IEEE Power Electronics Magazine - June 2020 - 48

Codesign

expertise-became generically known as the engineer's
feel for a problem.
Codesign is far more than a method of designing an electriWe can call such expertise-driven models low-fidelity
cal circuit, optimized or otherwise, and going through the
or coarse models. Coarse, but physically meaningful modmotions of double-checking that the topology will maintain
els, were good enough for practical purposes before the
decent thermal conditions due to losses, ease of mainteformal exploitation of mathematically based optimization
nance, or vibration requirements. It is also not so simple as
algorithms. And they still are!
determining a model for each domain and iteratively runCoarse models remain essential to the engineer's underning through each model until a desired outcome for all
standing of their specialized fields (such as equivalent circonsiderations is created. No, codesign requires a thoughtcuits in electrical engineering) as well as to meeting the
ful process of integrating each domain to succeed in the
mounting challenges of approaching
overall design of the system.
a desired optimal design employUsing transformer design as an
ing highly accurate, computationexample of this process, let's consider
Only with the combially intensive, physically based, or
the potential domains. The electrination of the two
electromagnetically based simulators.
cal requirements are the primary to
Computationally intensive but highly
secondary voltage and current ratio.
techniques can the
accurate simulators or devices under
When implemented in a nonideal setdesign be physically
test can also be called high-fidelity or
ting, leakage inductance, magnetizing
fine models.
inductance, and parasitic capacitances
implemented to be
The question is: how can we make
occur. These parasitic capacitances
within
the
multidointelligent,
effective use of both coarse
stem from the physical implementaand
fine
models
in the same problem? The
tion of the transformer itself. For exammain constraints of
answer should not come as a shock
ple, factors that affect them are core
the optimization
to anyone, because we all effectively
structure, number of turns and correprocedure.
iterate between coarse and fine modsponding layers, and the physical locaels in our everyday lives, whether we
tion of the primary winding in relation
know it or not. But it did. The simple
to the secondary winding. Proximity
answer shocked engineers when Bandler first announced
losses are also of concern, which can create more heat than
the space mapping concept in the early 1990s [1], and even
expected and impact the thermal estimations of the origidecades later, some engineers and mathematicians are
nal design.
still amazed.
In summary, transformer design ultimately needs to
Space mapping is common sense in action. We go back
happen in the physical realm. While many models account
and forth between our coarse and fine models. We try our
for the physical structure and have high accuracy, they can
best with our coarse model, and we see what our correbe seen as too complex when viewed from a system level
sponding fine model produces. If unsatisfactory, we recaliof design, where the transformer is just one of many combrate our coarse model and try again. We don't abandon our
ponents to be integrated. However, codesign falls short
coarse model. Instead, we evaluate and update a "mapping"
when used in an optimization procedure. This is due to the
between our two models and try again.
sequential nature of the coding algorithm. In this way, engiLet's return to the early engineers who designed and
neers are forced to select a code layout where an outcome
built workable, highly complex electrical devices and strucof one model is inserted into another domain's model. This
tures before the advent of electronic computers. They iterlimits the impact of this sequential design procedure unless
ated intelligently between their fast-to-evaluate but highly
it can be corrected. Enter space mapping.
effective coarse model and their expensive-to-realize fine
model, that is, a prototype or device under test.
Space Mapping
Intuitively, they used space mapping. Its astonishingly
So, what is space mapping? First, we have to agree on some
simple formulation was first published in 1994 [1], followed
engineering fundamentals.
by Aggressive Space Mapping (ASM) in 1995 [2]. Space
How did engineers design and build workable, highly
mapping asks us to compute a simple mathematical mapcomplex electrical devices and structures before the
ping between corresponding coarse and fine models. What
advent of electronic computers, let alone today's highdistinguishes different algorithms is how this mapping is
speed computers? Of course, they used models: mental
calculated or improved-explicitly or implicitly-either
models and/or mental models augmented, for example,
before or during the design optimization process.
by paper-and-pencil calculations and/or experimental prototypes. These models were perfected by their
common sense or augmented by years of specialized
ASM Methodology
study and experience, by data sheets and other means.
Preferably using all available prior iterations of the algoThe fruits of this experience and know-how-their
rithm, the aim of ASM is to predict a set of fine-model

IEEE POWER ELECTRONICS MAGAZINE

z June 2020

IEEE Power Electronics Magazine - June 2020

Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - June 2020