Antenna Engineering - Startseite TU Ilmenau Engineering Prof. Dr. M. Hein Summer semester 2017 RF &...

Antenna EngineeringProf. Dr. M. Hein

Summer semester 2018

RF & Microwave Research Labwww.tu-ilmenau.de/hmtSince 1961

Antenna EngineeringRelevance – Practical issues – Current research




1. Wireless technologiesBrief introduction and example applicationsPropagation of electromagnetic waves: Free space vs multipathRequirements for antennas (receive and transmit)

Antenna Engineering Lecture: Content

Content

2. Fundamentals of antenna engineeringElectrodynamic foundations and theoretical approachBasic radiating elementsExamples of practical radiating elements

3. Antenna arraysDisplacement principlePerformance figures of linear arraysBeam forming and spatial signal processing

4. Practical aspects of antenna engineeringPackaging and protectionDesign and numerical simulationAntenna measurements




Seminar topics50% tutorial, 50% revision: See homework topics

• Loop antennas• Patch antennas• Broadband antennas• Tracking antennas• Antenna measurements (anechoic chamber)

Homework topicsPartly to be solved during the seminar, partly by yourself in a small group or at home

See current internet version: www.tu-ilmenau.de/hmt Education

Content

Further interactive formats




Literature (selection)S. Drabowitch, A. Papiernik, H. Griffiths, J. Encinas, B.L. Smith, "Modern antennas",2nd edition, Springer, 2005 (1st edition: Chapman & Hill, 1998).Signature: ELT ZN 6440 D756(2)C.A. Balanis, “Antenna theory: analysis and design”, Wiley, 1997.Signature: ELT ZN 6440 B171(3)J. Volakis Ed., “Antenna Engineering Handbook”, 4th edition, New York, McGraw-Hill,2007.Signature: ELT ZN 6440 A627(4)Rothammels Antennenbuch (in German), 12th edition, DARC Verlag Baunatal, 2001.J.D. Kraus und R.J. Marhefka, "Antennas for all applications", McGraw-Hill, 2002.K. Fujimoto and J.R. James Eds., “Mobile Antenna Systems Handbook”, 2nd edition,Artech House, 2001.T. Weiland, M. Timm, and I. Munteanu: A Practical Guide to 3-D Simulation, IEEEMicrowave Magazine, Dezember 2008, pp.62-75; DOI10.1109/MMM.2008.929772D.G. Swanson, Jr., W.J.R. Hoefer: Microwave Circuit Modeling Using ElectromagneticField Simulation, 2003 ARTECH HOUSE, Norwood, MA , ISBN 1-58053-308-6

Literature




Antenna = Part of a system

Mobile antenna system

s handbook, K. Fujimoto and J. R

. James Eds, Artech H

ouse, 2001

• „Air interface“• Transmitter or receiver

or transceiver• Combination of analog

RF and IF with digital baseband

• Function convolved with radio wave transmission (wireless channel)

• Antenna parameters enter link budget calculations




Functions: Antennas ...

... convert the mode of propagation

... select spectrum and spaceTime frequencies: Single resonance – multi-

resonant – ultra-widebandSpatial frequencies: Omnidirectional – directive –

multi-beam

Antenna arrays for diversity (multipath propagation, MIMO)Phased-arrays (electronic beam-steering, radar)Adaptive arrays (tracking, reconfigurability, multi-user systems)

Antennas

Radiated wave guided-wave (RX/TX, omnidirectional / directive)Matching: Power (TX), noise (RX), bandwidth

... are (analog) signal processors

AntennaWaveguide

RX

AntennaWaveguide

TX




Frequency f (MHz)

Wavelength (m)

Designation Propagation loss (dB) (4r/)2 at r = 10 km

< 0.003 > 100,000 ELF < 0 – 200.003...0.03 100,000...10,000 VLF 0 – 20 ... 0

0.03...0.3 10,000...1,000 LF 0 + 0 ... 200.3...3.0 1,000...100 MF 0 + 20 ... 403.0...30 100...10 HF 0 + 40 ... 6030...300 10...1 VHF 0 + 60 ... 80300...3,000 1...0.1 UHF 0 + 80 ... 1003,000...30,000 0.1...0.01 SHF 0 + 100 ... 12030,000...300,000 0.01...0.001 EHF 0 + 120 ... 1400.3-3 THz 1-0.1 mm Sub-mm-waves3-400 THz 100-0.75 mm Infrared400-750 THz 400-750 nm Visible light

Frequency ranges

RF

micro-waves

mm

0 20log(4 ) 22 dB

Multitude of services allocated to wide frequency range; inter/national regulation




Research and development of antennasFrequency: High centre frequencies, broad bandwidthsSpectral efficiency, data rates, range, mobility (communications, multimedia, localisation, radar, hybrid)

Design and numerical simulationOptimal results: Radiation pattern, efficiency, frequency, bandwidth, sizeOptimal methods: Geometric and electromagnetic boundary conditions, CPU time and efficiencyMiniaturisation, integration (on-chip, packaging)

Added performanceSelective / Diversity (space, mode, and polarisation)Adaptive (beam steering, smart antennas, ad-hoc networks)Cognitive (spectral and spatial adaptation, RX and TX)

Antennas




Specular and diffuse reflectionSpecular reflectionRegion of reflection is perfectly flat on scale of wavelengths (h /16)Reflection law applies (geometrical optics)One well-defined directed reflected beam exists (depending on angle of incidence)

