Algebraic Structure of Knot Modules

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.