Hi Bill,
Sorry I have taken so long to get back to you. You know how it is. Some days you've got too much time on your hands, some times you just don't have enough.
I've collected some of the things I have written on the topic of second order gradients over the past couple years. I hope someone finds them interesting. I'll be honest, you have to be really over the edge to try building yourself a second order gradient, but they are without doubt the best way to get big room bass in a small room. If anybody has any questions just ask...
John
PS: thanks for reading my website--at least now I know the effort wasn't in vain.
What is a second order gradient?
Second order gradients are easier to invision if you explain them in the context of dipoles and cardioids.
A monopole is a zero order gradient. Dipoles and cardiods are first order gradients. Dipoles are two monopoles separated by a distance and operated out of phase. A cardioid is two monopoles separated by a distance and operating out of phase, with one monopole delayed by an amount equivalent to the physical separation between the two monopoles, eg. if the monopoles are 1 meter apart, one monopole is delayed by 1/344th of a second. A unidirecctional second order gradient is like a cardiod, except it is constructed with two dipoles instead of two monopoles: two dipoles separated by a distance and operated out of phase with one dipole delayed by an amount equivalent to the physical separation. Dipoles and cardioids have directionalaty indices of 4.8dB. Second order unidirectional gradients have a directionality index of 8.8dB. The price you pay for the better directional control is 12dB per octave of phase cancelation. But that's OK as long as you don't try to use it down too low.
Olson wrote a paper on gradient loudspeakers in the JAES and it is reprinted in the AES loudspeaker anthology volume 1. There are commercial second order gradient microphones. However, I have never seen a second order gradient loudspeaker. It is not the least expensive way to build a speaker, but it does get you good directional control in the bass frequencies without having to resort to monstrous horns. It is a living room solution, not a stadium solution.
John
Second order gradients are easier to invision if you explain them in the context of dipoles and cardioids.
A monopole is a zero order gradient. Dipoles and cardiods are first order gradients. Dipoles are two monopoles separated by a distance and operated out of phase. A cardioid is two monopoles separated by a distance and operating out of phase, with one monopole delayed by an amount equivalent to the physical separation between the two monopoles, eg. if the monopoles are 1 meter apart, one monopole is delayed by 1/344th of a second. A unidirecctional second order gradient is like a cardiod, except it is constructed with two dipoles instead of two monopoles: two dipoles separated by a distance and operated out of phase with one dipole delayed by an amount equivalent to the physical separation. Dipoles and cardioids have directionalaty indices of 4.8dB. Second order unidirectional gradients have a directionality index of 8.8dB. The price you pay for the better directional control is 12dB per octave of phase cancelation. But that's OK as long as you don't try to use it down too low.
Olson wrote a paper on gradient loudspeakers in the JAES and it is reprinted in the AES loudspeaker anthology volume 1. There are commercial second order gradient microphones. However, I have never seen a second order gradient loudspeaker. It is not the least expensive way to build a speaker, but it does get you good directional control in the bass frequencies without having to resort to monstrous horns. It is a living room solution, not a stadium solution.
John
building a second order gradient
One of the things that fascinates me Harry Olson is the degree to which he managed to optimize his second order gradient setup with only the aid of intuition and what would now be considered rather rudimentary measurement techniques. I have spent hours and hours trying out different setups using finite element analysis--different baffles, different amounts of acoustic resistance, different everything. With FEA modeling, I could try a different setup in a matter of minutes, Whereas for Olson, it must have taken days to try something new. In all my experiments, I never managed to better the setup he describes in his JAES paper on gradient speakers. That was one smart dude!
The second order gradient that Olson describes in his paper amounts to two identical drivers mounted one in front of the other. The distance between the drivers is equal to the diameter of the drivers. There is no box or baffle, just a frame to hold the drivers in place. The back side of the drivers are covered by a perforated sheet, which forms an acoustic RC filter that rolls off the high frequencies coming from the rear side of the driver diaphragm. The drivers are wired out of phase and the rear driver has a delay applied to it equal to the physical separation between the drivers divided by tghe speed of sound. Olson didn't reveal all the secrets in his paper, though, and with the help of DSP, it is possible to do even better than the analog filtering he was implementing. The following paragraphs are some items I've managed to sort out.
