Audio Speaker Design

Formulas for Calculating
Volume and Port Dimensions

Driver 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 * Qts^2.87

Fb = 0.42 * Fs / Qts^0.9

F3 = 0.26 * Fs / Qts^1.4

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 Butterworth crossover

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 = 10^db/20 * Rt / ( 1 – 10^db/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.