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Planar mid/tweeter

Calculations (or things passing as calculations)


As far as I can tell, it is going to be next to impossible to fully predict the behavior of the driver. While equations exist for a simple ribbon, this system is more complex and I don't know of any equations that fully apply. However, I believe that their basic form will hold true and that they can give some insight as to how best to proceed.

Diaphram design

From (1) we have:

where E is the efficiency in percent, A is the diaphram raidiator in cm2, B is the field strength in Tesla (10k gauss), M is the moving mass, and F is the fraction of the mass belonging to the conductor.

From this, we can see that efficiency is raised by increasing the diaphram size, field strengh and fraction of the mass accounted for by the conductor. Unlike pure ribbon drivers, this driver will consist of a series of conductors bonded to a thin film, making the driver wider. The wider driver clearly raises our A, which being squared will certainly help our efficiency. Of course, we must keep the overall mass low and keep the conductor:diaphram mass ratio high. The optimal value of F is 0.5, but keep in mind this includes the air-load mass.

5 micron Al has a mass of about 1.4mg/cm2 for a total here of 320mg. Our diaphram has an area of approx. 710cm2 which with 0.3 mil Kapton (1kg/93m2) works out to 760mg. Without adhesive, we're looking at something slightly over 1g.

Impedance

For our impedance, 5 micron Al has a resistance of about 0.006 ohms / cm2. Given 1.25cm (0.5") gaps between the magnets, 0.5cm conductors will fit. Four conductors at 112cm equals 448cm or a length-width ratio of 896. This yields 5.376 ohms putting us within our target range. If needs be, to increase power handling, slightly thicker or wider strips could be employed, but for now, this is what I'm working with.

Magnet gap

The flux in this design runs parallel to the diaphram and should be nicely linear. I've yet to do the math on what the B will actually be. For now, I've chosen to stick with Ceramic 5. The Alinco bars I've seen in the Magnet Source's catalog are oriented the wrong way (being bars and not blocks) and don't seem economical. If we look at max BH/ $ for an inch of ~0.5"x ~0.5" magnet in lots of 100: Ceramic 5= 16, Alinco 5=1.8, Neodymium 28 (bulk sale) = 6.1 or 12.2 (half width). Similarly if we limit ourselves to 264" or $100 (whichever comes first) per speaker, BH*#magnets: Ceramic 5=482 ($52), Alinco 5=88.5 ($100), Neodymium 28=308 ($100). Doubling the price cap lets Neodymium win out here (616), but we've doubled the price cap. FWIW, Ceramic 8 is what Gold Ribbon Concepts uses and its BH is 3.5 vs. 3.4 of Ceramic 5.

Diaphram design
Impedance
Magnet gap

Planar mid/tweeter - 15 OCT 1996
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