This course provides a comprehensive treatment of some of the most fundamental concepts in electromagnetics. Following a review of vector algebra and vector calculus concepts in the three useful coordinate systems (rectangular, cylindrical, and spherical), the course examines the fundamental phenomena associated with distributions of electric charge at rest (known as electrostatics) and those associated with constant currents (known as magnetostatics), as well as the laws that govern these phenomena. When these quantities vary in time, they generate electromagnetic waves that propagate, which are studied as solutions to Maxwell's famous equations. These concepts are essential to several areas of electrical engineering, and underlie everything from voltage and current inside a circuit, to radio-wave propagation between antennas, to the interaction of light and matter at the nanoscale.

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The equations of standard circuit theory are obtained from the general equations governing all electromagnetic phenomena, known as Maxwell's Equations, in the extreme low-frequency (static) limit. On the other hand, at extremely high frequencies, standard circuit theory fails, and a complete electromagnetic solution is required. Between these two frequency extremes lies the RF/microwave spectrum (from hundreds of Megahertz to hundreds of Gigahertz), where techniques from circuit theory are useful but incomplete, and a full electromagnetic solution is superfluous and often too abstract to offer any useful intuition. The growing number of commercial, industrial, scientific, medical, and military applications utilizing this frequency spectrum (e.g. heating, biomedical imaging, high-speed electronics, wireless and satellite communications, radar, sensing, astronomy, etc.) demand a systematic approach to the design of components and devices that supplements the simplicity of basic circuit theory with a knowledge of the underlying electromagnetic phenomena. This, in a nutshell, defines the field of microwave engineering, and the components and devices designed for operation at RF/microwave frequencies are microwave circuits.

In this course, students are introduced to the transmission-line (TL) theory of wave-propagation, which forms the cornerstone of many fields in electrical engineering and may be used to describe the propagation of signals along anything from PCB traces to coaxial cables to nerve fibres to the space separating transmitting and receiving antennas. It is intrinsically associated with fundamental concepts like propagation, attenuation, transmission/reflection, impedance, impedance matching, and network analysis. This course provides an emphasis on engineering techniques, which are applied towards the analysis and design of a variety of fundamental passive RF/microwave components like power dividers/combiners, couplers, matching networks, and filters, as well as active devices like transistor amplifiers. These concepts are reinforced through hands-on laboratories that engage students in the conceptualization, analysis, simulation, fabrication, and test of practical passive and active microwave circuits using industry-standard simulation and measurement tools. Although the concepts conveyed in this course are ideally suited for the RF/microwave frequency range, they are straightforwardly adapted for use in the optical or quasioptical regimes. Thus, a student of microwave engineering is also well-equipped to appreciate the techniques of optical engineering.

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Antennas are fundamental and indispensable components of telecommunications systems. Whereas microwave signals may be guided using transmission lines and processed using a variety of microwave circuits, antennas are a means for communicating information contained in these signals via radiating electromagnetic waves that propagate over large distances in free space. The unprecedented proliferation of wireless handheld devices such as smartphones and tablets, for example, is preceded by decades of antenna research and development. Today, antennas represent one of the most active areas in research and development, as antenna designers continue to strive for smaller, more broadband, and more efficient antennas for the next generation of communications technologies. This graduate-level course begins with a comprehensive treatment of antenna theory, including mechanisms of radiation, radiation patterns, quantities such as gain, directivity, impedance, efficiency, and studies the canonical dipole antenna and loop antenna. Array theory is presented as a tool to synthesize radiation patterns, and is followed by a treatment of important physical principles such as mutual coupling, reciprocity, and equivalence, which are best illustrated in the context of antennas. The remainder of the course is an application of these theories to the analysis and design of several classes of antennas, including resonant antennas such as the microstrip patch and Yagi-Uda antennas, broadband antennas such as the helix and leaky-wave antennas, and aperture antennas such as the horn antenna. The course concludes with a discussion on useful antenna-measurement techniques, recent trends in antenna miniaturization, and the use of novel materials - such as metamaterials - in antenna design.

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