Combined acoustic/electric rolloff

[niacin]

I read that Joe D'Appolito had an interesting idea:

You take a small sealed box with Q=1.0.

You add a first order electronic highpass ahead of the amp (or just an R-C network): Butterworth, Q=.707.

You end up with a combined acoustic/electronic rolloff that is 3rd order Butterworth, Q=.707.

Question: assume my enclosure f3 is 150Hz. To what frequency do I set the R-C highpass to make this work, and what is the new f3 of the overall system?

Sounds like a neat trick, supposedly described in Speaker Builder 4/84, which I don't have, and my library doesn't carry, and I'm too cheap to spend $20 for a reprint, just to get one lousy equation!

Plus, I bet one of you smarties has the answer on the top of your head!


I'm planning to adapt this technique to a slightly different use too. I'm making some very tiny line arrays for PA use---for busking. I have 1016-type piezo horns, fs=3500 Hz, Q=1.0 (or very nearly) as I observe from the response graphs.

I want to add a crossover where a coupling cap feeds a resistive voltage divider (about 50 ohms total) then the voltage divider feeds the piezo.

On the one hand I get the attenuation I need to match the mids, on the other I get another rolloff pole making a combined 3rd order butterworth response. Then I just need a 3rd order lowpass for my mids. Voila. The classic odd-order crossover, MTM D'Appolito setup-- sort of

My mids only go up to 7K, not a lot of room to put a "normal" crossover between 3.5K and 7K, that's why I want to look at this technique. Plus it's simpler.

Can somebody remember the equation for this? .707 or 1.414 or whatever it is? Pretty please? W/sugar and cream?

[Saturnus]

I can answer the first part. You set the input filter at the same frequency as the box roll off is tuned to. If you use a different box Q, you'll have to experiment with the correct frequency.

[niacin]

Thanks....

But if my second-order speaker box is already -3dB at 150 Hz, and my first-order filter is also -3dB at 150 Hz...

That means my total response is now -6dB at 150 Hz, which means my -3dB point for the whole system has shifted upward to some new, higher frequency.

But are you pretty sure that the right way to do this is to cascade a first order butterworth filter Q=.707 with the second order chebychev speaker Q=1.0 at exactly the same frequency to make a compound third order butterworth overall response?

That info alone is a great help!.... I could probably figure the new f3 frequency just by carefully measuring from a 3rd order Butterworth response graph.... how far in frequency between the -3dB and -6dB points.....

[Saturnus]

Not quite. The point is that if the box Q is 1 then it's 0db at the tuning frequency and has a 1.25db peak at 1.414 times the tuning frequency. Combined with a Butterworth filter at the same frequency as the box is tuned at, it gives a combined N order Butterworth filter. Where N is the order of the Butterworth filter plus 2 from the acustic roll-off in a closed box.

This trick has been used for decades in prospeaker boxes. I think it was JBL that pioneered it.

It's an absolute must that the box Q is exactly 1. It is very hard to predict the behaviour otherwise, and it's likely that it wouldn't have the same effect at all.

EDIT: If you're certain that the box Q is 1 and the -3db point is 150 Hz, then the box tuning frequency is 1.207 higher, ie 181 Hz.

[niacin]

Well my box program, (AJ sealed designer), says that for Q=1.0, I will have:

an F3 of 171.3
and an Fb of 217.9

Those are in the ratio of 1.27 not 1.207 as you indicated. Typo? or is my box program wrong?

I see from the program's graph that the frequency response crosses 0dB at the box tuning of 217, and the peak is at 1.404 the box freqeuncy, exactly as you said.

So if I add a 1st order highpass filter before the amp, which is -3dB at 217Hz, my overall response should go from 0dB at 217, to -3dB at 217 Hz.

So that's my new F3 point for the system-- it just shifted up a bit from 171 to 217. And now it's 3rd order butterworth overall.

Cool!


Now I will REALLY stick my neck out and use the same technique on my piezo tweeter that seems to be Q=1.0 as well!

[Saturnus]

Originally posted by niacin
Those are in the ratio of 1.27 not 1.207 as you indicated. Typo? or is my box program wrong?

The result of too much alcohol intake over the years I guess. I was just writing it from memory. So the program is probably right.

[niacin]

Yeah tell me about it.! But only the weakest brain cells die, so we who drink are actually smarter. Survival of the fittest. Ha ha

Thanks for the valuable input on this project idea, O esteemed Copenhagian, I will try it...

We are making this micro-PA for our local Fire spinning group, who learned at Burning Man...

Thanks again.

[sreten]

Originally posted by niacin


Now I will REALLY stick my neck out and use the same technique on my piezo tweeter that seems to be Q=1.0 as well!

Hi,

Read the wiki on peizo's. Things are not what they seem........

/sreten.

[richie00boy]

This added 1st-order filter technique does not lower F3, in fact it makes bass response less extended as well as more thin-sounding. What it does do is provide some protection for the speaker and facilitate a certain type of crossover to be implemented.

The added filter resonance frequency must be the same as the box resonance frequency Fb, not F3. So taking your given example it would be 217.9 Hz.

[Saturnus]

Originally posted by niacin
Yeah tell me about it.! But only the weakest brain cells die, so we who drink are actually smarter. Survival of the fittest. Ha ha

An interesting theory which I'll take upon myself to test ... thoughroughly ... forthwith.