Audio Speaker DesignFormulas for Calculating
Volume and Port DimensionsDriver Parameters
Ro = Rmax / Re
Rx = Re * ( Ro )1/2
Qms = Fqr * [( Ro ) / ( F2 – F1 )]1/2
Qes = Qms / ( Ro – 1 )
Qts = Qms / Ro
Sd = 3.14159 * ( Dia / 200 )2
Cms =
[ 1 / ( 12.56636 * ( M / 1000 ) ) ] * [ (Fqr + Fqs) * (Fqr – Fqs) / (Fqr2* Fqs2) ]
Vas = 140000000 * Cms * Sd2
EMP = Fqs / Qes
L = X /6283.18 X = ( R2 – Re2)1/2
Sealed Enclosures
Qts = Qes * Qms / ( Qms + Qes )
Fcb = Fs * [ ( Vas / Vb ) + 1 ]1/2
Qtc = Qts * [ ( Vas / Vb ) + 1 ]1/2
db = 20 * log10[ Qtc4 / ( Qtc2– 0.25 ) ]
Fdb = Fcb * [1 – ( 1 / ( 2 * Qtc2 )]1/2
F3 = Fcb * [ ( a + (a2 + 4)1/2 ) /2 ]1/2
a = [ 1 / (Qtc * Qtc) ] – 2
Dual driver
Qes = Qes / 2
Vas = 2 * Vas
Quad driver
Qes = Qes / 4
Vas = 4 * Vas
Vented Enclosures
Vb = 15 * Vas * Qts2.87
Fb = 0.42 * Fs / Qts0.9
F3 = 0.26 * Fs / Qts1.4
db = 20 * log10 [ 2.6 * Qts * ( Vas / Vb )0.35]
Recalculations
Fb = [ Vas / Vb ] 0.32
F3 = Fs * [ Vas / Vb ] 1/2
Single port
Vb_in = Vb * 61.016949
R_in = 0.393701 * Dp / 2
Lp_in = [ ( 14630000 * R_in2 ) / ( Fb2* Vb_in ) ] - [ 1.463 * R_in ]
Lp = Lp_in * 2.54
Dual port
Dp = [(Dp * Dp) + (Dp * Dp)]1/2 - for calculation of Lp
Dual driver
Qes = Qes / 2
Vas = 2 * Vas
dd = 68600.0152 / Fqx
Dimension calculations
y = [ (Vb * 1000) + (Vdr * 1000) / ( 1.618 *0.618 ) ]1/3
W = y
H = y * 1.618
D = y * 0.618
3rd order 2 way Butterworthcrossover
C1 = 106103 / ( Fc * Rt )
C2 = 318391 / ( Fc * Rt )
C3 = 212207 / (Fc * Rw)
L1 = 119.37 * Rt / Fc
L2 = 238.73 * Rw / Fc
L3 = 79.58 * Rw / Fc
1st order 3 way crossover
ratio = Math.round [ ( FqH / FqL ) – 1 ]
FqL2 = ( FqL * FqH / ratio )1/2
FqH2 = FqL * FqH / FqL2
C1 = 159155 / ( FqH * Rt )
C2 = 159155 / ( FqL2 * Rm )
L1 = 159.155 * Rm / FqH2
L2 = 159.155 * Rw / FqL
Attenuation network
Rp = 10db/20 * Rt / ( 1 – 10db/20)
Rs = Rt – [ ( 1 / Rp ) + ( 1 / Rt ) ]–1
Impedance compensation network
Rc = 1.25 * Re
C = 1000 * Ld / ( Rc * Rc )
Please see the Online Enclosure Calculators for definitions of variables.
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