introduction to antennas dr costas constantinou school of electronic, electrical & computer...

Introduction to Antennas

Dr Costas ConstantinouSchool of Electronic, Electrical & Computer Engineering

University of BirminghamW: www.eee.bham.ac.uk/ConstantinouCC/

E: c.constantinou@bham.ac.uk

2

Recommended textbook

• Constantine A. Balanis, Antenna Theory: Analysis and Design, 3rd Edition, Wiley-Interscience, 2005; ISBN:0-471-66782-X– Chapters 1 & 2

3

Antennas

• An antenna can be thought of as a transition / transducer device

• Two ways of describing antenna operation– Field point of view– Circuit point of view

4

Antenna examples

• Wire antennas– Monopoles– Dipoles– Arrays

5

Antenna examples

• Aperture Antennas– Reflectors– Lenses– Horns– Patches– Planar inverted F

6

Antennas

• Most antennas are resonant structures– Narrowband– Size is inversely

proportional to frequency of operation

• Travelling wave antennas also important– Wideband– Size dictates lowest

frequency of operation

1000 ft diameter; 50 MHz to 10 GHz

chip size = 2 x 1 mm2; 60 GHz antenna

7

How does it work? – radiation

8

How does it work? – radiation

9

How does it work? – radiation

10

How does it work? – radiation

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How does it work? – radiation

B

A

Sphere grows with time (i.e. delay increases with distance)

12

How does it work? – radiation

13

Source: MIT Open Courseware

How does it work? – radiation

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Source: MIT Open Courseware

How does it work? – radiation

15

Antennas – TV aerial• Radiation of power in space can be controlled by

carefully arranging the patterns of electron motion• This is the same as their sensitivity to received signals

from different directions in space

16

Fundamental antenna parameters

• Radiation pattern; radiation power density; radiation intensity

• Beamwidth; directivity; sidelobe levels• Efficiency; gain• Polarisation• Impedance• Bandwidth• Vector effective length and equivalent area• Antenna temperature

17

Radiation pattern

• A mathematical and/or graphical representation of the properties of an antenna, usually the radiation intensity vs. spatial direction coordinates sufficiently far from the antenna

• Is polarisation specific• Spherical polar coordinates

are always usedSource: C.A. Balanis©

18

Radiation pattern

Polar pattern

Linear pattern

Source: C.A. Balanis©

19

Radiation pattern

Linear pattern

Source: C.A. Balanis©

E plane is plane of electric field H plane is plane of magnetic fieldIf field direction not known, do not use E or H plane

20

Omnidirectional antenna radiation pattern

H-plane E-plane

λ/2 dipole antenna radiation pattern

Source: C.A. Balanis©

21

Radiation pattern definitions

• Isotropic antenna– Radiates equally in all directions in space; physically

unrealisable• Omnidirectional antenna– Radiates equally in all directions in one plane only; e.g.

dipoles, monopoles, loops, etc.• Directional antenna– Radiates strongly in a given direction; has a principal or

main lobe, the maximum of which point in the direction of the antenna’s boreside

– Can you guess what is meant by front-to-back ratio?

22

Field regions• Reactive near-field

– Phases of electric and magnetic fields are often close to quadrature

– High reactive wave impedance– High content of non-propagating stored

energy near the antenna

• Radiative near-field (Fresnel)– Fields are predominantly in-phase– Wavefronts are not yet spherical; pattern

varies with distance

• Radiative far-field (Fraunhofer)– Electric and magnetic fields are in-phase– Wavefront is spherical; field range

dependence is e-jkr/r

– Wave impedance is real (Eθ/Hφ = 120π = 377 Ω)

– Power flow is real; no stored energy

• Field regions have no sharp boundariesSource: C.A. Balanis©

23

Reminder on angular units

RadiansSteradiansFor the whole sphere,

2 2

0 0 0 0

0

sin sin

2 cos 2 1 1

4 Sr

d d d d

Source: C.A. Balanis©

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Radiation power intensity and density

• Poynting vector

• Time-averaged Poyting vector

• Radiation power density

• Radiation intensity

• Total radiated power

2Wm S E H

* 21Re Wm

2 S E H

2m, WW S

2rad avg

22*

rad

0 0

1ˆRe .

