Spring 2006 Dr. Stuart Long - University of Houston

Chapter 11Chapter 11FrequencyFrequency

Independent Independent AntennasAntennas

ECE 5318/6352ECE 5318/6352Antenna EngineeringAntenna Engineering

Spring 2006Spring 2006Dr. Stuart LongDr. Stuart Long

2

THE BEGININGTHE BEGINING

Before 1950’s no antennas with bandwidth > 2 : 1

V.H. RumseyV.H. Rumsey – University of Illinois 1955-1958

Antenna performance is typically a function of “ length / wavelength “ λ

l

Important characteristic Important characteristic

3

SCALING PRINCIPLESCALING PRINCIPLE

Scale size by ratio of frequency and get similar behavior

e.g. decrease antenna dimensions by factor of 2 and increase frequency by factor of 2

⇒ same performance (both are the same size in wavelengths)

depends on some ““characteristic lengthcharacteristic length””

4

SCALING PRINCIPLESCALING PRINCIPLE(CONT)(CONT)

Basic structural feature for frequency independent operation is the absenceabsence of any ““characteristic lengthcharacteristic length””

⇒ self -scaling

5

ANGLE PRINCIPLEANGLE PRINCIPLE

need a structure completely described by angles

““ANGLE PRINCIPLEANGLE PRINCIPLE””

α

6

TRUNCATION PRINCIPLETRUNCATION PRINCIPLE

but practical structures need to be finite in sizesomehow currents need to fall off rapidlyenough so that terminating the structure at some finite length does not alter its characteristics

““TRUNCATION PRINCIPLETRUNCATION PRINCIPLE””

7

TRUNCATION PRINCIPLETRUNCATION PRINCIPLE(CONT)(CONT)

infinite biconical infinite biconical infinite biinfinite bi--fin (bow tie)fin (bow tie)

Why ne

ed su

ch

broad

band

? e.g. TV. channelsJammers

ExampleExample

8

EQUIANGULAR SPIRAL EQUIANGULAR SPIRAL (log spiral) (log spiral)

Boundaries given by

aoe

φρ ρ=Except for a rotation in space it looks the same for all frequencies

9

EQUIANGULAR SPIRALEQUIANGULAR SPIRAL(CONT)(CONT)

Earlier work by H.G. BookerH.G. Booker on impedance relationship between a slot and its complementary dipole

41

22

2

2

⋅=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

=⎟⎠⎞

⎜⎝⎛=⋅

o

oo

o

ods

ZZZεμε

μ

10


if could somehow make an antenna and its complement the same, then the impedance would have to be constant, independent of frequency

[ ]Ω==⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛== 189

22

21

2' oo ZZZZ

called

““ SELFSELF--COMPLEMENTARY COMPLEMENTARY ””

11


DysonDyson tried to build a self-complementary spiral;

found ⇒ a constant and radiation pattern over several octaves; also had circular polarization

0→I

⇒ current “ I ” fell off faster than over a

frequency independent band before truncationr1

inZ

12


λ=

found ⇒ lost frequency independent behavior; frequency was lowered to pointwhere diameter

(upper limit on frequency depends only on the accuracy of the feed region)

But needed linear polarization (LP)LP) as well as circular polarization (CP)CP)

13


Fig. 11-2 Spiral plate and slot antennas

14


Fig. 11.4 Conical spiral metal strip antenna

15

LOG PERIODICLOG PERIODIC

DuHamelDuHamel – University of Illinois ⇒ altered the bi-fin antenna

linear polarization, satisfied ANGLE PRIN., but not TRUNCATION PRIN.

needed to cause currents to fall off more rapidly

⇒ introduced discontinuities – “teeth” in fins –to increase radiation and increase decay of “I “

16

LOG PERIODICLOG PERIODIC(CONT)(CONT)

To satisfy ANGLE PRINCIPLE concept of RumseyRumsey, teeth were made along circular arcs so their length was determined by an angle

BUT HOW TO DETERMINE SPACING ?

