Small loop antenna (magnetic dipole)

Dipole antenna generates high radiation resistance and efficiencyFor far field region,

where

0cos( cos ) cos( )

2 22 sin

j rl l

I eH j a

r

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202

15( , ) ( ) ,r

IP r F a

r

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2

cos( cos ) cos( )2 2( )

sin

l l

F

max

( )( )

( )n

FP

F

Half-wave dipole2

2max

cos ( cos )( ) 2( )( ) sinn

FP

F

p = 7.658, Dmax = 1.64, Rrad = 73.2

Image theory is employed to build a quarter-wave monopole antenna.

4

5

6

Monopole antenna is excited by a current source at its base.

Directivity is doubled and radiation resistance is half of that of dipole antenna.

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The best operation: ground is highly conductive (or use counterpoise in case of remote antenna)

Shorter than /4 antenna arises highly capacitive input impedances, thus efficiency decreases.

Solution: inductive coil or top-hat capacitor

Inductive coil Top-hat capacitor

A group of several antenna elements in various configurations (straight lines, circles, triangles, etc.) with proper amplitude and phase relations, main beam direction can be controlled.

Improvement of the radiation characteristic can be done over a single-element antenna (broad beam, low directivity)

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To simplify,1. All antennas are identical.2. Current amplitude is the same.3. The radiation pattern lies in x-y

plane

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From

Consider ,

00 sin ,

4

j rIl eE j a

r

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2 0

0 .4

j rIl eE j a

r

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Let I1 = I0, I2 = I0ej,

since r1 and r2 >> d/2 for far field,

we can assume 1 2 and r1 r2 r.

10

1 21 0 2 0

1 24 4

j r j r

totI l I le e

E j a j ar r

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11

0 20 2 cos( cos )4 2 2

j r j

totI l e d

E j e ar

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But the exponential terms cannot be approximated, then

1 cos2d

r r

2 cos2d

r r

2 2 2

20 02 2( , ) 4cos ( cos )

2 232r

I l dP r a

r

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We can write this as

Funit = a unit factor or the maximum time-averaged power density for an individual element at

Farray = array factor =

whereThis depends only on distance d and relative current phase, .We can conclude that the pattern function of an array of identical elements is described by the product of the element factor and the array factor.

12

( , , )2

runit arrayP r F F a

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2

24cos ( )2

cos .d

We will simplify assumptions as follows:1. The array is linear, evenly spaced along the

line. 2. The array is uniform, driven by the same

magnitude current source with constant phase difference between adjacent elements.

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2 3 ( 1)1 0 2 0 3 0 4 0 0, , , ,...j j j j N

NI I I I e I I e I I e I I e

2 ( 1)00 (1 ... )4

j rj j j N

totI l e

E j e e e ar

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2

2

sin ( )2

sin ( )2

array

N

F

(Farray)max = N2

Yagiuda (rooftop antenna)

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Parasitic elements are indirectlydriven by current induced in themfrom the driven element.

Consider power transmission relation between transmitting and receiving antennas where particular antennas are aligned with same polarization.

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Let Prad1 be Ptotal radiated by antenna 1 have a directivity Dmax1,

11 max12( , , )

4radPP r Dr

12 1 2 max1 22( , , ) .

4rad

rec

PP P r A D A

r

With reciprocal property,

Therefore, we have

21 2 1 max2 12( , , ) .

4rad

rec

PP P r A D A

r

max1 max2

1 2

.D DA A

Each variable is independent of one another, so each term has to be constant, we found that

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max1 max22

1 2

4.

D DA A

Effective area (Ae) is much larger than the physical cross section.

More general expressions

We can also write

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22

1( , , )rec

e

PA

P r

2 ( , ) ( , )4rad

rec t r

PP D A

r

2

( , ) ( , ) .4

rect r

rad

PD D

P r

Finally, consider Prad = etPin, Pout = erPrec, and Gt = etDt, Gr = erDr

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2

( , ) ( , ) .4

outt r

in

PG G

P r

Friis transmission equation

Note: Assume - matched impedance condition between the transmitter circuitry/antenna and receiver

- antenna polarizations are the same.

Additional impedance matching network improves receiver performances

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2 2

2( ) 4oc oc

recant in rad

V VP

Z Z R

in antZ Z

Since the receiver is matched, half the received power is dissipated in the load, therefore

Without the matching network,

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212 2

Lrec

L

VP

Z

.LL oc

L ant

ZV V

Z Z

A monostatic radar system Some of energy is scattered by target so called

‘the echo signal’ received at the radar antenna.

Let Prad be the radiated power transmitted by the radar antenna, then the radiated power density P1(r, , ) at the target at the distance r away is

The power scattered by the target is then

s = radar cross section (m2)

11 2( , , ) ( , )

4radPP r Dr

2 1( , , )rad sP P r

This scattered power results in a radiated power density at the radar antenna of

Then

By manipulation of these equations, we have

or

2 12 2 2 2( , , ) ( , )

4 (4 )rad rad

s

P PP r D

r r

1 2 ( , , ) .rec eP P r A

221

3 41

( , )4

rec s

rad

PD

P r21

4 21

.4

rec se

rad

PA

P r

Radiation patterns for dipole antenna

http://www.amanogawa.com/archive/DipoleAnt/DipoleAnt-2.html

Ex1 Suppose a 0.5 dipole transmitting antenna’s power source is 12-V amplitude voltage in series with a 25 source resistance as shown. What is the total power radiated from the antenna with and without an insertion of a matching network?

0.5