Reciprocity, Babinet principle, slot, microstrip and wideband antennas

P. Hazdra, M. Mazanek,….hazdrap@fel.cvut.czDepartment of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org

v. 14.3.2016

Outline

• Effective height and aperture of an antenna• Reciprocity and reaction theorem• The Babinet principle• The slot antenna• The slot waveguide antenna• Microstrip antennas• Frequency‐independent antennas• Helix antennas

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Transmitting and receiving antennas

3

Maximum power delivered to antenna occurs for conjugate matching  Z∗

Induced voltage

Maximum power delivered to load occurs for conjugate matching  Z∗

Receiving antenna – effective height

4

⋅

effective length

1d

/

/

0.64 0.5

0.64 0.5

Antenna as an aperture - Effective area

5

• Describes power capturing characteristics of the antenna when a wave impinges on it.• Relation between power at load and incoming power density

12 . . forconjugatematchingandlosslessantenna 8

1

Available power at the terminals of a receiving antenna 

Power density of incident plane wave  / (Poynting vector)

example: Maximum effective area of a elementary( ≪ ), lossless ( 0) dipole

81

202

38 0.119

⋅

Effective area (aperture)

6

4 4

4Maximum effective area of antenna with maximum directivity 

Directivity of any antenna is proportional to its aperture

Power at the receiver 4

38 Constant ⋅ D 4 ⋅

32

Elementary dipole

, 4 ,

Maximum effective aperture of antenna

7

The physical significance of these apertures is that power from the incident plane wave is absorbed over an area of this size by the antenna and is delivered to the terminating resistance

4 4 10 . / 0.131

!vs physical aperture!

f 440MHz14 3 3 20

4 4 10 . / 3.7

Small dipole illuminated by plane wave

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/10Physical vs. effective area

Small dipole illuminated by plane wave

9

/10

Physical vs. effective area

Reciprocity theorem for antennas

10

• Voltage  is applied to the terminals of an antenna A, current  at the terminals of another antenna B is measured

• Voltage  is applied to the terminals of an antenna B, current  at the terminals of another antenna A is measured

linear, passive, isotropic medium

If  then More generally

Reciprocity and reaction theorem for antennas

11

⋅ ⋅ ⋅

Two set of sources  ,  that generate fields  , 

0 for

⋅ ⋅ 0 0

Reaction (coupling) between a source and a field  ,

• “in any network composed of linear, bilateral, lumped elements, if one places a constant current (voltage) generator between two nodes (in any branch) and places a voltage (current) meter between any other two nodes (in any other branch), makes observation of the meter reading, then interchanges the locations of the source and the meter, the meter reading will be unchanged”.

0 for source‐free region

, ,

Arbitrary RLC 

network, In terms of reactions:

Physical and circuit antenna parameters

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The Babinet principle

13

Complementary screen

The impedance of complementary antennas

Dipole antenna (“metal”)

Slot antenna (“air”)

435476

The slot antenna

14

. .

/2 @ 3 GHz

/50

35476

2/ /2

The slot antenna

15

Radiation pattern of slot and dipole

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The slot antenna

17

3547673 486Ω

The slot antenna

18

35476

The slot antenna

19

The slot antenna

20

The bat-wing antenna

21

The slot antenna array – radiating cavity (standing-wave array)

22

The slot antenna array – radiating cavity (standing-wave array) 8 x slot

23

• Common phase• Arbitrary amplitude distribution

The slot antenna array – radiating cavity

24

Surface current

/2Few λ

The slot antenna array

25

FTR

The slot antenna array – radiating cavity (standing-wave array) 4 x slot

26

The slot antenna array

27

Microstrip antennas

28

• Planar resonator designed to radiate, 70s• Printed on substrate  cheap, reproducible, mass producement• Moderate gain (single element 7‐9 dBi, arrays..)• Can easily produce CP• Integration with microwave circuit (active antenna)• Usually low bandwidth• Losses in substrate should be considered

Rectangular patch antenna

29

Surface current density J .. Jx

2Δ

Rectangular patch antenna

30

Ez

Hy

Model of radiation: two slots of length W, separated by distance L

2 2 3 3

Microstrip antennas - feeding

31

sin

H

Lp x Wp

Lv

Lh

Proximity feeding with L‐probe

Microstrip line feed

Probe feed (coaxial connector)

Microstrip antennas – circular polarization

32

Microstrip antennas – circular polarization

33

Re (Z)

Im (Z)

Microstrip antennas – circular polarization

34

LHCP RHCP

ARS

Compact Microstrip antennas

35

Frequency independent antennas

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4

• Constant pattern, impedance, polarization and phase center• Antenna specified by angles rather than by linear dimensions• Self‐scaling behavior• Babinet principle self‐complementary antenna (translation, rotation)

4 .

Self-complementary spiral antenna

37Piksa, P., Mazanekm, M.: A Self‐Complementary 1.2 to 40 GHz Spiral Antenna with Impedance Matching, Radioengineering, 2006

1.2 – 40 GHz

38

Log-Periodic Antennas• Entire shape cannot be solely specified by angles  not truly frequency independent• A log‐periodic antenna is defined as a structure whose electrical properties vary 

periodically with the logarithm of frequency.• Current distribution is the same for two frequencies separated by ratio ln 1/

⋯,  is geometric ratio 

100‐1100MHz, Gain ~ 6dBi• Moving phase center

Helix antennas

39

x

z

Diameter D

Turn spacing S

Circumference CGround Plane > /2

Number of turns N

Normal mode of radiation (broad side) x Axial mode of radiation (end fire)

Pitch Angle α

tan

John D. Kraus, 1947

Helix antennas

40

x

z

Diameter D

Entire

helix

length Ly

Normal mode of radiation (broadside) appears if:

D <<  ,   entire L << radiation like from small 

dipole

Standing‐wave current

Linear polarization

Helix antennas

41

x

z

y

C ~  (3/4 < C/ < 4/3)• Travelling current

• Circular polarization

• Narrow mainbeam with minor sidelobes (Gain 10‐15dBi)

• HPBW ~ 1/N

• Wide bandwidth (30%)

Circumference 

Axial Mode of Radiation (endfire) occurs if:

15C

1402 12

≅ /4

≅ 12 14∘

2

Helix antennas

42

1Standing wave current

Normal mode (broadside)

1Travelling wave currentAxial mode (endfire)

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Helix antennas 0.42

D 0.1470.46

0.93D 0.33

1.03

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Helix antennas 0.42

D 0.1470.46

0.93D 0.33

1.03

Electric field above the helix

Helix antennas

45

The effective area of antenna - derivation

46

Flux density in the „matched“ polarization

Random wave (noise from blackbody radiation), the two orthogonal polarization components (V/H or RHC/LHC) will vary 

rapidly in intestity (unpolarized radiation), but have equal powers when averaged over long times

P12 , Ω A

122

4

Blackbody cavity

Noise power (per Hz) generated by a resistor at temp. Tk .. Boltzmann constant

Blackbody radiation flux (Rayleigh‐Jeans) approximation

A 4

Microstrip antennas – fractal geometry

47

polarization

0.21λc x 0.21λc x 0.15λc