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22nd April 2004, 09:48 PM  #21  
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22nd April 2004, 10:10 PM  #22  
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And you don't hear people referring to capacitors or inductors as "AC generators." The cone's mass and its compliance are energy storage mechanisms just as inductors and capacitors are. And in fact the cone's mass and compliance have their electrical analogues in inductance and capacitance respectively, which is why dynamic loudspeaker drivers are modeled electrically using R, L and C elements. se 

22nd April 2004, 10:12 PM  #23  
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22nd April 2004, 10:29 PM  #24  
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22nd April 2004, 10:48 PM  #25 
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On the subject of speaker electrical models.
The speaker has the additional complexity of being coupled to air and of drive units being physically coupled to one another through the speaker box and the air within the speaker box. Speakers are also microphones, so there will be cone movements which are temporally delayed from the original signal and these will create impedance changes as seen by the amplifier. Also, the speaker cables form transmission lines which can have very big effects on impedance seen by the amp at HF (as Nelson knows well). Just for completeness. 
22nd April 2004, 10:59 PM  #26  
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22nd April 2004, 11:10 PM  #27  
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that's the TS model that I referred to in the original thread. Nobody including Graham picked it up, tho, yeah, if you write out the differential equiations describing the electromechanical movements of a real speaker, you get the same differential equations describing that RLC network presented by TS. so as far as the amp is concerned, the rlc network and its equivalent speaker are one and the same. 

23rd April 2004, 12:13 AM  #28  
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23rd April 2004, 02:21 AM  #29  
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Well I thought the part where he quoted a paragraph of mine was just great. Also, I think there is some merit to the weighting of harmonics in evaluating harmonic distortion. I know I'd rather listen to 1% 2nd or 3rd than 1% 4th and 5th. "You cannot get accurate spectral analysis results with an FFT of one cycle....That is a horrible window." You're right. I'd have to see some evidence of how you can accurately get Spice to model THD on a waveform start that has to be full of harmonics by itself, much less steady state. 

23rd April 2004, 04:16 AM  #30  
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f_{bin}= m*f_{s}/N where m=0, 1, 2, ...N1 and N is the number of DFT samples and f_{s} is the sampling frequency. The f_{bin} are the frequency "bins", that is, where the DFT is telling us the frequency components of the signal are, as opposed to where they really may be. Suppose we choose the sampling frequency f_{s} to be exactly N times the fundamental frequency of the periodic signal we're sampling. That is, choose: f_{fund}=f_{s}/N Reffering to "Understanding Digital Signal Processing" by Lyons, page 72, he says this: "The DFT produces correct results only when the input data sequence contains energy precisely at the analysis frequencies given in Eq. 324, at integral multiples of our fundamental frequency f_{s}/N" Andy's note: his equation 324 is the same as what I've written above for the f_{bin}. So if we choose our sampling frequency as exactly N times the fundamental frequency of the signal we're sampling (where N is again the number of DFT points), the bins will line up exactly with the frequency components of the signal we're sampling (assuming that signal is truly periodic). If we don't establish this relationship, the signal will appear spread out in all the DFT bins in general. How do we make this work with SPICE? SPICE wants to pick its own, often nonuniform time steps based on the time rate of change of the signal. But we can specify a minimum time step, and if that minimum time step is way smaller than what SPICE would compute on its own, we'll get uniform time steps. We can choose these time steps, together with the number of points in the FFT to make the sampling frequency f_{s} an exact integer multiple of the fundamental frequency of the sine wave we're applying. But the typical approach is to do the analysis on the last cycles of the sinusoid, so that any transient will have died out. Note that this is the opposite of what GM suggests. But GM's measurement really indicates the closeness of the first cycle to that of an ideal sinusoid. This isn't really distortion in the nonlinear sense. Note that I don't necessarily agree with this approach. I'm just trying to explain what I think he's doing. 

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