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Classical Circuit Theory

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Omar Wing
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Classical circuit theory is a mathematical theory of linear, passive circuits, namely, circuits composed of resistors, capacitors and inductors. Like many a thing classical, it is old and enduring, structured and precise, simple and elegant. It is simple in that everything in it can be deduced from ?rst principles based on a few physical laws. It is enduring in that the things we can say about linear, passive circuits are universally true, unchanging. No matter how complex a circuit may be, as long as it consists of these three kinds of elements, its behavior must be as prescribed by the theory. The theory tells us what circuits can and cannot do. As expected of any good theory, classical circuit theory is also useful. Its ulti mate application is circuit design. The theory leads us to a design methodology that is systematic and precise. It is based on just two fundamental theorems: that the impedance function of a linear, passive circuit is a positive real function, and that the transfer function is a bounded real function, of a complex variable.
"This book begins with the basic principles of circuits, derives their analytic properties in both the time and frequency domains, and states and proves the two important theorems. It then develops an algorithmic method to design common and uncommon types of circuits, such as prototype filters, lumped delay lines, constant phase difference circuits, and delay equalizers. The material also discusses the relation between gain and phase, linear and minimum phase functions, group delay, sensitivity functions, scattering matrix, synthesis of transfer functions, approximation of filter functions, all-pass circuits, and circuit design by optimization.
This book fills a need for a modern text on the mathematical foundations of passive circuits in general and passive filter design in particular. The mathematical foundations are what classical circuit theory, which is the subject of this book, is all about. It is old, but it has survived the test of time and it is still relevant today because it is basic."
Fundamentals.- Circuit Dynamics.- Properties in the Frequency Domain.- The Impedance Function.- Synthesis of Two-Element-Kind Impedances.- Synthesis of RLC Impedances.- Scattering Matrix.- Synthesis of Transfer Functions.- Filter Design.- Circuit Design by Optimization.- All-Pass Circuits.

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