Hi Craig!> 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.Ok, I'll do that! < How exactly are you doing the mathematical> modeling of the linear system, are you receiving the subharmonics as a > result of the input of micYes.> 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,Matlab->DAC->amp->speaker->mic->mic-preamp->ADC->Matlab The amp is an high-end transistor amp with flat frequency response through the bandwidth of the system. Both the mic and the preamp are expensive B&K equipment. The speaker is measured in a well damped room with a floating floor.> 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
speaker modeling
Started by ●July 1, 2003
Reply by ●July 2, 20032003-07-02
Reply by ●July 3, 20032003-07-03
Alan wrote:> ... > 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?Hi Alan, you didn't mention the excitation frequency. If the membran is not able to follow the excitation because the frequency is too high, this might cause partial excitation, so that part of the membran is moved forth and back with the excitation frequency. This might cause the whole system to move with such a frequency, of which the excitation frequency is a harmonic. That's nothing strange - to my opinion. If you excite a system with an Dirac impulse. It will respond with the "impulse response" showing not so much the impulse itself, but mainly the characteristics of the system - if it's band limited you'll find a response which shows the limits somehow, often in a declining pulse which rings with a frequency inside the band until it's faded away. Sorry, that this is not a fine mathematical explanation. HTH Bernhard -- before sending to the above email-address: replace deadspam.com by foerstergroup.de
Reply by ●July 3, 20032003-07-03
"Bernhard Holzmayer" <holzmayer.bernhard@deadspam.com> skrev i meddelandet news:3119716.rhjChok3aq@holzmayer.ifr.rt...> Alan wrote: > > > ... > > 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? > > Hi Alan, > you didn't mention the excitation frequency.The sub-harm were only added at some freq and it seems that these are the resonance freq of the speaker and/or cabinet. Also, the cabinet is half-closed.> That's nothing strange - to my opinion. > If you excite a system with an Dirac impulse. > It will respond with the "impulse response" showing not so much the > impulse itself, but mainly the characteristics of the system - if > it's band limited you'll find a response which shows the limits > somehow, often in a declining pulse which rings with a frequency > inside the band until it's faded away.Yes I know about impulse responses, but do you really think they'll be helpful here?> Sorry, that this is not a fine mathematical explanation.I can do without to much maths ;-) /A
Reply by ●July 3, 20032003-07-03
"Alan" <alan@swipnet.uk> wrote in message news:<90%Ma.15066$mU6.15081@newsb.telia.net>...> "Bernhard Holzmayer" <holzmayer.bernhard@deadspam.com> skrev i meddelandet > news:3119716.rhjChok3aq@holzmayer.ifr.rt... > > Alan wrote: > > > > > ... > > > 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? > > > > Hi Alan, > > you didn't mention the excitation frequency. > > The sub-harm were only added at some freq and it seems that these are the > resonance freq of the speaker and/or cabinet. Also, the cabinet is > half-closed.That would be consistent with the notion of cone break-up being responsible (ie. the cone not behaving as a rigid body and doing so in a non-linear fashion) because the momentum would be at a maximum at the resonant frequency for a fixed input level. Note that break up in the form of waves propagating along the surface of the cone out to the roll surround occur predominantly at high frequencies but these modes are approximately linear in behaviour. IMHO only at high deflections are you likely to get strong non-linear behaviour and I believe this is more likely to occur at frequencies around the speaker resonance. Regards, Paavo Jumppanen. Author of AtSpec : A 2 channel PC based FFT spectrum analyzer http://www.taquis.com
Reply by ●July 3, 20032003-07-03
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 think you need to look at Volterra series perhaps to understand this.
