1. The document introduces microwave engineering concepts over 4 weeks, covering Maxwell's equations, plane wave solutions, propagation in lossy media, and S-parameters. 2. It describes applications of microwave engineering like wireless devices, 5G networks, satellite links, and direct broadcast. Maxwell's equations describe macroscopic electric and magnetic phenomena. 3. Plane waves have electric and magnetic fields perpendicular to the direction of propagation. The wave equation relates wavelength, frequency, and speed of waves. Plane waves in lossy media have complex propagation constants that cause amplitude changes over distance.

1. INTRODUCTIONTO
MICROWAVE ENGINEERING

2. WEEK 1
• CLASS 1: Introduction to Microwave Engineering,
Applications of Microwave Engineering, Maxwelll’s
Equations
• CLASS 2:The wave equation and basic plane wave
solutions, Poynting’sTheorem and Wave Power

3. WEEK 2
• CLASS 3: Plane wave reflection from a media
interface, Refraction, Diffraction
• CLASS 4: S-Parameters, Propagation in good
conductors: skin effect

4. INTRODUCTION
What is “Micro”wave?
3 x 10^8 Hz
(lambda = 1m)
3 x 10^11 Hz
(lambda = 1mm)

5. SO WHAT?
The complication of small
wavelengths are many….
Because the size of the device is ~ lambda, the phases
of voltage and current over the device changes

6. APPLICATIONS
OF
MICROWAVE
ENGINEERING
Why Study Microwave?

7. Our love for small (and thin!) wireless devices
If we operate at smaller lambda
(err…higher frequencies), our
devices become BIG
(electronically!)

8. The 5G standard
(operating at 28 GHz) will be 100
times faster than 4G,
with data rate of ~ 10GB/sec!
Our love for juice!

9. Microwave signal travel by LOS,
enabling high capacity satellite
links!Thus live footballs!
Our love for direct broadcast!

10. REVISITING OUR ELDERS
“IF I HAVE SEEN FURTHER, IT IS BY STANDING ON THE SHOULDERS OF GIANTS”
- ISAAC NEWTON
!THE MAXWELL’S EQUATIONS !
(Macroscopic electric and magnetic phenomena are described by these equations)

11. Differential Form of
Maxwell’s Equation
Gauss’s Law
Gauss’s Magnetism
Law
Faraday’s Law
Ampere’s Law

12. DIVERGENT
VS.
CURL

13. Electric Flux
Density
#1 Gauss’s Law
{
Electric charge acts as sources or sinks for Electric Fields
Electric Charge
Density
{

14. Magnetic Flux
Density
#2 Gauss’s Magnetism Law
{
Magnetic monopoles do not exist!

15. #3 Faraday’ Law
A magnetic field changing in time gives rise to an E-field circulating around it
https://phet.colorado.edu/sims/html/faradays-law/latest/faradays-law_en.html

16. #4 Ampere’s Law
A time-changing Electric Flux Density
(D) gives rise to a Magnetic Field that
circles the D field
A flowing electric current (J) gives rise
to a Magnetic Field that circles the
current
In Wires In Wireless

17. DC
Conclusion of Maxwell’s Equation
{
{
AC
A changing magnetic field gives rise to a changing electric field…and a changing
electric field gives rise to a changing magnetic field - which itself will produce a
changing electric field which will give rise to .....
?!??!!

18. Electromagnetic Propagation

19. THE WAVE (MOVING, OR, PROPAGATING!)
• The wave equation and basic plane wave solutions, Poynting’s
Theorem and Wave Power

20. THE WAVE EQUATION
In general, the wave equation is a mathematical relationship between the
speed (v) of a wave and its wavelength (λ) and frequency (f).
v = λf
From the two equation, we see that the EM wave (E and H) is varying in
space (x, y, z) and also time (t)
HW1:
Derive this!

21. THE PLANE WAVE
A special case when E and H is not varying in x and y direction, forming
only a “plane” moving upwards/downwards along z-axis
z
(-kz)
E0
x
E0
Equation (1) - Board

22. What happens to H?
By solving the wave equation for an x directed E-field (as was derived
on the board) travelling in the z-direction, we find that it is always
ACCOMPANIED BY A y-DIRECTED H-FIELD
z
(-kz)
E0
x
E0
y
Equation (2) - Board

23. If both E and H is travelling in the z-direction
perpendicular to each other (TEM Wave),
WHAT DOES IT’S PROPAGATION REPRESENT?
ENERGY
TEM WAVE
Poynting
Vector, P
ENERGY
P = E X H

24. z
(-kz)
E0
x
E0
y

25. • Example Question (on board)

26. PROPAGATION IN LOSSY MEDIUM
• CLASS 3: Plane wave reflection from a media interface,
Refraction, Diffraction

27. The wave equation remains same but the
“wave number/propagation constant” is COMPLEX
We’re introduced to a new term that
symbolises loss. In a lossless media (i.e, free-space),
sigma =0
MAIN ISSUE

28. The general effect of a complex “k” is a travelling wave that
changes its amplitude with distance
Equation (3) - Board
WAVE EQUATION WITH COMPLEX ‘K’

29. REGARDLESS OF PROPAGATION
(IN FREE SPACE/ A MEDIUM)…
What is the speed of the electromagnetic wave?
Equation (4) - Board

30. PLANE WAVE REFLECTION FROM A MEDIA
INTERFACE
Free-Space
Derivation on the Board

31. S-PARAMETERS…
OR,“scattering” parameters are measures of reflection and transmission of voltage
waves through a two-port electrical network.

32. S-parameters come in a matrix, with the number of rows and columns equal
to the number of ports
}
{
REFLECTED
TRANSMITTED

33. THE END CH 1