1 ELEC 401 MICROWAVE ELECTRONICS Lecture 1Instructor: M. İrşadi Aksun Acknowledgements: Two animations on Faraday’s law were taken from the following web page: Artworks used to discuss Faraday’s law, Ampere’s law, Gauss’s law were taken from the following web page:

2 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

3 Review of EM Wave TheoryGoverning 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

4 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

5 Review of EM Wave TheoryFaraday-Maxwell Law

6 Review of EM Wave TheoryFaraday-Maxwell Law

7 Review of EM Wave TheoryFaraday-Maxwell Law

8 Review of EM Wave TheoryGeneralized Ampere’s Law

9 Review of EM Wave TheoryGauss’ Law

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

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

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

13 Review of EM Wave TheoryPhenomenological Picture of Wave Generation

14 Review of EM Wave TheoryTime-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,

15 Review of EM Wave TheoryAs 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

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

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