ETEN10:1 Antenna Technology - eit.lth.se · Alternative literature: Antenna Theory: Analysis and...

ETEN10:1 Antenna Technology

Mats Gustafsson

Department of Electrical and Information Technology

Lund University

ETEN10, HT2, 2015

Outline

1 ETEN10 overview

2 Antenna background

3 Antenna parameters

Mats Gustafsson, ETEN10:1(2)-2015, EIT, Lund University, Sweden

ETEN10 Antenna technology: AimThe student shall

SonyEricsson T68,2001 [7]

VLA in New Mexico 2006

I acquire fundamentalknowledge of antenna theory.

I acquire good ability toanalyse and design antennas.

I acquire good knowledge ofantenna parameters such asdirectivity and radiationpattern.

I carry through and documenta project in which an antennais designed, fabricated andmeasured.

Rome 2012.

Patch antenna, cf., the labproject.


Examination

In order to pass the course you must:

1. do all laboratory sessions

2. write a laboratory report (covering thelaboratory sessions)

3. do a written five hour examination (max60p, grade 3 for 30-39p, 4 for 40-49p, and 5for 50-60p).

Pass on the electronic quiz offers 5 bonus pointson the written exam in January 2016.Retake exams in April and August. Note, nobonus points on the retake exams.


Overview

I 2 lectures per week.

I 1 problem solving class (computer exercise)/week.

I 3 laboratory sessions.

I Electronic quiz (7 tests, 5p on the written exam inJanuary 2016).

I Written examination (max 60p, pass 30p).

I http://www.eit.lth.se/course/ETEN10

I Mats Gustafsson, Anders J. Johansson, DorukTayli, Zachary Miers


Overview: Literature

I (KM) Antennas by J.D. Kraus and R.J. Marhefka.

I (S0) Electromagnetic Waves and Antennas by S.J.Orfanidis.(www.ece.rutgers.edu/~orfanidi/ewa/)

I Chapter 8 and 9 in (RB) ’Fundamentals ofEngineering Electromagnetics’ by R. Bansal.

I Parts of chapter 7 in (BRI) ’ComputationalElectromagnetics’ by A. Bondeson, T. Rylanderand P. Ingelstrom.

I Download the e-books from the homepage.

I Lecture notes (download from moodle).Alternative literature: Antenna Theory: Analysis and Design by Balanis, Antenna Theory andDesign by Stutzman and Thiele, Foundations of Antenna Engineering by Kildal (downloadfrom http://www.kildal.se), ...


http://www.kildal.se/

http://www.kildal.se

Schedule 2015

See homepage for details. Laboratory lessons preliminary for week3, 5, and 6, see the homepage.


Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance

reflectioncoefficient

Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field

Many different types, sizes, and shapes ofantennas. Some common antenna typesare:

Antenna elements collected into arrays.

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

Parameters used to characterize antennasinclude:

Radiation intensitynormalized by theaccepted power.G = P/PT

Radiation intensitynormalized by theaverage radiatedpower. D = P/Pave

The impedance at theantenna terminalsZ = V/I

Reflected signal ΓUin,

Γ =Z−Z0Z+Z0

. Often

|Γ | ≤ 1/3 formatched antennas.

Stored energynormalized by theaverage dissipatedenergy Q =2ω maxWe,Wm

Pd.

Fractional bandwidthB ≈ 0.7/Q forΓ0 = 1/3.

Radiated powernormalized by theinput power.

Common applications for antennas include:

Antennas are measured using: Antennas are analyzed using e.g., :

Method of Moments(integral solver forMaxwell’s eq.)

Finite Differences inthe Time-Domain.

Finite ElementMethod.

Geometrical optics andphysical optics. Highfrequencyapproximations forMaxwell’s eq.

modal solutions toMaxwell’s eq.

Stored energy in fieldsor currents.

Fourier transform todetermine the far-fieldfrom a current density.

First three lectures:

I dipole antennas

I antenna parameters

I determine thefar-field from currentdistributions

I Method of momentsin the computerexercise


Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.




Antennas are measured using:

Antennas are analyzed using e.g., :









I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.