Diffuse reflectionRegion of reflection is uneven on scale of wavelength (Rayleigh, h > /16)Huygens‘ priniciple: Superposition of point sources; incident wave is scattered in many directions (tendentially independent of angle of incidence)Ideal diffuse surface: Lambert‘s law

Mixed reflection

0P( ) P cos

specular directive diffuse Wave propagation




Fresnel reflection

Statement of problemContinuity conditions for E- and H- fields across interfaces depend on • Angle-of-incidence• Material• Polarisation

2r

h 2r

sin cos

sin cos

2r r

v 2r r

sin cos

sin cos

Propagation scenarioTwo-path model (applies often)Line-of-sight (air) plus single reflection (ground)

ApproximationFlat geometry ( 0)|r| 1 (e.g., water)Asymptotically for 0: v = h –1 (180o phase jump)

sin Csin C

br

b 1 for V polC with

b 1 for H pol

h1 h2

r1 r2

r = r1+ r2

Wave propagation

LOS




Atmospheric attenuation

Resonant absorptionDominated by oxygen and water at microwave frequencies55 and 118 GHz (O2)22 and 180 GHz (H2O)




Fresnel zone – or „how thick is a ray?"

Undisturbed transmissionCertain space between transmitter S and receiver E free of obstacles (otherwise direct and reflected or diffracted wave portions may interfer)Of special relevance: Region around line-of-sight (LOS) with additional path lengths up to /2 (NLOS): First Fresnel zone

GeometryRotational ellipsoid with focal points S and E, path difference /2 along edge reflections compared to LOS

http://ww

w.radartutorial.de, http://de.wikipedia.org/w

iki/FresnelzoneS E

S E

S E

S Ed1

rF,1

d2

dF,1 er d 1 1 1e 1 2d d d




0 F F

E 1 1 j h hC jSE 2 2 r r

F

0

rE(P) 1E 2 | h |

Asymptotic for v2 1 (“shadow”)

Asymptotic for v > 1 (“light”)21 1C(v) sin v

2 v 2

21 1S(v) cos v2 v 2

Wave propagation

Shadow Light

x2

2o

C(x) cos( u )du x

22

o

S(x) sin( u )du

F er d rF = Fresnel radius

0

0.2

0.4

0.6

0.8

1

1.2

-3 -2 -1 0 1 2 3

E/E0

h/rF

Fresnel integrals

asymptotic, h>0asymptotic, h<0

Diffraction: analytical results

Nearly undisturbed “beam” for h > rF/2Height of antenna mounting is relevant

h = distance beam – diffracting edge




Two-path model (LOS and specular reflection off ground)

Analytical result(flat geometry, plane waves)

ges 1 2

0

| E | h h2 sin 2

E (r) r

Case 1: Variation with distanceAt given antenna heights

Case 2: Variation with heightAt given distance and height h1

0

1

2

0 2 4 6 8 10

Rel

ativ

e fie

ld s

treng

th |E

ges|/E

0

Normalised distance r/rref

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4

Rel

ativ

e fie

ld s

treng

th |E

ges|/E

0Normalised height h

2/h

2,ref

ges 21E (r)r

Pathloss exponent nTPM = 4




Constituents of multipath propagation

A. Paulraj, R. Nabar, D. Gore, “Introduction to Space-Time Wireless Communications,” 2003.

n(r) r

Average behaviour r = 3…300 m ( ) r = 0.3…0.6 m ( )

Wave propagation

Path loss exponent nLine-of-sight (LOS) 2

Single specular reflection

2

LOS + single specular reflection

4

Diffraction 1

Diffraction + reflection (obstacle gain)

5

Scattering (radar eq.) 4




Radiation pattern

Wave propagation

G (dB)

(or )

-60-50-40-30-20-10

0

0

30

60

90

120

210

240270

300

330

Isotropic radiator (hypothetic, d )

Patch (d)

Rectangular aperture (d )

Normalised angular distribution of radiation parameters, e.g.

• Gain or directivity• Field amplitude• Phase of field

Distinguish between • Main lobe• Side lobes• Backward radiation

Normalisation of G0 lin (dBi)

Isotropic radiator 1 0

Rectangular patch (TM100) 6 7.8

Rectangular aperture (10 ×10 , homogeneous) 1200 30.8




Effective area of an antenna Aeff

2eff

0

AG 4

The effective area Aeff describes the capability of collecting power from a power density (Poynting vector).

1. Hertzian dipole (lossless, HD)

Two examples

Definition and constituing equation

The ratio of effective area Aeff tomax. antenna gain G0 is constant(thus equal for every antenna).

2HD 2eff

3 1A2 4 8

PR 2eff physA A d

4

2 2

20

d dG 10

2. Parabolic reflector antenna (diameter d, PR)

Wave propagation




Radio links: Friis equation

Customised version (matched antennas)

System-oriented version (max. gains G0) • EIRP = PTX·GTX0 defined bystandards

• SNR determined by BER• Range rmax determined by

mobility and data rate

22 0max TX

min B RX

G 1r EIRP4 T SNR k B F

RX

TX2

2TX RX TX RX

P 1P ( , )

G ( , ) G ( , ) e e4 r

• Path loss FS

• Matching (orientation, polarization, impedance)

• Antenna gain → link budget• Antenna Frontend

Wave propagationTX RX

TX RX(dB) 92.4 20 logf(GHz) 20 logr(km) 10 logG 10 logG




Parameter space of wireless data transmission

Wave propagation

Stat

iona

ryN

omad

icM

obile

22max Tx

sys B min Rx

G 1r EIRP4 T k BW SNR

User data rate (bps)

