©Thomas H. Lee, rev. October 17, 2004; All rights reserved
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A solid understanding of feedback is critical to good circuit design, yet many practicing
engineers have at best a tenuous grasp of this important subject. We agree with MIT Pro-
fessor Jim Roberge’s feeling that “feedback is so fundamentally important that analog
engineers who don’t understand it should be legally barred from circuit design.” This
chapter is intended as but a brief overview of the foundations of classical control theory,
that is, the study of feedback in single-input, single-output, time-invariant, linear continu-
As usual, we’ll start with a little history to put this subject in its proper context.
A Brief History of Modern Feedback
Although application of feedback concepts is very ancient (Og annoy tiger, tiger eat Og),
mathematical treatments of the subject are a recent development. Maxwell himself offered
the first detailed stability analyses, in a paper on the stability of the rings of Saturn (for
which he won his first mathematical prize
), and a later one on the stability of flyball-gov-
ernor controlled steam engines (“On Governors,”
Proc. Royal Soc.
, no. 100, 1868).
The first conscious application of feedback principles in electronics was apparently by
rocket pioneer Robert Goddard in 1912, in a vacuum tube oscillator which employed pos-
As far as is known, however, his patent application was his only writing
on the subject (he was more than a little preoccupied with rocketry, after all), and his con-
temporaries were largely ignorant of his work in this field.
Armstrong and the Regenerative Amplifier
Edwin Howard Armstrong’s 1915 paper
on vacuum tubes contained the first published
explanation of how positive feedback (which he called regeneration) could be used to
increase greatly the voltage gain of amplifiers. Although engineers today have a prejudice
against positive feedback, progress in electronics in those early years was largely made
possible by Armstrong’s regenerative amplifier, since there was no other economical way
to obtain large amounts of gain from the primitive (and expensive) vacuum tubes of the
The Adams Prize, which he won in 1857. Maxwell argued that stability of the rings was possible only if
they consisted of small particles. We now know from direct observation by Voyager that Maxwell was right.
U.S. Patent #1,159,209, filed 1 August 1912, granted 2 November 1915.
“Some Recent Developments in the Audion Receiver,”
Proceedings of the IRE
, v.3, pp. 215-247, 1915.
The effective internal “
” of vacuum tubes back then was only on the order of five, so the gain per
stage was typically quite low, requiring many expensive stages if conventional topologies were used.