1

EMLAB

Antennas

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EMLAB

Hertzian dipole antenna

Heinrich Hertz (1857-1894)

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EMLAB

Schematic diagram of Hertz’ experiment

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EMLAB

Electric field : red

Magnetic field : blue

Propagation of electromagnetic wave

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EMLAB

V

Reception of EM wave

current

Transmitting antenna Receiving an-

tenna

E

The charges on the receiving antenna move toward the antenna terminal, which causes voltage drop across them.

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EMLAB

E

H

J

Example – Radiation from current filament

R

S

t

SR

ej

jkR

4

][

4)ˆ(ˆ)(

J

JRRJrE

)]/(ˆ[ˆ)/(][ crtcrt JRRJJ

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EMLAB

Example – Radiation from a dipole antenna

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EMLAB

Far field radiation from a dipole antenna

2/

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EMLAB

Example – Radiation from current loop

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EMLAB

Radiation from a tapered transmission line

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EMLAB

Dipole antenna - resonance

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EMLAB

Example of resonance

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EMLAB

Advantage of a resonant circuit

CLjR

VI S

1

SCSLS

R VCRj

VVR

LjV

R

VI

1

,,

SVCRR

LQ

1

SC VQV SL VQV

At resonance

SSCL VVQVV

Generate higher voltage than input voltage.

Maximum current level depends on internal resistance.

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EMLAB

How to generate time varying currents

Electronic circuit generate oscillating voltages

Output voltage

Alternating currents accel-erate electrons which emit electromagnetic waves propagating in perpendicu-lar direction

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EMLAB

Antenna types

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EMLAB

Radiation from an infinitesimally small current segment

V

jkR

dR

kRjkR

R

kRjkR

R

e

k

j

)()(33)(1

4),( 4

2

2

2

2 JRRJrE

Exact solution :

V

jkR deR

jkR

2

1ˆ4

1),( JRrH

22 f

k

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EMLAB

V

jkR

dR

ej

4)ˆ(ˆ)( JRRJrE

V

jkR

dR

ejk

)ˆ(

4)( JRrH

Far field approximation

Electrostatic solution

V R

d2

ˆ

4

11),(

RJArH

Vd

R

24

ˆ)(),(

RrrE

Biot-Savart’s law

)0( k

Coulomb’s law

V dtR

)]ˆ(ˆ[4

1JRRJE

)1( kR

V

jkR

dR

e

j

)ˆ(ˆ

4

1),(

3JRRJrE

V

jkR

dR

e

2

ˆ4

1),( JRrH

Near field approximation )1( kR

ER

H

ˆ

Vt

jkR

dtdR

e

)]ˆ(ˆ[4

13

JRRJE

ERH ˆRj

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EMLAB

Radiation pattern of an infinitesimally small current

R

ezIjd

R

ej

jkR

V

jkR

4sinˆ

4)]ˆ(ˆ[

JRRJE

sinˆ)cosˆˆ()ˆ(ˆ

ˆ

00

0

JzJ

Jz

rJrrJ

J

ˆ

ˆˆ

0sincos

cossincossinsin

sincoscoscossin

ˆ

ˆ

ˆ r

z

y

x

z

r

sinz

I

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EMLAB

Isotropic pattern

Omnidirectional pattern

Directional pattern

Gain and directivity of an antenna

0

),(),(

U

UD

in

radrad P

P),(),( DG rad

: Gain takes into account losses and reflections of the antenna.

Directivity 정의 :

(Efficiency)

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EMLAB

][W/m 4

22

T

r

PSaverage

][W/m 4

),(),(),( 2

2T

R

GPGSS average

TRT

eTT

eTr PR

GGA

R

GPASP

2

2

2 )4(

),(),(),(

4

),(),(),(

][T WGPEIRP T

Friis equation

transmitter receiver

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EMLAB

Example – half wavelength dipole antenna

cos)ˆˆ()ˆˆ(222 zrrrrrrrR rrrrrr

z

o

C

zjkjkr

V

jkR

zdezJr

ej

dR

ej

cos)(4

sin

4)ˆ(ˆ)( JRRJrE2/l

2/l

02/)2/(sin

2/0)2/(sin)(

0

0

zlzlkI

lzzlkIzJ

2coscos

2cos

2sin 0 klkl

r

eIj

jkr

rr ˆr

rr ˆr

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EMLAB

Array antenna

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EMLAB

r

z

z

o

r

R

cosz

cos)ˆˆ()ˆˆ(222 zrrrrrrrR rrrrrr

zrr ˆr

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EMLAB

C

zjkjkr

C

rjkjkr

zdezJr

ejdezJ

r

ej

cos)ˆˆ( )(

4sin)(

4sin)( rrrE

N

n

njn

N

n

dnjkn eIeIAF

11

cos Array factor :

Array factor

1I

2I

3I

1z

2z

3z

4z

x

y

z

4I

r

z-directed arrayrr ˆr

rr ˆr

d

),cos( jnnn eIIkd

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EMLAB

N

n

xjkn

jkrN

nn

neIer

klj

0

cos

0total sin

4ˆ

θEE

d

z

x0I 2I

xl

1I

d

Array factor

0x 1x 2x

x-directed array

Top view

1R 2R

1 2

1r 2r

r

Ox

r

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EMLAB

Typical array configurations

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EMLAB

How to change currents on elementary antennas?