Because of the 12dB per octave phase cancellation, if you are going to get meaningful output over more than an octave from a second order gradient, you will need to use it above the point where a true second order gradient starts to lose directional control--above the point where the front and back dipoles are separated by a half wave. The things Olson didn't reveal are related to how to get a tight directionality pattern above this point:
1) Use big drivers. Above the half-wave point, the directionality of the front driver is what keeps the directionality of the system tight. I was making a system for 300Hz down. A 15 inch driver is the minimum for this application. 18 inches is better.
2) The perforated covering on the back of the driver, which forms an aoustical resistance, should have holes opening about 1/3 to 1/2 of the surface area. The acoustic filter should already be reducing the output of the rear wave by the 1/2 wave point.
3) Don't use a baffle. The lack of a baffle is surprisingly important. I thought at first, "why doesn't he use a baffle to decrease the amount of cancellation?" I don't have a good explanation for why a baffle screws everything up, but it does. No baffle also means the holes on the back cover have to go all the way to the edge of the driver.
4) Ideally, the delay on the back dipole should not exceed 1/2 wave. You can get close to this by putting the knee of your analog delay filter below the 1/2 wave point--this also reduces the amount of insertion loss (smaller inductors). If you are using a digital filter to implement the delay (I was) you can have a linear phase shift below half a wave and then constant phase shift above it.
5) Olson inserted an inductor in series with the back dipole to reduce the output above the half wave point. This inducter needs to be sized so that the rear dipole is already down about 3dB at the 1/2 wave point--otherwise you get a quarter wave transmission line resonance problem. It would be nice to reduce the output of the rear dipole at an even faster rate than 6dB per octave, but if you are using an analog filter, this would increase the phase shift, which you don't want. If you are using a digital filter, it is, of course possible to reduce the output without creating phase shift.
John
One of the things that fascinates me Harry Olson is the degree to which he managed to optimize his second order gradient setup with only the aid of intuition and what would now be considered rather rudimentary measurement techniques. I have spent hours and hours trying out different setups using finite element analysis--different baffles, different amounts of acoustic resistance, different everything. With FEA modeling, I could try a different setup in a matter of minutes, Whereas for Olson, it must have taken days to try something new. In all my experiments, I never managed to better the setup he describes in his JAES paper on gradient speakers. That was one smart dude!
The second order gradient that Olson describes in his paper amounts to two identical drivers mounted one in front of the other. The distance between the drivers is equal to the diameter of the drivers. There is no box or baffle, just a frame to hold the drivers in place. The back side of the drivers are covered by a perforated sheet, which forms an acoustic RC filter that rolls off the high frequencies coming from the rear side of the driver diaphragm. The drivers are wired out of phase and the rear driver has a delay applied to it equal to the physical separation between the drivers divided by tghe speed of sound. Olson didn't reveal all the secrets in his paper, though, and with the help of DSP, it is possible to do even better than the analog filtering he was implementing. The following paragraphs are some items I've managed to sort out.
Because of the 12dB per octave phase cancellation, if you are going to get meaningful output over more than an octave from a second order gradient, you will need to use it above the point where a true second order gradient starts to lose directional control--above the point where the front and back dipoles are separated by a half wave. The things Olson didn't reveal are related to how to get a tight directionality pattern above this point:
1) Use big drivers. Above the half-wave point, the directionality of the front driver is what keeps the directionality of the system tight. I was making a system for 300Hz down. A 15 inch driver is the minimum for this application. 18 inches is better.
2) The perforated covering on the back of the driver, which forms an aoustical resistance, should have holes opening about 1/3 to 1/2 of the surface area. The acoustic filter should already be reducing the output of the rear wave by the 1/2 wave point.
3) Don't use a baffle. The lack of a baffle is surprisingly important. I thought at first, "why doesn't he use a baffle to decrease the amount of cancellation?" I don't have a good explanation for why a baffle screws everything up, but it does. No baffle also means the holes on the back cover have to go all the way to the edge of the driver.
