IEEE Circuits and Systems Magazine - Q1 2023 - 44

rates. Most typically, in an energy equation, the
flow rate through a volume boundary port must
be multiplied by the enthalpy inside the volume
if the fluid is exiting, and by the mix of enthalpies
appearing at the port outside if the fluid is entering.
The management of this complexity source is
offered in Modelica by declaring transported variables
as stream in a connector with one flow variable.
Then, a model using that connector has to
assign to each stream variable the value it takes
inside the component, and when that variable
appears in a balance equation, to apply to it the
actual-stream operator; the tool will generate all
the required conditional equations transparently.
This capability is exploited in Listing 3, which also
employs some of the electric components defined in
Listing 1. Thanks to the manipulation capability already
mentioned as a peculiarity of EBM tools, the Example
model shows how simple and fast it is to mode a cascade
of an arbitrary number of " resistor in duct " elements-
apparently, an almost prohibitive (or at least
much more time-consuming) task to carry out in imperative
form directly.
D. Abstracting With an Eye on IC Cooling
We start from some general facts, that the examples
above should have clarified. First, as EBM tools allow
to write declarative models, the analyst is relieved from
the D2I burden. This burden can be high, and in general
must be re-incurred every time the structure of the
model is modified.
On the other hand, if one accepts to do the D2I translation
manually, most often the obtained imperative code
will be significantly more efficient than that generated
by a declarative model translated by an EBM tool. We do
not explain the reasons here as this would be quite long
and inessential for our purposes; the interested reader
can refer, e.g., to [16].
Now let us focus on ICs, and reconsider Examples 1
and 2 above. Example 1 is in fact a toy version of a 3D
chip thermal model (1D geometry instead of 3D, only
one heat source, constant material properties, and so
on). Building on Algorithm 1, it is possible to create an
extremely fast imperative model, realistic enough for a
real chip, and that can be adapted to any case at hand
by just compiling configuration files; the D2I translation
can still be costly but is needed only once. With further
additions not relevant at this point, such a configurable
model is exactly what 3D-ICE and similar tools provide.
Example 2 is an equally toy version of an air cooling
network inside a rack (only one stream, no pressure
drops described, no air humidity, and so on). In
such a context, for the imperative approach it would
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IEEE CIRCUITS AND SYSTEMS MAGAZINE
Listing 3. D2I example 2, the declarative way.
FIRST QUARTER 2023
be evidently prohibitive to follow the variety of possible
cooling network (thus model) topologies - let
alone, for example, extensions to fluid phase changes,
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