Antennas are measured using:

Antennas are analyzed using e.g., :









I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





Antennatechnology

antennaelements

dipole

monopole

helixYagi-Uda

DRA

patch

hornlens

reflector

Arrays

beamsteering

side lobes

array factor

MIMO

patternsynthesis

Parameters

directivity

gain

efficiency

inputimpedance


Q-factor

Applica-tions

radar

mobilephones

powertransfer

radio, TV

astronomy

RFID

nano,optics

Measure-ments

far field

near field

anechoicchamber

VNA, S-parameters

SAR

Analysis

MoMFDTD

FEM

GO,PO

modes

energy

current tofar field



0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB

0o

180o

90o

90o

45o

135o

45o

135o

−10−20−30dB






Γ =Z−Z0Z+Z0

. Often



Pd.













I dipole antennas





CST Microwave studio

I Commercial program (www.cst.com).I You can run the program on your PC.I

I

I Also available in E:4118, E:4119, use: Note, create your ownfolder (use your name) and store your data on some externalmemory, e.g., USB.




I





I



First computer exercise

In this first computer exercise you should

1. investigate basic properties of dipole antennas.

2. practice on antenna parameters such as reflection coefficient,impedance, radiation pattern, and directivity.

3. get familiar with the program CST. You will use it later in thecourse and in the laboratory part of the course.

Preparation: Study the lecture notes and Ch. 15 in Orfanidis. Dothe exercises in Ch. 15, see the instructions (ETEN10_E1.pdfdownload from moodle).


Moodle (lecture notes and electronic quiz)

You log in using your STIL or lucat identity. More about moodleand the quiz next lecture.








Outline

1 ETEN10 overview




Antennas

Antenna definition (IEEE)

”That part of a transmitting or receiving system that is designed toradiate or to receive electromagnetic waves.”

Transmission line

Antenna

with guided EM-waves

EM-waves in free space

I Transition from guidedwaves on transmissionlines to free space waves.

I EM waves on transmissionlines are studied in othercourses (e.g., Ch. 10)

I EM waves in free spaceare studied in othercourses (e.g., Ch. 2)

See also http://en.wiktionary.org/wiki/antenna andhttp://en.wikipedia.org/wiki/Antenna_(radio)


http://dx.doi.org/10.1109/IEEESTD.1993.119664

http://en.wiktionary.org/wiki/antenna

http://en.wikipedia.org/wiki/Antenna_(radio)

Early history I

J.C. Maxwell [1]

G. Marconi [5]

I 1800s Wire telegraph

I 1864 James Clerk Maxwell (EM-theory)

I 1887 Heinrich Rudolf Hertz (Experimentalverification of EM waves)

I Guglielmo Marconi develops ”wireless” andradio (Nobel Prize 1909)

and Loomis, Popov, Tesla,...


http://en.wikipedia.org/wiki/James_Clerk_Maxwell

http://en.wikipedia.org/wiki/Heinrich_Hertz

http://en.wikipedia.org/wiki/Guglielmo_Marconi

Early history II

Heinrich Rudolf Hertz [6]

I Heinrich Rudolf Hertz (1857–1894)

I Experimental verification of EM waves.

Hertz did not realize the practical importance ofhis experiments. He stated that,

”It’s of no use whatsoever[...] this is just an exper-iment that proves Maestro Maxwell was right - wejust have these mysterious electromagnetic wavesthat we cannot see with the naked eye. But theyare there.”

Asked about the ramifications of his discoveries,Hertz replied,

”Nothing, I guess.”


http://en.wikipedia.org/wiki/Heinrich_Hertz

Applications

SonyEricsson T68, 2001

VLA in New Mexico [4]

RFID-TAG [3]

I CommunicationRadio, TV, mobile phone, Satellite

I Radar (RAdio Detection And Ranging),Ground-penetrating radar (GPR), Microwavetomography

I RFID (Radio-frequency identification)

I Positioning, e.g., GPS

I Radio astronomy

I Optics, nano antennas


http://en.wikipedia.org/wiki/Radar

http://en.wikipedia.org/wiki/Ground-penetrating_radar

http://en.wikipedia.org/wiki/Radio-frequency_identification

http://en.wikipedia.org/wiki/Global_Positioning_System

http://en.wikipedia.org/wiki/Radio_astronomy

Wireless communications

Base station in Nattavaara by.

Base stations:

I High efficiency

I Directivity

Terminal antennas:

I Many small antennas inmodern mobile phones.

