I'm in the beginning of a small student project where I'm trying to simulate a guitar speaker cabinet (Marshall 1x12, half closed). I'm using high-end equipment for measurements like B&K mic, National Instr DAC cards etc. My approach is to model the speaker as a static nonlinear system followed by dynamic linear system. As you probably know, a static nonlinear system will produce harmonics as multiples of the fundamental. During the identification process of the speaker system, I got some strange results. Say that the input signal, a sine, has a frequency = f, then apart from the harmonics 2f, 3f, 4f, ... I also got harmonics 1/2f. How is this possible? The only explanation I can come up with is frequency modulation. Does any one know the physical explanation behind this phenomena? Could you get harmonics one octave below the fundamental and where do they come from in reality? Regards, /A
speaker modeling
Started by ●July 1, 2003
Reply by ●July 1, 20032003-07-01
Alan wrote:> > I'm in the beginning of a small student project where I'm trying to simulate > a guitar speaker cabinet (Marshall 1x12, half closed). I'm using high-end > equipment for measurements like B&K mic, National Instr DAC cards etc. My > approach is to model the speaker as a static nonlinear system followed by > dynamic linear system. As you probably know, a static nonlinear system will > produce harmonics as multiples of the fundamental. > > During the identification process of the speaker system, I got some strange > results. Say that the input signal, a sine, has a frequency = f, then apart > from the harmonics 2f, 3f, 4f, ... I also got harmonics 1/2f. How is this > possible? The only explanation I can come up with is frequency modulation. > > Does any one know the physical explanation behind this phenomena? > Could you get harmonics one octave below the fundamental and where do they > come from in reality? > > Regards, /AI don't know, but I can tell you that subharmonics -- that's what fractional frequencies are called -- can be produced by resonant circuits (or their physical equivalents) with non-linear elements. The standard telephone ringing frequency in the US is 20 Hz. Very early PBXs (Private Branch Exchanges) had hand-cranked ringing generators. Later installations, starting around 1950, used capacitors and non-linear inductors to generate 20 Hz ringing current when excited by 60 Hz power. You might search Western Electric archives for the explanation of how it worked. (I understood it once, but I've forgotten.) With your working simulation, you are in a better position than most to dig out an explanation. Plot some of the waveforms developed at intermediate nodes and the mechanism in your particular case may become clear. I recall reading about woofer subharmonic generation in a paper by George Briggs of Wharfdale. <rembrance of thing past> In 1955, when I was 23, I was reading Briggs's "Sound Reproduction" -- the dust jacket was still new and legible -- on the IRT subway. A woman sitting across the aisle (she looked like a test pilot for a broom factory) was making a big production of wrinkling her nose at me, as if I had dog doo on my shoe. When I finally realized what was happening, I said, "Lady, you have a dirty mind. This is a book about loudspeakers." She walked to the other end of the car and got off at the next stop. </rembrance of thing past> Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 1, 20032003-07-01
Hi and thanks for your answer! Do you think that the "Doppler effect" could explain the behaviour? On the other hand, shouldn't that affect all the frequencies then? Here, it's only some fundementals that get subharmonics. /A "Jerry Avins" <jya@ieee.org> skrev i meddelandet news:3F01C711.5A409175@ieee.org...> Alan wrote: > > > > I'm in the beginning of a small student project where I'm trying tosimulate> > a guitar speaker cabinet (Marshall 1x12, half closed). I'm usinghigh-end> > equipment for measurements like B&K mic, National Instr DAC cards etc.My> > approach is to model the speaker as a static nonlinear system followedby> > dynamic linear system. As you probably know, a static nonlinear systemwill> > produce harmonics as multiples of the fundamental. > > > > During the identification process of the speaker system, I got somestrange> > results. Say that the input signal, a sine, has a frequency = f, thenapart> > from the harmonics 2f, 3f, 4f, ... I also got harmonics 1/2f. How isthis> > possible? The only explanation I can come up with is frequencymodulation.> > > > Does any one know the physical explanation behind this phenomena? > > Could you get harmonics one octave below the fundamental and where dothey> > come from in reality? > > > > Regards, /A > > I don't know, but I can tell you that subharmonics -- that's what > fractional frequencies are called -- can be produced by resonant > circuits (or their physical equivalents) with non-linear elements. The > standard telephone ringing frequency in the US is 20 Hz. Very early PBXs > (Private Branch Exchanges) had hand-cranked ringing generators. Later > installations, starting around 1950, used capacitors and non-linear > inductors to generate 20 Hz ringing current when excited by 60 Hz power. > You might search Western Electric archives for the explanation of how it > worked. (I understood it once, but I've forgotten.) > > With your working simulation, you are in a better position than most to > dig out an explanation. Plot some of the waveforms developed at > intermediate nodes and the mechanism in your particular case may become > clear. I recall reading about woofer subharmonic generation in a paper > by George Briggs of Wharfdale. > > <rembrance of thing past> > In 1955, when I was 23, I was reading Briggs's "Sound Reproduction" -- > the dust jacket was still new and legible -- on the IRT subway. A woman > sitting across the aisle (she looked like a test pilot for a broom > factory) was making a big production of wrinkling her nose at me, as if > I had dog doo on my shoe. When I finally realized what was happening, I > said, "Lady, you have a dirty mind. This is a book about loudspeakers." > She walked to the other end of the car and got off at the next stop. > </rembrance of thing past> > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������
