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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’s Theorem and Wave Power
WEEK 2
• CLASS 3: Plane wave reflection from a media interface, Refraction, Diffraction
• CLASS 4: S-Parameters, Propagation in good conductors: skin effect
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
Our love for small (and thin!) wireless devices
If we operate at smaller lambda (err…higher frequencies), our
devices become BIG (electronically!)
The 5G standard (operating at 28 GHz) will be 100
times faster than 4G, with data rate of ~ 10GB/sec!
Our love for juice!
Microwave signal travel by LOS, enabling high capacity satellite
links! Thus live footballs!
Our love for direct broadcast!
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)
Differential Form of Maxwell’s Equation
Gauss’s Law
Gauss’s Magnetism Law
Faraday’s Law
Ampere’s Law
Electric Flux Density
#1 Gauss’s Law
{
Electric charge acts as sources or sinks for Electric Fields
Electric Charge Density{
#3 Faraday’ LawA 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
#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
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 ..... ?!??!!
THE WAVE (MOVING, OR, PROPAGATING!)• The wave equation and basic plane wave solutions, Poynting’s
Theorem and Wave Power
THE WAVE EQUATIONIn 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!
THE PLANE WAVEA 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)
E0x
E0
Equation (1) - Board
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 alwaysACCOMPANIED BY A y-DIRECTED H-FIELD
z (-kz)
E0x
E0
y
Equation (2) - Board
If both E and H is travelling in the z-direction perpendicular to each other (TEM Wave),
WHAT DOES IT’S PROPAGATION REPRESENT?
ENERGYTEM WAVE
Poynting Vector, P
ENERGY
P = E X H
PROPAGATION IN LOSSY MEDIUM• CLASS 3: Plane wave reflection from a media interface,
Refraction, Diffraction
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
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’
REGARDLESS OF PROPAGATION(IN FREE SPACE/ A MEDIUM)…
What is the speed of the electromagnetic wave?
Equation (4) - Board
S-PARAMETERS…OR, “scattering” parameters are measures of reflection and transmission of voltage
waves through a two-port electrical network.
S-parameters come in a matrix, with the number of rows and columns equal to the number of ports
}{
REFLECTED
TRANSMITTED