Reply by ●July 4, 20032003-07-04
Paavo Jumppanen wrote:> That would be consistent with the notion of cone break-up being > responsible (ie. the cone not behaving as a rigid body and doing > so in a non-linear fashion) because the momentum would be at a > maximum at the resonant frequency for a fixed input level. > > Note that break up in the form of waves propagating along the > surface of the cone out to the roll surround occur predominantly > at high frequencies but these modes are approximately linear in > behaviour. IMHO only at high deflections are you likely to get > strong non-linear behaviour and I believe this is more likely to > occur at frequencies around the speaker resonance. >I agree to this. If I interpret it backwards: Except for saturation effects, you should be able to find a linear model which is good enough to model the behaviour - and much easier to be understood. It should even reveal the subharmonics if it's properly done. Impulse response technics may help you to find the correct model. As long as you deal with linear models, it leads you directly to the transfer function, which essentially describes your system. Another point: Did you take into account that the speaker reflects energy into the cable? Did you model your amplifier and cable properly? Bernhard -- before sending to the above email-address: replace deadspam.com by foerstergroup.de
Reply by ●July 4, 20032003-07-04
Bernhard Holzmayer <holzmayer.bernhard@deadspam.com> wrote in message news:<1674026.D71KQjRvpg@holzmayer.ifr.rt>...> Paavo Jumppanen wrote: > > > That would be consistent with the notion of cone break-up being > > responsible (ie. the cone not behaving as a rigid body and doing > > so in a non-linear fashion) because the momentum would be at a > > maximum at the resonant frequency for a fixed input level. > > > > Note that break up in the form of waves propagating along the > > surface of the cone out to the roll surround occur predominantly > > at high frequencies but these modes are approximately linear in > > behaviour. IMHO only at high deflections are you likely to get > > strong non-linear behaviour and I believe this is more likely to > > occur at frequencies around the speaker resonance. > > > > I agree to this. > If I interpret it backwards: > Except for saturation effects, you should be able to find a linear > model which is good enough to model the behaviour - and much easier > to be understood. It should even reveal the subharmonics if it's > properly done.Do you know any examples of linear models that generate subharmonics? Or did you mean that the subharmonic terms should be included as auxilliary source terms? Rune> Impulse response technics may help you to find the correct model. > As long as you deal with linear models, it leads you directly to the > transfer function, which essentially describes your system. > > Another point: Did you take into account that the speaker reflects > energy into the cable? > Did you model your amplifier and cable properly? > > Bernhard
Reply by ●July 4, 20032003-07-04
> > Paavo Jumppanen wrote: > > > > > That would be consistent with the notion of cone break-up being > > > responsible (ie. the cone not behaving as a rigid body and doing > > > so in a non-linear fashion) because the momentum would be at a > > > maximum at the resonant frequency for a fixed input level. > > > > > > Note that break up in the form of waves propagating along the > > > surface of the cone out to the roll surround occur predominantly > > > at high frequencies but these modes are approximately linear in > > > behaviour. IMHO only at high deflections are you likely to get > > > strong non-linear behaviour and I believe this is more likely to > > > occur at frequencies around the speaker resonance. > > > > > > > I agree to this. > > If I interpret it backwards: > > Except for saturation effects, you should be able to find a linear > > model which is good enough to model the behaviour - and much easier > > to be understood. It should even reveal the subharmonics if it's > > properly done. > > Do you know any examples of linear models that generate subharmonics? > Or did you mean that the subharmonic terms should be included as > auxilliary source terms?Exactly! How could Impuls response tech help here? I don't see it. For the moment I'm not sure what model structure to use, but I think there's a physical explanation: At some input-freq f_0, the cabinet will oscillate due to its eigenvalues. These freqs depends on the shape and the material of the cabinet. When the cabinet vibrates at f = f_0/2, the freqs of the speaker cone will be affected by the freqs of the cabinet, and hence, we have frequency modulation only at those freqs that influence the eigen-freqs of the cabinet. /A> > Impulse response technics may help you to find the correct model. > > As long as you deal with linear models, it leads you directly to the > > transfer function, which essentially describes your system. > > > > Another point: Did you take into account that the speaker reflects > > energy into the cable? > > Did you model your amplifier and cable properly? > > > > Bernhard
Reply by ●July 7, 20032003-07-07
