Greater than 20dB gain at DC with Linkwitz Transform - bad?

[Jim85IROC]

I've been playing with the FRD Consortium's subwoofer designer spreadsheet to get some ideas for a tiny-box subwoofer.

Anyway, I've read online that you shouldn't allow your DC gain to exceed 20dB, but nobody really seems to say why. I designed a transform filter, supplimented by a high Q 2nd order high pass. The resulting Linkwitz transform gives 20.8dB of gain at DC, but the graphs indicate that with 100 watts, I'll be below xmax at all frequencies, and in fact, when I do reach x-max, it's at approximately 32hz, not any lower thanks to the high Q high-pass that I've implimented

So... is there a circuit-based reason why this "20dB" number can't be exceeded, or is this just a safety precaution to prevent overexcursion at subsonic frequencies?

[mazurek]

The real key is that when you design and test the circuit, you should measure the actual dc gain on it. More than ~40 mV will yield an audible pop on turn on, if you get to a couple hundred mV or higher, you are just wasting power and heating up your voice coil, and potentially not making the psu happy.

You can play with your filter structure to mediate the DC problem by putting high pass after the linkwitz transform, or dc blocking caps. Also pick op amps with a low dc offset.

[Jim85IROC]

The high-Q high-pass that comes after the Linkwitz transform should knock down virtually all of the DC gain before it ever gets to the amplifier, so I'm not really worried about a DC offset at the output of the amp. I'm more concerned about overloading the output transistor of the Linkwitz circuit or perhaps an input buffer that may be present on the inputs of the plate amp before the high-pass can knock down the gain.

[gmikol]

Originally posted by Jim85IROC
I'm more concerned about overloading the output transistor of the Linkwitz circuit or perhaps an input buffer that may be present on the inputs of the plate amp before the high-pass can knock down the gain.

This is a legitimate concern. A typical full-scale input of about 1Vrms below the tuning frequency of the LT (like something you might find in the WOTW DVD from what I hear), turns into a 10Vrms = 14.14Vpeak output. This will almost certainly send your opamp into clippng, unless it's designed for rail-to-rail swing at those kind of supply voltages, or maybe if your opamp is running off 18V rails like the OPA2134 can.

You run the risk of higher noise, but you may want to scale down your input to the Linkwitz circuit by 6dB or even more.

Also, I'm not sure having a "high-Q" HPF after the Linkwitz is such a good idea. That's adding even more boost near the corner frequency of the HPF. The only way this makes sense is if your Linkwitz Q is <<0.7, like you would for a 4th-order Butterworth where 1st-stage Q is 0.541 and 2nd-stage Q is ~1.3.

Hope this helps.

--Greg

[AndrewT]

Hi,
I have never built nor even investigated a Linkwitz transform, so I might start talking through a hole in my hat. But here goes anyway and if I'm wrong please put me right.

That gain of +20.8db is relative the the rest of the frequency range.

If the bass unit and the rest of the speakers are the same sensitivity then it follows that when the bass unit reaches it's 100W limit the rest of the speakers are receiving 830mW of power.

That puts the SPL at a fairly low level for normal speakers.

Buying more powerful bass drivers only helps a little since the extra power is often swapped for reduced sensitivity.

Let's try a 1000W 87db/2.83V bass driver with 20.8db gain then the main speakers at 90db/2.83V would need 3db less than before i.e. 830mW multiplied by that factor of 10 and devided by 2.
The result is the main speaker is now up to just 4.15W when the 1000W speaker reaches it's new limit.
Your overall SPL is about 6.2db (4.15W) + 90db = 96.2db loud but not particularly so if the average level is 20db below this peak level. (76db is a conversation at 500mm).

I see three options:-
less transform gain.
high bass driver sensitivity
quiet listening only.

The pre-amp overload problem is easily overcome by adjusting the bass amplifier gain.

[Jim85IROC]

Originally posted by gmikol



Also, I'm not sure having a "high-Q" HPF after the Linkwitz is such a good idea. That's adding even more boost near the corner frequency of the HPF. The only way this makes sense is if your Linkwitz Q is <<0.7, like you would for a 4th-order Butterworth where 1st-stage Q is 0.541 and 2nd-stage Q is ~1.3.

I'd show the transform, but it's on my work computer and I'm home right now.

If memory serves me, the F3 of the woofer is about 66hz and the Q is .7. The new F3 selected is 18 or 20hz with a Q still of .7. The resulting plot shows a smooth rolloff, but the whole pass band is about 3dB below the 100hz-up response. I then selected a high pass with a Q of about 2 at 35hz. This gave a boost that brought up the area below 100hz, and also rolled off the response below 35hz rather sharply. I adjusted it until the output followed the x-max slope of the driver at 100 watts. The result is a dual 8" woofer enclosure of .3 cubic foot volume that should achieve SPLs in excess of 105dB, and will never exceed x-max as long as power is kept under 100 watts.

This of course assumes that the electronics don't hate the design.

[gmikol]

First...what's the 8" driver that you're using?

If the Fc of your HPF is at 35Hz, Q=2, there's no reason to extend the Linkwitz all the way to 18Hz. You're eating up overhead for no reason. I go back to the suggestion I made in my previous response. Try modeling the following:

Linkwitz Fc=35Hz, Q=0.54
HPF Fc=35Hz, Q=1.3

This gives you close to a 4th-Order Butterworth (maximally flat) response out to 35Hz. You can push the Fc down a little bit, but keep an eye on excursion. This should limit the DC gain of the LT, and still provide a fairly steep roll-off below 35Hz.

I'm at work, too, so I don't have the graphs to prove it, but I think that this will provide for a lower group delay at 35Hz. If the difference is big enough, it could be audible as "tighter" or less "flabby" bass.

If you do nothing else, you could probably pull your LT back to 25Hz and lose about 4dB of DC gain.

Hope this helps.

--Greg

[Jim85IROC]

I tried the configuration that you suggested, and it seems to give a rolled-off low end:



Here's my original configuration with an LT of fp=20hz and Qp=.7 along with a high-pass at 35hz with a Q of 1.5. As you can see from the plot, I stay just under max excursion with a 100 watt input. While the dB gain of the LT is 20.8dB, the max gain of the entire transfer function is under 15dB thanks to the high-pass filter.



Your suggestion for moving the fp up to 25hz seems like a very good idea also. This only results in about a 1dB loss in output at 35hz, and since this is likely to be used for music only, would probably be inaudible.

[richie00boy]

There are a few reasons why 20dB is an guideline max.

1) As Andrew has pointed out, your main speakers will only be seeing 1/100 the power.

2) That is a lot of gain at very low frequency which can lead to hum pickup and DC problems.

3) The massive gain means that only small input signals can be handled.

That's not to say 20dB is the end of the world. I have made a sub before with such high gain. It's not ideal really though.

[consort_ee_um]

Why not go for a classic sixth order design? You do not need the Linkwitz transform, just need the 2nd order high pass filter. Try doing it without the Linkwitz. I found the best compromise is Keeles sixth order alignment where you use a boost of 6db and the equations (for his technique)
fb=f3=faux =0.3fs/Qts
and Vb = 4.1Qts^2 Vas
and faux is the 6db peak of the underdamped 2nd order high pass filter