passive Linkwitz transform calculator?

rjj45 · November 2019

Looking at a sealed RS270 three way similar to Tony Gee's "BllackBox" with a passive Linkwitz transform
Thinking about a larger box than the 24 Liters he used, but can't find any calculator or formula for the uF capacitor
I would need. Anyone have the formula or link for a solution?

Thanks.

Ed_Perkins · November 2019

I didn't think a passive Linkwitz Transform was possible as you need gain for the LT. Do you mean a single, large capacitor to change the knee of the roll-off?

dcibel · November 2019

You can look up Tony Gee's writeup on the wayback machine, without pictures unfortunately.

https://web.archive.org/web/20100325072004/http://www.humblehomemadehifi.com/Black Box.html

"Determining the correct value for the woofer high-pass capacitor is a little fuzzy and besides calculations, involves some empirical determination. The German magazine Hobby-Hi-Fi has done some research the last few years and have come up a simple calculation. The basic formula for working out the rough value of the capacitor is: C=(K x Qts) / (Re x fs). The value of Qts should include all series resistances as mentioned earlier. The value of the constant K depends on the voice-coil inductance. For woofers with a small voice-coil inductance K = 316.000 and for woofers with very large voice-coil inductance, like many sub-woofer drivers, K = 100.000. For standard types like the Dayton RS270S-8 choose K = 265.000. In this situation the formula results in a value of about C = 580uF to 600uF. By fine-tuning the final value of the capacitor one also match the loudspeaker with the room-acoustics. If the capacitor is chosen a little on the small side, say about 10-20% smaller, this will give the loudspeaker a more lean sounding character. This could be ideal for bass-heavy rooms or positioning close to a rear wall."

What I would do is forget the math exam and use a combination of PCD and WBCD to simulate the effect without the guesswork. Import the impedance of your woofer into PCD, skip the FRD and apply a series cap to simulate the effect it has on the response as a raw transfer function. You may need to import as a tweeter to apply the series cap. You can then export the resulting response using the "output total high pass response to FRD file" button, and import to WBCD using the "Import External Filter Response" button. Turn on the filter section, include the imported filter, and turn off all other filters. Off to the races

Ed_Perkins · November 2019

Here's a link to Tony Gee's write up with pics.

http://www.humblehomemadehifi.com/download/Humble%20Homemade%20Hifi_Black%20Box.pdf

Wolf · November 2019

I usually use the midrange section as you can do both the LP and HP, and it's called a 'Passive Assist'. This changes the sealed rolloff to a 3rd order and raises the knee. LSDC says make the box Qtc 1.1, have a woofer with large Xmax capability, and a Qms of 7-10. The Qtc in combination with the Fsb being higher in the smaller box, coupled with the 3rd order rolloff makes the increase possible.

rjj45 · November 2019

Thanks everyone!
Sheesh, I already had the PDF from Tony's writeup, and somehow missed the docs on calculation <doofus> - but in any case, y'alls tips on PCD/WBCD should help empirically.

rjj45 · November 2019

I've got a 37 liter test box in the "lab", so I just decided to fire the damn thing up.
Stock RS270-8 in that box gave a 53 Hz F3. Not good enough!
Scrounged up about 600uF and tried it again. 43 Hz F3 - just about what I was looking for, and
the ZMA plot shows protection for extreme bass. The build is on.
I expected the impedance peak to shift, lower, but no real change. No matter.
Stock (no cap) ZMA

Image: https://diy.midwestaudio.club/uploads/editor/jq/v6y5ci3sp2vi.png

Here is the ZMA with 600uF inline.

Image: https://diy.midwestaudio.club/uploads/editor/1y/4qwd9vy1i1po.png

Image: https://diy.midwestaudio.club/uploads/editor/0j/j41n1mlebneh.png

Just what I wanted! - stock (no cap) vs added 600uF inline.

ani_101 · November 2019

How is the f3 measured/determined in the above images?

rjj45 · November 2019

ani_101 said:

How is the f3 measured/determined in the above images?

Very good question
Between 125 and 175Hz I swagged the average (max error maybe .25 dB), then manually found the -3dB point.
The Unibox model predicts a .5dB peak at 96Hz for the stock box model, and you can see a little bit of a rise in the
black (stock) FR. OTOH, the box Qt is .86, which is a bit low for the Linkwitz transform, so you see a little droop in the red (600uF) FR.
Comparing the original Unibox model shows it predicts a 53Hz F3 for the stock box, so measurements agree exactly.

Image: https://diy.midwestaudio.club/uploads/editor/ml/0d47ceteh67g.png

Image: https://diy.midwestaudio.club/uploads/editor/ax/4jgmxtqwym7a.png

I have NO frickin' idea why Unibox F3 and Fb are different between the params and max SPL screens. Wierd.