Mobility / Range

TX RX

Bluetooth

DECT

GSMGPRS

EDGE

WLAN802.11x

3G

UMTSHSDPA

.16x

WMAN

4G LTE

PersonRoom

Noma-dic

Pedes-trian

Urban

High-way

Rural

100k 1M 10M 100M 1G 10G 100G

WiGigWLAN802.11ad




Antenna noise temperatureBlack body radiationEvery object emits radiation (T > 0 K)

(emissivity)B physT ( , ) ( , ) T

Example values (radiometry)• Dark sky (average background): 3 K• Earth (on average): 290 K• Human body: 310 K

Advancing Pahoehoe toe, Kilauea Hawaii 2003

Images obtained with a THz scanner

2

B0 0

A 2

0 0

T ( , ) G( , )sin d dT

G( , )sin d d

http://hvo.wr.usgs.gov/kilauea/update/archive/2003/May/main.html

Antenna noise temperatureMean environmental temperature, weighted by antenna gain pattern

http://www.tsa.gov/graphics/images/approach/mmw_large.jpg




Electromagnetic foundations

E j H (Faraday 's law)

H j E (Ampere's law)

E H 0 (Sourcelessness, free space)

dJdt

Constituing vector fields Sources of electromagnetic fields

Maxwell‘s equations (f-domain)Free space (no sources)Harmonic time-varying fieldsLinear isotropic media

Fundamentals

Electrical field EElectrical displacement DMagnetic field HMagnetic flux density BComplex material parameters: permittivity , permeability

Stationary: Charge density Moving: Current density J

Conservation of charge

Electromagnetic potentialsMagnetic vector potential AElectric scalar potential

A B

A j

j A E




Electromagnetic properties of matter

Medium Material Propagation Wave impedance

Free space(Vacuum, air)

= 0

= 0

= 0

Perfect(lossless)dielectric

= 0r real = 0 r real = 0

Dielectricwith losses

= ‘ - j ‘‘ = ||e-j

= 0 r real

= 0

Good metallicconductor

arbitrary = 0 r real ||

0 0 0k / c

0 0v c 1/

k / v

r rv c /

k ' | | cos 2 /

r rv c / cos | |

k '' | | sin 1/

k ' k '' 2 / 1/

2/

0 0 0Z /120377

Z /

j / 2Z / | | e

s sZ R (1 j)

sR 1/2

propagation cons tant j jk k '' jk '

Fundamentals




Why do antennas radiate?Cases to be distinguished1. Static fields 2. Stationary fields 3. Time varying fields

Double curl coupling: Equivalent to charges being accelerated

H

Et

E

Ht

J(t) 0

E(t),H(t) const.

J(t) const.

E(t) H(t) 0t t

J(t) 0t

E(t) H(t)0, 0t t

H

E

Et

Ht

FundamentalsAccelerated charges cause electromagnetic radiation




Derivation of radiation parametersFull electrodynamic solution

Fundamentals

Far-field approximation

Radiated power density and total radiated power

Antenna parameterse.g., G, D, SLL

Electromagneticpotentials

Wave equations, Lorenz gauge

Electric andmagnetic fields

Near fields andfar fields

Electromagneticsources

Time-varyingcharge and current

densities

Radiated power density and total radiated power

Antenna parameterse.g., G, D, SLL

Distribution of electric or magneticfields across radiating aperture

Aperture illumination

Electric andmagneticfar fields2D Fourier

transformation




Fourier transform between real domain and image domainFourier transformationTime – frequency domain

j t1G(t) G( )e d2

Radiation source in (x,y)-planeSpatial – image domain (k-space)

Wave vector

jk( x y)2

1G( , ) G(x,y)e dxdy

Tk | k | ( , , )

Time domain – frequency domain Spatial domain – spectral domain (2-dim)

t x, y kx, ky

Phase t Phase kxNormalisation 2/ = T Normalisation 2/|k| = t·c = |r|, ·c = k |r| / c = t, |k| / c =

Fundamentals

j t1G( ) G(t)e dtT

Corresponding terms

jk( x y)G(x,y) G( , )e d d




Determination of radiation field by tangential components in aperture

Follows from Maxwell‘s equations and absence of sources in propagation region (Verification: see homework)

z x y1divE 0 E E E

2x x y

1H E 1 EZ

2y x y

1H 1 E EZ

z x y1H E EZ

z x y1divH 0 H H H

2x x y

ZE H 1 H

2y x y

ZE 1 H H

z x yE Z H H

E-field given H-field given(electrical antenna) (magnetic antenna)

Fundamentals




Four key rules of antenna theory

Every field component is fully determined by its value in the aperture plane (free space: no sources)

Far field = Superposition of plane waves along direction of propagation, weighted by the field distribution in aperture plane G(,,0+)

Far field determined by tangential field components in aperture plane

Far field proportional toFourier transform of aperture illumination

jkr

FF 0 0t 0eE (x,y,z) j 2 k E ( , ,0 ) zkr

jk( x y z)G(x,y,z) G( , ,0 ) e d d

Fundamentals

1.

2.

3.

4.

FF 0 FF1H (x,y,z) k E (x,y,z)Z

(No information about near-field through 2D-FT; accessible through em potentials)




Radiation fields

Fourier transform

jk( x y)

21G( , ) G(x,y)e dxdy z

Aperture plane

Radiating area or aperturein (x,y)-plane (at z = 0)

y

x

Q1(x,y,0)

Q2(x,y,0)

Q3(x,y,0)

M(x,y,z)

Distribution of sources Qi

Function G(x,y)

Example2

1 for x a,y b ab sin(k a / 2) sin(k b / 2)G(x,y) G( , )0 for | x | a,| y | b k a / 2 k b / 2

Fundamentals




Fourier transformation: Trade-off between D and SLL

Solution: Adjust aperture distribution (amplitude tapering)

0

0.2

0.4

0.6

0.8

1

-4 -2 0 2 4

Nor

mal

ised

ape

rture

fiel

d di

strib

utio

n

Position along aperture (a.u.)

