1

Chapter 15Chapter 15ReflectorReflectorAntennasAntennas

ECE 5318/6352ECE 5318/6352Antenna EngineeringAntenna Engineering

Dr. Stuart LongDr. Stuart Long

2

GEOMETRICAL CONFIGURATIONSGEOMETRICAL CONFIGURATIONS

large flat sheetlarge flat sheet

corner reflectorcorner reflector

small flat sheetsmall flat sheet

parabolic reflectorparabolic reflector

(wide freq. range) (narrow freq. range)

3

FLAT REFLECTORFLAT REFLECTOR

image drivenelement

d

Image Theory AnalysisImage Theory Analysis

Source polarization and spacing used to control radiating properties

4

FLAT REFLECTORFLAT REFLECTOR

Gain relative to a Gain relative to a λλ//22 dipole in free spacedipole in free space

losses decrease gain at small spacing

larger spacing – less gain– more bandwidth

.5λ λ

d/λ

G

imperfect conductors1

2

5

CORNER REFLECTORCORNER REFLECTOR

Electrostatic ImagingElectrostatic Imaging

nfor 180

=α ,

,

3#1 4# 2 3

imagesin phasein phase but negative

φ1

2

3

4

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛≈ φ

λπφ

λπ

φ sin2coscos2cos ddE

6

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

GainGain

region w/ gain < 0 dB

⇒ main lobe in another direction

7

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

if spacing gets too large, multilobe patterns in real plane

d = 0.5λ

d = 1.5λ

d = 1.0λ

G = 3.1

G = 3.8

G = 4.4

MultilobesMultilobes

8

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

MultilobesMultilobes appear whenappear when

1.2λ2.5λ30°

0.85λ1.2λ45°

0.65λ0.95λ60°

0.5λ0.7λ90°

0.2λ0.3λ180°

1st. max. at d=(multilobe)α

9

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

Design and GeometryDesign and Geometry

NOTEpoint A is 1.4 S from corner

the only waves reflectedfrom an infinite casebut not from the finite caseare those radiated intosector η

10

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

absence of reflectorbeyond point B does not have a large effect-slightly larger beamwidth-null not exactly at 45°(at a somewhat larger φ)

L ≈ 2 d is good practical size

Design and GeometryDesign and Geometry

11

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

NOTE

for smaller α gain goes up;but need to use larger dand point A is now at1.73 d from corner

⇒ larger reflector size neededonly small increase in gain

Design and GeometryDesign and Geometry

LA

B

1.73dη

φα=60°

d

12

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

Practical DesignPractical Design

L= 2d d = 0.35λ⇒ aperture of 1.0λ

2d

0.7

λ

0.35λ1.0 λ

13

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

Practical DesignPractical Design

L= 2d d = 0.5λ⇒ aperture of 1.4λ

2d

1.0

λ

0.5λ1.4 λ

14

CORNER REFLECTORCORNER REFLECTOR(CONT)(CONT)

WireWire--grid arrangementgrid arrangement

to reduce wind resistanceand weight a grid of wires can be used for the reflector

g

h2d

2d

g < 0.1λh > 0.6λ

(to prevent “spill-over”)

15

PARABOLIC REFLECTORPARABOLIC REFLECTOR

given a point sourcewant to produce a planewave front over an aperture

want path lengths from source to reflectorto aperture plane to be equal

aperture

16

PARABOLIC REFLECTORPARABOLIC REFLECTOR

eqn. of a parabola with focus at F

)cos1(2

θ+=⇒

LR

)cos1(2want θ+= RL

pathFOF

pathFPB

Design and Geometry Design and Geometry

P

R

B’

B

A’

A

S Q

R cosθ

θL O F

17

PARABOLIC REFLECTORPARABOLIC REFLECTOR

Design and GeometryDesign and Geometry

⇒ also means that distancefrom point P on the parabola to the focus at F is equal to the ┴ distanceto a fixed line directrix

P

R

B’

B

A’

A

S Q

R cosθ

θL O F

18

PARABOLIC REFLECTORPARABOLIC REFLECTOR

Design and Geometry Design and Geometry

- thus all waves from an isotropicsource at the focus, reflectedfrom a parabola arrive at lineAA’ with equal phase

- wave AA’ appears to have come from a plane wave at thedirectrix Q

QSPQQSPFPSPFQPQSPS

PQPF

=−+=+−=

=

P

R

B’

B

A’

A

S Q

R cosθ

θL O F

19

PARABOLOIDPARABOLOID(PARABOLA OF REVOLUTION)(PARABOLA OF REVOLUTION)

a portion A of the sourceradiation is interceptedby the paraboloid and reflectedas a plane wave of circularcross-section

Design and Geometry Design and Geometry

20

PARABOLOIDPARABOLOID(CONT)(CONT)

wavesreflected of region central reinforces source feed

from radiation direct so

odd with choose nnλ L4

=

feed source

Design and Geometry Design and Geometry

21

PARABOLOIDPARABOLOID(CONT)(CONT)

feed source

LD

LD

LD

∠

⇒

for small, outer edges of

paraboloid get smaller illumination

for more uniform, make illumination smaller by increasing and keeping

the same

large

Design and Geometry Design and Geometry

22

PARABOLOIDPARABOLOID(CONT)(CONT)

feed source

largevery is

telescopes optical for

DL

F D L

Design and Geometry Design and Geometry

23

PARABOLOIDPARABOLOID(CONT)(CONT)

feed source

Polarization depends on primary feedtypically – horn – linearly polarized

presence of primary source in path of reflected waves-cause mismatch-obstruction (blockage)

Can displace feed

Design and Geometry Design and Geometry

24

PARABOLOIDPARABOLOID(CONT)(CONT)

feed source

front-fed Cassegrain-fed

Feeds Feeds

25

CORNER REFLECTORCORNER REFLECTORVS.VS.

PARABOLAPARABOLAfeed

source

NOTE

wave from corner reflectortravels shorter distance by (OO’)

patternssamefor

patternsdifferentfor

⇒=⇒=

⇒=⇒=

12'35.

5.0'2

λλ

λλ

OOAF

OOAF

26

CORNER CORNER VS. VS. PARABOLAPARABOLA(CONT)(CONT) feed

source

if AF is small, the exact shape of the reflector is unimportant

practical advantage of corner is itssimplicity and ease of construction

27

YAGIYAGI--UDA ARRAYSUDA ARRAYS

llrld

sr

sd

directors

reflectordriven

element

28

YAGY UDA YAGY UDA (CONT)(CONT)

[ ]

[ ]

[ ]dBSLR

dBBtoF

dBG

10

3020

128

=

−=

−=

TypicalForward gain G

Input impedance Z

Front to back ratio F-B

Sidelobe ratio SLR

Characteristics

29

YAGY UDAYAGY UDA(CONT)(CONT)

impedance and gain affect and

gain not but affects

and affect does

much gain affect tdoesn'

dd

r

r

ls

Zl

F-BZs

s

Design

λ25.0=rs

λ45.04.0 →=dl

λ55.05.0 →=rl

)(2

lessslightlyl λ=

λ4.03.0 →=ds