ECE 344

Microwave Fundamentals

Assistant ProfessorDr. Gehan Sami

Course Objectives

The course aimed to:

Describe principles of microwave engineering and technology.

Derive and solve the wave equations in many microwave structures such as transmission lines and waveguides to analyze the wave propagation along them.

Use of Smith chart for determining the wave characteristics on a transmission line and determine the input impedance and calculate perform the impedance matching .

Investigate different passive microwave components such as: power dividers/combiners, couplers, resonators and cavities.

No. Topics

1 Course Objectives and Outline & Review of Electromagnetic Fields

2 General Transmission Line Theory & Circuit Model of Transmission lines

3 General Transmission Line Equations & Standing Wave Properties

4 Transmission Line Parameters & Lossless Transmission Line

5 Matching techniques - Quarter wavelength transformer - Smith chart - Single stub matching-Double stub matching

6 Advanced Design System (ADS) program- Simulation for microwave circuits

7 Rectangular Waveguide

8 Power transmitted in rectangular waveguide

9 Microstrip Transmission Line Structure &Stripline Transmission Line Structure

10 Microwave network analysis-S matrix-Z matrix-Y matrix-ABCD matrix

11 Microwave Passive devices- analyze and design Directional coupler

12 Microwave Passive devices- analyze and design Power dividers

Course Contents

List of ReferencesTextbook:

D.M. Pozar “Microwave Engineering”, third edition, Wiley publishing

• Related readings:

R.E. Collin “Foundations for microwave engineering”, McGraw-Hill, 2nd

ed., 1992

-ECE 5317_6351 Microwave Engineering Prof. David R. Jackson

Simulators

- HFSS High Frequency Structure Simulator.

- ADS Advanced Design System

Course Assessment

Part 1 Dr. Gehan Sami

• Attendance 5

• Midterms 15

• Project 5

• Final Exam 50

• Total 75

Introduction• Microwave refer to alternating signals with frequencies between 300MHz

and 300GHz,with wavelength between λ=c/f=1m and 1mm.

• Why we use microwaves

microwave signals offer wide bandwidths, and have the added advantage of being ableto penetrate fog, dust, foliage, and even buildings and vehicles to some extent

Microwaves are widely used for point-to-point communications because their small wavelength allows conveniently-sized antennas to direct them in narrow beams, which can be pointed directly at the receiving antenna

high frequency of microwaves gives the microwave band a very large information-carryingcapacity.

Gain of a Typical 6 Foot Dish Antenna (with Losses)

Antenna gain is proportional to the electric size of theantenna. for Dish antenna physical size almost equal to

Electrical size

f ↑, gain ↑

Microwave ApplicationsThree main applications of microwaves in everyday life:

1- Heating-Microwave ovens

2- Remote sensing- Radars (radio direction and ranging),detect object position or velocity (or both).- RFID

-Radio astronomy

3- Communications-satellite, radio, television, wireless phone and data transmission applications

• Other applications as:-Medical applications

-Directed energy weapons

https://www.microwaves101.com/

Microwave ovens

Microwave Applications

f=2.45GHz

RFID System

Microwave Applications

Microwave ApplicationsMedical applicationsPatient monitoring

Microwave ApplicationsMedical applications

Free-range Resonant Electrical Energy DeliverySystem (FREE-D) for a Ventricular Assist Device

University of Washington

GROUND PENETRATING RADAR AND MICROWAVE TOMOGRAPHY

Microwave Applications

Transmission Line

A Monolithic Microwave Integrated

Circuit, or MMIC

(sometimes pronounced "mimic"), is a type

of integrated circuit (IC) device that

operates

at microwave frequencies (300 MHz to

300 GHz). These devices typically perform

functions such as microwave mixing,

power amplification, low-noise

amplification, and high-frequency

switching. Inputs and outputs on MMIC

devices are frequently matched to

a characteristic impedance of 50 ohms.

This makes them easier to use, as

cascading of MMICs does not then require

an external matching network.

.

