Depending on where you place the RC it could require more difficult calculations. Place an RC in front of a State Variable Filter and you need to account for the input resistor, and you could end up with a shelving filter if the input impedance is low. Raise the input impedance and you need to scale everything up to very high impedance, increasing the susceptibility to EMI and increase resistor noise. It might be easier to implement it in a separate stage or between the second order filter and the output buffer.
Funny thing - Reading the specs of your crossover, it uses 3rd order Butterworth electrical filters. Unless your drivers are flat well beyond the crossover point you will have something other than a Butterworth acoustic response. Use that filter on a Seas T25CF001 at 1600 Hz and your acoustic response is LR4. Hmm, you could be a Linkwitz Reilly fan and not even know it
I agree with many aspects design philosophy you presented (even if the writeup has a lot of marketing hype mixed in), I just disagree with presenting it as "THE ONLY WAY".
Funny thing - Reading the specs of your crossover, it uses 3rd order Butterworth electrical filters. Unless your drivers are flat well beyond the crossover point you will have something other than a Butterworth acoustic response. Use that filter on a Seas T25CF001 at 1600 Hz and your acoustic response is LR4. Hmm, you could be a Linkwitz Reilly fan and not even know it
I agree with many aspects design philosophy you presented (even if the writeup has a lot of marketing hype mixed in), I just disagree with presenting it as "THE ONLY WAY".
Check this out:
An externally hosted image should be here but it was not working when we last tested it.
True. You could just glom these on externally if you are really averse to using another gain stage.
Well, this is strictly true, but not in an engineering sense. If the distortion is vanishingly small, then twice the distortion is still vanishingly small. This is one reason why I am using high end op amps, so that the number of op amps is not really of major concern.
Also, you have to keep in mind the big picture. These circuits will be used as crossovers for loudspeakers. Loudspeaker drivers convert an electrical signal in to a mechanical one (e.g. sound waves) with an inherent distortion that is often on the order of 0.1%, or 1% if SPLs are "high" and the driver is reaching Xmax. So chasing distortion in the crossover circuit that is much smaller in magnitude really does not make all that much practical sense. The loudspeaker driver distortion dominates.
-Charlie
I presented it as "only way" because odd-order Butterworth filters are the only way to sum constant axis power + constant total power. (Assuming driver phase errors have been accouinted for.)
JAES has articles with detailed mathmatical analysis.
You cannot twist the laws of physics to suit your favorite notion.
JAES has articles with detailed mathmatical analysis.
You cannot twist the laws of physics to suit your favorite notion.
Alex,
I was aware of how to construct a 3rd order filter around a Sallen-Key second order block. But... seeing the diagram made me think that it really wouldn't be all that difficult (assuming that there is room on the board to do it) to add places for the extra two components. The series component location could be bridged with a link if not used and the grounded component left unfilled... I suppose that wouldn't cause any problems, so I will think about implementing that. Thanks for the suggestion.
-Charlie
Alex's topology is multiple feedback, not Sallen Key. In any case, we must take into account the loading of the RC filter by the components that follow. The negative op amp input is a virtual ground, so you need to consider the parallel impedances connected to ground when designing the RC. The resistor at the input of the State Variable filter sets the filter's input impedance.
If the impedance of the second RC is roughly 10x the impedance of the second, you can safely ignore it when calculating the first (meaning less than 10% error). So, you have two options if you want simple calculations. High impedance in the second order section or low impedance in the first order section. Going high means susceptibility to EMI and increased resistor noise, going low means the preamp may be loaded beyond its ability to deliver a clean signal.
I suggest that the extra RC be placed at the output of the second order filter before the output buffer. That would allow purists to easily take the output directly from the filter without a buffer if desired.
If the impedance of the second RC is roughly 10x the impedance of the second, you can safely ignore it when calculating the first (meaning less than 10% error). So, you have two options if you want simple calculations. High impedance in the second order section or low impedance in the first order section. Going high means susceptibility to EMI and increased resistor noise, going low means the preamp may be loaded beyond its ability to deliver a clean signal.
I suggest that the extra RC be placed at the output of the second order filter before the output buffer. That would allow purists to easily take the output directly from the filter without a buffer if desired.
regarding power response...
