Page 33 - Analog Circuit Design Art, Science, and Personalities

Analogs Yesterday, Today, and Tomorrow

should begin with drastic approximations to the nonlinear features, which are refined
in stages as the project develops. Each step should be simple and well defined, with
continual checking of the assumptions, and of those portions which are assumed to
be complete, before forging ahead. Of course the parallel development of rudimen-
tary overall models is in order if it is understood that they should be taken with a
grain of salt: they may impart some idea of the flavor of the final concoction. Aspects
of a system suitable for separate analog study will depend on the nature of the
system; this is the age of broadness of system definition, extending even to all of
Society. Taking such a case, one might study population density, political stability,
wealth and commerce, considering these somewhat independently before they are
all joined in one model. Again, the study in each case might be from the viewpoints
of transients, or cycles, or statistics (possibly introducing random perturbations from
independent sources). Still further, the item of interest might be tolerance to para-
metric changes, transitions from one regime to another, extrapolations backward
and forward in time, and so on. But my prognostications have turned into a ramble.
As an offshoot of specialized training applications, analogs should find growing
applications to pedagogy of a more general kind. This is partly owing to the per-
sonal experience which the subject may be afforded, but also to the interest which is
induced by living analogies. The speed at which dynamic models may be operated
is another factor in maintaining interest, and in saving time as well. If fast repetitive
operations are employed, an introductory step may involve slower demonstrations,
better to enable the mental transformation of time scale. Block diagrams or signal
flow graphs become immediately more meaningful if tangible analog apparatus is
made available to fulfill them. The innate property of causality, for example, is
given memorable and dramatic emphasis. Feedback is of course the big thrill to the
innocent in its general framework, along with its embodiment in differential equa-
tions, automatic controls including servomechanisms, and vibrations.
Models and analogs, even as concepts, are powerful teaching means in any case.
Symbols themselves are rudimentary analogs, striving close to reality in mathemat-
ical operators. Words and languages are analogs right down to the ground. Physicists
think and talk in models, the very best of them saying that models are their most
powerful tools. Similitude conditions apply equally to all physical phenomena,
along with dimensional analysis, so called. The unification of a set of properties in
one structure, suggestive of an underlying organization and beauty, gives power and
appeal to the model concept in the education of students: and students we all should
remain, every one. So we close with a student’s recollection.
Emerging many years ago from the old Jefferson Physical Laboratory at Harvard,
one could read on the Music Building opposite, cut into the stone under the eaves,
an inscription which should still be there:

To charm, to strengthen, and to teach,
These are the three great chords of truth.

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