I MIMO (many antennas),RFID, TV...

I Co-exist with camera,battery, ..., user

I Must be cost efficient.

SonyEricsson T68, 2001 [7]


http://en.wikipedia.org/wiki/Wireless

http://en.wikipedia.org/wiki/MIMO

http://en.wikipedia.org/wiki/Radio-frequency_identification

Radio astronomy

I Often large reflector antennas.

I Often large arrays.

I The VLA (Very Large Array) inSocorro, New Mexico has 27antennas that together offer aresolution of approximately0.2 arcsec ≈ 1µrad atλ = 3 cm.

The VLA and Washington DC


http://en.wikipedia.org/wiki/Radio_astronomy

http://en.wikipedia.org/wiki/Very_Large_Array

http://en.wikipedia.org/wiki/Very_Large_Array

Outline

1 ETEN10 overview




Antenna characteristicsWhat parameters are interesting?

Antenna

Radiated EM-waves


Antenna characteristics

V+

-I

J

Radiated EM-waves

Power flowin direction, µ,'

z

x

µ

Circuit (transmission line) properties:

I Input impedance Z(ω) and reflectioncoefficient Γ = Z−Z0

Z+Z0.

I Matched antennas |Γ | ≈ 0

I Determine Z = V/I in the feed point

I Or measure the reflection coefficient Γ .

Radiation properties:

I Radiated power in direction θ, φ.

I Determine the currents on the antennaand integrate to obtain the far-field.

I Or measure the received (ortransmitted) field.


Circuit (transmission line) parameters (Ch. 10)

+

-

VZ

IAntenna input impedance, Z(ω)

The impedance at the antenna terminals. Functionof the (angular) frequency ω = 2πf .

Reflection coefficient, Γ (ω)

The reflected signal on the transmission line (char-acteristic impedance Z0) is Γuin, where

Γ =Z − Z0

Z + Z0and Z = Z0

1 + Γ

1− Γ

Measure with a network analyzer.

Standing wave ratio (SWR or VSWR)

Voltage standing wave ratioVSWR = Vmax/Vmin = (1 + |Γ |)/(1− |Γ |)


Antenna radiation parametersCoordinate system (Ch. 14.8)

x

y

z

φ

θ

Use the spherical coordinatesystem r, θ, φ with

x = r cosφ sin θ

y = r sinφ sin θ

z = r cos θ

The radiation pattern depends on θ, φ. We also consider thepolarization, often expressed in the directions θ and φ directions,see also 39 .



x

y

z

φ

θ

θ

φ

r Use the spherical coordinatesystem r, θ, φ with

x = r cosφ sin θ

y = r sinφ sin θ

z = r cos θ




x

y

z

φ

θ

θ

φr

Use the spherical coordinatesystem r, θ, φ with

x = r cosφ sin θ

y = r sinφ sin θ

z = r cos θ



Latitude, longitude, and cardinal directions

Earth.

Radiated EM-waves


z

x

µ

Radiated field.

We can compare the spherical coordinatesystem that we use to describe antennaparameters with a geographic coordinatesystem.On earth, we want to describe

I positions.

I directions.

This is similar to the radiation pattern froman antenna, where we want to describe

I the radiation intensity far away from theantenna (cf., the position on earth).

I polarization of the E-field (directions onearth).


Latitude, longitude, and cardinal directions

Latitude and longitude on a sphere.Lund at 55N, 13E

longitude

latitude

−180−150−120 −90 −60 −30 0 30 60 90 120 150 180−90−75−60−45−30−150153045607590

Latitude and longitude in a Cartesiancoordinate system.

Use a set of coordinates that describepositions and directions on earth (here weneglect altitude).

I Latitude, angle between −90 (southpole) and 90 (north pole).

I Longitude, angle between −180 (west)and 180 (east) from the referencemeridian, 0 at Greenwich, UK.

I Directions: north (latitude) and east(longitude).

I Note the change of area close to thenorth and south poles.


Spherical coordinates for antennas

Á=0 Á=30

Á=60

Á=330

µ=0

µ=30

The θ, φ coordinate system on asphere.

Á0 30 60 90 120 150 180 210 240 270 300 330 360

0153045607590105120135150165180

µ

The θ, φ coordinate system.