I'm not familiar with the JAES pubs you refer to... can you please post the references?
Are you familiar with John Kreskovsky's study of power response for odd ordered Butterworth and (even order) Linkwitz-Riley filters (see link below)? These largely support your claim, BUT John assumed that the drivers acoustic centers are time-aligned, and this is not the case in general. So you can get some additional phase differences that can cause on and off axis power to droop, unless you compensate for the difference in acoustic centers (typically by delaying the tweeter signal, or sometimes by using asymmetric crossovers).
Here is the five page study by John K (make SURE to read past page 1):
Note on page 2 he shows that power is not flat, even for odd-ordered Butterworth filters. It's only under the simplifying assumption that the drivers are point sources (never true) that the BUT3 yields flat power response for all frequencies.
Not that I am trying to bash what you are saying/claiming about odd-ordered Butterworth filters, but I think the situation is not as clear cut as you might be asserting. There are other variables to consider, too. For instance, if you look at the off-axis behavior of the LR4 crossover, while you do get a dip in the power response around the crossover point, it is nicely symmetric around the crossover point and power could easily be filled using EQ via a BP filter. Can't exactly do that for the BUT3, because it so happens that the power response sums to flat because on one side of "on axis" there is a response peak and on the opposite side of "on axis" there is a response dip, and these just happen to cancel out. But, depending on where you are listening, the direct sound could be way off "flat", and since on-axis sound dominates, this would not be all that great. Also, off-axis/power response is most important in small listening spaces, where you do get a lot of sound energy coming back to the listening location from the room for all frequencies (not the same as the room resonance modes). But in larger spaces, relatively much less power reaches the listener from the room compared to the direct sound, so power response is far less important. In fact one could use an adjustable EQ to fill any hole in the symmetric LR4 power response, so that the speaker can be matched better to the room.
-Charlie
I'm not familiar with the JAES pubs you refer to... can you please post the references?
Are you familiar with John Kreskovsky's study of power response for odd ordered Butterworth and (even order) Linkwitz-Riley filters (see link below)? These largely support your claim, BUT John assumed that the drivers acoustic centers are time-aligned, and this is not the case in general. So you can get some additional phase differences that can cause on and off axis power to droop, unless you compensate for the difference in acoustic centers (typically by delaying the tweeter signal, or sometimes by using asymmetric crossovers).
Here is the five page study by John K (make SURE to read past page 1):
Note on page 2 he shows that power is not flat, even for odd-ordered Butterworth filters. It's only under the simplifying assumption that the drivers are point sources (never true) that the BUT3 yields flat power response for all frequencies.
Not that I am trying to bash what you are saying/claiming about odd-ordered Butterworth filters, but I think the situation is not as clear cut as you might be asserting. There are other variables to consider, too. For instance, if you look at the off-axis behavior of the LR4 crossover, while you do get a dip in the power response around the crossover point, it is nicely symmetric around the crossover point and power could easily be filled using EQ via a BP filter. Can't exactly do that for the BUT3, because it so happens that the power response sums to flat because on one side of "on axis" there is a response peak and on the opposite side of "on axis" there is a response dip, and these just happen to cancel out. But, depending on where you are listening, the direct sound could be way off "flat", and since on-axis sound dominates, this would not be all that great. Also, off-axis/power response is most important in small listening spaces, where you do get a lot of sound energy coming back to the listening location from the room for all frequencies (not the same as the room resonance modes). But in larger spaces, relatively much less power reaches the listener from the room compared to the direct sound, so power response is far less important. In fact one could use an adjustable EQ to fill any hole in the symmetric LR4 power response, so that the speaker can be matched better to the room.
-Charlie
Op amps are LME49740 (quad) and LME49720 (dual).
Caps are all PP type, Vishay and Wima. What do you mean by "large". I hope you are not referring to axial caps! Save those for passive crossovers.
-Charlie
Yup, MFB, I didn't look closely. Good points about the interaction of the extra components without isolation from another amplifier, Bob.
I wouldn't like to see components after the op-amp, unless there was another high impedance stage following, otherwise you will just have a different set of problems. The only place I would suggest for it would be at the input to the power amp. But you need to know the amps input configuration and impedance.