4) Ideally, the delay on the back dipole should not exceed 1/2 wave. You can get close to this by putting the knee of your analog delay filter below the 1/2 wave point--this also reduces the amount of insertion loss (smaller inductors). If you are using a digital filter to implement the delay (I was) you can have a linear phase shift below half a wave and then constant phase shift above it.
5) Olson inserted an inductor in series with the back dipole to reduce the output above the half wave point. This inducter needs to be sized so that the rear dipole is already down about 3dB at the 1/2 wave point--otherwise you get a quarter wave transmission line resonance problem. It would be nice to reduce the output of the rear dipole at an even faster rate than 6dB per octave, but if you are using an analog filter, this would increase the phase shift, which you don't want. If you are using a digital filter, it is, of course possible to reduce the output without creating phase shift.
John
why directional control is important in the bass
Linkwitz does a good job of discussing the advantages of directional speakers regarding improved clarity and reduced room mode problems on his web site and I won't try to rehash the subject. Directionality in the bass is also important for getting a sense that you are listening in a large room even though you're really in your living room...
"I guess I was still operating under the mistaken impression that below 100 Hz and without significant upper harmonics, we were hard pressed to identify a source."
That is precisely the problem, it is more difficult for the brain to localize low frequency sources, especially when they come from the medial plane--in front, behind, above or below. When the brain cannot localize the source, it sounds like it is coming from inside your head. A feeling I personally can't stand. Pay attention next time you're listening and you'll know what I mean.
The solution to this problem is to increase the lateral arriving energy relative to the medial arriving energy in the bass region. This can be done by increasing the directivity of your bass speakers and locating them at the sides of the room. You can also decrease the amount of bass reverberation in the room by a) adding more absorption--not very effective in the bass region or b) get a bigger room--somewhat expensive. Another trick that Dave Griesinger uses is to put in a 90 degree delay on one of the woofers below around 100Hz (you'll need to also add a 3dB boost of you do this).
The end result if you do all this is that your brain still won't be able to localize the bass, but it will recognize that it is not coming from inside your head. In my room, I find that just going to dipoles is enough to get the bass out of my head. In addition, the directivity of a dipole woofer is a much better match to a horn mid and treble than for a monopole. I found when I had monopole woofers that if I equalized the on axis response, then the bass sounded boomy. If I equalized the power response, the bass lacked dynamics. The dipoles sound dynamic, but not boomy. I'll never go back to monopoles.
John
Linkwitz does a good job of discussing the advantages of directional speakers regarding improved clarity and reduced room mode problems on his web site and I won't try to rehash the subject. Directionality in the bass is also important for getting a sense that you are listening in a large room even though you're really in your living room...
"I guess I was still operating under the mistaken impression that below 100 Hz and without significant upper harmonics, we were hard pressed to identify a source."
That is precisely the problem, it is more difficult for the brain to localize low frequency sources, especially when they come from the medial plane--in front, behind, above or below. When the brain cannot localize the source, it sounds like it is coming from inside your head. A feeling I personally can't stand. Pay attention next time you're listening and you'll know what I mean.
The solution to this problem is to increase the lateral arriving energy relative to the medial arriving energy in the bass region. This can be done by increasing the directivity of your bass speakers and locating them at the sides of the room. You can also decrease the amount of bass reverberation in the room by a) adding more absorption--not very effective in the bass region or b) get a bigger room--somewhat expensive. Another trick that Dave Griesinger uses is to put in a 90 degree delay on one of the woofers below around 100Hz (you'll need to also add a 3dB boost of you do this).
The end result if you do all this is that your brain still won't be able to localize the bass, but it will recognize that it is not coming from inside your head. In my room, I find that just going to dipoles is enough to get the bass out of my head. In addition, the directivity of a dipole woofer is a much better match to a horn mid and treble than for a monopole. I found when I had monopole woofers that if I equalized the on axis response, then the bass sounded boomy. If I equalized the power response, the bass lacked dynamics. The dipoles sound dynamic, but not boomy. I'll never go back to monopoles.
John
Hi John,
Thanks for starting this thread.
