Notes 21

Introduction to Antennas

1

ECE 3317 Applied Electromagnetic Waves

Prof. David R. Jackson Fall 2018

Introduction to Antennas

Antennas

An antenna is a device that is used to transmit and/or receive an electromagnetic wave.

Examples:

Cell-phone antenna (transmit and receive) TV antenna in your home (receive only) Wireless LAN antenna (transmit and receive) FM radio antenna (receive only) Satellite dish antenna (receive only) AM radio broadcast tower (transmit only) GPS position location unit (receive only) GPS satellite (transmit only)

Note: The antenna itself can always transmit or receive, but it may be used for only one of these functions in an application.

2

Introduction to Antennas (cont.)

For communication over long distances, to have lower loss (see below)

Where waveguiding systems (e.g., transmission lines) are impractical or inconvenient

When it is desired to communicate with many users at once

Antennas are often used for a variety of reasons:

Power loss from waveguiding system:

Power loss from antenna broadcast: 21/ r2 re α−

(always better for very large r)

3

rA B

Main properties of antennas:

Radiation pattern Beamwidth and Directivity (how directional the beam is) Sidelobe level Efficiency (power radiated relative to total input power) Polarization (linear, CP) Input Impedance Bandwidth (the useable frequency range)

4

Introduction to Antennas (cont.)

Reflector (Dish) Antenna

Very high bandwidth Medium to high directivity (directivity is determined by the size) Linear or CP polarization (depending on how it is fed) Works by focusing the incoming wave to a collection (feed) point

5

Ideally, the dish is parabolic in shape.

Introduction to Antennas (cont.)

Dipole Wire Antenna

Very simple Moderate bandwidth Low directivity Omnidirectional in azimuth Most commonly fed by a twin-lead transmission line Linear polarization ( Eθ , assuming wire is along z axis) The antenna is resonant when the length is about one-half free-space wavelength

Current

0 / 2L λ≈

6

(resonant)

Introduction to Antennas (cont.)

[ ]73inZ = ΩAt resonance :

Dipole Wire Antenna (cont.)

7

Introduction to Antennas (cont.)

The bow-tie antenna has flared dipole arms, which increases the bandwidth.

Folded Dipole Antenna

8

Introduction to Antennas (cont.)

The folded dipole is a variation of the dipole antenna. It has an input impedance that is 4 times higher than that of the regular dipole antenna.

[ ]292inZ = ΩAt resonance :Compatible with TV twin lead

[ ]0 300Z = Ω

Monopole Wire Antenna

This is a variation of the dipole, using a ground plane instead of a second wire.

Similar properties as the dipole Mainly used when the antenna is mounted on a conducing object or platform Usually fed with a coaxial cable feed

9

Introduction to Antennas (cont.)

Feeding coax

0 / 4h λ≈h

[ ]36.5inZ = ΩAt resonance :

Monopole Wire Antenna (cont.)

10

Introduction to Antennas (cont.)

Yagi Antenna

This is a variation of the dipole, using multiples wires (with one “reflector” and one or more “directors”.

Low bandwidth Moderate to high directivity Commonly used as a UHF TV antenna

Prof. Yagi

11

Introduction to Antennas (cont.)

Yagi Antenna (cont.)

UHF Yagi VHF Log-periodic

UHF Yagi

UHF Yagi

12

Introduction to Antennas (cont.)

Log-Periodic Antenna

This consists of multiple dipole antennas of varying lengths, connected together.

High bandwidth Moderate directivity Commonly used as a VHF TV antenna

13

Introduction to Antennas (cont.)

Beam

Log Periodic Antenna (cont.)

14

Introduction to Antennas (cont.)

Typical Outdoor TV Antenna

VHF Log-periodic

UHF Yagi

15

Introduction to Antennas (cont.)

Horn Antenna

It acts like a “loudspeaker” for electromagnetic waves.

High bandwidth Moderate directivity Commonly used at microwave frequencies and above Often used as a feed for a reflector antenna

16

Introduction to Antennas (cont.)

Horn Antenna (cont.)

Arno A. Penzias and Robert W. Wilson used a large horn antenna to detect microwave signals from the “big bang”

(Nobel Prize, 1978).

17

Introduction to Antennas (cont.)

Horn Antenna (cont.)

This is a variety called the “hoghorn” antenna (a combination of horn+reflector).

18

Introduction to Antennas (cont.)

Microstrip (Patch) Antenna

It consists of a printed “patch” of metal that is on top of a grounded dielectric substrate.

Low bandwidth Low directivity (unless used in an array) Low-profile (h can be made very small, at the expense of bandwidth) Can be made by etching Easily fed by microstrip line or coaxial cable Can be made conformable (mounted on a curved surface) Commonly used at microwave frequencies and above

01/ 22d

r

L λλε

≈ =

19

Introduction to Antennas (cont.)

Current

rεx

y

hL

W

Microstrip (Patch) Antenna (cont.)