-Charlie
Butterworth 3rd order on and off-axis response
Alex,
Here are the results of a model of the BUT3 crossover filter. The model conditions are:
Note that reversing the driver phase by 180 degrees (e.g. exchanging the leads) only swaps the dashed and solid lines, (e.g. the lobing behavior flips about the on axis plane) but the responses are the same.
As the model shows, on axis response is flat, but off axis (in vertical plane, e.g. up and down) the response is quite different depending on which direction you go. In one direction there is a partial null and in the other direction there is a peak. These cancel, leading to a flat power response (under these conditions).
But as I mentioned, if you are not listening right on axis, the direct sound will not be flat. When the off-axis FR responses are not presented along with the power response, the BUT3 can look very good, but the details of the off-axis FR can be just as important as the power response, if not more so, unless you want to require people to be exactly lined up with the speakers on-axis "sweet spot".
-Charlie
Alex,
Here are the results of a model of the BUT3 crossover filter. The model conditions are:
no inter-driver time delay / pathlength difference
assumes point sources
on axis point lies on a horizontal plane midway between driver acoustic centers
vertical driver separation = 0.153m = 6 in = 0.45 wavelength at crossover freq.
crossover frequency = 1k Hz (although this really has no bearing on the result)
assumes point sources
on axis point lies on a horizontal plane midway between driver acoustic centers
vertical driver separation = 0.153m = 6 in = 0.45 wavelength at crossover freq.
crossover frequency = 1k Hz (although this really has no bearing on the result)
Note that reversing the driver phase by 180 degrees (e.g. exchanging the leads) only swaps the dashed and solid lines, (e.g. the lobing behavior flips about the on axis plane) but the responses are the same.
As the model shows, on axis response is flat, but off axis (in vertical plane, e.g. up and down) the response is quite different depending on which direction you go. In one direction there is a partial null and in the other direction there is a peak. These cancel, leading to a flat power response (under these conditions).
But as I mentioned, if you are not listening right on axis, the direct sound will not be flat. When the off-axis FR responses are not presented along with the power response, the BUT3 can look very good, but the details of the off-axis FR can be just as important as the power response, if not more so, unless you want to require people to be exactly lined up with the speakers on-axis "sweet spot".
-Charlie
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Charlie :
I did the research over 25 years ago and do have the exact references. Do a search for A. N. Thiele
I did the research over 25 years ago and do have the exact references. Do a search for A. N. Thiele
If you "have the exact references", can you please post/list them, instead of telling me to "go do a search..."???
I would honestly like to read them. TIA-Charlie
Charlie :
I am familiar with the off-axis response anomolies for 3rd Butterworth, but have found it to be less objectionable than the problems with other configurations. If drivers are in a vertical array, then side-to-side movement will have minimal effect on perceived response. These same phase funnies are going to be present in any multi-way speaker system. In my opinion, 3rd Butterworth response anomolies are least audible compared to those of all the other configurations.
I enjoy being able to move about in the sound fiels while the music is playing and not have the soundstage collapse.
Have you actually implemented a 3rd Butterworth configuration as I suggested in my original post to this thread and listened to the sound character?
I am familiar with the off-axis response anomolies for 3rd Butterworth, but have found it to be less objectionable than the problems with other configurations. If drivers are in a vertical array, then side-to-side movement will have minimal effect on perceived response. These same phase funnies are going to be present in any multi-way speaker system. In my opinion, 3rd Butterworth response anomolies are least audible compared to those of all the other configurations.
I enjoy being able to move about in the sound fiels while the music is playing and not have the soundstage collapse.
Have you actually implemented a 3rd Butterworth configuration as I suggested in my original post to this thread and listened to the sound character?
Charlie :
Haven't you already done your homework by researching past issues of technical journals on audio crossovers? I would have to go back to the engineering library and do a search to find all of the original articles with references. I gleened the relevant info from the journals and proceeded forward, not anticipating ever becoming a teacher. All I have found in my papers so far is an excerpt from AUDIO, August 1978, but no author. I believe it was A. N. Thiele. I remember there were many articles in JAES, and the one above may have been a synopsis of one for publication in Audio. If I find more, I'll post the info.