17


Looking at equiangular spiral on a radial line from center the spacing of the arms are in a constant ratio

τρρρρρρ ππφφ ==⇒== −+ aa

oa

o eee 2

2

1)2(21

11

τ=−

n

n

RR 1

So radii of successive teeth were chosen suchthat

18


Resulting structure is not exactly frequency independent, but it should have identical characteristics at a discrete number of frequencies

ExampleExample

τof

If the p-th tooth is at then the

(p-1)th tooth is at

of10λ

10λ

19


as long as the structure is accurate at the feedand there are negligible currents at the

truncation point.

…… ,,,,,,, 31

211

13

12

11 ττττττ fffatandffff

⇒ so identical performance at

20


Fig. 11-6 Planar and wire logarithmically periodic antennas

21


Since

performance is periodic function of the log of the frequency

( ) ( ) ⎟⎠⎞

⎜⎝⎛+=⇒= ++ τ

τ 1lnlnln 11 nnnn ffff

LOG-PERIODIC ANTENNAS

Experimentally, they found that the variation in pattern between the periods were relatively minor for designs

where τ was not too far from 1.0

22


Still this periodic antenna was bi-directional and had a broad pattern

BI-FIN had fieldspolarized in dir.Some models of log-periodic were found to have linearpolarization in the

dir.(along dir. of teethinstead of perpendicularto them)

xxE

zE

BI-FIN LOG PERIODIC

z z

xx

z

23


IsbellIsbell – ignored restrictions on planar structures by Babinet.folded planar L-P structure into a wedgegot unidirectional pattern off the tipsame bandwidth

-dir polarization

could be made straight (trapizodal)most currents were in teeth whose length was near

4λ

x

[see model]

Also found they could only just outline the peripheryof the sheet structure with a wire and it would still work

24


Fig. 11-6 Planar and wire trapezoidal toothed log - periodic antennas

25

LOGLOG--PERIODICPERIODIC(CONT)(CONT)

Fig. 11.8 Linearly polarizedflush mounted cavity-backedlog-periodic slot antenna

26


Isbell Isbell -

α

Wanted to develop a broad band array of more conventional elements

Array of dipoles - lengths determine by angle

- spacing chosen in log-periodic style

27

ZoutZCin

LLin LLout

ZCinSource

LOGLOG--PERIODIC DIPOLE ARRAY PERIODIC DIPOLE ARRAY --LPDALPDA

28

LOGLOG--PERIODIC DIPOLE ARRAY PERIODIC DIPOLE ARRAY -- LPDALPDA

n

n

n

n

RR

ll 111 ++ ==

τ 1

1

2 +

+ −=

n

nn

lRRσ

29

LPDALPDA(CONT)(CONT)

BUT HOW TO EXCITE?

Using successful trapezoidal wedgecenter portion was like transmission line feeding teeth as radiatorsteeth connected in shuntwhen wedge folded back soparallel pairs of equal length teeth almost lined upsuccessive teeth came out in opposite direction.

Equivalent to criss-crossing wire between elements introducinga 180° phase shift between successive elements

Feeding structure ⇒

Source

30


criss cross connection

alternate coaxial connection – alternate pairs from opposite sides

31


IsbellIsbell’’ss investigation

showed ⇒ that for a proper choice of α and τtypical range )95.7.45210( ≤≤≤≤ τα and

2λ

the structure was indeed broadband, linearly polarized and unidirectional

found ⇒ currents mostly on elementsnear in total length

frequency band bounded on high sideby size of smallest element, and on lowend at frequency where largest dipole is approximately in length

