Audio Engineering

Loudspeakers 697

23.17 Motional Impedance .............................................................................................

The moving coil system is a reversible transducer, a current through the coil will produce
a force, and the resultant velocity of the coil will produce an EMF. This voltage will be
a function of velocity, conductor length, and magnetic fi eld strength; thus if an external
EMF is applied to the coil the resultant motion will generate a back EMF (180° out
of phase), which will tend to counteract the forward current fl ow, thus increasing the
electrical impedance. This is “ motional impedance. ”

If the motion of the system can be prevented by applying an infi nite mechanical
impedance (Z mx in Figure 23.16 ), there will be no back EMF and the electrical
impedance will be only the voice coil resistance and inductance (blocked impedance).
Reducing the mechanical impedance (reducing mass and resistance and increasing
compliance) will result in an increase in velocity and the motional impedance will be
increased. Intuitively, this indicates that motional impedance will be proportional to Bl
and an inverse function of the mechanical impedance. The common factor is the velocity
of motion.

Back EMF EBlvb V (23.26)

from ( ) velocity v

Force

ZZ

m/s.

mm

15 26. 

Bli

(23.27)

Thus motional impedance

Kg/s ohms

cm

b

ml

mem

Z

E

i

Bl

Z

ZZ





22

(23.28)

from Equations (23.27) and (23.28)

Z

Bl

RL

C

em

mm

m

j





22

1

ω

ω

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

(23.29)

Z

em YGjBem em em

 ,



11

(23.30)