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Exploring the overlap of mathematics and engineering network synthesis, this book presents a rigorous treatment of the key principles underpinning linear lumped passive time-invariant networks. Based around a series of lectures given by the author, this thoughtfully written book draws on his wide experience in the field, carefully revealing the essential mathematical structure of network synthesis problems. Topics covered include passive n-ports, broadband matching, the design of passive multiplexes and two-state passive devices. It also includes material not usually found in existing texts, such as the theoretical behavior of transverse electromagnetic (TEM) coupled transmission lines. Introducing fundamental principles in a formal theorem-proof style, illustrated by worked examples, this book is an invaluable resource for graduate students studying linear networks and circuit design, academic researchers, and professional circuit engineers.