608 Chapter 17
cause the voice coil resistance to increase to 40% above
its ambient value. The following equation give voice
coil resistance at any temperature in degrees Celsius
(17-1)where,
RT is the resistance at temperature T in ohms,
Ro is the resistance at ambient temperature To in ohms,
T and To have units of °C.
The operating temperature of the voice coil, TVC, is
determined by ambient temperature, the amount of
power being dissipated in the coil, and a parameter
called thermal resistance, expressed in degrees Celsius
per watt, °C/W. The thermal resistance is a measure of
the ability of an object to transfer heat away from itself.
The lower the value of the thermal resistance, the more
effective the object is at this transfer. As power is
doubled, final temperature rise above ambient is
doubled. Heat transfer in a loudspeaker is a function of
the air gap design, voice coil design, and the ability of
the loudspeaker frame and magnet to dissipate heat to
the surrounding or ambient air. Referring to Fig. 17-25,
the thermal rise TVC of a stationary voice coil in an air
gap is
(17-2)where,
TVC is the temperature of the voice coil in °C,
Ts is the temperature of structure (magnet) in °C,
Q is the electrical heating power (IR) in watts,
L is the effective air gap length in inches,
AT is the total gap area in square inches exposed to the
voice coil,
K is the conductivity of air or 7 × 10–4 W/°C.
As the air gap length is decreased and the area
increased, heat transfer increases (or, equivalently,
thermal resistance decreases). Making the voice coil
former of aluminum will increase effective heat transfer
area; the thicker the aluminum, the greater the effect.
Voice coils wound on aluminum formers with large
diameters in magnets with large gap areas and very tight
coil to gap tolerances are capable of handling high elec-
trical power due to good heat transfer in the air gap. In
short, large, accurately constructed loudspeakers can
usually handle more power. As the loudspeaker moves,
it may be able to pump the air in the gap to improve
heat. The loudspeaker designer may be able to exploit
this behavior. Given voice coils of the same length, the
underhung and equal-length configurations will have
greater heat transfer capacity. The overhung coil would
only conduct heat well in the gap region, while the coil
ends remaining out of the gap would be more likely to
suffer damage at high power level because of relatively
poor heat transfer. Typical thermal behavior for most
coils is on the order of 0.5°C/W to 3°C/W input.
A heat-conducting magnetic liquid may be used to
improve heat transfer. Known as ferrofluids, these fluids
will be retained in a magnetic air gap due to magnetic
attraction. Their thermal conductivity is seven to ten
times higher than that of air. Since ferrofluid alters the
mechanical damping of the moving assembly, its use
has implications for the design of the motor assembly.
There are also issues related to compatibility of ferro-
fluid with adhesives and materials used in the construc-
tion of a transducer. For these reasons, ferrofluids
should generally be designed into a loudspeaker, rather
than added on.
Temperature rise in voice coils is not instantaneous.
It is directly related to mass. As one might suspect, light
voice coils have short thermal rise times, and vice versa.
The thermal time constant of a loudspeaker coil (the
time required for the coil to reach 63% of its final value)
is given by:(17-3)where,
t is the time constant in seconds,
M is the mass of the coil,
C is the specific heat of voice coil material in joules per
gram in degrees Celsius,
'T/Q is the thermal resistance in degrees Celsius per
Figure 17-25. Heat conduction in magnetic loudspeakers. watt.
RT Ro+= 0.004 TT– o'TVC TVC–= Ts
QL
ATK= ----------Top plateMagnetFormerATBack plate Voice coilL 2 L
1tMC'T
Q= ------ -MCL
ATK= ----------