Page 29 - Analog Circuit Design Art, Science, and Personalities

Analogs Yesterday, Today, and Tomorrow

scale factors relating them in pairs. Basic parameters, when the scale ratios are prop
erly assigned, turn out to be numerical, and apply equally to model and to proto-
type. This doctrine, whereby characteristic system parameters are dimensionless, is
applicable to all modelling procedures. The transformation concept, so clear and
concise for scale models, carries over with little confusion to modelling in which
the physical form is changed, and ultimately to electronic analogs where transfor-
mation includes transmogrification. The scale ratios in general, however, are no
longer numbers, but the basic parameters may be. This sort of introduction is
recommended for physicists and applied mathematicians who may be coming sud-
denly into modem analog contacts, since it utilizes some of the ideas and precepts,
however badly expressed here, of the more classical fields.
Another sort who is momentarily taken aback by the liberties permitted in analog
models is typified by an engineer who has been too long away from the time domain.
Often brought up, pedagogically, on linear systems and frequency analysis, he (or
she) may even be suspicious of a mechanism which gives solutions as functions of
time, perhaps not realizing that it will provide amplitude and phase spectra as well
if one merely applies a different stimulus to the same model structure. It is frequently
worthwhile, in these cases, to introduce the analog from the viewpoint of the fre-
quency domain, shifting later from the familiar to the strange and magical. Oddly
enough, the most confirmed practical and the most profoundly theoretical of engi-
neers will both be found to favor the time domain, with or without computing equip-
ment. In the former case this is by virtue of convenience in handling real equipment,
and in the latter it is since-among other reasons-he finds it better to approach
nonlinear problems in the time domain than in the frequency domain.
Analog engines have not always been as respected as they are now becoming.
Analogy itself we have been warned against, in proverb and in folklore, as being
dangerous and requiring proof. Parenthetically, this is good advice. Simulation has
had connotations of deceit, empiricism of quackery. It was stylish, even recently, to
say that the only good electronics is that which says Yes or No. There is nothing to
be gained in disputing these allegations, least of all by excited rejoinder. The con-
tinuous active analog is in its infancy, and time is (literally) running in its favor.
Time as an independent variable, given at low cost by Nature, has the advantage
of nearly, if not actually, infinite resolution. This continuity, coupled with the conti-
nuity of voltage and charge, leads to the ability to close loops at very high frequency,
or with short time intervals. As a consequence one may approach the ideals of dif-
ferentiability which are inherent in the infinitesimal calculus, which postulates the
existence of a continuum. While most contemporary analog apparatus does not
press these limits, it is comforting to know that there is room left to maneuver in.
In modest applications to on-line measurement and data-processing, it is quite
generally conceded that the advantages of continuous analog apparatus make it
irresistible. This is partly owing to the simplicity and speed which its continuity
makes possible, and partly to the fact that almost every input transducer is also
“analog” in character, that is to say continuous in excursion and time. Storage and
sampling, for example are frequently unnecessary in such applications, as in many
others. When we turn from simpler to more involved data processing, to ambitious
simulation, or when in general we pass from modest to more pretentious computa-
tions, there has been some feeling that digital means should automatically be substi-
tuted, especially if funds are available. In this connection we should like to quote,
on the other side of the argument, no less a figure than Dr. Simon Ramo, writing on
Systems Engineering in a collected volume called Purts und Wholcs (edited by
Daniel Lerner; Macmillan, New York, 1963). The following is admittedly taken out
of context:

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