Radiated EM-waves


z

x

µ

Place the antenna in the center of a sphere(the earth). Use a spherical coordinatesystem (similar as the latitude and longitude)with θ = 0 at the north pole, θ = 180 atthe south pole, and 0 ≤ φ < 360.


Spherical coordinates for antennas

Á

µµ

Á=0

Á

Á=30

Á=60

Á=330

µ=0

µ=30

Spherical coordinates, θ, φ, on a

sphere with the directions θ and φ.

Á0 30 60 90 120 150 180 210 240 270 300 330 360

0153045607590105120135150165180

µ

Á

µ

Á

µ

The θ, φ coordinate system.

Place the antenna in the center of a sphere(the earth). Use a spherical coordinatesystem (similar as the latitude and longitude)with θ = 0 at the north pole, θ = 180 atthe south pole, and 0 ≤ φ < 360.

Directions:

I The unit vector θ is in the direction ofincreasing θ, i.e., towards south. This isalso the polarization (direction of theelectric field) of an z-directed dipoleantenna.

I The unit vector φ is in the direction ofincreasing φ, i.e., towards east.

I Note the change of area close to thepoles, cf., the sin θ in many integrals.


Spherical coordinate system

x

y

z

φ

θ

θ

φ

r

x

y

z

φ

θ

θ

φr

Useful vector formulasr = x sin θ cosφ+ y sin θ sinφ+ z cos θ

θ = x cos θ cosφ+ y cos θ sinφ− z sin θ

φ = −x sinφ+ y cosφ

andx = r sin θ cosφ+ θ cos θ cosφ− φ sinφ

y = r sin θ sinφ+ θ cos θ sinφ+ φ cosφ

z = r cos θ − θ sin θ

You have them in the formula sheet, see also43 .


Antenna radiation parameters (Ch. 15.2)

VV1

y

x

z

Anechoic chamber at EIT, LU [2]

Radiation intensity P (θ, φ)

Angular distribution of the radiated power aroundthe antenna.

Directivity D(θ, φ) = P (θ, φ)/Pave

Radiation intensity normalized by the isotropic (av-erage) intensity Pave = Prad/(4π). The directionof maximum radiation is implied if no direction isspecified, i.e., D = maxθ,φD(θ, φ).

Gain G(θ, φ) = P (θ, φ)/(PT/(4π))

Radiation intensity normalized by the power ac-cepted by the antenna.

Efficiency εr = Prad/PT

Radiated power normalized by the input power.


Electromagnetic fields

J.C. Maxwell [1]

∇×E = −jωB

∇×H = J+jωD

PhysWorld 2004

I Electric field intensity E unit V/m.

I Magnetic field intensity H unit A/m.

I (Electric) current density J unit A/m2.

I Poynting vector S = 12E ×H

∗ unit W/m2.

I Frequency f , angular frequency ω = 2πf ,wavenumber k = ω/c0, wavelengthλ = c0/f = 2π/k.

I Free space impedance η0 ≈ 377 Ω.

I Speed of lightc0 = 299792458 m/s ≈ 3 108 m/s.

Time harmonic fields, e.g., E(t) = ReEejωt.


http://en.wikipedia.org/wiki/James_Clerk_Maxwell

http://en.wikipedia.org/wiki/Poynting_vector

http://en.wikipedia.org/wiki/Speed_of_light

Current to radiation pattern I

J(r )

E(r)

r

µ

^

^r

0

r 0

The radiated field is determined from the currentdensity, J , on the antenna element as

F (θ, φ) = F (r) =

∫J(r′)ejkr·r

′dV′,

where F is the radiation vector 44 and

r = x cosφ sin θ + y sinφ sin θ + z cos θ.

The electric field far from the antenna is

E(r) = −jkη0e−jkr

4πrF⊥(r)

= −jkη0e−jkr

4πr

(θFθ + φFφ

).


Current to radiation pattern II

VV1

y

x

z

The Poynting vector (power flux) far from theantenna is

ReS =1

2ReE ×H∗ =

P (θ, φ)

r2r,

with the radiation intensity

P (θ, φ) =η0k

2

32π2|F⊥(θ, φ)|2.