I think I'm beginning to understand this concept.
Let me run the following idea by you for a 2OG to cover 50-300Hz:
I'm picturing 4 15" woofers per channel (2 front, 2 back) in twin vertical frames (~15"x34") separated by 15". Instead of perfed sheet, how about stuffing between the drivers?
For the EQ, I'm picturing a Behringer 8024 per channel feeding the two signals to the front and back halves, the back delayed ~1ms. Each channel out of the 8024 would go into a dual integrator with the upper knee setting the preferred lowpass point. Each integrator would then feed an amp powering its respective half. If a phase reinforcement peak is in the passband, you could use the digital PEQ on the 8024 to notch it out.
Does this setup make sense? Using 4 15s per channel, could I get decent SPL down to 50 Hz?
Thanks for starting this thread.
I think I'm beginning to understand this concept.
Let me run the following idea by you for a 2OG to cover 50-300Hz:
I'm picturing 4 15" woofers per channel (2 front, 2 back) in twin vertical frames (~15"x34") separated by 15". Instead of perfed sheet, how about stuffing between the drivers?
For the EQ, I'm picturing a Behringer 8024 per channel feeding the two signals to the front and back halves, the back delayed ~1ms. Each channel out of the 8024 would go into a dual integrator with the upper knee setting the preferred lowpass point. Each integrator would then feed an amp powering its respective half. If a phase reinforcement peak is in the passband, you could use the digital PEQ on the 8024 to notch it out.
Does this setup make sense? Using 4 15s per channel, could I get decent SPL down to 50 Hz?
So you're saying that this method adds directionality to the lower frequencies, which is fascinating, but doesn't your brain give the bass directionality depending on the upper, more directional frequencies coming from the same source? In other words, when a car explosion eminates from the center channel down to 50 hz, doesn't that sound give directionality to the bass coming from the remotely located subwoofer, so the bass seems to come from that center channel?
I am just trying to understand where you are coming from so I don't miss anything.
I am just trying to understand where you are coming from so I don't miss anything.
John, could you provide a link to your homepage?
Keltic: I'd like a scan please.
On a side note:
Wvier (http://www.wvier.de/download.htm) propagate Unipoles. Some of the articles are even in English. A Unipole is a dipole and a monopole used on top of each other. They say this is the best way to get an efficient excitation of all modes.
In my eyes, they - being PA driven - are striving for an efficient and uniform excitation of modes.
For the most natural sound reproduction (including temporal decay characteristics!), I think we should be striving for an efficient non-excitation of modes.
Regards,
Eric
Keltic: I'd like a scan please.
On a side note:
Wvier (http://www.wvier.de/download.htm) propagate Unipoles. Some of the articles are even in English. A Unipole is a dipole and a monopole used on top of each other. They say this is the best way to get an efficient excitation of all modes.
In my eyes, they - being PA driven - are striving for an efficient and uniform excitation of modes.
For the most natural sound reproduction (including temporal decay characteristics!), I think we should be striving for an efficient non-excitation of modes.
Regards,
Eric
Capslock:
Please email me your Email address. DIYAudio Email cannot send scans.
The article is 8 pages. Have scanned in GIF, and each page is about 150 KB. How many pages would you like me to send you each day? I don't want to clog your mailbox.
Am researching how to put these into pdf files for smaller file size. but6 I can send you eight 150 KB files if you wish.
Please send me your Email address for the scans.
Thanks.
Please email me your Email address. DIYAudio Email cannot send scans.
The article is 8 pages. Have scanned in GIF, and each page is about 150 KB. How many pages would you like me to send you each day? I don't want to clog your mailbox.
Am researching how to put these into pdf files for smaller file size. but6 I can send you eight 150 KB files if you wish.
Please send me your Email address for the scans.
Thanks.
Mefistofelez:
Haven't gotten the Email yet. Please email through diyAudio mail and I will send them to you right away.
There are eight pages that average 160 KB. Am working on compressing them, but I'm not there yet. Please give me an email address capable of taking that big of a file, or include other Email adderess that I can spread them around. I can also send a couple a day to you. For instance, Hotmail only allows 2.0 MB in emails-I do not know what your Email allows. I don't want to overflow your Email address.