Magnitudes and phases of currents on elementary antennas can be changed by amplifiers and phase shifters.

N

n

dnjkneIAF

1

cos

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EMLAB

Huygens principle

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EMLAB

Equi-phase surface

Equi-phase surface

,1,1,1,1,1 44

33

2210

jjjj eIeIeIeII

Pattern synthesis

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EMLAB

1R 2R

1 2

1r 2r

r

Ox

r

(1) Two element array

2,1,1 10

dII

10

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180 0

10

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180 0

,12

,1,1

10

10

II

dII

(2) Two element array

Examples

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EMLAB

10

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180 0

10

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180 0

(3) Five element array

,2

.1,1,1,1,1 44

33

2210

d

eIeIeIeII jjjj

(4) Five element array

0,2

.1,1,1,1,1 44

33

2210

d

eIeIeIeII jjjj

(5) Five element array

0,8.0

.1,1,1,1,1 44

33

2210

d

eIeIeIeII jjjj

10

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180 0

3dB Beamwidth

Beam direction

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EMLAB

phi=0:0.01:2*pi; %0<phi<2*pik=2*pi;d=0.5;% 0.5 lambda spacing.shi=k*d*cos(phi); alpha = pi*0.0;beta = exp(i*alpha);%Currents=[1,2*beta, 3*beta^2,2*beta^3,1*beta^4]; %Current excitationsCurrents=[1, 1*beta, 1*beta^2, 1*beta^3,1*beta^4]; %Current excitations E=freqz(Currents,1,shi); %E for different shi values E = DB(E)+30; % 최대값에서 30dB 범위까지 그림 .E = (E>0.).*E; polar(phi,E); %Generating the radiation pattern

Sample MATLAB codes

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EMLAB

N-element linear array antenna

Uniform Array : Magnitudes of all currents are equal. Phases increase monotonically.

cosd

z

d

d

d

1r

cosd

2r3r

4r

Nr

1

2

3

4

N

y

1 cos1cos2cos

1

cos1

kdNjkdjkdj

N

n

kdnj

eee

eAF

)cos (

1

1

kd

eAFN

n

nj

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EMLAB

121 Njjj eeeAF

)2/sin(

)2/sin(2/)1(2/2/

2/2/2/

2/

Ne

ee

ee

e

eAF Nj

jj

jNjNjN

j

jNNjjjj eeeeAFe 12

Difference :

j

jNjNj

e

eAFeAFe

1

1 1)1(

)2/sin(

)2/sin(

N

NAF

• Universal Pattern is symmetric about y = .p

• Width of main lobe decrease with N

• Number of sidelobes = (N-2)

• Widths of sidelobes = (2π/N)

• Side lobe levels decrease with increasing N.

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EMLAB

Visible and invisible regions

kdkd 0

Array Factor 의 특성

Array factor has a period of 2 p with re-

spect to ψ.

Of universal pattern, the range covered by

a circle with radius “kd” become visible

range.

The rest region become invisible range

)2()( AFAF

2

1

1

1coskd

kd

visible region

2nAF

Visible range of the lin-

ear array

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EMLAB

Grating Lobes Phenomenon

2

122 dkd

If the visible range includes more than

one peak levels of universal pattern,

unwanted peaks are called grating

lobes.

To avoid grating lobes, the following

condition should be met. 2

1)(f

1

1coskd

kd2

visible region

grating lobes

major lobe

They have the same strength !

2

Example :2

1/22 and For dkd , no grating lobe occurs

1/2 and 0For dkd , no grating lobe occurs

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EMLAB

77GHz 에서 array element 들이 모두 동위상을 갖도록 설계함 .

10mm

17mm

두께 0.127mm비유전율 2.2

표면 전류 분포

Example : array antenna (77GHz)

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EMLAB

Radiation pattern (77GHz)

elementary pattern

Radiation pattern of 8-element array

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EMLAB

Automotive radar antenna

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EMLAB

Analog beamforming : phase shifter

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EMLAB

LPF A/D

DigitalSignal

Processing(Amplitude

&Phase)

~

Desired signal

direction

LPF A/D

LPF A/D

LPF A/D

Interference or

multipath

signal direction

Beamforming Approaches : Digital Beamformer (DBF)