Analysis of Hertzian Dipole

Analysis of Hertzian Dipole

Antenna Antenna EngineeringEngineering

CHO, Yong HeuiCHO, Yong Heui


EM Wave LabEM Wave Lab2

E and H fields

1. Field analysis

Vector potential

Vector potential approach

AB

V

jkR

VdJR

eA

4

222 )()()( zzyyxxrrR

AH 1

Hj

E 1



Hertzian dipole

1. Field analysis

Current density approximation

2/2/for

ˆ)()(

zzz

zyxIJ



Vector potential

1. Field analysis

Current vs. vector potential

zr

zeI

zIdR

ezA

jkr

z

z

z

jkR

ˆ4

4ˆ

0

2/

2/

sin

cos

z

zr

AA

AA



H field

1. Field analysis

ˆsin1

4

1ˆ11

rjk

r

zeI

ArArr

AH

jkr

r



E field

1. Field analysis

ˆsin1

4

ˆcos12

1ˆsinsin

1ˆ

1

1

2

2

kr

j

rjk

r

zeI

rkr

j

r

zeI

rHrr

Hrr

j

Hj

E

jkr

jkr



Electric dipole moment

1. Field analysis

Current vs. electric dipole moment

dt

dp

dt

zdQz

dt

dQzI



Far-field

1. Field analysis

Dr

ˆsin4

jkr

zeIH

jkr

ˆsin4

jkr

zeIE

jkr

*Re2

1HES



Radiated power

1. Field analysis

2

22

0 0 2

22

22

*

3

sinsin

42

sin42

1

2

1

Re2

1

zI

ddrr

kzI

dSjkr

zeIdSH

SdHEP

S

jkr

S

Sr



Radiation resistance

1. Field analysis

rr RIzI

P2

2

2

1

3

2

3

2

zRr

Open transmission line

)2/cot(0in zjZZ



Simple calculation

1. Field analysis

Far-field calculation

r

zeIA

jkr

z

4

zz AjE sinzEE

ErH ˆ1



Radiation pattern

1. Field analysis

Power and field pattern dB scale: Half-power beamwidth: Main beam:

sin),( E

sin),( H

2sin),( rS

22Dr

Far-field condition: phase condition

9090(BW)3dB

),(log10 10 rS



Antenna gain

1. Field analysis

Directivity: 3/2 for Hertzian dipole Gain and efficiency Isotropic radiation dBi

DG

lossloss RR

R

PP

P

r

r

r

r

210

44),(

rP

U

U

UD SrU 2



(Lorentz) Reciprocity theorem

1. Field analysis

The same propagation characteristics: Tx and Rx

Antenna measurement

1I 2V

1V 2I

21Z

12Z

1221 ZZ



Antenna characteristics

Antenna gain: anisotropic radiation (G > 1)isotropic radiation (G = 1)

Directivity and efficiency: Angular beamwidth: 3dB

Radiation pattern [dBi]: dB isotropic

DG

1. Field analysis



Friis power transmission formula

Microwave radio link

R

tP rP

2. Microwave link



Transmitted power

Power density:

EIRP (Effective Isotropic Radiated Power)

Radiation pattern [dBi]: dB isotropic

22

/4

mWGR

PS t

t

2. Microwave link

tP

ttGPEIRP



Received power

Received power:

Effective area

-

er SAP

4

2r

e

GA

WR

GGP

Prt

t

r

2

4

Friis transmission formula

2. Microwave link



Effective area

Reciprocity theorem:

Effective area:

1221 AGAG

2. Microwave link

er SAP

22

rms1 8

3

4

SR

V

S

PA

r

r

r

rr R

VRIP

44

2rms

2rms zEV rmsrms

2rmsE

S

2

31 G

4

22

2

GA



Free space loss

Free space loss:

Received power

2

FS

4

R

L

]dB[EIRP FS rr GLP

WL

GG

P

P rt

t

r

FS

2. Microwave link



0.6

dishdiameter 4

]GHz[14

]W[100

m

f

P

u

t

0.55

2

]GHz[12

]W[10

3dB

θ

f

P

d

t

Uplink and downlink

2. Microwave link

][000,40 kmR



tt

et

tt

DG

AD

GP

2

4

EIRP

Uplink calculation

2. Microwave link

rr

r

DG

D

21

4

2

FS

4

R

L

]dB[EIRP FS rr GLP



rr

r

DG

AD

max2

4

Downlink calculation

2. Microwave link

tt

t

tt

DG

D

GP

21

4

EIRP

2

FS

4

R

L

]dB[EIRP FS rr GLP



Noise power

Thermal noise: white noise, Nyquist formula

Thermal noise

BNN

kTBPn

0

Noise temperature

kB

NT

2. Microwave link



Carrier to noise ratio

TkB

C

BN

C

N

C

0

C/No: related to carrier to noise ratio G/T: Figure of merit

Carrier to noise ratio

]dB[EIRP FS rGLC

G/T: sensitivity of receiver

2. Microwave link

Date post:	07-Dec-2014
Category:	Technology
Upload:	yong-heui-cho
View:	5,416 times
Download:	3 times

Analysis of Hertzian Dipole

Technology