2

ˆ. .

sin

r

r

P P d r d

P r d d

E e

S e

H

A S

2, W/SrU r W

25

Directivity

avg rad

max maxmax

0 rad

10 max

, 4 ,,

4

dB 10log dimensionless

U UD

U P

U UD

U P

D D

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Directivity

• Isotropic antenna

• Current element L << λ

max 1 or 0dBavgU U D D

2max, sinU U

23 2

rad max max

0 0 0

12

max max

1

sin 2 sin sin

82 1

3

P U d d U d

U u du U

max ma

max

maxrad

x

max

31.76dB

2

4 483

U UD D

UD

Por

27

Directivity

• Half wave dipole L = λ/2 2

2max

cos cos,

sinU U

222

rad max

0 0

22

max

0

max

cos cossin

sin

cos cos2

sin

2 1.22

P U d d

U d

U

max maxmax

rad maxmax

4 4

1.221.6

24 2.15dB

U UD

P UD or D

28

Beamwidth

• Current element L << λ• The half-power angles in E-plane are given by,

• Halfwave dipole – a similar numerical calculation for the two roots of

2max, sinU U

23dB max max 3dB

3dB 3dB,1 3dB,2

3dB,2 3dB,1

1, sin

21 3

sin ,

9

42

0

4

U U U

HPBW

2 3dB

3dB

cos cos 1

sin 278HPBW

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Beamwidth vs. directivity

• The narrower the beamwidth of an antenna, the bigger its directivity

• For a single main beam antenna where ΩA is the main lobe half power beam solid angle

• Kraus approximation for non-symmetrical main lobes

• Tai & Pereira approximation for non symmetrical main lobes

max 4 AD

max1 2 1 2

4 41,253

r r d d

D

max 2 2 2 21 2 1 2

32ln 2 72,815

r r d d

D

Source: C.A. Balanis©

30

Antenna efficiency, ηant

• In an antenna, we experience reduction in radiated power due to– Reflection at the input

terminals (impedance mismatch)

– Ohmic conductor losses (c) in the antenna conductors

– Dielectric losses (d) in the antenna dielectrics

– The latter two are grouped under the term antenna radiation efficiency

2

ant in1 c d

radrad

inc d

P

P

Source: C.A. Balanis©

Typical antenna efficiency valuesDipole ηant ~ 98%Patch antenna ηant ~ 90%Mobile phone PIFA ηant ~ 50%

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Antenna Gain

in

max max

10 max

4 ,, ,

dB 10log dimensionless

a

a

UG D

P

G D

G G

Antenna Absolute Gain 2

abs in, 1 ,aG D

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Bandwidth

• Many properties vary with frequency and deteriorate in value from their optimum values:– Pattern bandwidth

• Directivity/gain• Sidelobe level• Beamwidth• Polarisation• Beam direction

– Impedance bandwidth• Input impedance• Radiation efficiency

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Polarisation

• Antenna polarisation refers to the orientation of the far-field radiated electric field vector from the antenna– A vertical dipole radiates a vertical electric field– A horizontal dipole radiates a horizontal electric field– A general (e.g. horn) antenna with a vertical aperture

electric field radiates a vertical electric field in the E-plane and H-plane only; everywhere else the electric field vector is inclined to the vertical and changes with angular direction

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Polarisation

• The polarisation of an electromagnetic wave can be– Linear (as in all previously discussed examples)– Circular (e.g. using a helical antenna to transmit)– Elliptical (e.g. circular after reflection from a lossy

interface)• Circular and elliptical

polarisations have a sense of rotation– Positive helicity (or right hand, clockwise)– Negative helicity

Source: C.A. Balanis©

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Polarisation

Source: C.A. Balanis©

1

OAAR

OBAR

Axial ratio,

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Polarisation

• Linearly polarised uniform plane wave (E0x and E0y real)