RectangleTriangleGaussian

-60

-50

-40

-30

-20

-10

0

-4 -2 0 2 4

Dire

ctiv

ity p

atte

rn ~

|E|2

(dB

)

Image domain (k-space) (a.u.)

RectangleTriangleGaussian

-13 dB

-26 dB

Fundamentals




Example

Important consequences

Horn antenna (nearly homogenous aperture illumination)

Principles of antenna theory

The far field of an antenna is determined by the 2D Fourier transform of the field distribution in the aperture plane.

Fundamentals

1. Electrical size of an antenna ↔ Capability of spatial focusing (Least focusing antenna: Hertzian dipole)

2. Homogeneous illumination Maximal directivity3. Side lobe level varies in an opposite way as directivity (SLL↑ ↔ D↓)




Elementary dipole: Geometry

x

y

z

r

k0

r0

0

0

Electrical dipole (Hertzian dipole)Straight wire element in originConstant current, length

Electrical dipole moment Current density

jkr

0 0t 0eH(x,y,z) j 2 k H ( , ,0 ) xkr

0t 0 02

1H ( , ,0 ) I y const.2

jkr

0jk eH (r, , ) I sin4 r

0I z

0 0 0 0k r r

Fundamentals

Dq u

DJ I (x) (y) (z) u




Field components of the Hertzian dipoleDistinguish between contributions in the near field and the far field (stored energy, reactive power vs effective power)

Radially directed power flow (radiation)

Tangential power flow (near field) Fundamentals

jkr0I e 1H j sin 12 r jkr

jkr0

2

I e 1 1E jZ sin 12 r jkr (kr)

jkr0

r 2

I e 1 1E jZ cosr jkr (kr)

rH H 0

E 0

Zero Near field Far field

×

××




Antenna dPrad(,)/dS Prad Directivity D(,) Dmax

Hertzian (electrical) dipole

Fitzgerald (magnetic) dipole

Homogeneously illuminated aperture S 2

Rectangular, aperture ab 2

[cos] radiation into half-sphere

Power-based antenna parameters

2 2

21 I sinZ8 r

2IZ3

23 sin( )

23 (1.76dB)2

22 2

2 24 IS sinZ8 r

22

2IS4 Z

3

21A cos ,r 2

2A

1

2 ( 1) cos

22

2

1 | E( , ) |2Z r

22| E | d d

2Z

jk( x y) 2

S2 22

S

| E(x,y)e dxdy |4 4 S

| E(x,y) | dxdy

24 ab

0 2

ab sin( a / ) sin( b / )E Ea / b /

Fundamentals

sin cossin sin

=1: 4 (6 dBi) =2: 6 (7.8 dBi)




The size of antennas

• Radius, length• Limited by specific

application (e.g., mobile handset)

Physical size (m)

• Directivity and beamwidth• Input matching • Radiation quality factor

and matched bandwidth• Radiation efficiency• Realised gain

Electrical size /(1)determines:

Electrically small large

-40

-30

-20

-10

0

10

20

-2 -1.5 -1 -0.5 0 0.5 1N

orm

alis

ed a

nten

na p

aram

eter

(dB

)

Electrical size of antenna, log(/)

Radiation quality factor Q

rad ~1/BW

Input matching ||

Maximum directivity D

max Efficiency

Realised gain Geff




Dipole antennas

FeaturesCurrent varies along lengthRequires symmetric feedDiameter neglected (slim wire)

0I(z ) I sin k | z |2

Far fieldLinear phase-correct superposition of the field contributions from elementary dipoles along current axis

J.D. K

raus, R.J. M

arhefka, Antennas for all applications,

McG

raw-H

ill 2002

Fundamentals




Electrical dipole: Radiation patterns

n

n ncos cos cos2 2( )

sin

Fundamentals

• Radiation pattern n() for n = n/2• n 2: Nulls along dipole axis at

cos0 = ± 1• n > 2: Additional nulls at n

n

1 31, , n oddn n

ncos 1, 0 even2

1 n1, oddn 2

H.D.n=1/2 n=1 n=3/2 n=2

n=2n=5/2n=3




C.A. Balanis, „Antenna theory“, John Wiley, 1982.

l/ 3dB(o)

D0(dBi)

Rrad()

1 90 1.76 0

1/4 87 1.9 < 10

1/2 78 2.14 73.2

3/4 64 2.8 200

1 47.8 3.82 200

Dipole antennas: Radiated power and directivity

2

rad

120D( ) ( )R ( )

Fundamentals

/2-dipole -dipole




Antenna design for manufacturabilityApplicationBroadcast, P2P, communications, radar, sensing, navigation, direction-finding, tracking, ...EnvironmentLand, sea, air, spaceNearfield, far fieldFree space, implanted, embeddedPerformanceSpectral f0, BW, ...Spatial Pattern, G, 3dB, SLL, ...Polarisation Linear, dual, circular, ellipticFunction fixed, switched, phased-

array, adaptive, ...Operation stationary, nomadic, mobile

ImplementationRadiator Elements, arrays,

geometry, homo-geneous, periodic

Feed Active, passive, hybrid

Assembly Geometry, materials, interfaces

Package Shape, volume, mass, integration, stability

CostManufacture, installation, power consumption maintenance,




Antennas: Geometries and shapes (categories)