Transmission Line

Transmission Line

Planar Transmission Lines •Microstrip.

•Slot Line.

•Coplanar waveguide.

•Coplanar lines.

Transmission Line

Can propagate a signal at any frequency (in theory) Becomes lossy at high frequency Can handle low or moderate amounts of power

Does not have Ez or Hz components of the fields (TEMz)

Properties

Coaxial cable (coax)

Transmission Line (cont.)

Microstrip

h

w

er

er

w

Stripline

h

Transmission lines commonly met on printed-circuit boards

Coplanar strips

her

w w

Coplanar waveguide (CPW)

her

w

19

Fiber-Optic Guide

Has minimal signal distortion Very immune to interference Not suitable for high power

Has both Ez and Hz components of the fields

Properties

Wave guides

Waveguides

Has a single hollow metal pipe

Can propagate a signal only at high frequency: > c

The width must be at least one-half of a wavelength Has signal distortion, even in the lossless case Immune to interference Can handle large amounts of power Has low loss (compared with a transmission line)

Has either Ez or Hz component of the fields (TMz or TEz)

Properties

http://en.wikipedia.org/wiki/Waveguide_(electromagnetism) 21

Transmission Line (cont.)

Transmission lines are commonly met on printed-circuit boards.

A microwave integrated circuit

Microstrip line

22

Lumped circuits: resistors, capacitors, inductors

neglect time delays (phase)

account for propagation and time delays (phase change)

Transmission-Line Theory

Distributed circuit elements: transmission lines

We need transmission-line theory whenever the length of a line is significant compared with a wavelength.

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electrical wavelength is much larger than the physical dimension of the circuits

Transmission Line

2 conductors

4 per-unit-length parameters:

C = capacitance/length [F/m]

L = inductance/length [H/m]

R = resistance/length [/m]

G = conductance/length [ /m or S/m]

Dz

24

An engineering problem is to transfer signal from generator to load.

A transmission line is a part of circuit that link between generator and load; Theory of

transmission line applied on all types of transmission lines.

Transmission Line (cont.)

zD

,i z t

+ + + + + + +- - - - - - - - - - ,v z tx x xB

25

RDz LDz

GDz CDz

z

v(z+Dz,t)

+

-

v(z,t)

+

-

i(z,t) i(z+Dz,t)

( , )( , ) ( , ) ( , )

( , )( , ) ( , ) ( , )

i z tv z t v z z t i z t R z L z

t

v z z ti z t i z z t v z z t G z C z

t

D D D

D D D D D

Transmission Line (cont.)

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RDz LDz

GDz CDz

z

v(z+Dz,t)

+

-

v(z,t)

+

-

i(z,t) i(z+Dz,t)

at a time t

Hence

( , ) ( , ) ( , )( , )

( , ) ( , ) ( , )( , )

v z z t v z t i z tRi z t L

z t

i z z t i z t v z z tGv z z t C

z t

D

D

D D D

D

Now let Dz 0:

v iRi L

z t

i vGv C

z t

“Telegrapher’sEquations”

TEM Transmission Line (cont.)

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2 2

2 2( ) 0

v v vRG v RC LG LC

z t t

The same equation also holds for i.

Hence, we have:

2 2

2 2

v v v vR Gv C L G C

z t t t

TEM Transmission Line (cont.)

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2

2

2( ) ( ) 0

d VRG V RC LG j V LC V

dz

2 2

2 2( ) 0

v v vRG v RC LG LC

z t t

TEM Transmission Line (cont.)

Time-Harmonic Waves:

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Note that

= series impedance/length

2

2

2( )

d VRG V j RC LG V LC V

dz

2( ) ( )( )RG j RC LG LC R j L G j C

Z R j L

Y G j C

= parallel admittance/length

Then we can write:

2

2( )

d VZY V

dz

TEM Transmission Line (cont.)

30

Let

Convention:

Solution:

2 ZY

( ) z zV z Ae Be

1/2

( )( )R j L G j C

principal square root

2

2

2( )

d VV

dzThen

TEM Transmission Line (cont.)

is called the "propagation constant."

