rdp@teddy.UUCP (10/15/85)
[] I received the following today, and attempted to reply by EMAIL, but was thwarted. Anyway, the questions asked might be of general interest. > From: muller@brl-tgr > > First let me say how much I have enjoyed your contributions to net audio. > It is refreshing to see someone with experiance to back up his views. > Gee whiz, I twiddle my kneecaps in virtual gratitude! :-) > I am very interested in speaker design and have started by studying some of > the literature on Theil-Small parameters. This aspect of speaker design > seems to be fairly well developed but as you said in your article, crossover > design is far behind. > Far behind for some people. Those that have the tools seem to do just fine, thank you. > My main question is how do you model a driver for SPICE. To me, it seems > that you would use a resistor in series with an inductor. The value of the > inductor would be a function of voice coil position which in turn would > depend on the resonant frequency of the driver and the enclosure, and of > course the frequency being applied to the driver. This is just an > intuitive guess. In fact, the SIMPLE model is more complex than that. First of all, while the driver is operating in its linear region, the voice coil inductance is pretty independent of position. I have been unable to find the slightest variation in inductance vs. position as long as I kept excursions small (on the order of .25 inch or so for woofers). Usually, the inductance changes at high levels, not because the voice coil is positioned far enough away from the pole, but because you've hit the mechanical limits of the suspension. If your trying to do that at frequencies where the inductance is an issue (above rim resonance or 1 kHz or so for woofers) then the inductance will end up being totally unmeasurable, as you have just vaporized the voice coil. The SIMPLE model involves modelling both the voice coil inductance and the mechanical resonance. The voice coil inductance can, indeed, be modelled by a simple inductance. The non-linearities in this region due to rim resonance effects are small enough to ignore for crossover considerations. The DC resistance of the voice coil is real simple, just measure it and use a resistor of the appropriate value! The mechanical resonance is a little tougher. A reasonable model can be built using an RLC parallel tank, where the R is determined by the maximum impedance at resonance minus the DC resistance, and the L and the C are determined by the actual characteristics of the impedance curve. The net result is a driver model (for woofers) that consists of a series combination of three basic elements. First, a resistor corresponding to the DC resistance of the voice coil. Second, an inductance corresponding to the voice coil inductance. Third, a parallel RLC tank which models the resonance. Note that determining the voice coil inductance is not trivial. The figures given (when they are) by the manufacturer are often for a voice coil held rigid in the magnet assembly, or (worse) the voice coil in free air! The method I have found most reliable is a figure derived from the measured impedance. For a woofer, look at the impedance at, say 8 kHz. This impedance is the vector sum of the inductance, the DC resistance, and the remaining radiation resistnace reflected back through the motor assembly (which, for a woofer at these frequencies, is damned small). Knowing two of these allows you to derive the third (the DC resistance you measure, the radiation resistance you ignore). Now the kicker, do this at several frequencies, and you discover that the measured inductance is not constant! The result is a model which works quite well for the pruposes of measuring or verifying crossover performance. Note that the model described above knows nothing about the transfer function of the driver as a whole. That's a lot tougher! > Another question is what is your opinion of a 6th order design (2nd order > active filter and 4th order vented enclosure)? I have misgivvings about such high-order designs. As was alluded to earlier in the occasionally enflamed discussion on digital filters, high-order filters are much more component-variation sensitive (intolerant) than low order filters. Slight variations in some parameters (driver mass, air mass) can severely effect tuning and performance. If you are planning on using such things as paper or other pulp-based cones, then the problem of tuning is a real one. Paper can absorb and release sufficient moisture from the air to change its mass by as much as 50% (wow! I can't believe it!). That could well be enough to screw up your design completely. (Note that the tuning parameters of such a system would be different in the winter than the summer!). The British long ago (1960?) recognized this fact, along with the intractability and dependability of paper, and started looking into alternative materials. EMI tried (somewhat successfully) fiberglas cones, while KEF led the pursuance of rubber-modified polystyrene ("bextrene"). B&W later used bextrene and cross-linked poly-amide fibers in some of their cones (DM-6, et al). I have a passive radiator system at home, the KEF RS-104AB, and part of its success in consistant performance is due to its non hygroscopic/phobic materials. Note also that this speaker was an early successful example of designing the crossover from amplifier to air, as they were able to achieve the desired crossover response acoustically. > I was very interested by your comments on an audio magazine and was wishing > I knew enough to contribute. > Me too! :-) Dick Pierce