-pole elements with global feedback around the whole lot. Structurally much more like those allpass filters we were discussing in another thread, in fact.

Yep, I did see the similarity.

It's four first order highpass filters. I don't see anything second order about it, although that may be equivalent.

It's pretty common in filter language to bundle two first orders and consider these a second order with Q=0.5. It then becomes

fairly obvious that the peakyness goes up and the (initial) roll-off goes up as you increase the Q. Second order Q=0.5 is *identical* to two first orders in cascade which have the same frequency w0.

(this is drawn with the same asymptotic roll-off vs frequency.)

I don't agree about "sloppy rolloff". Your graph shows a drop of around 75dB in the decade from 1KHz down to 100Hz. That's pretty close to the theoretical 24dB/oct that we expect, and if you measure it better than me eyeballing it, you might find that's exactly what it is.

Sure, but that's the slope some distance away from the cut-off; the so called asymptotic roll-off which depends only on the order of the filter. The Q has the most effect near the cut-off. It's a very strong effect.

Here's four high pass filter responses with matching -3dB points

- 1x second order Butterworth (Q=0.707); total order 2

- 2x second order Butterworth (Q=0.707) in cascade; total order 4

- 1x fourth order Butterworth (Q=1.307 and Q=0.541); total order 4

- 2 x second order Q=0.5 (critically damped); total order 4

As you can see the roll-off rate near cut-off of the 4th order 2xQ=0.5 is in the ball-park of the 2nd order Butterworth. The true 4th order Butterworth has the highest roll-off rate near the cut-off of all the examples.

*Why* do we want to do this? What's wrong with the perfectly good 4-pole highpass filter you've already got?

The reason why we care is the OP already has a design which is a 2nd order Butterworth. So going to a 4th order 2xQ=0.5 isn't going to add a lot but it's a lot more complex.

The ultimate aim is to model the horn speaker of the megaphone. Some horns have fairly steep initial roll-off so the next step up from the existing 2nd order Butterworth design would be a 4th order filter based on highish Q's

Here's a horn tweeter response. Obviously the cut-off frequency is higher than a megaphone but look at the roll-off. About 26dB in an *octave*; so close to the 4th order Butterworth case.

I don't understand this. Boosting the feedback boosts the Q, and the Q makes a peak. What did you expect the Q to do if not this?

Flipping the phase of the feedback is obviously going to break things.

All I was saying is the way I've drawn it is the best peak you are going to get. I *tried* the opposite peak in case I'd got the phase of the feedback wrong in the sim. Also since the loop is 4th order the flip might put a peak in another place.