Audio Engineering

Loudspeakers 701

LCBlcm md^22 Henries (23.41)

R

Bl

em Rem

 Ohms

22

(23.42)

Rc and Lc are the “ blocked ” impedance values and not the DC resistance and inductance
measured in “ air. ”

C

Bl

A Sd

a

        Farads

ρ

(^22) π

8

3

(23.43)

R

Bl

A CSd

 Ohms,

22

ρ 0

(23.44)

where a is diaphragm radius and Sd is diaphragm area.

It should be noted that the factor 8a/ π in Equation (23.43) is actually the “ end correction ”
used to describe the accession to inertia acting on one side only of a rigid piston of radius
‘ a ’ vibrating in an infi nite baffl e. The air loading on the back side of the diaphragm is
determined by the loading presented by the enclosure.

Figure 23.20 shows the impedance of a 300-mm (12-inch) loudspeaker in an 85-liter
enclosure (3 ft^3 ). It will be seen that the modulus of impedance rises to 125 ohms at
the mechanical resonant frequency of 55 Hz, drops to 8 ohms at the series resonance,
and rises to 40 ohms at 10 kHz. Of equal interest is the reactive component: below the
fi rst resonance an inductive reactance is presented to generator (rising to infi nity at
resonance), while between the two resonances a capacitive reactance is presented. At
100 Hz the effective capacitance is about 90 μ F, and at that frequency the phase angle

E

Lc Rc

B^2 l^2 Cmd B^2 l^2

Rmd B^2 l^2

Mmd

B^2 l^2

CSd

B^2 l^2

8aSd

3 π

Figure 23.19 : Analogue referred to electrical input.