20

Introduction to Antennas (cont.)

Dielectric Resonator Antenna (DRA)

It consists of a dielectric material (such as ceramic) on top of a grounded dielectric substrate.

Moderate to large bandwidth Low directivity (unless used in an array) Commonly used at microwave frequencies and above

The dielectric resonator antenna was invented by our

very own Prof. Long! rε

Cylindrical DRA

21

Introduction to Antennas (cont.)

Dielectric Resonator Antenna (cont.)

GPS antenna

22

Introduction to Antennas (cont.)

Leaky-Wave Antenna

23

2

0 00

1k kk aπβ

= − <

The wave is a “fast wave.”

pv c>

0pv c

kω ωβ

= > =Note:

This allows the wave to radiate from the slot.

Introduction to Antennas (cont.)

Rectangular waveguide

Slot

Air

x

y

24

0 0coszk k θ β= =

0 0cos / kθ β=

A narrow beam is created at angle θ0.

Leaky-Wave Antenna (cont.)

Introduction to Antennas (cont.)

0kβ <

0θ

z

y k

b

Antenna Radiation

We consider here the radiation from an arbitrary antenna.

The far-field radiation acts like a plane wave going in the radial direction. 25

r →∞"far field"

+ -

( ), ,r r θ φ

S

x

y

z

r

How far do we have to go to be in the far field?

26

2

0

2Drλ

>

Antenna Radiation (cont.)

+ -

( ), ,r r θ φSphere of minimum diameter D that encloses the antenna.

r

A derivation is given in the Antenna Engineering book: C. A. Balanis, Antenna Engineering, 4th Ed., 2016, Wiley.

Antenna Radiation (cont.)

The far-field has the following form: ˆ ˆ

ˆ ˆE E E

H H Hθ φ

θ φ

θ φ

θ φ

= +

= +

0EH

θ

φ

η=

0

EH

φ

θ

η= −

27

TMz

TEz

Depending on the type of antenna, either or both polarizations may be radiated (e.g., a vertical wire antenna radiates only TMz polarization.

x

y

z

E

HS

x

y

z

EH

S

The far-field Poynting vector is now calculated:

( ) ( )( )

*

* *

* *

0 0

22

0 0

121 ˆ ˆ ˆ ˆ21 ˆ2

1 ˆ2

1 ˆ2

S E H

E E H H

r E H E H

EEr E E

EEr

θ φ θ φ

θ φ φ θ

φθθ φ

φθ

θ φ θ φ

η η

η η

= ×

= + × +

= −

= + = +

0EH

θ

φ

η=

0

EH

φ

θ

η= −

28

Antenna Radiation (cont.)

Hence we have

( )22

0

1ˆ2

S r E Eθ φ η

= +

2

0

ˆ2E

S rη

=

or

Note: In the far field, the Poynting vector is pure real (no reactive power flow).

29

Antenna Radiation (cont.)

Radiation Pattern

The far field always has the following form:

( ) ( )0

, , ,jk r

FeE r Er

θ φ θ φ−

=

( ),FE θ φ ≡ Normalized ar - field electric fieldf

In dB:

( )( )( )10

,dB , 20log

,

F

Fm m

EE

θ φθ φ

θ φ

=

( ),m mθ φ = direction of maximum radiation

30

Radiation Pattern (cont.)

The far-field pattern is usually shown vs. the angle θ (for a fixed angle φ) in polar coordinates.

( )( )( )10

,dB , 20log

,

F

Fm m

EE

θ φθ φ

θ φ

=

31

0 dB

θ 30° 30°

60°

120°

150° 150°

120°

60°

mθ

0φ =

-10 dB

-20 dB

-30 dB

z

A “pattern cut”

Radiated Power

The Poynting vector in the far field is

( )( ) 2

20

, 1ˆ, ,2

FES r r

rθ φ

θ φη

=

The total power radiated is then given by

( )( ) 2

2 22

00 0 0 0

,ˆ sin sin

2

F

rad

EP S r r d d d d

π π π π θ φθ θ φ θ θ φ

η

= ⋅ =

∫ ∫ ∫ ∫

Hence we have

( )2

2

0 0 0

1 , sin2

FradP E d d

π π

θ φ θ θ φη

= ∫ ∫32

Directivity

In dB,

( ) ( )( )2

,,

/ 4r

rad

SD r

P rθ φ

θ φπ

≡ → ∞

The directivity in a particular direction is the ratio of the power density radiated in that direction to the power density that would be radiated in that direction if the antenna were an isotropic radiator (i.e., one that radiates equally in all directions).

( ) ( )dB 10, 10log ,D Dθ φ θ φ=

The directivity of the antenna in the directions (θ, φ) is defined as

Note: The directivity is sometimes referred to as the

“directivity with respect to an isotropic radiator”. 33

Directivity (cont.) The directivity is now expressed in terms of the far field pattern.