/2jz z e

j

0, 0

attenuationcontant

phaseconstant

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TEM Transmission Line (cont.)

0 0( ) z z j zV z V e V e e

Forward travelling wave (a wave traveling in the positive z direction):

0

0

0

( , ) Re

Re

cos

z j z j t

j z j z j t

z

v z t V e e e

V e e e e

V e t z

g0t

z

0

zV e

2

g

2g

The wave “repeats” when:

Hence:

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One of the solutions

Phase Velocity

Track the velocity of a fixed point on the wave (a point of constant phase), e.g., the crest.

0( , ) cos( )zv z t V e t z

z

vp (phase velocity)

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Phase Velocity (cont.)

0

constant

t z

dz

dt

dz

dt

Set

Hencep

v

1/2

Im ( )( )p

vR j L G j C

In expanded form:

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Characteristic Impedance Z0

0

( )

( )

V zZ

I z

0

0

( )

( )

z

z

V z V e

I z I e

so 00

0

VZ

I

+

V+(z)

-

I+ (z)

z

A wave is traveling in the positive z direction.

(Z0 is a number, not a function of z.)

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Use Telegrapher’s Equation:

v iRi L

z t

sodV

RI j LIdz

ZI

Hence0 0

z zV e ZI e

Characteristic Impedance Z0 (cont.)

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From this we have:

Using

We have

1/2

00

0

V Z ZZ

I Y

Y G j C

1/2

0

R j LZ

G j C

Characteristic Impedance Z0 (cont.)

Z R j L

Note: The principal branch of the square root is chosen, so that Re (Z0) > 0.

37

• a fundamental parameter of transmission

line is its characteristic impedance z0 and

propagation constant γ.

z0 describe the relation between the

current and voltage travelling waves

z0 is function of dimensions of T.L. and

dielectric constant

for most RF systems z0 is either 50 or 75

ohms.(Notice z0 is real for low losses)

For low power (cable TV for example ) coaxial lines are optimized for low loss z0 =75 ohms,

for radar applications high power is encountered coaxial line is designed to compromise

Between max power handling and minim um losses ,it designed to have z0 =50 ohm

Characteristic impedance of transmission line:

appendix J for standard

coaxial cable, most designed

for z0 between 50-75

00

0 0

j z j j z

z z

z j zV e e

V z V e V

V e e e

e

e

0

0 cos

c

, R

os

e j t

z

z

V e t

v z t V z

z

V z

e

e t

Note:

wave in +z

direction wave in -zdirection

General Case (Waves in Both Directions)

40

Backward-Traveling Wave

0

( )

( )

V zZ

I z

0

( )

( )

V zZ

I z

so

+

V -(z)

-

I - (z)

z

A wave is traveling in the negative z direction.

Note: The reference directions for voltage and current are the same as for the forward wave.

41

General Case

0 0

0 0

0

( )

1( )

z z

z z

V z V e V e

I z V e V eZ

A general superposition of forward and backward traveling waves:

Most general case:

Note: The reference directions for voltage and current are the same for forward and backward waves.

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+

V (z)

-

I (z)

z

1

2

12

0

0 0

0 0

0 0

z z

z z

V z V e V e

V VI z e e

Z

j R j L G j C

R j LZ

G j

Z

C

I(z)

V(z)+

-z

2

mg

[m/s]pv

guided wavelength g

phase velocity vp

Summary of Basic TL formulas

43

Lossless Case

0, 0R G

1/ 2

( )( )j R j L G j C

j LC

so 0

LC

1/2

0

R j LZ

G j C

0

LZ

C

1pv

LC

pv

(indep. of freq.)(real and indep. of freq.)44

Lossless Case (cont.)

1pv

LC

In the medium between the two conductors is homogeneous (uniform) and is characterized by (e, ), then we have that

LC e

The speed of light in a dielectric medium is1

dce

Hence, we have that p dv c

The phase velocity does not depend on the frequency, and it is always the speed of light (in the material).

(proof given later)

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