[sdiy] inductors, B fields, and confusion

[Scott E.]

Hmmm... I think I'll just stick to 8 ohm drivers. :)

Scott E.
============================================================
Magnus Danielson wrote:
>        rho
>           0    B²l²Sd²
> eff = ------ * --------
>       4*pi*c   Re * Mm²
> 
> Where rho0 is the density of the air.
> 
> True, but there is another thing... are you really using the same gauge of
> wire?
> 
> If we assume we have about the same cross-section area of copper wire on the
> coil (the coil thickness doesn't vary very much), then we would require a
> smaller gauge of wire. The resistance per meter of wire varies reciprocal to
> the wire radius in square, that is reciprocal to the per-wire-area.
> 
> The cross-sectional of the coil will be the number of turns N times the
> effective area (there is some space inbetween the wires) so we have:
> 
> A    = N * A     * geometry-factor
>  tot        Wire
> 
> (The geometry factor handles the geometry-depending area-scaling which is due
> to the detailed packing geometry of the wires. It's a constant for our
> purposes. I'll assume it to be 1 for simplicity.)
> 
> Now, there is a connection between N and l due to the geometry, a rought
> equalent would be:
> 
> l = 2*pi*r*N
> 
> where r is the effective radius of the coil wires as they are wound around the
> coil. r is assumed to be a constant for us as well.
> 
> The wires area is found as
> 
>             2
> A     = pi*r
>  wire       wire
> 
> Where rwire is the wires radius.
> 
> The resistance Re is formed by
> 
>      rho * l   rho*2*pi*r*N
> Re = ------- = ------------
>       A           A        
>        wire        wire    
> 
> where rho is the resistivity constant for copper wire.
> 
> It's just that N depends now on the Awire so:
> 
>     A
>      tot
> N = -----
>     A
>      wire
> 
> So 
> 
>      rho*2*pi*r*A
>                  tot
> Re = ---------------
>           2
>          A
>           wire
> 
> If we now stuff this into the efficient formula we have:
> 
> l = 2*pi*r*N
> 
> 
>     A
>      tot
> N = -----
>     A
>      wire
> 
> l = 2*pi*r*Atot/Awire
> 
>        rho                 rho             4*pi²*r²*A²         A²
>           0    B²l²Sd²        0    B²Sd²             tot        wire
> eff = ------ * -------- = ------ * ----- * ------------- * ---------------
>       4*pi*c   Re * Mm²   4*pi*c    Mm²        A²          rho*2*pi*r*A
>                                                 wire                   tot
> 
> this reduces down to
> 
>        rho             2*pi*r*A      rho            r*A
>           0    B²Sd²           tot      0   B²Sd²      tot
> eff = ------ * ----- * ----------- = ---- * ----- * ------
>       4*pi*c    Mm²        rho       2*c     Mm²     rho
> 
> Now look at this formula. The things we can play with to change the resistance
> comes in the total area cross-section of the coil Atot, the radius of the coil
> r and the resistivity of the coil wire rho. The impedance we select to create
> is for all practical purposes an independent variable for the efficiency.
> 
> Oh, and if anyone wonders, here is is the speed of sound in air and not the
> speed of light in vacuum. ;O)