Starting Qtc for Speaker used for Linkwitz Transform

[ctrlx]

If your box size gives a hi q, peaked up response, then your circuit values will need to be more exact to cancel out that peak, whereas a lower q starting point say <0.8 will be more tolerant of circuit values.

 

[phase_accurate]

Exactly

 

[Fernando R]

The Linkwitz transform is more than just a shelving filter like the ones used in tone controls. It is a little more refined shelving filter (a biquadratic filter to be exact) because it is able to correct fc and Qtc.
In its original form it is restricted in terms of the achievable Qtc and fc ratios. With more complicated topologies one could go a little further. it is not restricted to the use of frequency Extension - it can also be used for the reduction of frequency response in order to achieve a target acoustic transfer function of a crossover/driver combination.

I wouldn't use it for the correction of very high Qtc values either (like over 2). But corrections like EQing a closed box with a Qtc of 1.0 to a Qtc of 0.5 one octave lower is easily doable.


Regards

Charles

My original use of the Linkwitz Transform was as you described, for correction for tweeter Fs and Qts in an electronic 4th order crossover network. One filter section was a high pass Sallen and Key second order, the second section was the Linkwitz Transform which essentially works as another second order above fs and no filter below fs, giving an acoustic fourth order in conjunction with the driver.

 

[eriksquires]

So, I can see the extension possibilities, and the ability to flatten the bottom of the response, but this filter does not reduce excursion or distortion. All of that will still be present.

So, hmmmmm...

E

 

[Fernando R]

Correct

 

[Doppler9000]

So, I can see the extension possibilities, and the ability to flatten the bottom of the response, but this filter does not reduce excursion or distortion. All of that will still be present.

So, hmmmmm...

E

You are correct with regard to excursion - this isn't a magical potion. If you want to go deeper, you will always require more excursion, all else equal. #Newton.

If you read the article linked above you will discover, however, that the transformed system can perform better in the time domain, so it can improve distortion, at least in that aspect.

 

[eriksquires]

Doppler:

Now that IS interesting, certainly when comparing a sealed + Linkwitz system vs. ported.

 

[Doppler9000]

Doppler:

Now that IS interesting, certainly when comparing a sealed + Linkwitz system vs. ported.

it is a very clever solution.

 

[Doppler9000]

Dr. Linkwitz adds insights.

In order to further the discussion, I reached out to the man himself. Dr. Linkwitz was very generous and took the time to respond. I am including the conversation here, with Dr. Linkwitz’s permission.

My Question:

Dear Dr. linkwitz,

I am wondering if there is an optimal Qtc starting point for a speaker that will undergo a Linkwitz Transform. Is there a point or range beyond which the result become less usable?

For example, will a properly transformed system with a starting Qtc of 1.2 sound the same as a system with a starting Qtc of 0.577, assuming the appropriate curves have been applied, and all else equal?

Does the starting transient response affect the final performance?

What is the practical upper limit to the starting Qtc for a "perfect" final curve?

Thank you so much.

Dr. Linkwitz's response:

Hi There,

I have never investigated how the starting Qtc or Qz, Fz and the desired Fp, Qp relationship affects the final acoustic performance, which means the amount of distortion produced by the driver.

Keep in mind that the LT assumes linear behavior of the driver, but we know that the lower frequencies demand increasing volume displacements, which become more and more non-linear.

I like to use drivers with Qtc or Qb=Qz (when in a box) of less than 0.5. In that case equalization can be simply done with shelving filters. Also and probably more importantly, Qtc<0.5 means that the motor is very strong in how it controls the voice coil motion. Below driver resonance the compliances, spider and surround, dominate the linearity. Above resonance the moving mass of the driver dominates, which does not change with excursion. Working a driver below its mechanical resonance as done with a LT, extends the bass but may come with excessive distortion.

Linkwitz Lab - Loudspeaker Design filters.htm#9

Have fun,

SL

PS:

F0 and Q0 should be determined by an impedance measurement of the mounted driver the way it will be used, either in a sealed box or open baffle. If vented box, then seal the vent for this measurement. See Figures 17 to 19 of SB1980-3way.

So, it would seem that while the Linkwitz transform is very good at extending (or otherwise altering) response, the ability to reduce cabinet size while extending response lower, is modest.

 

[eriksquires]

The Qtc < 0.5 is also quite limiting, no? That would be a normally over-damped (and therefore larger) enclosure to start with.

Am I misreading?

Best,

E

 

[scottjoplin]

So, it would seem that while the Linkwitz transform is very good at extending (or otherwise altering) response, the ability to reduce cabinet size while extending response lower, is modest.

If that is your primary objective the ESP solution may be better though it depends on your intended Xover frequency

 

[Doppler9000]

If that is your primary objective the ESP solution may be better though it depends on your intended Xover frequency

I am looking to be able to use a ready-made device - either a DSP or a Marchand BASSIST.

 

[scottjoplin]

You could do it with DSP, I don't know what BASSIST is? The principle is outlined here Sub-Woofer Controller

 

[Fernando R]

The Qtc < 0.5 is also quite limiting, no? That would be a normally over-damped (and therefore larger) enclosure to start with.

Am I misreading?

Best,

E

Note that he said he likes to use <.5, not that you have to use. There is an article he wrote around 1982 that is available on the net. He describes using it with, if I remember correctly, a KEF B139. That was the oval 13X9 that had an area about the size of a 10.

 

[scottjoplin]

SB1980-3way

 

[Fernando R]

That is the one

 

[Doppler9000]

...I don't know what BASSIST is? The principle is outlined here Sub-Woofer Controller

Sorry, added a T for some reason.

BASSIS - a Linkwitz transform-capable equalizer from Phil Marchand, in all its analog, 70s, literally, styling glory.




It is a one trick pony, however, so the DSP certainly has large cost advantages.