Quasi-planar Volumetric, conformal

Aperture antennas (fields)

PatchSlotSurface wave Leaky traveling waves, coupled elements

Waveguide Aperture and leaky waveReflector Single, multipleDielectric lens

Wire antennas

(currents)

Linear Straight, folded

Loop Elliptical, rectangular

Circular symmetric Bi-conical, discone, ...Helix, ferrite

Hybrid Multitude of combinations / variations

Fundamentals




Aperture antennas

Radiating elements

Horn, lens, reflector, surface wave (leaky waves)

J.D

. Kra

us a

nd R

. J. M

arhe

fka,

Ant

enna

s fo

r all

appl

icat

ions

, M

cGra

w H

ill (2

002)

Fundamentals

Radiation pattern

Aperture distribution E(,)

Far field E(x,y)

Homogeneous aperture distribution Maximal directivity Pronounced sidelobes

Reduced sidelobes Inhomogeneous aperture

distribution (amplitude taper)

~






ww

w.2cool4u.ch/microw

ave/rifu_anforderungen/rifu_anforderungen.pdf

1 – Main reflector (Rotational paraboloid, Focus F, Apex S)

2 – Sub-reflector (Focal widths f1 and f2)

3 – Focal point of main reflector

4 – Focal point of sub-reflector

5 – Feed horn

Direct feed Indirect feed (Cassegrain)

Rotational paraboloids

Shell antenna

Reflector antennas

Horn parabol

Direct feed Indirect feed (Gregory)

Fundamentals




Parabolic reflector antenna

Gain

3-dB beamwidth

G(dBi) 20.4 10log 20log D(m) f(GHz)

3dB D G

2 22 D DG 10

3dB0.12

D(m) f(GHz)

Rule-of-thumb (simplification)

Fundamentals

After http://commons.wikimedia.org/wiki/File:Parabel-def-p.png

Q

Relevant geometry parameters

| FS | f| PQ | D

15

20

25

30

35

40

45

50

55

1 10 100

D=0.6mD=1.2mD=1.8mD=2.4mD=3.0mD=3.7mD=4.5m

frequency f (GHz)G

ain

G (d

Bi)




H-sector horn antenna

Aperture distribution corresponds to waveguide mode, e.g., TE10:Ey(x) = E0x·cos(x/A), Ey(y) = E0y

E

x

y

z

Fundamentals

Gain

Rule-of-thumb (simplification, fundamental mode)Geometry

b

a

AR

HRG 3

b 0.25

optA R1.73

HRG (dBi) 7.4 5log

H,3dB0.125

R

3-dB beamwidth http://www.feko.info/applications/white-papers/naval-radar-analysis-with-utd30. May 2012

a 0.5




Microstrip patch antennaDielectric resonator (modes: standing waves)Field distribution and radiation pattern

2 2 2

mnpr

c m n pfa b h2

TM100 TM020

Fundamentals

h p 0




Patch antenna

Fundamental modeEz(y) = E0

Ez(x) = E0·cos (x/a), a g/2Virtual magnetic dipole sources:

Two narrow slits constructiveConstant field distributionTwo-element array pattern

Two long slits destructiveIn (y,z)-plane as well as in opposing (x,z)-plane.

z

y

x

b

a

h

Fundamentals

E

H

M

E

M 2n E




10-4

10-3

10-2

10-1

100

0

30

6090

120

210

240270

300

330

E-planeH-plane

Patch antenna: radiation patternC

.A. B

alanis, „Antenna theory“, John W

iley, 1982.

Broad beam perpendicular to surface of patch (array pattern)

E|E|

aC cos sin

bH|E| b

sin sinC cos

sin

Fundamentals

E-plane

H-plane




Patch antenna: Directivity

1. Estimated from radiation mechanismTwo elementary dipoles: 1.76 dBi + 3 dBReflection from groundplane: + 3 dB

2e 3

4 4D 6 (7.8 dBi)

D 7.8 dBi (factor 6)

2. Estimation from radiation patternEffective aperture angle about 120 deg

Fundamentals

3. Analytical approximationTwo-slit array

b/ D D (dBi)1 6.6 8.2

1 8·b/ 9+10·log (b/)




Polarisation of patch antennasLinear polarisationPolarisation determined by surface currents on patch controlled by feed point

Circular polarisationSuperposition of two linear polarised fields in quadrature (either dual-feed or mode mixing)

x

y

Fundamentals




http

://en

.wik

iped

ia.o

rg/w

iki/F

ile:G

SM

_bas

e_st

atio

n_2.

JPG

Examples of array antennas




Displacement principle

Two identical sources O and O'Distant observation point in far field

00

jkr

0

jkk djkr jkrjkk d

0 00

jkd

eE f (k )kr

e e eE f(k ) f (k ) ekrk(r k d)

E E e

Arrays

Simplifying assumptions

Displacement in spatial domain (x,y,z) corresponds to phase shift in spectral domain (kx,ky,kz)

0

0

| r | | r | k d

k d d cos

r,k

r

d

O

O

y

x

0k d




nk0

θ d

A0 A1 A2 An

0

nAdAsinθ

an

f()

L = Nd

a0

1 n

Line

ar a

rray

(pha

sed

arra

y)

Uniform linear arrangement of N identical radiation elements

Arrays




Normalised array factor RN'(,0)