( ) ( )( )2

,,

/ 4r

rad

SD r

P rθ φ

θ φπ

≡ → ∞

( )

( )

( )

2

20

22

2

0 0 0

, 12

, 41 , sin

2

F

F

Er

D r rE d d

π π

θ φη

θ φ πθ φ θ θ φ

η

= → ∞

∫ ∫

Therefore,

( )( )

( )

2

22

0 0

4 ,,

, sin

F

F

ED

E d dπ π

π θ φθ φ

θ φ θ θ φ=

∫ ∫

Hence we have

34

Resonant half-wavelength dipole:

35

( )/ 2,maxD D D π φ= =

/ 2mθ π=

-9 -3 -6

0 dB

θ30° 30°

60°

120°

150° 150°

120°

60°

z

Short dipole

Directivity (cont.)

1.643D =

Feed 2l h=

x

y

z

h

h−

Short dipole: 1.5D =

( ) ˆsinFE θ θ θ=

Short dipole

Beamwidth

The beamwidth measures how narrow the beam is. (The narrower the beamwidth, the higher the directivity).

HPBW = half-power beamwidth

36

Sidelobes

The sidelobe level measures how strong the sidelobes are.

37

In this example the sidelobe level is about -13 dB

Sidelobes

Sidelobe level

Main beam

13dB−

Gain and Efficiency The radiation efficiency of an antenna is defined as

radr

in

PeP

≡

The gain of an antenna in the directions (θ, φ) is defined as

( ) ( ), ,rG e Dθ φ θ φ≡

( ) ( )dB 10, 10log ,G Gθ φ θ φ=

In dB, we have

38

rad

in

PP

==

power radiated by antenna

power input to antenna

Gain and Efficiency (cont.) The gain tells us how strong the radiated power density is in a

certain direction, for a given amount of input power.

39

( ) ( ) ( )2, / 4 ,r r inS e P r Dθ φ π θ φ =

( ) ( ) ( )2, / 4 ,r inS P r Gθ φ π θ φ =

( ) ( )( )2

,,

/ 4r

rad

SD r

P rθ φ

θ φπ

≡ → ∞

( ) ( ) ( )2, / 4 ,r radS P r Dθ φ π θ φ =

Therefore, in the far field:

Recall that

Receive Antenna

The Thévenin equivalent circuit of a wire antenna being used as a receive antenna is shown below.

Th inZ Z=

40

+

- ThVincE

+ - ThV

ThZ

2

2

0

W/m2

incinc

d

EP

η =

2W/mincdP = incident power density

[ ] ( )73inZ = Ω resonant half - wavelength dipole

41

The effective area determines the Thévenin voltage.

Assume an optimum conjugate-matched load:

+ -

*L ThZ Z=

incL eff dP A P=

Receive Antenna (cont.)

ThZ

ThV

LP = power absorbed by load

effA = effective area of antenna

2W/mincdP = incident power density

42

We have the following general formula*:

( ) ( )20, ,

4effA G λθ φ θ φπ

=

*A poof is given in the Antenna Engineering book: C. A. Balanis, Antenna Engineering, 4th Ed., 2016, Wiley.

Receive Antenna (cont.)

( ),G θ φ = gain of antenna in the direction of the incident signal

This assumes that the incoming signal is polarized in the optimum direction.

43

( ) ( )

( )

2o o 0

20

2

90 , 90 ,4

1.6434

21.643

4

effA G

l

λφ φπ

λπ

π

=

=

=

Effective area of a lossless resonant half-wave dipole antenna:

( )o 290 , 0.5230effA lφ =

Hence

Assuming the incident electric field is aligned along the wire and θ = 90o:

( )0 / 2l λ=

Receive Antenna (cont.)

+ - ThV

l

incE

44

Example

Find the receive power in wireless system shown below, assuming that the receiver is connected to an optimum conjugate-matched load.

[ ][ ]

[ ]

1 GHz

10 W

1 kmin

f

P

r

=

=

=

[ ]( )0 29.979 cmλ =

Receive Antenna (cont.)

Assume lossless antennas (G = D =1.643)

Receive Transmit

o90θ =

* 73 [ ]L ThZ Z= = Ω

x

z

r

2W/mincdP

rad inP P=

[ ]WinP

o90θ =

45

( ) ( )2

o 0290 , 1.643 , 1.643

4 4inc rad

eff dPA P

rλφπ π

= =

incL eff dP A P=

( )20

21.643 1.6434 4

radL

PPr

λπ π

=

81.54 10 [W]LP −= ×

Hence

The result is

Receive Antenna (cont.)

Recall: Gain of transmit antenna Gain of receive antenna

46

Effective area of dish antenna

( ) ( ) 20

4, ,effG A πθ φ θ φλ

=

eff phy apA A e=

In the maximum gain direction:

The aperture efficiency is usually less than 1 (less than 100%).

Receive Antenna (cont.)

phy

ap

Ae

=

=

physical area of dish

aperture efficiency