Rune Allnor wrote:> Bernhard Holzmayer <holzmayer.bernhard@deadspam.com> wrote in > message news:<1674026.D71KQjRvpg@holzmayer.ifr.rt>...>> .... Except for saturation effects, you should be able to find a >> linear model which is good enough to model the behaviour - and >> much easier to be understood. It should even reveal the >> subharmonics if it's properly done. > > Do you know any examples of linear models that generate > subharmonics? Or did you mean that the subharmonic terms should be > included as auxilliary source terms? >I thought of oscillators which are pumped by sources which are not running at the resonance frequency but at a higher frequency. But after some thinking I'm not quite sure if this would work if the excitation would be a signal which consists of only exact harmonics. If I reason that such a harmonic excitation signal injects power only at perfectly orthogonal frequencies, therefore I guess that it's impossible that power is transferred to a subharmonic in a completely linear system. In practice, this will probably work only because systems are not perfect and because the excitation is not purely harmonic. Examples would have been: tuning fork excited with a pulse. Or my guitar. Exciting a flageolett tone (this is cause a fractional swing of the string) will cause it to emit a harmonic tone at first, which fades away until you hear the fundamental tone (which is then a subharmonic) in the end. But this may be a misinterpretation, because I might have excited both tones at first without noticing the lower tone at first - I'm not sure. But now take a gear box: exciting one (smaller) wheel with a certain rotation frequency would cause a subharmonic rotation on the other side (of the bigger wheel). What is this? - Clearly power at one frequency is transferred into power at another frequency which has at least a fractional relationship - could be a subharmonic. Has it to do with it? Or is the direct coupling something different, because the system is completely stiff? Bernhard -- before sending to the above email-address: replace deadspam.com by foerstergroup.de
Reply by ●July 7, 20032003-07-07
Bernhard Holzmayer wrote:> > Rune Allnor wrote: > > > Bernhard Holzmayer <holzmayer.bernhard@deadspam.com> wrote in > > message news:<1674026.D71KQjRvpg@holzmayer.ifr.rt>... > > >> .... Except for saturation effects, you should be able to find a > >> linear model which is good enough to model the behaviour - and > >> much easier to be understood. It should even reveal the > >> subharmonics if it's properly done. > > > > Do you know any examples of linear models that generate > > subharmonics? Or did you mean that the subharmonic terms should be > > included as auxilliary source terms? > > > > I thought of oscillators which are pumped by sources which are not > running at the resonance frequency but at a higher frequency. > But after some thinking I'm not quite sure if this would work if the > excitation would be a signal which consists of only exact > harmonics. If I reason that such a harmonic excitation signal > injects power only at perfectly orthogonal frequencies, therefore I > guess that it's impossible that power is transferred to a > subharmonic in a completely linear system. > In practice, this will probably work only because systems are not > perfect and because the excitation is not purely harmonic. > > Examples would have been: tuning fork excited with a pulse. > Or my guitar. Exciting a flageolett tone (this is cause a fractional > swing of the string) will cause it to emit a harmonic tone at > first, which fades away until you hear the fundamental tone (which > is then a subharmonic) in the end. > But this may be a misinterpretation, because I might have excited > both tones at first without noticing the lower tone at first - I'm > not sure. > > But now take a gear box: > exciting one (smaller) wheel with a certain rotation frequency would > cause a subharmonic rotation on the other side (of the bigger > wheel). What is this? - Clearly power at one frequency is > transferred into power at another frequency which has at least a > fractional relationship - could be a subharmonic. Has it to do with > it? Or is the direct coupling something different, because the > system is completely stiff? > > Bernhard > > -- > before sending to the above email-address: > replace deadspam.com by foerstergroup.deBernhard, Your agile mind usually delights me. Sometimes I find it hard to follow your path, but it's worth the effort. Sometimes, like now, you stimulate me to think beyond what I have taken for granted. I take as given that subharmonics will not appear in linear, time- invariant systems. In the example of pumping a pendulum with a double- frequency vertical drive, the drive actually couples to the double- frequency vertical motion in the pendulum itself. Even if the pendulum were perfectly linear (as a cycloidal pendulum is), the vertical motion would exist. Electronic parametric amplifiers exploit non-linearities and work in sufficiently similar ways so that the pendulum is often used to explain them. I find your question about how a gear train fits into the scheme of things disturbing, hence interesting. An ideal gear train is certainly linear. A gear train can produce not only subharmonics, but any integer ratios. What puts it outside the the paradigm that we normally use when discussing linear systems? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