In power flux is in the radial direction r, decaysas r−2, and depends on the direction θ, φ.Approximate current distributions are known forsome simple antennas. We use this approach toanalyze dipole, loop, and patch antennas. Accu-rate current distributions require numerical solu-tions, e.g., with MoM.


Near field and far field

I Reactive near field: the region closeto the antenna where the reactive fielddominates.

I Radiative near field (Fresnelregion): weak reactive fields butradiation in different directions.

I Far field (Fraunhofer region): theregion far from the antenna where thefields decay as 1/r, i.e.,

E(r) ≈ −jkη0e−jkr

4πr F⊥(r). Oftendefined as distances r > rf = 2D2/λand r λ, where D denotes thediameter of the antenna.

Far-field region

Radiative near field

Reactive near field

D rf

We analyze the far-field (radiation pattern) in this course.


Receiving antenna parameters

Z0

E

k

in

Reciprocity

Most antennas are reciprocal, i.e., they have simi-lar properties in transmission and reception.

Effective area (aperture) A(θ, φ) = PR/PinWhere PR is the power absorbed by the antenna inwatts, and Pin is the power density incident on theantenna in watts per square meter. It is assumedthat the antenna is terminated with a matchedload.

Gain and effective area

A(θ, φ) =λ2G(θ, φ)

4πand G(θ, φ) =

4πA(θ, φ)

λ2


Friis transmission equation

Transmitting

antenna

Receiving

antenna

r

P , G , ATTTP , G , ARRR

The radiated power density at the distance r from the transmittingantenna is Pin = P/r2 = PTGT/(4πr

2). The received power ishence

PR = PinAR =PTGT

4πr2AR = PT

GTGRλ2

(4πr)2= PT

GTGR

(4πr/λ)2

Here, we assume that the antennas are matched and have alignedpolarizations. This will be generalized later in the course.Harald T. Friis, Proc. IRE, 1946.


http://dx.doi.org/10.1109/JRPROC.1946.234568

Next lecture

date Lec. Exe. Lab S.O. K.&M. R.B. topic11-02 1 15 2 Introduction, antenna parameters11-04 1 Computer exercise (E:4118, E:4119)11-05 2 16 2,6 Dipoles, antenna parameters, MoM

I Computer exercise in E:4118 and E:4119, preparations: definitions andterminology e.g., input impedance, reflection coefficient, directivity,gain, radiation pattern. Read these lecture notes and Orfanidis Ch 15.Download the exercise instructions ETEN10 E1.pdf from moodle.

I Lecture 2: dipole antennas, short dipole, half-wave dipole, simpleanalytic expressions, download the lecture notes ETEN10 2.pdf frommoodle. Read before next lecture.


References

[1] James Clerk Maxwell. http://en.wikipedia.org/.

[2] The anechoic chamber at EIT, LU, 2002. LTH-Nytt.

[3] RFID TAG, 2008. http://en.wikipedia.org/.

[4] Hajor. The Very Large Array at Socorro, New Mexico, US,2004. http://en.wikipedia.org/.

[5] Nobel foundation. Marconi, 1909. http://nobelprize.org/.

[6] Oliver Heaviside: Sage in Solitude. Heinrich Rudolf Hertz,1894. http://en.wikipedia.org/.

[7] Sony Ericsson. T68, 2001.


Outline

4 Appendix: Additional materialVectorsPotentials and far fields


Appendix: vectors

We use vectors to describe positions and directions. In a Cartesiancoordinate system x, y, z, we have r = xx+ yy + zz andr′ = x′x+ y′y + z′z with the scalar product

r · r′ = (xx+ yy + zz) · (x′x+ y′y + z′z) = xx′ + yy′ + zz′

as x · x = 1, x · y = 0, x · z = 0,...The length of a vector is

r = |r| =√r · r =

√x2 + y2 + z2

The distance between the two points r and r′ is

|r−r′| =√

(r − r′) · (r − r′) =√

(x− x′)2 + (y − y′)2 + (z − z′)2

or|r − r′| =

√(r − r′) · (r − r′) =

√r2 − 2r · r′ + r′2


Vector fields

The electric field E(r), magnetic field H(r), and current densityJ(r) are vector fields, where a vector is assigned to every point inspace.