Arrays

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Mag

nitu

de p

atte

rn |R

'()|

Direction = sin

real(visible) region

virtual(invisible)

virtual(invisible)

=/d

0

Auxiliary parametersAngular direction = sinElectrical element separation = d/

0N 0

0

sin[N ( / 2)]R ( , )N sin( / 2])




Array pattern RN'(,0)

• Determined by electrical element spacing and phase gradient 0

• Main beam direction: 0 = 2·0

• Main lobes periodic: = 1/• Unambiguity: ≥ 2 ( 1/2)• Beamwidth: R'N (1/2) = 1/2• Beamwidth varies with steering:

Scan loss (broadfire – endfire)• Scan range max: < (1+sinmax)–1

Arrays

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Mag

nitu

de p

atte

rn |R

'()|

Direction = sin

real(visible) region

virtual(invisible)

virtual(invisible)

=/d

0

0N 0

0

sin[N ( / 2)]R ( , )N sin( / 2])




Linear phased-arrays

Feed networkPower distribution, matching, de/coupling (angle-dependent reflections)

Phase shiftersElectronic beam steering (as opposed to mechanical)

Antenna elementsSuperposition of the field-patterns (amplitudes and phases) of the individual radiation elements in a certain array configurationAntennas potentially complemented by focusingreflector or lens

Arrays

nu

θ d

A0An AN-1

Array

Phaseshifters

a0

b0

an

bn

aN-1 bN-1

Feed and distribution network

Driver

ProcessorTransceiver

...

.........




Active arrays

Transmit (TX)Compensate attenuation between feed and radiatorDistributed power control (high total power, e.g., tube amplifier required for full array)Improved reliability (drop-out of single elements, graceful degradation)Improved phase accurady (small-signal operation before amplifier)

Receive (RX)Adaptive amplitude and phase control for each individual radiating elementPhase → direction of main beam. Amplitude: Beam forming and null steering

TX-RX switching (duplex)Speed, power, circuit technology, MMIC solutions (Si, GaAs or SiGe)

Each radiating element equipped with its own amplifiers (RX and TX) → Maximal variability Maximal complexity

Arrays




Beam forming: Switched-beam N-element arrayArray provides set of M ≤ N predefined beams (e.g. sectorial antenna) Simple implementation (single frontend for entire array) Limited adaptivity (no beam forming)

Arrays

C.A. Balanis, „Antenna theory“, John Wiley, 1982.




Beam forming: Adaptive N-element array

Arrays

C.A

. Balanis, „A

ntenna theory“, John Wiley, 1982.

Frontend

Frontend

N complete frontends (RF to baseband),1 beamformerDigital signal processing (direction estimation, complex-weight pattern adaptation)




Beam forming: Spatial division multiple access (SDMA)

Arrays

C.A

. Balanis, „A

ntenna theory“, John Wiley, 1982.

N complete frontends (RF to baseband),M N beamformers Ultimate adaptivity (multiple adaptive subsystems) Ultimate complexity (signal processing, power consumption, size & weight)




Analog beam forming networks

vv

v

12

3

A

B• Provides amplitudes and phase gradients

for M N patterns• Low-loss. Matched. Wideband or selective.

Power transfer from feed into far field• Excites “independent” beams

No exchange of power, “orthogonality”• Analog HW implementation of a linear set of

equations (N+M) (N+M) matrix, function can be implemented in the digital domain

A1 A2 A3

B1 B2 B3

A1 B1

A2 B2

A3 B3

0 0 a a a0 0 a a a

a a 0 0 0a a 0 0 0a a 0 0 0

A B 1 2 3AB123

N-element antenna array → N different beams or N-1 different nulls

M-port beam forming network

Arrays

Losslessness: Orthogonality:N 2

ipi 1

S 1

N

*ni pi np

i 1S S

A Ba a 1 *

A Ba a 0

A lossless reciprocal network is orthogonal.

aAbA

a3b3




Fading minima depend strongly on antenna position:• Multiple displaced receive antennas beneficial (antenna arrays)• Risk of all antennas undergoing a deep fade simultaneously reduced• Signal optimised by coherent combination (e.g., maximum ratio combining)

Mitigating fading by spatial diversity with antenna arrays

CombinedAntenna 1 Antenna 2

Time or receiver position

SNR

(dB

)

Enhanced stability and reliability of the link

Arrays




No signal-strength fluctuationDistribution function: unit step

Diversity antennas: Statistical description of fading

Line-of-sight transmission (LOS)

Received power “fades” (fluctuates) upon movement of mobile stationRayleigh distribution function

Non-line-of-sight (NLOS)

Deep fades are less likelyRice-factor KDistribution functions "intermediate"

Combined LOS and NLOS fading

Arrays




Diversity antennas (Rayleigh fading)

Array size: N elements• SNR improves with N (link budget)• Probability for deep fades decreases

with N (link reliability and quality)Arrays

N 1 r

0

1CDF( ) r e dr(N 1)!




