ELECTROMAGNETICS AND APPLICATIONS

Lecture 20Transmitting Antennas

Luca Daniel

L20-2

• Review of Fundamental Electromagnetic Laws• Electromagnetic Waves in Media and Interfaces• Digital & Analog Communications• Wireless Communications

o Radiation Fundamentalso Transmitting Antennas, Gain

Radiated Power from an Antenna Antenna [Directivity] Gain Example: Dipole Directivity Gain Short Dipole Radiation Resistance Arrays of Antennas Wire Antennas

o Receiving Antennas; Wireless Communicat. Systemso Aperture antennas; Diffraction

• Acoustic waves and Acoustic antennas• e.g. speakers, musical instruments, voice

Outline

TodayToday

L20-3

I(,,r) = Transmitted Intensity [W/m2]

Radiated Power

For isotropic antenna:

Steradian: unit of solid angled, d: units of radians.Spheres: span 4 steradiansd (steradians)

2 2R 0 0

P I( , ,r)r sin d d

Isotropic:

I(,,r)area =r2(d)(sin d)

d steradians

r

x

z

main beam

backlobessidelobes

Antenna pattern:

I(r)

R2

PI( , ,r) constant

4 r

PR = Total power radiated [W]

For non-isotropic antenna:

L20-4

Antenna [Directivity] Gain G(,)

Intensity at receiver:

[Directivity] Gain over Isotropic, G(,):

Actual intensity radiated in (, ) direction

Intensity if PR were radiated isotropically

backlobessidelobes

G(,)

Isotropic gain

2R

I( , ,r)G( , )

P / 4 r

2R2

PI( , ,r) G( , ) [W/m ]

4 r

Intensity if the powerwere to be radiated“isotropically”

[Directivity] GainThink of it as a“shaping factor”

L20-5

Short Dipole Antennas – Directivity Gain

Currents on Short Dipole:

q qo oq effv v

dJ dv I (z)dz I d I2

Radiated Intensity [W/m2] (from last time):2

2oo effkI dI( , ,r) sin

2 4 r

0

I

+Io -

z z

d

deff

I(z)

Io

R

22o eff

o0 0

kI dP I( , ,r) (r sin d ) r d

3 2

Power Radiated [W]:

Gain of a short dipole:

22

R

I( , ,r) 3G( , ) sin2P / 4 r

z

y

x

L20-6

2o eff

oI d

3

Short Dipole Antennas - Radiation Resistance

Currents on Short Dipole:

q qo oq effv v

dJ dv I (z)dz I d I2

Radiated Intensity [W/m2] (from last time):2

2oo effkI dI( , ,r) sin

2 4 r

Radiation Resistance Rr:

R2

o r1P I R [W]2

0

I

+Io -

z z

d

deff

I(z)

Io

Io

+

-

Rr

Equivalent resistance

R

22o eff

o0 0

kI dP I( , ,r) (r sin d ) r d

3 2

Power Radiated [W]:

o eff2

r2 d

R = ohms3

L20-7

How to Increase Antenna Gain G() in some directions?

Focus the energy

Lenses

Mirrors

Phasing

L20-8

Antenna Arrays

Radiation from a Pair of Short Dipoles:

Example, D = /2:

Io

Io

+-

+-

z

I

y

x

I

y

x

D

x

y

3Null if , etc.2 2

Null

NullsinD

Null

2sin

2

S

φ

oNull 90

Superposition applies

Null2

sin oNull 30Example, D = :