Rick,

The question about the dielectric thickness lowering the temperature
rise (thus enabling higher power densities) depends on the presence of a
copper plane on the opposite side of the core. We call this the "Volcano
Curve," it was published in PC Fab about twenty years ago (it was so old
we didn't have it as a digital file but had to scan and attached it as a
JPEG photo). The left side of the curve in the absence of heat sinking
shows rising power density with increasing dielectric thickness but the
right side of the curve with reverse cladding shows rising power density
with decreasing dielectric thickness. This is very old technology and
the relevance of the large surface resistors to modern embedded
miniature resistors is only to demonstrate the theory.

Today, we use power density curves that relate power to area in the
absence of heat sinking (the left side of the curve only). Miniature
resistors with power rating of less than 50 milliwatts operate at the
equivalent power densities of hundreds of watts per square inch because
they readily dissipate heat into the surrounding material. Furthermore,
the PCB structures are usually embedded microstrip or stripline
constructions with thin dielectric spacing and adjacent power or ground
planes so even smaller resistors can be made if the the heating sinking
effects are considered. We receive inquiries as to the physical
properties of the OhmegaPly like volume resistivity and thermal
conductivity whenever someone is doing thermal modeling, however, our
preference is to do step-tests-to-failure studies and build in safety
factors by derating the resistor elements. We simplify the design
process by providing power density constants to the PCB designers.

Power density constants assume uniform current flow across the resistor
elements. Hot spots at the center of the resistor elements are only hot
relative to the cooling at the terminations but true hot spots can be
created by "neck-downs" such as where we make fuses designed to blow in
the center at specific amperages. Laser trimming also creates true hot
spots. The idea that you can cool a hot spot by moving it to the
termination (laser trimming alongside a termination edge) is a
reliability concern because those edges are the line of greatest
thermal-mechanical stress and when thermal shock stress-to-failure
testing is done, that's where they fail. We prefer to keep the hot spots
in the center as far as possible from the the terminations.

Best regards,

Dan Brandler