Handbook for Sound Engineers

370 Chapter 13

13.1.3.1 Thermal Resistance

The total thermal resistance between the junction and
the air is the sum of the individual thermal resistances

(13-1)

where,
I is the thermal resistance in degrees Celsius per watt
(°C/W),
JC is the junction to case,
CI is the case to insulator,
IS is the insulator to heatsink,
SA is the heatsink to air.

The temperature at the junction can be determined
from the ambient temperature, the thermal resistance
between the air and the junction, and the power dissi-
pated at the junction.

(13-2)

where,
TA is the temperature of the air,
TJA is the thermal resistance from the air to the junction,
PD is the power dissipated.

If the junction temperature was known, then the
power dissipated at the junction can be determined

(13-3)

where,
'T is TJ  TA.

13.1.3.2 Heatsink Materials and Design

Heatsinks are generally made from extruded aluminum
or copper and are painted black, except for the areas in
which the heat-producing device is mounted. The size
of heatsinks will vary with the amount of heat to be
radiated and the ambient temperature and the maximum
average forward current through the element. Several
different types of heatsinks are pictured in Fig. 13-2.
The rate of heat flow from an object is

(13-4)

where,

Q is the rate of heat flow,

K is the thermal conductivity of material,

A is the cross-sectional area,

'T is the temperature difference,

L is the length of heat flow.

For best conduction of heat, the material should have

a high thermal conductivity and have a large

cross-sectional area. The ambient or material tempera-

ture should be maintained as low as possible, and the

thermal path should be short.

The heat may also be transferred by convection and

radiation. When a surface is hotter than the air about it,

the density of the air is reduced and rises, taking heat

with it. The amount of heat (energy) radiated by a body

is dependent on its surface area, temperature, and emis-

sivity. For best results, the heatsink should:

• Have maximum surface area/volume (hence the use
  of vertical fins).

Figure 13-1. Series thermal resistance/temperature circuit.

J (Junction) C (Case) S (Sink) A (Ambient)

Junction

temperature

Case

temperature

Sink

temperature

Ambient

temperature

TJ QJC TC QCS TS QSA TA

6T T= JC+++TCI TIS TSA

TJ TA+= TJAPD

PD 'T

6T

------ -=

Q KA'T

L

=---------------

Figure 13-2. Conduction type heatsinks used for cooling

diodes and transistors. Courtesy Wakefield Engineering Co.

A. Small heat sinks used with diodes and transistors.

Their diameter is less than a dime.

B. Large heat sink for use with heavy current rectifiers.

The stud of the rectifier is screwed into the center fin

of the sink.