⇒

2λ

Source

32


⎟⎟⎠

⎞⎜⎜⎝

⎛=<= +−

n

n

n

n

RRor

RR 11 11

ττdefine

33


n

n

n

n

n

n

n

n

n

n

ll

RR

Rl

Rl

Rl 11

1

1

1

1 −−

−

−

+

+ ==⇒== τ

1

1

/ 2 / 2tan n n

n n

l lR R

α +

+

= = =…

/2nl

nR

α

( ) nnnnnnn RRRRRRR τττ −=−=−⇒= −− 111

1

11

22 +

+− −=

−=

n

nn

n

nn

lRR

lRRσspacing factor

but

34


( )α

τα tan2

1tan2 1

nnn

nn

lRRlR −=−⇒= −

⎥⎦⎤

⎢⎣⎡ −

=στα

41tanor 1-

from geometry ⇒

( )ατ

ατσ

tan41

2tan21

21 −

=⋅

−=

−= −

n

n

n

nn

ll

lRR

2/nl

nR

α

35


Fig. 11.13 Computed contours of constant directivity versus σ and τ for log-periodic dipole arrays

Note: horizontal axis is

decreasing

36


BANDWIDTHS

( )( )τ1ln

ln1# sBNelem +==

maxλ

2λ

sB

( ) ατ cot17.71.1 2−+=arB

ars BBB ⋅=

αλ cot114max

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

sBLlength

design BW

active region correction

desired BW

so longest element is

at low freq. end of band

Source

37


If longest element = ; the next is , , ,……maxl maxlτ max2 lτ max

3 lτ

2minλ

sBuntil shortest element is shorter than (high end of band )

38

1 1tan4

ar s

calculate

B and B

τασ

− −⎡ ⎤= ⎢ ⎥⎣ ⎦

ProcedureProcedure

LandNfind define lengths and

positions of elements

( )dBDoGiven

.11.13

find optimumand

from Figσ τ

LPDA DESIGNLPDA DESIGN(CONT)(CONT)

39

ExampleExample

917.0;172.0

1311.

==

−

τσoptimumFigFrom

MHzBW 6020−⇒

dBDo 9=

88.64

1tan 1 =⎥⎦⎤

⎢⎣⎡ −

= −

στα

( )21.1 7.7 1 cot 1.54

60 1.54 4.5620

ar

s

B

B

τ α= + − =

⎛ ⎞= ⋅ =⎜ ⎟⎝ ⎠


40

ExampleExample

2 1 2

1

1 2

1 2

1 1 2

To center around 4.56 and 1 120 60

more generally want 1 1

centered so same % above and below andwhere and are ends of bandand and are ends of band

2 15.9 and 72.41

s

L H

L H

s

L H

s

H L

f f fB Bf

f ff f

f ff f B

f f B

f f MHz f MBf f

⇒ = − = −

− = −

⇒ = ⇒ = =⎛ ⎞

+⎜ ⎟⎝ ⎠

Hz


41

ExampleExample

[ ]

[ ]

1

2

2

1

1 max1

maxmax

15.9check: .795 20.5% below2072.4 1.205 20.5% above60

72.4and 4.5615.9

Longest element at low frequency of2

at 15.9 18.9

9.432

L

H

s

ffffff

B

cf MHz mf

l m

λ

λ

λ

= = ⇒

= = ⇒

= =

=

= ⇒ = =

= =


42

ExampleExample

max

1 11 cot 1.62 30.5 [ ]4

ln ln 4.561 1 18.5 18 19 elements1 1ln ln

.917

s

s

L L mB

BN or

αλ

τ

⎛ ⎞= − = ⇒ =⎜ ⎟

⎝ ⎠

= + = + = ⇒⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠


43

ExampleExample

LTotal

max max

max max

2 2max max

17max

18 18max max

min

9.43 39.18.65 35.8

7.93 32.6

2.16

1.98 8.2

2.072

l Rl R

l R

l

l R

τ τ

τ τ

τ

τ τλ

= == =

= =

=

= =

⎡ ⎤ =⎢ ⎥⎣ ⎦

][9.302.81.39Total mL =−=


Spring 2006 Dr. Stuart Long - University of Houston

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