feedback system

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Feedback Systems
1.0 Introduction
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 Professor
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 continuous-
time systems.
As usual, we’ll start with a little history to put this subject in its proper context.
2.0 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 prize1), and a later one on the stability of flyball-governor
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 positive
feedback.2 As far as is known, however, his patent application was his only writing
on the subject (he was more than a little preoccupied w

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