How to model active baffle step compensation in PCD?

[charlielaub]

Here's another PCD question for ya, Jeff:

I'd like to use PCD to model the response of a system using an active crossover. Part of the crossover will be baffle step compensation - e.g. a shelving LP filter. How do you model that in PCD? I couldn't figure it out.

-Charlie

[Jeff B.]

Re: How to model active baffle step compensation in PCD?

Here's another PCD question for ya, Jeff:

I'd like to use PCD to model the response of a system using an active crossover. Part of the crossover will be baffle step compensation - e.g. a shelving LP filter. How do you model that in PCD? I couldn't figure it out.

-Charlie

On the low pass filter you can use the Linkwitz Transform.

I just switched a project I am currently working on over to all active for modeling to see how it would do. For my 9" wide baffle I "dialed in" perfect BSC using F0= 500Hz, Q0= .70, Fp= 350 Hz, and Qp= .60. The gain works out to 6.2dB. Then I needed to lower the woofer level a few dB to match things back up. I dialed this in manually by just adjusting the parameters in the LT section until I "tuned" the circuit to give me the response I wanted.

Another option, would be to change the active low pass section to "User Entered Coefficients" and by dialing those in you can arrive at a similar transfer function shape. However, you would need to be able to translate these into an actual active circuit. If you are working with a digital filter that would be pretty easy, but it might not be with analog circuits, for those the LT may be a viable alternative.

If you want I can send you the file I was just working with (RS180 MTM with RS28a), so you can see what I did and how it worked out as a result.

Jeff

[charlielaub]

Re: How to model active baffle step compensation in PCD?

Close, but no cigar. :D

The LT is most like a second order shelving filter, so unless one was planning to use an LT for baffle step compensation (ehh, I guess you could) than this is not exactly mimicking the typical baffle step compensation circuit, namely a first order shelving filter.

I don't think that one could use your generalized filter function to emulate a shelving filter transfer function, either. I have to admit, though, that I'm not exactly sure how the shelving factors in to the transfer function, or how to translate that in to your generalized polynomial formula.

Any ideas?

I am planning to implement this with active circuity.

-Charlie

[charlielaub]

Re: How to model active baffle step compensation in PCD?

Jeff,

I found on one of Linkwitz's web pages, the transfer function (e.g. Vout/Vin or in SL's notation, V2/V1) for the first order shelving filter:


How do you put this in to your polynomial in powers of s?

I have to admit, I have never been all that clear on your polynomial approach, and always preferred the transfer function notation. Is there a method to go back and forth between the two that you could share?

-Charlie

[Jeff B.]

Re: How to model active baffle step compensation in PCD?

Jeff,

I found on one of Linkwitz's web pages, the transfer function (e.g. Vout/Vin or in SL's notation, V2/V1) for the first order shelving filter:


How do you put this in to your polynomial in powers of s?

I have to admit, I have never been all that clear on your polynomial approach, and always preferred the transfer function notation. Is there a method to go back and forth between the two that you could share?

-Charlie

Indeed it does work, just as I described. First we need to remember that simple baffle step compensation is about the same as textbook filters, because true baffle response is more complex with a changing slope merging to a peak that needs to be accounted for. It is only first order for a limited bandwidth.

Second, we need to realized that by changing the Q values in the Linkwitz Transform we can adjust these slopes over narrow bandwidths, and it is quite easy to tune it to accomplish the result you need. (Did you see my recent paper in Understanding Diffraction).

The graph below shows the actual response of the RS180 on the 9" baffle that I mentioned above. The resulting response is the LT with parameters I gave above and a third order Butterworth filter applied at the end. So, both of these are easily implemented into an active analog circuit.



Here's the information on the polynominal from the User Guide. It is a standard 4th order polynominal. Some digital filters use these same coefficients, which make knowing them useful.



Later I will prepare the file for download and send you the link, so you can see what I did.

[charlielaub]

Re: How to model active baffle step compensation in PCD?