• Radiation matrix [H] = [1] – [S]H[S]• Efficiency

• Depends on feed vector (array element excitation, "illumination")• Determined by radiation matrix (S-parameters, radiation patterns)• Enables quantitative comparison of different arrays

Generalised efficiency

H

r adH

avail

P a [H]a(a)P a a

C. Volmer, Dissertation, Ilmenau 2009 Arrays

Radiation matrix of a lossless N-element antenna array




Diversity gain Gdiv• Given outage probability tolerated

by the radio link (e.g., 1%)• SNR-difference between N-element

array and single radiator at same probability (e.g., Gdiv,3(1%) = 16.3 dB for N = 3)

Gdiv,N(p) = Power that could be saved by spatial diversity – without affecting reliability nor coverage

16.3 dB • Approximationp

1

div,N

tr [H]qG (p) 1 qp N N 1

Nq N! p det [H]

C. Volm

er, Dissertation, Ilm

enau 2009

Arrays




Diversity loss Ldiv

• Accounts for radiation coupling

• Marks the SNR-difference between coupled diversity antenna (real) and fully decoupled version (ideal)

Mutual element coupling always reduces diversity gain

• Approximation

Ldiv

div,N10L (dB) log det [H] 0N

Arrays

C. Volm

er, Dissertation, Ilm

enau 2009

div,Ndiv,N

1L !G




Packaging issues of antennas

Transmission lineDefined by geometrical dimensions and material parameters (, , )Propagating modes: TEM (broadband), TE vs TM vs hybrid (low-/high-pass)

Practical aspects

Matching networkMatching of impedance, effective power, propagating modeLumped vs distributed vs hybrid (affects frequency, bandwidth, losses, size)

RadomeMechanical and environmental ruggedness, affects electrical properties

Example: Transmit antenna




Types of transmission lines (selection)

Strip transmission linesMicrostrip, slotline, coplanar waveguide, coplanar slot (Principle of duality, characteristic impedance, field concentration, power handling)

Hollow-tube waveguidesDifferent contours (e.g., rectangular, circular)Different cross-sections (e.g., ridged, fin-line)Different environments (substrate-integrated waveguides, via fences)

Coaxial linesPower handlingFlexibility vs dissipation losses

Wire transmission linesOpen and shielded geometries (simplicity vs performance)




Impedance matching using transmission line elements

Practical aspects

0 Lin L

L 0

Z cos jZ sinZ Z

Z cos jZ sin

/ Z0 = 0 (short circuit) Z0 → (open circuit)

< /2 < 1/4

= /2 = 1/4

< < 1/2

= = 1/2




Baluns: NecessityR

othamm

els Antennenbuch, 12. A

uflage (in Germ

an)http://de.w

ikipedia.org/wiki/B

aluneven mode

odd mode

Current distribution at unbalanced-balanced transition

Dipole radiation pattern with (top) and without balun (bottom)

Mode matching and/or suppression of ground currents required




Baluns: Types and example implementations

1 Differential transformers

2 Half-wave line baluns

3 Quarter-wave baluns (loop, collinear: Marchand)

4 Reactance networks (lumped elements, distributed line elements)

5 Radials, bazooka, coil baluns (suppress sheath currents)

6 Absorbers (ferrites)

Practical aspects

1 2 5

3 3

4 4 6




Antenna radomesFunction• Protective enclosure• Minimal impact on performance

Implementation• Sandwich, space frame,

dielectric, solid laminate• Ceramic and organic materials




Simulated influence of a radome (direction finding antenna at 950 MHz) on electromagnetic fields

Direction of propagation (plane wave)

Courtesy R

ohde & S

chwarz, D

r. M. P

auli, Nov. 2010




Radome materials (selection)

Practical aspects

MaterialMass density (g/cm3)

Dielectric permittivity r

Loss tangent103·tan

Al2O3/AlN 3.69 9.28 0.3

Aluminum oxide 3.32 7.85 0.5

Beryllium oxide 2.88 6.62 1

Boron nitride 2.13 4.87 0.5

Silica-fiber composite 1.63 2.90 4

Silicon nitride 2.45 5.50 3

Ceramics

Material (g/cm3) r 103·tanLexan 1.2 2.86 6

Teflon 2.2 2.10 0.5

Epoxy-E glass cloth 1.9 4.40 16

Polyester-quartz cloth 3.70 7

Quartz-reinforced polyimide 1.3 3.2 8

Duroid 5650 2.2 2.65 3

Organics and composites




Circuit analysis versus field simulation

Practical aspects

Circuit elements of uniform cross-section can be modeled by conventional circuit analysis (transmission line models), including simple types of discontinuities (steps, vias, ...)

Engineered transformations of field distributions and/or radiation effects require numerical field simulation




Classification of field problems

Practical aspects

Keyword Description

Electrical size Number of variables

DomainTime domain (broadband, switching)Frequency domain (resonant, high-Q)Related by FT in linear systems

BoundariesElectric (PEC, E, H||) Magnetic (PMC, H, E||) Space (matched, absorptive)

Dimensionality1d (transmission lines)2/2.5d (PCB, symmetric 3d problems)3d full complexity

3minN ~ /




Classification of simulation methods

Practical aspects

Keyword Description

General Procedure

Wave equations potentials fields parameters like impedance, gain/directivity/efficiency, radiation pattern, ...

Boundary conditions

Geometry Material(s)Ports (position, type)Excitation (current/voltage, E/H fields, modes)

Solver

Analytical: Closed form, simple problems, reference solution (e.g., Hertzian dipole)Semi-analytical: Integral expression numerical computation high computational efficiency(specific problems, limited validity, e.g., /2-dipole)Numerical: Wave equation @ discrete lattice, local interpolation




Finite-element method

Practical aspects

Complex and inhomogeneous field problems are split into homogeneous simple sub-structures with known solutions

Discretisation of a planar problem using a triangular mesh

Example for an Ansoft HFSS microstrip mesh

11 11 1

2 2 2 2

3 33 3

c 1 x yc 1 x y

1 x yc

212

V

| | dV min




Finite-difference time domain models

Practical aspects

Example FDTD grid, formed by brick-shaped hexahedral cells

Solution of wave equations on a discrete lattice (mesh)

2 2 2

2 2 2 0x y z

l 1,m,n l 1,m,n1

x 2h

l,m,n l 1,m,n l 1,m,n

l,m 1,n l,m 1,n

l,m,n 1 l,m,n 1

6 ...

