H-infinity engineering continues to establish itself as a discipline of applied mathematics. As such, this extensively illustrated monograph makes a significant application of H-infinity theory to electronic amplifier design, demonstrating how recent developments in H-infinity engineering equip amplifier designers with new tools and avenues for research. The amplification of a weak, noisy, wideband signal is a canonical problem in electrical engineering. Given an amplifier, matching circuits must be designed to maximize gain, minimize noise, and guarantee stability. These competing design objectives constitute a multiobjective optimization problem. Because the matching circuits are H-infinity functions, amplifier design is really a problem in H-infinity multiobjective optimization. To foster this blend of mathematics and engineering, the author begins with a careful review of required circuit theory for the applied mathematician. Similarly, a review of necessary H-infinity theory is provided for the electrical engineer having some background in control theory. The presentation emphasizes how to (1) compute the best possible performance available from any matching circuits; (2) benchmark existing matching solutions; and (3) generalize results to multiple amplifiers. As the monograph develops, many research directions are pointed out for both disciplines. The physical meaning of a mathematical problem is made explicit for the mathematician, while circuit problems are presented in the H-infinity framework for the engineer. A final chapter organizes these research topics into a collection of open problems ranging from electrical engineering, numerical implementations, and generalizations to H-infinity theory
CONTENT
1 Electric Circuits for Mathematicians -- 2 The Amplifier Matching Problem -- 3 H? Tools for Electrical Engineers -- 4 Lossless N-Ports -- 5 The H? Framework -- 6 Amplifier Matching Examples -- 7 H? Multidisk Methods -- 8 State-Space Methods for Single Amplifiers -- 9 State-Space Methods for Multiple Amplifiers -- 10 Research Topics -- A The Axioms of Electric Circuits -- A.1 Krein Spaces and Angle Operators -- A.2 N-Ports ?Angle Operators -- A.3 Time Invariance ?Convolution -- A.4 Causality ? Analyticity -- Existence -- B Taylorโ{128}{153}s Expansion and the Descent Lemma -- Taylorโ{128}{153}s Expansion -- The Kolmogorov Criterion -- 237 -- 245
Mathematics
Applied mathematics
Engineering mathematics
System theory
Mathematical optimization
Control engineering
Robotics
Mechatronics
Mathematics
Systems Theory Control
Applications of Mathematics
Optimization
Appl.Mathematics/Computational Methods of Engineering