Reply by ●July 1, 20032003-07-01
Alan wrote:> > Hi and thanks for your answer! > > Do you think that the "Doppler effect" could explain the behaviour? > On the other hand, shouldn't that affect all the frequencies then? Here, > it's only some fundementals that get subharmonics. > > /A >... Two opinions: Doppler effect has nothing to do with it. (But it can have a different manifestation.) Subharmonic generation depends on resonances. Only some frequencies are affected. Apparently, subharmonic generators are used today in telephone centrals. From http://www.telephonetribute.com/switches_survey_chapter_12.html: "In the smaller offices being engineered today, 60 cycle power from the commercial service is converted to 20 cycles by a static type subharmonic generator which also supplies audible ringing tone, 420 cycles modulated by 40 cycles. During power failures, a rotary converter is automatically started, converting battery power to a-c to keep the ringing generator in operation. These static type generators are economical up to 50 watts output, the 5 to 25 watt models being in widespread use in community dial, manual and PBX applications. Tones are also derived from 60 cycle power by other static type generators which use saturable transformers and tuned filters to select 60 cycle harmonics; 540 cycles for high tone and 600 modulated by 120 cycles for low tone." Details of their operation ought to be currently available. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 1, 20032003-07-01
I would strongly recommend you borrow or read Loud Speaker Design Cookbook by Dickason, it will help you understand more of what is occuring inside the box. How exactly are you doing the mathematical modeling of the linear system, are you receiving the subharmonics as a result of the input of mic, or you getting that from your own simulation model. What type of controls are you using to limit what goes in and out, are you performing tests in noise free environment etc.....kinda give a discription of your setup, and maybe I can provide some more detailed background of what is most likely occuring, I could make a guess at what is happening, but it would be a blind stab in the dark. Jerry is right on there are a lot of factors it could be, I would follow his advice too! Craig Jerry Avins <jya@ieee.org> wrote in message news:<3F01C711.5A409175@ieee.org>...> Alan wrote: > > > > I'm in the beginning of a small student project where I'm trying to simulate > > a guitar speaker cabinet (Marshall 1x12, half closed). I'm using high-end > > equipment for measurements like B&K mic, National Instr DAC cards etc. My > > approach is to model the speaker as a static nonlinear system followed by > > dynamic linear system. As you probably know, a static nonlinear system will > > produce harmonics as multiples of the fundamental. > > > > During the identification process of the speaker system, I got some strange > > results. Say that the input signal, a sine, has a frequency = f, then apart > > from the harmonics 2f, 3f, 4f, ... I also got harmonics 1/2f. How is this > > possible? The only explanation I can come up with is frequency modulation. > > > > Does any one know the physical explanation behind this phenomena? > > Could you get harmonics one octave below the fundamental and where do they > > come from in reality? > > > > Regards, /A > > I don't know, but I can tell you that subharmonics -- that's what > fractional frequencies are called -- can be produced by resonant > circuits (or their physical equivalents) with non-linear elements. The > standard telephone ringing frequency in the US is 20 Hz. Very early PBXs > (Private Branch Exchanges) had hand-cranked ringing generators. Later > installations, starting around 1950, used capacitors and non-linear > inductors to generate 20 Hz ringing current when excited by 60 Hz power. > You might search Western Electric archives for the explanation of how it > worked. (I understood it once, but I've forgotten.) > > With your working simulation, you are in a better position than most to > dig out an explanation. Plot some of the waveforms developed at > intermediate nodes and the mechanism in your particular case may become > clear. I recall reading about woofer subharmonic generation in a paper > by George Briggs of Wharfdale. > > <rembrance of thing past> > In 1955, when I was 23, I was reading Briggs's "Sound Reproduction" -- > the dust jacket was still new and legible -- on the IRT subway. A woman > sitting across the aisle (she looked like a test pilot for a broom > factory) was making a big production of wrinkling her nose at me, as if > I had dog doo on my shoe. When I finally realized what was happening, I > said, "Lady, you have a dirty mind. This is a book about loudspeakers." > She walked to the other end of the car and got off at the next stop. > </rembrance of thing past> > > Jerry