... ...

... 0




Numerical simulation tools: summary

Practical aspects

FDTD FEM

ExampleCST Microwave Studio Many other codes available

Ansoft HFSSMany other codes available

Domain Time FrequencySolution Iterative time steps Matrix equationCell geometry Rectangular / cubic Triangular / tetrahedral

Advantages

Low memory requirementsEfficient for broadband problems and physical transitionsElectrically large geometries

Adaptive discretisation of complex structuresRapid computation for single frequency points (e.g. high-Q devices) and multi-port devices

Dis-advantages

Less efficient for curved structuresEach port requires separate simulation

Electrically small geometriesHigh memory requirementsCPU time increases with number of frequency points




Port modeling and mode matching

Practical aspects

Port parameters (mode specific) define incident power flowCurrents and voltages (circuit design) must be related to field parameters requires a reference path 1 for integration

cond

portI Hd

1 2 pathA

Ed j BdA 0

1

port

2

port 12

A

( Ed )Z

(E H*)dA




Input matchingReflection coefficient

Standing wave ratio

Return loss

Matching (Reciprocity)Voltage ratio

1 | |S1 | |

RL 20log | |

0

0

Z / Z 1Z / Z 1

1 1 2 2

1 1 2 2

RxFS AUT2 2

Tx T SA AUT R

V e et (1 )V 1 e 1 e

Practical aspects

0

5

10

15

20

25

30

0 2 4 6 8 10

Ret

urn

loss

RL

(dB)

Standing wave ratio S

S ~ 5.8

S ~ 1.9

S ~ 1.2




• Known reflections or none• Natural or artificial environment• Defined methods

(e.g., far/near field; frequency/time domain)

• Calibrated precision measurements (distances, power levels, phase centres, …)

Radiation measurements

Free space www.orbitfr.comAnechoic chamber (HMT)

"Virtual road" antenna and channel measurements (HMT)




Rad

iatio

n m

easu

rem

ent s

chem

es

http://ww

w.cuminglehm

an.com/pdf/m

ag.pdf (12.07.2017)

Rectangular anechoic chamber Compact antenna test range

Outdoor elevated range Ground reflection range

Planar near-field Cylindrical near-field Spherical near-fieldPractical aspects




Anechoic chamber measurementsReflections damped by absorbers (-30 ... -50 dB)Absorber: Height reflects wavelength, shape matches impedance (free space – metal shield)Chanber size: Far field conditions, constant amplitude under rotation Specific adaptations w.r.t. frequency ranges and test specs

Practical aspects

http://ww

w.m

vg-world.com

/en/products/field_product_family/absorber-6 12.07.2017

ECCOSORB® HHP-60-NRL




From near field to far field

Near field: reactive (stored energy)Far field: plane waves (E H z)

Rayleigh Fresnel Fraunhofer

Electrically small antennas:rff / < 1

Given value of D/ 1/2: rff / ≈ 1

High gain:rff / 1

Example: parabolic reflector antenna

2ffr D2

22

parabolDG

ffparabol2

r 2 G

Practical aspects




Radiation measurement uncertaintiesMajor influencesMeasurement setup Quiet zone, electrical distance, calibration, dynamic range, e.g. for high frequenciesNear field Region ≈ , environmental effects, e.g. SARNon-idealities Phase centre variation upon rotation, parasitic radiation from cables, shadowing from positioner, calibration

Require careful adjustment and critical analysisPractical aspects

H. Eder, A. Wiedenhofer, http://www.mobilfunkundschule.bayern.de, 2012

After Jeffrey A. Fordham, Microwave Instrumentation Technologies, LLC




Examples of measured radiation patterns

Commercial GNSS antennaTallysmanTM TW3870

Graphical display of measured data: AUT Studio, www.lisa-analytics.de

Polar

Cartesian

Elevation Azimuth




Doppelsteg-Hornantenne (im Prinzip für große Bandbreiten geeignet)

Examples of measured radiation patterns (UWB)U

. Schw

arz, TU Ilm

enau, Dissertation in Vorbereitung (2008)

Practical aspects




Dispersion: frequency dependent impulse responsesRadiation patterns in time domain

W. W

iesbeck, „Ultrabreitbandantennen“, KIT, 2008

Non-resonant(Vivaldi)

Resonant(Log-periodic)

E-plane H-plane

time(ns)

Azimuth (deg)Practical aspects




G/T-measurements

G – Antenna gainTsys – System noise temperature – Power flux1 sfu = 10-22 W/m2Hz

N,B2

sys N,0

PkG 4 1T P

Data (Sun)Power flux of the sunData updated on daily basisFrequency specific analysis

Other astronomic radiating sources:Cassiopeia A, 3Cxyz, Cygnus A, ... Practical aspects

http://www.ips.gov.au/Solar/3/4 (12.07.2017)

101

102

103

102 103 104Sol

ar fl

ux

S(f)

in "s

olar

flux

uni

ts"

Frequency f (MHz)

Steady contribution (quiet solar)Learmonth /Australia

22.01.200427.01.200626.01.200710.07.200809.07.200903.04.201029.06.201012.07.201110.07.201208.07.201304.07.201413.07.201511.07.201612.07.2017

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Antenna Engineering - Startseite TU Ilmenau Engineering Prof. Dr. M. Hein Summer semester 2017 RF &...

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