Also, there are articles that give the formulas to calculate the R and C values relevant to the schematics I previously posted. I don't have it either, I use the PC program XOVER as supplied with 3PX8 xover I purchased from "un-named company".
Haven't you already done your homework by researching past issues of technical journals on audio crossovers? I would have to go back to the engineering library and do a search to find all of the original articles with references. I gleened the relevant info from the journals and proceeded forward, not anticipating ever becoming a teacher. All I have found in my papers so far is an excerpt from AUDIO, August 1978, but no author. I believe it was A. N. Thiele. I remember there were many articles in JAES, and the one above may have been a synopsis of one for publication in Audio. If I find more, I'll post the info.
Also, there are articles that give the formulas to calculate the R and C values relevant to the schematics I previously posted. I don't have it either, I use the PC program XOVER as supplied with 3PX8 xover I purchased from "un-named company".
Yes, I have a Behringer DCX2496 connected to my DIY speakers and I can instantly switch back and forth between crossover types and orders on the fly, including your beloved Butterworth 3rd order.
Each one sounds different because each has its own on and off axis behavior and one or the other might happen to match the particular speaker at hand and room/environment. If you feel the Butterworth 3rd order is "best under all conditions" then I am glad you have found your happy place. Hey, it is a good crossover in terms of its simple implementation, relatively good selectivity, and low order (so transient response is not in the crapper). Like I mentioned a few posts ago, all the crossover types have tradeoffs with frequency and time responses, and you need to go with what you like and what is best for your application. But it would be awesome if you could share some data or research that backs up what you are saying. This is why I want to take a look at those papers you mentioned because if there is some good data on why BUT3 is so superior then I would sure like to know about it. If you have some hard evidence from the published literature, or from your own work from the past, apart from opinion, please share it here.-Charlie
Charlie :
I meant to say:
I did the research over 25 years ago and DO NOT have the exact references. Do a search for A. N. Thiele
Sorry.
Haven't you already done your homework by researching past issues of technical journals on audio crossovers? I would have to go back to the engineering library and do a search to find all of the original articles with references. I gleened the relevant info from the journals and proceeded forward, not anticipating ever becoming a teacher. All I have found in my papers so far is an excerpt from AUDIO, August 1978, but no author. I believe it was A. N. Thiele. I remember there were many articles in JAES, and the one above may have been a synopsis of one for publication in Audio. If I find more, I'll post the info.
Also, there are articles that give the formulas to calculate the R and C values relevant to the schematics I previously posted. I don't have it either, I use the PC program XOVER as supplied with 3PX8 xover I purchased from "un-named company".
I meant to say:
I did the research over 25 years ago and DO NOT have the exact references. Do a search for A. N. Thiele
Sorry.
Haven't you already done your homework by researching past issues of technical journals on audio crossovers? I would have to go back to the engineering library and do a search to find all of the original articles with references. I gleened the relevant info from the journals and proceeded forward, not anticipating ever becoming a teacher. All I have found in my papers so far is an excerpt from AUDIO, August 1978, but no author. I believe it was A. N. Thiele. I remember there were many articles in JAES, and the one above may have been a synopsis of one for publication in Audio. If I find more, I'll post the info.
Also, there are articles that give the formulas to calculate the R and C values relevant to the schematics I previously posted. I don't have it either, I use the PC program XOVER as supplied with 3PX8 xover I purchased from "un-named company".
Using a Behringer digital crossover -- no wonder your observations are so off. I sold the one I had on eBay. Digital filters don't work, but let's not start that debate here.
Whatever dude.
Alex,
Here are the results of a model of the BUT3 crossover filter. The model conditions are:
no inter-driver time delay / pathlength difference
assumes point sources
on axis point lies on a horizontal plane midway between driver acoustic centers
vertical driver separation = 0.153m = 6 in = 0.45 wavelength at crossover freq.
crossover frequency = 1k Hz (although this really has no bearing on the result)
This plot only shows on/off-axis response. It conveniently overlooks the fact that while this response is happening, the total power into the room is constant and flat, regardless of position. This is only true for odd-order Butterworth filters.
Other filter topologies will exhibit the same off-axis responses, but will be plagued with non-flat total power into the room, and this effect is most definitely audible.
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