Reply by ●July 1, 20032003-07-01
Jerry Avins <jya@ieee.org> wrote in message news:<3F0200A5.D44FCAAC@ieee.org>...> Alan wrote: > > > > Hi and thanks for your answer! > > > > Do you think that the "Doppler effect" could explain the behaviour? > > On the other hand, shouldn't that affect all the frequencies then? Here, > > it's only some fundementals that get subharmonics. > > > > /A > > > ... > > Two opinions: > > Doppler effect has nothing to do with it. (But it can have a different > manifestation.)While I don't know a lot about the physics of speakers, I think it is true that Doppler effects can have an impact on the sound, at least to some extent.> Subharmonic generation depends on resonances. Only some frequencies > are affected.This is a more subtle point. A fellow student did some work on high-power ultrasonic propagation in some medium, I think it was air-filled shells submerged in water. The work was experimental, and his main conclusion was that subharmonics were generated in addition to the expected overharmonics. As far as I remember, these results got some attention because it was not clear at the time what physical process would generate subharmonics. What was clear, however, was that the cause was nonlinear, due to the high energy levels of the signals. I heard later that an explanation had been found, but I don't know what it was or who found it. The experiments were reported in an article I don't remember the name of that was published in the Journal of the Acoustical Society of America. The authors were Oddvar Lotsberg and Jens Hovem. I believe the article was printed in 1995 or 1996. Perhaps a search for articles that cite this work may produce something useful. Again, subharmonics and linear models may not be the best of mixes... Rune
Reply by ●July 2, 20032003-07-02
Rune Allnor wrote:> > Jerry Avins <jya@ieee.org> wrote in message news:<3F0200A5.D44FCAAC@ieee.org>... > > Alan wrote: > > > > > > Hi and thanks for your answer! > > > > > > Do you think that the "Doppler effect" could explain the behaviour? > > > On the other hand, shouldn't that affect all the frequencies then? Here, > > > it's only some fundementals that get subharmonics. > > > > > > /A > > > > > ... > > > > Two opinions: > > > > Doppler effect has nothing to do with it. (But it can have a different > > manifestation.) > > While I don't know a lot about the physics of speakers, I think it is > true that Doppler effects can have an impact on the sound, at least to > some extent.Indeed, but not subharmonic generation. High frequencies can be FMed by lows from the same cone, a sort of acoustic Zeeman effect.> > > Subharmonic generation depends on resonances. Only some frequencies > > are affected. > > This is a more subtle point. A fellow student did some work on high-power > ultrasonic propagation in some medium, I think it was air-filled shells > submerged in water. The work was experimental, and his main conclusion > was that subharmonics were generated in addition to the expected > overharmonics. As far as I remember, these results got some attention > because it was not clear at the time what physical process would generate > subharmonics. What was clear, however, was that the cause was nonlinear, > due to the high energy levels of the signals. I heard later that an > explanation had been found, but I don't know what it was or who found it. > > The experiments were reported in an article I don't remember the name of > that was published in the Journal of the Acoustical Society of America. > The authors were Oddvar Lotsberg and Jens Hovem. I believe the article > was printed in 1995 or 1996. Perhaps a search for articles that cite this > work may produce something useful. > > Again, subharmonics and linear models may not be the best of mixes... > > RuneNonlinearity is a sine qua non, and resonance also usually involved. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 2, 20032003-07-02
"Alan" <alan@swipnet.uk> wrote in message news:<eWiMa.14803$mU6.15043@newsb.telia.net>...> I'm in the beginning of a small student project where I'm trying to simulate > a guitar speaker cabinet (Marshall 1x12, half closed). I'm using high-end > equipment for measurements like B&K mic, National Instr DAC cards etc. My > approach is to model the speaker as a static nonlinear system followed by > dynamic linear system. As you probably know, a static nonlinear system will > produce harmonics as multiples of the fundamental. > > During the identification process of the speaker system, I got some strange > results. Say that the input signal, a sine, has a frequency = f, then apart > from the harmonics 2f, 3f, 4f, ... I also got harmonics 1/2f. How is this > possible? The only explanation I can come up with is frequency modulation. > > Does any one know the physical explanation behind this phenomena? > Could you get harmonics one octave below the fundamental and where do they > come from in reality? > > Regards, /AAs an extreme example any process whereby the output of your system is only under the influence of the input at certain states will give subharmonic behaviour. To illustrate, consider what would happen to your loudspeaker if you happened to detach the voice coil from the cone so that the only thing holding it in contact was the roll surround. On the first up cycle of the sinusoid the cone would follow the voice coil to it's peak displacement but then momentum would make the