58 September 2017
THE HAM‘S WIRELESS WORKBENCH ; BY WARD SILVER N0AX
Ohm’s Law for Heat
Everywhere current flows, heat is dissipated, and the
amount of heat is measured in watts; the same as electrical
power. For a resistor, the amount that must be dissipated
is Pd = I2R. In general, wherever a voltage drop and current
flow exist at the same time, Pd = V x I. Heat is released into
the surrounding environment through the component’s
body or via its leads into the supporting circuit board or
even other components.
If there is too much heat, the component can change
its characteristics or suffer damage. It’s up to the circuit
designer to “take the heat” and be sure that doesn’t
happen. To do that, you have to understand a fundamental
relationship of heat transfer.
Don’t panic — no thermodynamics involved! If you’re
comfortable with Ohm’s Law, you’ll recognize this new
equation right away. Instead of R for resistance, here’s a
new term: thermal resistance, θab. Thermal resistance is the
resistance to heat flow between two points: a and b.
Metals have a very low thermal resistance, and
insulating materials like glass or air have fairly high thermal
resistance. Although it’s not a hard and fast rule, the
thermal resistance for electrical conductors is low, and for
electrical insulators, it’s high. The analogy with electricity
even extends to this equation:
P x θab = Ta - Tb = Tab = ∆T
Temperature difference, ∆T, between the two points
(a and b) is equal to the power, P, flowing between the
points times the thermal resistance along that path, θab. If
you think this looks a lot like the V = I x R form of Ohm’s
Law, you’re right. T can be thought of as a “heat voltage,”
P as a sort of “heat current,” and θab as “heat resistance.” T
is usually specified in °C, P in watts, and θab in °C/W. (You
can see why the ancients thought heat must be some kind
The more power that flows through a given thermal
resistance, the higher the temperature difference will be.
If several different thermal resistances are encountered by
the flowing heat, then the total thermal resistance is θab =
θ1 + θ2 + ... + θn — just like resistors in series. Temperatures
at each step are calculated just like voltages in a voltage
Armed with this equation, we can now take four steps
to manage heat. Figure 1 illustrates how this works — just
like Ohm’s Law.
Picking a Heatsink
Websites and online catalogs have hundreds of
variations of heatsinks — how do you pick one? Like most
problems that look complicated, you can whittle them
down step-by-step until the choice has been narrowed to
just a few. The following four steps are how most design
engineers approach the problem (assuming they don’t have
fancy software to do it!).
Step 1 — Determine How Much Heat is Generated
Here is a list of the heat-generating equations for
Some Hot Topics for a Cool Hobby
hile not strictly a ham radio topic, hams certainly have to deal with
managing a surplus of heat. From an extra-hot 1/4 watt to getting
hundreds of watts away from the business end of a linear amplifier running a
“full gallon,” hot spots need attention! Let’s see about giving a few important
ideas the third-degree, including an easy experiment you can do on the bench.
; FIGURE 1. The basics of understanding how heat flow
turns into a temperature difference are very similar to
Ohm’s Law for voltage, current, and resistance.