1. ELEC 401 MICROWAVE ELECTRONICS Lecture 1
Instructor: 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 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

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 Theory
Faraday-Maxwell Law

6. Review of EM Wave Theory
Faraday-Maxwell Law

7. Review of EM Wave Theory
Faraday-Maxwell Law

8. Review of EM Wave Theory
Generalized Ampere’s Law

9. Review of EM Wave Theory
Gauss’ Law

10. 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

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

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

13. Review of EM Wave Theory
Phenomenological Picture of Wave Generation

14. 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,

15. 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

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

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