cone continue to move outward. When it would spring back to a position that is within the sphere of influence of the voice coil would depend upon the mass of the cone and the compliance of the roll surround but if the time it takes is greater than one cycle of the forcing sinusoid then subharmonics will be generated. Obviously this is far more extreme than what you can expect from a typical loudspeaker but it illustrates the type of non-linear behaviour that could give rise to sub harmonics. If I were to guess I suspect that cone break up may have alot to do with it. Have you ever noticed that the effective stiffness of a typical cone is direction dependent : that is if you poke your finger into the driver on the front side the cone shape is largely intact and follows the movement of your finger, whereas if you poke your finger from the other side the cone shape distorts dramatically. This is much like the crude example above where the time to recover will be related to the surface stiffness and mass per unit area of the cone material. The conical shape gives extra rigity to the cone but only on one side. One reasonable test to validate if cone break-up is responsible is to check what happens as you lower the amplitude of cone displacement. My guess is that the sub-harmonic components will reduce or even vanish below a certain level. Realistic models of speakers that include the effects of break-up would be very difficult to construct because your trying to make a lumped model of something that is inherently distributed. Maybe you should put sub-harmonics in the too hard basket and just include the others - unless you can think of a simple way to include this sort of behaviour. Regards, Paavo Jumppanen Author of AtSpec : A 2 channel PC based spectrum analyzer http://www.taquis.com
Reply by ●July 2, 20032003-07-02
Jerry Avins wrote:> > Rune Allnor wrote: > >...> > > > Again, subharmonics and linear models may not be the best of mixes... > > > > Rune > > Nonlinearity is a sine qua non, and resonance also usually involved. >For do-it-yourselfers: Consider a pendulum. (No. Not that one! The one I hung from the end of a cantilever.) As the bob swings from side to side, it also moves up and down. It moves up whichever side it swings to, so the vertical period is half the horizontal. The cantilever moves a bit, so if a "vertical pendulum" -- a weight suspended from a spring -- in resonance with the vertical motion is also attached, it will pump up and down whenever the bob swings. On the other hand, the ordinary pendulum has no apparent tendency to start swinging in response to the vertical pendulum's motion. Even so, it will start if the vertical drive is applied long enough. To try this, use a motor and crank instead of the vertical pendulum. This gizmo starts slowly. Pushing the horizontal pendulum doesn't often help much. The motions need to be in phase. Once the thing gets to swinging, keep it on in a back room, where you can use it as the clincher to win bets from people too young to know about parametric amplifiers. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 2, 20032003-07-02
> To illustrate, consider what would happen to your loudspeaker if you > happened to detach the voice coil from the cone so that the only thing > holding it in contact was the roll surround. On the first up cycle of > the sinusoid the cone would follow the voice coil to it's peak > displacement but then momentum would make the cone continue to move > outward. When it would spring back to a position that is within the > sphere of influence of the voice coil would depend upon the mass of > the cone and the compliance of the roll surround but if the time it > takes is greater than one cycle of the forcing sinusoid then > subharmonics will be generated. > > Obviously this is far more extreme than what you can expect from a > typical loudspeaker but it illustrates the type of non-linear > behaviour that could give rise to sub harmonics. If I were to guess I > suspect that cone break up may have alot to do with it. Have you ever > noticed that the effective stiffness of a typical cone is direction > dependent : that is if you poke your finger into the driver on the > front side the cone shape is largely intact and follows the movement > of your finger, whereas if you poke your finger from the other side > the cone shape distorts dramatically. This is much like the crude > example above where the time to recover will be related to the surface > stiffness and mass per unit area of the cone material. The conical > shape gives extra rigity to the cone but only on one side. >OK, thanks Paavo (Is that a Finish name?) I find your answer very intresting but a bit too technical for me at the moment. I think I'll have to dig into the Science of Acoustics first ;-)> One reasonable test to validate if cone break-up is responsible is to > check what happens as you lower the amplitude of cone displacement. My > guess is that the sub-harmonic components will reduce or even vanish > below a certain level. Realistic models of speakers that include the > effects of break-up would be very difficult to construct because your > trying to make a lumped model of something that is inherently > distributed. Maybe you should put sub-harmonics in the too hard basket > and just include the others - unless you can think of a simple way to > include this sort of behaviour.Yeah I've noticed that the behaviour depends on the amplitude of the input signal (another typical non-linear behaviour). Thanks again, Alan