@ani_101 - I respect your knowledge and analytics. Any feedback?

ani_101 · November 2019

hi Don

Yes the unibox figures seem to be switched. Didn't mean to be curt, but i was looking at the images on the phone and couldn't figure out shift in F3. I haven't figured out the low frequency measurements and simulations and seems more trial and error than measurement hence genuinely interested in know how you measured and what the inference were. Also i have very less experience with sealed boxes and none with caps in series before the woofer - i just go with the unibox simulation and may verify the system FB with DATS.

Also, I had to brush up on reading ZMA curves before tying the below question - so anybody reading this, please correct and educate...

Looking at the impedance images - ZMA, the system impedance look similar at the peak, so the system FB is the same, but you do have rising impedance at the lower frequency. I don't know what are the implications for it - would it serve to protect the woofer with lower frequency - rising resistance for lower frequency so lower power delivered? Usually there is rising impedance towards low frequency and this is due to voice coil inductance.

The third image is more interesting as you do see a flatter curve (red) vs the black which is assume is no cap. And the red curve is a bit more extended and given the flatter curve and lower extension, the F3 is indeed lowered by 10hz. What i don't know is how did you measure with omnimic, as usually i can measure up to 400-350 hz and nothing below. Is this purely near-field?

Another question is, Is there a SPL penalty for using the coil? The red curve is lower than the black curve, so looks like there is, but then the black curve would have been flattened with bsc and crossover, so maybe not much in real world after crossover, but you do gain more low end extension.

I am currently working on a box for a sealed project - this looks like a good experiment to try. Another question - what made you try 600uF?

From the PDF:
The basic formula for working out the rough value of the capacitor is: C=(K x Qts) / (Re x fs) . The value of Qts should include all series resistances as mentioned earlier. The value o f the constant K depends on the voice -coil inductance . For woofers with a small voice -coil inductance K = 316.000 and for woofers with very large voice- coil inductance , like many sub-woofer driver s, K = 100.000. For standard types like the Dayton R S270S -8 choose K = 265.000. In this situation the formula results i n a value of about C = 580uF to 600uF. By fine- tuning the final value of the capacitor one also match the loudspeaker with the room-acoustics. If the capacitor i s chosen a little on the small side, say about 10-20% smaller, this will give the loudspeaker a more lean sounding character.

rjj45 · November 2019

I probably should have documented conditions a bit more precisely.
I measured using Omnimic about 1/2 inch from the cone, near the RS270 phase plug.
I chose 600uF because that was most of the big NPEs I had on hand, and that's what Tony Gee used.
As far as I understand, there is not a SPL penalty per se, but you do have to pay attention to excursion issues
for the desired listening SPL since you are extended the bass response.
The ZMA rise at low frequencies is super neat, since it will assist the natural protection of a sealed box concerning Xmax.
Tony's original build used a 24 liter box (with a lot of wasted space for a crossover), but he really didn't document the F3 of the original or the transformed system. It may have been that he specifically wanted to start with a box Qt around 1.1 for the mod. I didn't need a box that small, and wanted to get more low end out the the wonderful RS270, and had the larger test box in my shop, so there. It's a workable size, and I can get the extension I want, so I'll probably build the production version that size.
You know how Unibox and WinISD simulations go - I initially used 100 watts, but was dismayed to find that the woofer exceeded Xmax about 55Hz. Then I realized that the passband showed something like 108 dB SPL, which I was never going to use. Reduced power to 50 watts still gives me 105 dB passband, with no Xmax issues, so I should be "golden" at 95dB max even with the added bass extension.
Really terrific mod, I'm looking forward to my first sealed box bass.
Did I answer all your questions?

ani_101 · November 2019

rjj45 said:

I probably should have documented conditions a bit more precisely.
I measured using Omnimic about 1/2 inch from the cone, near the RS270 phase plug.
I chose 600uF because that was most of the big NPEs I had on hand, and that's what Tony Gee used.
As far as I understand, there is not a SPL penalty per se, but you do have to pay attention to excursion issues
for the desired listening SPL since you are extended the bass response.
The ZMA rise at low frequencies is super neat, since it will assist the natural protection of a sealed box concerning Xmax.
Tony's original build used a 24 liter box (with a lot of wasted space for a crossover), but he really didn't document the F3 of the original or the transformed system. It may have been that he specifically wanted to start with a box Qt around 1.1 for the mod. I didn't need a box that small, and wanted to get more low end out the the wonderful RS270, and had the larger test box in my shop, so there. It's a workable size, and I can get the extension I want, so I'll probably build the production version that size.
You know how Unibox and WinISD simulations go - I initially used 100 watts, but was dismayed to find that the woofer exceeded Xmax about 55Hz. Then I realized that the passband showed something like 108 dB SPL, which I was never going to use. Reduced power to 50 watts still gives me 105 dB passband, with no Xmax issues, so I should be "golden" at 95dB max even with the added bass extension.
Really terrific mod, I'm looking forward to my first sealed box bass.
Did I answer all your questions?

yes, thanks for the details. This does answer all my questions.

Once you finish your build - or maybe you already have. Could you listen with the cap and without and give your impression of what the low end sounds like with the rest of the system / XO remaining the same?