Audio Engineering

Loudspeakers 699

and the mechanical impedance Zm will have a minimum value  Rm. The velocity will be
maximum, thus the back EMF and motional impedance will be maximum, indicating a
parallel resonance. It will be seen that series components in the mechanical circuit appear
as parallel components in the electrical side and vice versa.

23.17.1 Analogue Models

We can now assemble the various parameters to produce a basic analogue for a
loudspeaker. Figure 23.17 shows the low-frequency analogue referred to the mechanical
side. The quantityfc represents the total force acting in the equivalent circuit to produce
the voice coil velocity uc :

u

EBl

c RR X

g

c



(j

.

mm)

(23.39)

Let us divide the frequency region into fi ve parts and treat each part separately by
simplifying the circuit in Figure 23.18 to correspond to that part alone. In region A,
where the loudspeaker is stiffness controlled, the power output increases as the fourth
power of frequency, or 12 dB/octave. In region B, at resonance frequency 0) o the power
output is determined by the total resistance becauseXm passes through zero. For large
values of Bl and small values of Rc , the total circuit resistance becomes suffi ciently large
so that the resonance is more than critically damped. The sound pressure will increase
linearly with frequency (  6 dB/octave). In region C, the power output (and sound
pressure) approaches a constant value, provided that the circuit impedance approximates
a pure mass reactance. That is to say, RMR and Xm^2 both increase as the square of the
frequency.

Rmd

Rmd

Lmd

Mmd

uc

Cmd

B^2 I^2

Rc

L

(BI)^2

EBI

RjωL Fc

Figure 23.17 : A low-frequency mechanical analogue.