Spurred by another thread about tower floorstanding speakers versus bookshelf models https://www.audiosciencereview.com/...anders-really-bring-to-the-table.27360/page-3 I was spurred to finally dig out my copy of Richard Small's thesis and look up some things. (Once when I met him in Indiana and mentioned I had a copy he was astounded, he said only like 90 copies were printed. But my first employer had a copy in the corporate library and I photocopied the whole thing, over 2" thick. Still a great reference.)
The efficiency of a classical electrodynamic cone driver is set by a formula complicated to type here (thesis 1.28):
eta0 = (rho0/2*π*c) * (Bl)^2 *(Sd^2) / Re * (Mas^2)
eta0=reference efficiency. This is above resonance, but below cone breakup.
the second term is constants, which I'm forgetting and can't find in the previous umpteen thesis pages. rho0 = air density??? And c = air velocity? I don't think it's Einstein's speed of light ha ha.
Bl=magnetic strength, the product of the magnetic field + how much wire cuts the magnetic field.
Re=DC resistance of the voice coil. THIS is the biggest reason speakers tends towards 4 ohms-reducing the "ohms" directly increases efficiency. Because less power is burned up in resisitance, OK that's way oversimplified. Re is affected by the size of the wire and the length of it, and the wire in the magnetic field is affected by this.
Sd is the cone area, notice it is squared, this is a big factor, and why the most efficient direct radiator speakers have big woofers. Also why you don't see super-sensitive mids or especially tweeters. (Note: in Dick Small's thesis this is printed in the denominator however it is a typo and supposed to be in the numerator.)
Mas is the moving mass: cone + coil + part of the surround and spider + air loading.
- Translate this into Thiele-Small parameters and you get:
eta = (4*(π^2)) * fs^3 * Vas / (c^3 * Qes)
so notice here we see a foreshadowing that a "bigger volume" is more efficient (with a lot of other interrelationships).
The efficiency of a classical electrodynamic cone driver is set by a formula complicated to type here (thesis 1.28):
eta0 = (rho0/2*π*c) * (Bl)^2 *(Sd^2) / Re * (Mas^2)
eta0=reference efficiency. This is above resonance, but below cone breakup.
the second term is constants, which I'm forgetting and can't find in the previous umpteen thesis pages. rho0 = air density??? And c = air velocity? I don't think it's Einstein's speed of light ha ha.
Bl=magnetic strength, the product of the magnetic field + how much wire cuts the magnetic field.
Re=DC resistance of the voice coil. THIS is the biggest reason speakers tends towards 4 ohms-reducing the "ohms" directly increases efficiency. Because less power is burned up in resisitance, OK that's way oversimplified. Re is affected by the size of the wire and the length of it, and the wire in the magnetic field is affected by this.
Sd is the cone area, notice it is squared, this is a big factor, and why the most efficient direct radiator speakers have big woofers. Also why you don't see super-sensitive mids or especially tweeters. (Note: in Dick Small's thesis this is printed in the denominator however it is a typo and supposed to be in the numerator.)
Mas is the moving mass: cone + coil + part of the surround and spider + air loading.
- Translate this into Thiele-Small parameters and you get:
eta = (4*(π^2)) * fs^3 * Vas / (c^3 * Qes)
so notice here we see a foreshadowing that a "bigger volume" is more efficient (with a lot of other interrelationships).
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