Indeed it does work, just as I described. First we need to remember that simple baffle step compensation is about the same as textbook filters, because true baffle response is more complex with a changing slope merging to a peak that needs to be accounted for. It is only first order for a limited bandwidth.

Second, we need to realized that by changing the Q values in the Linkwitz Transform we can adjust these slopes over narrow bandwidths, and it is quite easy to tune it to accomplish the result you need. (Did you see my recent paper in Understanding Diffraction).

The graph below shows the actual response of the RS180 on the 9" baffle that I mentioned above. The resulting response is the LT with parameters I gave above and a third order Butterworth filter applied at the end. So, both of these are easily implemented into an active analog circuit.

Here's the information on the polynominal from the User Guide. It is a standard 4th order polynominal. Some digital filters use these same coefficients, which make knowing them useful.



Later I will prepare the file for download and send you the link, so you can see what I did.

Hi Jeff,

I'm not arguing whether or not you can use the LT to do baffle step compensation. I am only stating that the LT is not a first order shelving filter. It's transfer function is the ratio of two second order polynomials, so it's more like a second order shelving filter. It's also a more complicated circuit to implement via analog electronics.

For examples of baffle step compensation using a first order shelving filter, see:

http://www.trueaudio.com/st_diff1.htm

http://www.linkwitzlab.com/filters.htm#8

http://www.soton.ac.uk/~apm3/diyaudio/Diffraction.html

Since the first order shelving filter is the kind of circuit that I find is typically used for baffle step compensation, it seems only logical to include it in an active filter modeling program for loudspeaker design. Having the LT in there is great, but that is getting to a higher level of sophistication and complication. Also, while the LT may be more suited for baffle step compensation in some circumstances, the basic approach is still the first order shelving filter, or a shelving filter plus notch (See Linkwitz.com link above).

So I guess my question is:
Can one implement a first order shelving filter in the active filter section of PCD and, if so, how?

-Charlie

[Jeff B.]

Re: How to model active baffle step compensation in PCD?

Hi Jeff,

I'm not arguing whether or not you can use the LT to do baffle step compensation. I am only stating that the LT is not a first order shelving filter. It's transfer function is the ratio of two second order polynomials, so it's more like a second order shelving filter. It's also a more complicated circuit to implement via analog electronics.

For examples of baffle step compensation using a first order shelving filter, see:

http://www.trueaudio.com/st_diff1.htm

http://www.linkwitzlab.com/filters.htm#8

http://www.soton.ac.uk/~apm3/diyaudio/Diffraction.html

Since the first order shelving filter is the kind of circuit that I find is typically used for baffle step compensation, it seems only logical to include it in an active filter modeling program for loudspeaker design. Having the LT in there is great, but that is getting to a higher level of sophistication and complication. Also, while the LT may be more suited for baffle step compensation in some circumstances, the basic approach is still the first order shelving filter, or a shelving filter plus notch (See Linkwitz.com link above).

So I guess my question is:
Can one implement a first order shelving filter in the active filter section of PCD and, if so, how?

-Charlie

My point Charlie, is that articles like the True Audio link above misrepresent what real cabinet diffraction looks like, and therefore fall short in defining a solution. When dealing with real loudspeakers a simple first order shelf as described is no more effective in yeilding good results with baffle diffraction step than text book crossovers typically are at yielding a good acoustic crossover. On the other hand, due to the fact that real baffle diffraction peaks before the step (or at the top of the step depending on how you look at it) the Linkwitz Transform is a nearly ideal real-world solution, much better than the simple first order shelving network that has been described. It is also simpler than the shelving circuit with notch filter that you mentioned.

Here is another view of the real measured response of the RS180 on my 9" baffle with the tuned LT applied:


Up to 1200Hz how can we not say that the LT wasn't an ideal solution -providing neard perfect baffle diffraction step compensation.

Here is the transfer function of this circuit:

The Linkwitz Transform is easily tuned to this shape - it can be first order in a limited range if needed.

