Classical Circuit Theory

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. In this book, we begin with basic principles of circuits, derive their analytic properties in both the time and frequency domains, and state and prove the two important theorems. We then develop 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. Along the way, we learn about 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.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 first principles based on a few physical laws.

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