• Circularly polarised uniform plane wave (+/- corresponding to positive/negative helicity)

• Elliptically polarised uniform plane wave (+/- corresponding to positive/negative helicity; E0x and E0y real)

00 0ˆ ˆ, , , Re jk zj t

x x y yx y z t E E e e E e e

00 ˆ ˆ, , , Re jk zj t

x yx y z t E j e e E e e

00 0ˆ ˆ, , , Re jk zj j t

x x y yx y z t E E e e e E e e

0 0 0 0, , , 2 12x y x yE E n E E n or

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Polarisation• The radiation pattern performance of

antennas is often specified in terms of its co-polar and cross-polar components– Detailed mathematical definition is

Ludwig’s 3rd definition of cross-polarisation (A. Ludwig (1973), “The definition of cross polarization,” IEEE Transactions on Antennas and Propagation, 21(1))

– Co-polar radiation pattern of an antenna is measured with a suitably polarised probe antenna which is sensitive to the “wanted” polarisation

– Cross-polarised pattern is measured for linear polarisation by rotating the probe antenna by π/2 around the line joining the two antennas, or for circular/elliptical polarisation by changing the probe antenna helicity sign

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Impedance

• Transmitting operation • Receiving operation

generator(Zg = Rg + jXg)

receiver

(Zrx)

Thevenin equivalent circuit (suitable for electric radiators, e.g. monopole, dipole, etc.)

Norton equivalent circuit (suitable for magnetic radiators, e.g. loop, etc.)

RL

XA

Rr

Rg

Xg

Vg

a

b

Ig

RL

XA

Rr

Rrx

Xrx

a

b

Ia

Va

Ig Gg Bg Gr GL BA

a

b

Grx Brx Gr GL BA

a

b

Ia

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Impedance

• The antenna operation is characterised by an impedance ZA

– An equivalent radiation resistance, Rr

– A loss (ohmic and dielectric) resistance, RL

– A reactance, XA

• When connected to a generator, usually via a transmission line, the usual transmission line and circuit theories apply

• Radiated power• Maximum power transferred from generator to antenna

(maximum power transfer theorem)

• Half of generator power is consumed intenally, other half is shared between antenna losses and antenna radiation

212r g rP I R

&A r L g A gR R R R X X

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Impedance

2

2

2

2

2

2

8

8

;

1

8

4

g rr

r L

g LL

r L

r L g A g

g

r L gr L

g

T g r Lr L

V RP

R R

V RP

R R

R R R X X

VP P P

R R

VP P P P

R R

Since

Total

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Radiation efficiency

• We have come across radiation efficiency before, but now we express it in circuit theory equivalent terms

• Describes how much power is radiated vs. dissipated in the antenna

radr

r L

R

R R

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Antenna effective length

• The voltage at the antenna terminals is determined from the incident field

• The effective length is a vector

• When taking the maximum value over θ,φ this becomes

• For linear antennas

. . ,i ia OC e

C

V V E dl E l

.ia eV E l

physicale l Source: C.A. Balanis©

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Effective aperture area Ae

• This is usually assumed to refer to the co-polar radiation pattern on the boreside of an antenna

• The antenna effective aperture area is defined as a ratio

– PT is the power delivered to a matched load in W

– Wi is the incident wave power density in Wm–2

– Ae is the antenna effective aperture area in m2

• For any passive antenna we can invoke the principle of reciprocity to show that

Te

i

PA

W

2

4Tx

Rxe

G

A

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Antenna aperture efficiency

• For all aperture antennas

• This allows us to introduce the concept of antenna aperture efficiency

• For aperture antennas• For wire antennas where the physical aperture is taken

to be the cross sectional area of the wire

physicaleA A

physical

ea

A

A

1a 1a

45

Friis free-space transmission

• From your propagation lectures, assuming matched antennas,

• This expression is a statement of the principle of conservation of energy coupled with the notions of antenna gain and antenna effective aperture area

24Rx

Tx RxTx

P dG G

P