I personally don't believe a simple first order shelving circuit will provide ideal results for a real loudspeaker, at least not in many cases.

In answer to your last question, I don't believe a first order shelf can be modeled apart from the way I have done it here using PCD, And since I consider PCD's development closed, I don't think any more features will be added to the program.

Jeff

[charlielaub]

Re: How to model active baffle step compensation in PCD?

My point Charlie, is that articles like the True Audio link above misrepresent what real cabinet diffraction looks like, and therefore fall short in defining a solution. When dealing with real loudspeakers a simple first order shelf as described is no more effective in yeilding good results with baffle diffraction step than text book crossovers typically are at yielding a good acoustic crossover.
[snip]
I personally don't believe a simple first order shelving circuit will provide ideal results for a real loudspeaker, at least not in many cases.
[snip]

Jeff

I am not sure why you seem to be taking such a defensive stance regarding your use of the LT for baffle step compensation. If it works for you, have at it! I am NOT trying to tell you how to design your crossovers. I really only wanted to know how I could model a first order shelving filter in PCD's active circuit section, since I happen to like using it for baffle step compensation. Since you seem to have indicated that you can't model that in PCD, and that you aren't open to any more development with PCD, I think that is all that I need to know at this point.

But, seeing you went to great lengths to state that a first order shelving filter just can't do baffle step, I present exhibit A, a speaker that I just worked up today in fact, using a first order baffle step plus a notch. Seems to work fine. I worked this up using a Behringer DCX2496, while I performed measurements using a gated swept sine signal in ARTA. These are, therefore, measurements of an actual speaker's diffraction and the effect of the compensation circuit to combat it:


Active Crossover Information:
2nd order Linkwitz-Riley @ 3k Hz
6dB of baffle step (boost) using a 1st order shelving filter, FMID=400Hz
Notch filter: -2.5dB @ 1k Hz, Q=2.2

For comparison, here is the response of the raw drivers. Note the diffraction signature in the woofer - the bump around 1k Hz that is sitting in the middle of a gradual decrease in output (of about 6dB) between 2k Hz and 500 Hz:


The diffraction signature is shown in the True Audio web page, in the figure for a driver on a rectangular baffle. The frequency where the step and hump occur (a function of the actual baffle dimension) has shifted but the features remain the same:

-Charlie

[Jeff B.]

Re: How to model active baffle step compensation in PCD?

I am not sure why you seem to be taking such a defensive stance regarding your use of the LT for baffle step compensation. If it works for you, have at it! I am NOT trying to tell you how to design your crossovers. I really only wanted to know how I could model a first order shelving filter in PCD's active circuit section, since I happen to like using it for baffle step compensation. Since you seem to have indicated that you can't model that in PCD, and that you aren't open to any more development with PCD, I think that is all that I need to know at this point.

But, seeing you went to great lengths to state that a first order shelving filter just can't do baffle step, I present exhibit A, a speaker that I just worked up today in fact, using a first order baffle step plus a notch. Seems to work fine. I worked this up using a Behringer DCX2496, while I performed measurements using a gated swept sine signal in ARTA. These are, therefore, measurements of an actual speaker's diffraction and the effect of the compensation circuit to combat it:


Active Crossover Information:
2nd order Linkwitz-Riley @ 3k Hz
6dB of baffle step (boost) using a 1st order shelving filter, FMID=400Hz
Notch filter: -2.5dB @ 1k Hz, Q=2.2

For comparison, here is the response of the raw drivers. Note the diffraction signature in the woofer - the bump around 1k Hz that is sitting in the middle of a gradual decrease in output (of about 6dB) between 2k Hz and 500 Hz:


The diffraction signature is shown in the True Audio web page, in the figure for a driver on a rectangular baffle. The frequency where the step and hump occur (a function of the actual baffle dimension) has shifted but the features remain the same:

-Charlie

I wasn't defensive; I was only trying to pursue greater accuracy. The problem with the simple shelf circuit is that it can't be shaped to deal with the baffle peak, and it can reach +3db in some cases. The LT can compensate for it at the same it compensates for the step and its shape is infinitely variable in both corners. I'll quit beating the dead horse though. Poor ol' horse. ;)

Here are my thoughts on cabinet diffraction, including baffle step:

http://www.box.net/shared/f2jt7sjokm

Jeff

[charlielaub]

Re: How to model active baffle step compensation in PCD?