Haven't gotten the Email yet. Please email through diyAudio mail and I will send them to you right away.
There are eight pages that average 160 KB. Am working on compressing them, but I'm not there yet. Please give me an email address capable of taking that big of a file, or include other Email adderess that I can spread them around. I can also send a couple a day to you. For instance, Hotmail only allows 2.0 MB in emails-I do not know what your Email allows. I don't want to overflow your Email address.
Apparently a glitch in the Email system. I got Capslock's Email before, but not yours. Also, I have several diyAudio Emails informing me of new contributions to threads I am involved in.
Gotta run. When I return, I shall take Pinkmouse up on his generous offer to pdf the files, and relay them to you.
Gotta run. When I return, I shall take Pinkmouse up on his generous offer to pdf the files, and relay them to you.
Hello!
There have been at least one second-order gradient construction that I'm avare of. It was published in "Hifi", a hifi magazine here in Finland in the early 90's and also in the book called "Rakenna Hifikaiuttimet" by Pekka Tuomela, 2nd corrected print, Tecnopress 1993, ISBN:951-832-034-9.
The book is in finnish, if that makes sense to you
The loudspeaker was called Hifi-C1. The second-order gradient principle was employed in the 100-400Hz range by using 4+4 Seas P21REX elements, 4 in front group and 4 in the rear. These elements were placed in square around midranges and tweeter.
Other elements were Philips RT8 ribbon tweeter >4kHz, 2* Seas MP14RCY 400Hz-4kHz placed below and above the tweeter, and cardioid bass < 100Hz using 2* Seas P21REX and 2* Seas P17REX. Filters were passive.
From the looks of the book it sure looks an impressive idea for a loudspeaker! It was said have been used as a reference speaker in the mentioned Hifi magasine tests. I have never heard the speaker, though.
Also, it is stated in the book that the author made also design of the second-order cardioid speaker for a commercial manufacturer, but I have no info about that.
Yes, it is a rare consept that I would like to see used more often. Actually, I've had the second-order cardioid concept on my mind when thinking what kind of speakers to build, but I've neglected the idea as too expensive to realise at home.
-Elias
There have been at least one second-order gradient construction that I'm avare of. It was published in "Hifi", a hifi magazine here in Finland in the early 90's and also in the book called "Rakenna Hifikaiuttimet" by Pekka Tuomela, 2nd corrected print, Tecnopress 1993, ISBN:951-832-034-9.
The book is in finnish, if that makes sense to you
The loudspeaker was called Hifi-C1. The second-order gradient principle was employed in the 100-400Hz range by using 4+4 Seas P21REX elements, 4 in front group and 4 in the rear. These elements were placed in square around midranges and tweeter.
Other elements were Philips RT8 ribbon tweeter >4kHz, 2* Seas MP14RCY 400Hz-4kHz placed below and above the tweeter, and cardioid bass < 100Hz using 2* Seas P21REX and 2* Seas P17REX. Filters were passive.
From the looks of the book it sure looks an impressive idea for a loudspeaker! It was said have been used as a reference speaker in the mentioned Hifi magasine tests. I have never heard the speaker, though.
Also, it is stated in the book that the author made also design of the second-order cardioid speaker for a commercial manufacturer, but I have no info about that.
Yes, it is a rare consept that I would like to see used more often. Actually, I've had the second-order cardioid concept on my mind when thinking what kind of speakers to build, but I've neglected the idea as too expensive to realise at home.
-Elias
Thanks for doing this, Pinkmouse. I appreciate it.
I will try to load my own Optical Character Recognition Software. Neither the scanner no the OCR software worked very well at first with my 32MB 200 MHz computer back then. Now that I have upgraded to a slightly better computer and the scanner works very well, maybe the OCR software will, too.
Again, thanks.
I will try to load my own Optical Character Recognition Software. Neither the scanner no the OCR software worked very well at first with my 32MB 200 MHz computer back then. Now that I have upgraded to a slightly better computer and the scanner works very well, maybe the OCR software will, too.
Again, thanks.
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