−2 −1 1 2

−2

−1

1

2

x

y

xx+ yy√x2 + y2

= cosφx+ sinφy = r

−2 −1 1 2

−2

−1

1

2

x

y

−yx+ xy√x2 + y2

= − cosφx+ sinφy = φ


https://en.wikipedia.org/wiki/Vector_field

Matrix notation

A Cartesian coordinate system x, y, z with vectorsr = xx+ yy + zz can be identified with the matrix notation

r = xx+yy+zz = x

100

+y

010

+z

001

=

xyz

and r′ =

x′y′z′

where we have scalar (or inner) product

r · r′ =

xyz

Tx′y′z′

=(x y z

)x′y′z′

= xx′ + yy′ + zz′

The matrix notation is not suitable for spherical coordinatesystems and we do not use it in this course.



x

y

z

r

φ

θ

x

y

z

r

φ

θ

A vector r = xx+ yy + zz can be described ina spherical coordinate system r, θ, φ

x = r cosφ sin θ

y = r sinφ sin θ

z = r cos θ

I r = |r| =√x2 + y2 + z2 is the length of r

(the distance from the center of thecoordinate system to the point r).

I θ is the polar angle, i.e., the angle from zto r.

I φ is the azimuthal angle, i.e., the angle fromx to the projection of r in the xy-plane.



x

y

z

φ

θ

θ

φ

r

x

y

z

φ

θ

θ

φr

A spherical coordinate system r, θ, φ has theunit vectors

r = x sin θ cosφ+ y sin θ sinφ+ z cos θ

θ = x cos θ cosφ+ y cos θ sinφ− z sin θ

φ = −x sinφ+ y cosφ

that defines a local coordinate system with unitvectors

I r in the direction of increasing r.I θ in the direction of increasing θ.I φ in the direction of increasing φ.


Appendix: Potentials, far field, and radiation vector

The (time harmonic) Maxwell equations are (also assuming freespace D = ε0E, B = µ0H)

∇×E = −jωB

∇×H = jωD + J

∇ ·B = 0

∇ ·D = ρ

Continuity equation from ∇ · (∇×H) = 0

0 = jω∇ ·D +∇ · J = jωρ+∇ · J

orjωρ = −∇ · J


The divergenceless of B (∇ ·B = 0) implies the existence of avector potential A such that B = ∇×A. Moreover,∇×E = −jωB = −jω∇×A implies that there exists a scalarpotential φ such that E = −∇φ− jωA. The vector and scalarpotentials are not uniquely defined and here we impose the Lorenzgauge ∇ ·A = −c−20 jωφ. The vector potentials satisfy theHelmholtz equations

∇2φ+ k2φ = −ρ/ε0∇2A+ k2A = −µ0J


We have the solutions (Green’s function G(r) = e−jkr/(4πr),where r = |r|)

φ(r) =1

ε0

∫V

ρ(r′)e−jk|r−r′|

4π|r − r′|dV′ =

1

ε0

∫Vρ(r′)G(r − r′) dV′

A(r) = µ0

∫V

J(r′)e−jk|r−r′|

4π|r − r′|dV′ = µ0

∫VJ(r′)G(r − r′) dV′

giving the electric and magnetic fields (ωµ0 = kη0, k/η0 = ωε0)

E(r) =

∫V−jωµ0J(r′)G(r − r′) + ε−10 ρ(r′)∇′G(r − r′) dV′

= η0

∫V−jkJ(r′)G(r − r′)− 1

jk∇′ · J(r′)∇′G(r − r′) dV′

H(r) =

∫VJ(r′)×∇′G(r − r′) dV′


The expressions for the potentials and the fields simplify in the farfield. For r r′, we can approximate the distance

R = |r − r′| =√

(r − r′) · (r − r′) =√r2 − 2r · r′ + r′2

= r√

1− 2r · r′/r + (r/r′)2 ≈ r − r · r′

as r →∞, where r = |r|, r = r/r, and r′ = |r′|. The potentialsare

φ(r) ≈ e−jkr

4πε0r

∫Vρ(r′)ejkr

′·r dV′

A(r) ≈ e−jkrµ04πr

∫VJ(r′)ejkr

′·r dV′ =e−jkrµ0

4πrF (r)

where F is the radiation vector. The electric field is

E(r) ≈ −jω(r ×A(r))× r = −jkη0e−jkr

4πr(r × F (r))× r


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