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Bissell, Christopher
(2015).
DOI: https://doi.org/10.1007/978-94-017-9645-3_1
URL: http://www.springer.com/gb/book/9789401796446
Abstract
Towards the end of the nineteenth century electrical and telegraph engineers turned their attention both to modelling the phenomena they observed in the new technologies and to designing systems that would behave in the desired way. Although the mathematical techniques they used were well established, such engineers developed novel ways of developing and employing them. Oliver Heaviside, for example, as well as simplifying and re-casting Maxwell’s equations in the vector form that subsequently became universal, developed his operational calculus (effectively equivalent to Laplace transforms) to model the behaviour of electrical circuits. By the early decades of the twentieth century the whole array of Fourier techniques was being developed, including convolution in the time domain as an equivalent to multiplication in the frequency domain.
Feedback circuits presented a particular challenge, as they were known to become easily unstable. Researchers at Bell Labs studied this problem in detail, resulting in the Nyquist stability criterion of 1932 and Bode’s monumental work on circuit design some years later. Karl Küpfmüller in Germany carried out similar, but rather less well-known work.
Some of the most impressive, and still under-estimated, techniques involved graphical tools for design. The Nichols Chart removed the need for difficult computation of closed-loop behaviour based on open-loop modelling or experimental recording, while the Smith Chart provided a similar resource for engineers concerned with transmission lines. These charts now form an integral part of computer tools – not, now, to replace calculation, but because they are still unsurpassed as ways of presenting information to the skilled engineer.
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