ELEC 401 MICROWAVE ELECTRONICS Lecture 1 Instructor: M. İrşadi Aksun Acknowledgements: Two animations on Faraday’s law were taken from the following web page: http://web.mit.edu/jbelcher/www/inout.html Artworks used to discuss Faraday’s law, Ampere’s law, Gauss’s law were taken from the following web page: http://cobweb.ecn.purdue.edu/~ece695s/Lectures

Outline Chapter 1: Motivation & Introduction Chapter 2: Review of EM Wave Theory Chapter 3: Plane Electromagnetic Waves Chapter 4: Transmission Lines (TL) Chapter 5: Microwave Network Characterization Chapter 6: Smith Chart & Impedance Matching Chapter 7: Passive Microwave Components

Review of EM Wave Theory Governing equations of EM waves are: - Maxwell’s Equations in integral form: Electric Field Vector [V/m] Magnetic Field Vector [A/m] Electric Flux Density [C/m2] Magnetic Flux Density [W/m2] Current Density [A/m2] Charge Density [C/m3] - Continuity equation

Review of EM Wave Theory - Maxwell’s Equations in differential form: How do you get them from their integral forms? - Continuity equation Boldface and  are used throughout this course to represent vector and time-varying forms of the corresponding quantities, respectively

Review of EM Wave Theory Faraday-Maxwell Law

Review of EM Wave Theory Faraday-Maxwell Law

Review of EM Wave Theory Faraday-Maxwell Law

Review of EM Wave Theory Generalized Ampere’s Law

Review of EM Wave Theory Gauss’ Law

Review of EM Wave Theory What are the Maxwell’s Contributions? 1. Interpretation of Faraday’s Law C: Conducting Loop No need for a conducting loop to induce electromotive force

Review of EM Wave Theory What are Maxwell’s Contributions? 2. Correction of Ampere’s Law: Physical Original Ampere’s law Maxwell’s contribution

Review of EM Wave Theory What are the Maxwell’s Contributions? 2. Correction of Ampere’s Law: Mathematical Conservation of Charges

Review of EM Wave Theory Phenomenological Picture of Wave Generation

Review of EM Wave Theory Time-harmonic representations of Maxwell’s Equations: Maxwell’s equations are linear equations, as they involve linear operators like integrals or derivatives, Medium is assumed to be linear with linear relations between B and H, and D and E, Therefore, Time varying sources can be written in terms of pure sinusoids (harmonics) via Fourier transform, Superposition principle can be applied since the equations and the involved media are all linear,

Review of EM Wave Theory As a result, all involved field quantities have the same frequency of oscillations, and can be written as follows: For example: An x-polarized electric field may be given in time-domain as where all quantities are real. It can also be written in time-harmonic form (phasor form, frequency domain) as a complex quantity: Complex quantities

Review of EM Wave Theory Let us apply this representation to Generalized Ampere’s law: and the rest become

Review of EM Wave Theory As a result, we have the following sets of Maxwell’s equations in Integral form Differential form