Page 103 - Analog Circuit Design Art, Science, and Personalities

Propagation of the Race (of Analog Circuit Designers)

with using wideband amplifiers that limits their educational effectiveness. One of
the very satisfying features of the approximate methods that can be used to predict
feedback system performance is that they yield remarkably good results with mini-
mal effort if the system nzodel is accurately known. Unfortunately, strays complicate
the development of models for wideband systems. Students tend to blame their
inability to predict performance accurately on the approximations inherent to the
methods we suggest rather than their choice of a poor model.
We reduce the chances for this self-delusion by having this student use a pseudo
op amp that has been tamed by a combination of external compensation (an LM301A
is used as the building block) and a two-pole low-pass filter connected to its output.
The resultant pseudo-amplifier has a highly predictable transfer function that has a
unity-gain frequency low enough so that strays can safely be ignored and also has
negative phase margin at its unity-gain frequency. The students design compensa-
tors for various configurations using the pseudo-amplifier and verify performance.
There were several other experimental vehicles used in this version of the feed-
back subject. All were rather carefully selected (and possibly tweaked) so that the
students could develop accurate models for them in a reasonable period of time.
They were then able to experience the positive reinforcement that resulted when
their performance estimates were confirmed experimentally. It is our hope that this
experience will encourage them to spend the time necessary to develop accurate
models when they encounter more complex systems.
Classical feedback is taught in at least four different departments at M.I.T. Last
year we decided to modify the course described above so that it might be taught to a
group of students from several different disciplines. We have taught the new course
once to a population about equally divided between the department of Electrical
Engineering and Computer Science and the department of Aeronautics and
Astronautics.
The topics covered in this joint offering are the same as described earlier for
the original subject. The differences come in the examples, demonstrations, and
laboratory exercises. We frequently show how identical design and analysis
methods can be used in quite different systems. For example, we model a velocity
servomechanism where the motor dynamics are dominated by its mechanical time
constant and also model a noninverting amplifier using an operational amplifier
with a single-pole open-loop transfer function. The resultant block diagrams and
transfer functions are identical except for bandwith-related parameters.
The joint offering provides an excellent vehicle for expanding the horizons of
both groups of students. I feel that it is particularly important for electrical engineer-
ing students to learn how to model other than electrical systems, and they seem quite
willing to do this in the joint format.
We have introduced demonstrations that appeal to both groups. Additions to
our collection of EE-oriented demos include a magnetic suspension system and an
inverted pendulum. We are working on one that stabilizes two different-length
inverted pendulums on a single platform. (The analysis of this one is delightful. It
is possible to show that the maximum achievable phase margin for this system is
sin-'[(/? - I)/(R + 1 )], where R is the ratio of the natural frequency of the shorter
pendulum to that of the longer one. This result confirms the intuitive realization that
the task is not possible for equal-length pendulums.)
The differences in backgrounds of the two student groups convinced us that a
major modification of the laboratory was necessary. We have three different exper-
imental systems in various stages of development. One of these is a thermal control
system that maintains temperature stability to better than 1 millidegree C. The

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