FORMULAS & Electrical Units
Used in Speaker Circuits

Inductance

The unit of inductance in the henry.

All smaller units should be converted to henrys beforeusing the formulas.

1 millihenry (mH) = 0.001H  or 1 x 10^-3H

1 microhenry (mH) = 0.000001H or 1 x 10^-6H

Capacitance

The unit of capacitance is the farad.

All smaller units should be converted to farads beforeusing the formulas.

1 microfarad (mf) = 0.000001 farad or 1 x 10^-6

1 picofarad (pf) = 0.000000000001 farad or 10 x 10^-12farad

 

OHM'S LAW FOR SPEAKERS

For alternating current, the Ohms's Law formulas are:

E = I Z

I = E / Z

Z = E / I

E is the voltage in volts,

I is the current in amperes and

Z is the impedance in ohms

 

REACTANCE & RESONANCE

Capacitors

Capacitive reactance:

X_c = 1 / (2pƒC)

 

To get the value of a capacitor that will give a specified reactance at a given frequency:

C = 1 / (2pƒX_c)

Inductance

Inductive reactance:

X_L = 2pƒL

To get the value of a choke that will give a specified reactance at a given frequency:

L = X_L / (2pƒ)

Resonance

ƒ = 1 / [2psqrt(LC)]

Parallel Resistors

Where R₁ = R₂ = R₃, and N is the number of resistors.

Total (R_t) = R / N

 

For mixed value resistors:

R_t = 1 / [ (1/R₁) + (1/R₂)+ (1/R₃) + . . . ]

 

If N = 2

Rt = (R₁ *  R₂) / (R₁+ R₂)

Series Resistors

R_t = [R₁ + R₂ + R₃+ . . . ]

Parallel Capacitors

C_t = [C₁ + C₂ + C₃+ . . . ]

Series Capacitors

Where C₁ = C₂ = C₃, and N is the number of capacitors.

Total (C_t) = C / N

 

For mixed value capacitors:

C_t = 1 / [ (1/C₁) + (1/C₂)+ (1/C₃) + . . . ]

 

If N = 2

Ct = (C₁ *  C₂) / (C₁+ C₂)

Parallel Inductors (Chokes)

Where L₁ = L₂ = L₃, and N is the number of inductors.

Total (L_t) = L / N

 

For mixed value inductors:

C_t = 1 / [ (1/C₁) + (1/C₂)+ (1/C₃) + . . . ]

 

If N = 2

LCt = (L₁ *  L₂) / (L₁+ L₂)

Series Inductors (Chokes)

L_t = [L₁ + L₂ + L₃+ . . . ]

Resistor & Capacitor in Series

Z = sqrt ( R² + X_C² )

Resistor & Capacitor in Parallel

Z = [R * X₁] / [sqrt ( R² + X_L²)]

Resistor, Inductor, & Capacitor in Parallel

Z = [R * X_L * X_C] / sqrt[(X_L²X_C²)+ (R²(X_L - X_C)²]

 

CONVERSION FACTORS FOR SPEAKER COMPLIANCE

Speaker compliance is sometimes measured in cm/dyne- theCGS (centimeter-gram-second) system because the centimeter is a convenient unit to use in measuring cone diameter.   Sometimes compliance is shown in mixed units of mm/Newtonor even as its reciprocal term-stiffness-in Newton/Meter, the MKS (meter-kilogram-second)system.

To change cm/dyne to mm/Newton:

1cm = 10mm

1 * 10⁵dynes = 1 Newton

C_ms (cm/dynes) * 10⁶ = C_ms(mm/Newton)