I wasn't defensive; I was only trying to pursue greater accuracy. The problem with the simple shelf circuit is that it can't be shaped to deal with the baffle peak, and it can reach +3db in some cases. The LT can compensate for it at the same it compensates for the step and its shape is infinitely variable in both corners. I'll quit beating the dead horse though. Poor ol' horse. ;)

Here are my thoughts on cabinet diffraction, including baffle step:

http://www.box.net/shared/f2jt7sjokm

Jeff

Jeff, I fully understand what you are saying. The LT is a good solution to many baffle step frequency response irregularities. As I mentioned and showed above, and has been showed many times before, the baffle step response is well characterized and can easily be modeled using yout Diffraction modeling tool, the Edge, and other programs. Mark K has shown that the LT can be thought of as a second order shelving filter plus a notch. See his FAQ about the LT on his web site, here:

http://www.audioheuristics.org/primers/Linkwitz_transform/Linkwitz_transform.htm

The question is whether the LT's response shape is a good fit for the baffle step, and I think you have shown an example indicating that it can be. Regardless, I think it's equally valid to approach compensation for the baffle step using the LT or a first order shelving filter plus a notch and I think that both approaches should be in the tool set, so to speak.

From what I understand, you are using the LT to do baffle step compensation by aligning the LT's response (configured as the inverse of a high-Q sealed box response) with the baffle step signature. Since much less than an octave of 12dB/octave compensation is required, you can just reduce the LT "boost" to 6dB or less until the low frequency and mid frequency passband levels are about the same, and call it a day. With this approach, you will be stuck to the set of circuit shapes that the LT is capable of just as I will be stuck with the shapes that the shelving filter plus notch are capable of.

To-MAY-to, to-MAH-to.

As long as both approaches get you there, I don't think that one is better or worse than the other.

-Charlie

[charlielaub]

active baffle step compensation circuit

If anyone cares to do some baffle step compensation circuit design using my approach, here is a link to a pdf printout of the Excel worksheet I created, showing examples of the circuit. If you send me a PM I can send the worksheet to you so you can calculate your own values or play around with the circuit shape. You can also go to the links shown on Linkwitz's web site and get more info about the circuit.

http://audio.claub.net/temp/Active%20Baffle%20Step%20Compensation%20Design.pdf

-Charlie

[davidl]

Re: How to model active baffle step compensation in PCD?

Nahhhhhhhh I'd rather ask for help then argue with the person I asked help from and show them that their result, no matter how well done isn't correct for me :rolleyes:

[Jeff B.]

Re: How to model active baffle step compensation in PCD?

Nahhhhhhhh I'd rather ask for help then argue with the person I asked help from and show them that their result, no matter how well done isn't correct for me :rolleyes:

First, I would just like to state that I wasn't offended at all at Charlie's challenges. There's more than one way to skin a cat.

Also, I have reached a point where I do not blindly accept everything stated on websites as correct, even when they come from experts, if my understanding of the topic tells me different. As a result, I believe there are some oversimplifications, and therefore some error, on some of the websites he used for reference.

Finally, I still believe the Linkwitz transform is an excellent active solution to this issue because you can fine tune the two Q's of the transfer function to match your needs, and thereby address the diffraction peak as well as the step all in one circuit. For example, the correction curve Charlie shows in his pdf file above (shown below) is easily created with the Linkwitz Transform too.

This is nice, because this is a popular and well known circuit and there are several sources that will calculate the resistor and capacitor values for your circuit once you arrive at your desired transfer function.