Microwave engineering ch1

INTRODUCTION TO MICROWAVE ENGINEERING

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

INTRODUCTIONWhat is “Micro”wave?

3 x 10^8 Hz(lambda = 1m)

3 x 10^11 Hz(lambda = 1mm)

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

APPLICATIONS OF

MICROWAVE ENGINEERING

Why Study Microwave?

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

DIVERGENT VS.

CURL

Electric Flux Density

#1 Gauss’s Law

{

Electric charge acts as sources or sinks for Electric Fields

Electric Charge Density{

Magnetic Flux Density

#2 Gauss’s Magnetism Law

{Magnetic monopoles do not exist!

#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 ..... ?!??!!

Electromagnetic Propagation

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

z (-kz)

E0x

E0

y

• Example Question (on board)

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

PLANE WAVE REFLECTION FROM A MEDIA INTERFACE

Free-Space

Derivation on the 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

THE END CH 1