Linear (wire) antennas 1

Linear (wire) antennas 1P. Hazdra, M. Mazanek,…[email protected] of Electromagnetic FieldCzech Technical University in Prague, FEEwww.elmag.org

v. 7.3.2016

Linear (wire) antennas

• Current distribution on a wire antenna, natural resonances

• Radiation pattern, input impedance• The dipole• The folded dipole• Symmetrization, baluns• Monopole antennas

Katedra elektromagnetického pole 2

Linear (wire) antennas• Approximate solutions based on assumption that the

current distribution is only 1D, i.e. we go from surface density to ′ (1D integrals).

• Travelling wave / resonant.

3

Linear (wire) antennas - currentAt first we have to find the current on antenna• Numerical solutions based on variational principles (Method of Moments)• Approximate solutions in analytical form


Transmitting thin‐wire antenna

/Δ

⋅

Perfectly Electrically Conducting surfaces: Tangential E field on PEC = 0

known feeding

Unknown current function hidden inside the vector potential 4 ′

Assuming only z‐directed current (hence only component), this leads to integro‐differential equation for thin‐wire antenna

, /

/Interchanging integration with differentiation

′R

Current on linear antenna (dipole)


Center feeding

.

Whole dipole length

.

.

I 12

I sin 2

Triangular distribution

Sine distribution

small dipole

half-wavelength dipole

Linear (wire) antennas - current

6

sin12

I sin 2


7

We have very good approximation for current flowing along linear dipole in the form of

It follows from understanding the dipole as two‐wire open‐circuited transmission line – in other words the radiation is neglected in this model.

valid for thin dipoles only

I sin 2


8

+

+

+

+

++ + ++ + +

-

- - -

- -

+

out‐of phase currents sidelobes

Complete fields from linear antenna

9

, , 4 ′ ′/

/

Near field requires complete evaluations

Electric field (magnitude) of / dipole

Region separation (Rayleigh, Fresnel, Fraunhofer)

is expanded into series

• Linear term only: Fraunhofer (far field)

• Quadratic: Fresnel 0.62 /,

Radiation from linear dipole antenna

10

, sin

, , 4 ′ ′/

/

Far‐field approximation of the radiation integral

Δ cos ⋅Δ

R Δ ≅

, , 4 ′ ′/

/

The radiated field is proportional to Fourier transform of the source current!!

, , 4 sin ′ ′/

/

space factorelementary dipole! (element factor)

⋅

Radiation from linear dipole antenna

11

, , 30 sin sin 2 ′ 60cos 2 cos cos 2

sin

/

/

, , , ,

Radiation pattern – changes withdipole length

Sinusoidal current distribution assumed

Radiation patterns

12

/2

2.15dBi

1.5

“maximal dipole”

1.25

3.82dBi 5.16dBi 3.48dBi

current:

“One of the goals of antenna design is to place lobes at the desired angles.”

Directivity of a dipole

13

The dipole

14

• Its radiation pattern is omnidirectional in the H‐plane, which is required by many applications (including mobile communications).

• Its directivity (2.15 dBi) is reasonable – larger than short dipoles• The input impedance is not sensitive to the radius and is about 73 Ω, which is

well matched with a standard transmission line of characteristic impedance 75 or 50 Ω (with VSWR< 2). This is probably the most important and unique reason.

• dBd – decibels above /2 dipole, 0 dBd = 2.15 dBi

The dipole

15

, , 60cos 2 cos

sin

15 sin 15 2

1 cos≅ 2.435

22 ⋅ 15 ⋅ 2,435 ≅ 73Ω

Radiation resistance obtained from integration of the far‐field power density

Note: To obtain input reactance X too, we must integrate complex power‐flow in near fieldof an antenna (at antenna surface!). Then it could be shown that:

30 ∗∗

′sin

/

/

′/

/

30 ∗∗

′cos

/

/

′/

/

.

/2 dipole input impedance of infinitely thin dipole!

The dipole is not resonant ( ) and should be shortened a little, depending on radius

I sin I cos kz

Note – radiation resistance

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I sin 2

Radiation resistance is referred to the maximum current. For some lengths (0.5 ) this maximum does not occur at the input terminals (which we assume to be at the center) of the antenna and where we are measuring the .

2 2

0 I sin 2

sin 2

Peak value

sin 2

Thin center-fed dipole input impedance

17

3GHz, 0.1m, l 0.05m, a 0.2mm, Ω 2 ln 12.4

/2, 73 42.5Ω

≅ 0.48 , ≅ 72 0Ω

≅ %

% shortening to produce resonance req.

32

Resonance0

Antiresonance0


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3GHz, 0.2m, l 0.1m, a 0.2mm, Ω 2 ln 12.4

/


19

/ % shortening required

Resonant lengthΩ 2 ln

Dipole Thickness Class

10000 2 0.49λ 18.4 Very thin

1000 5 0.475λ 13.8 Thin

20 9 0.455λ 6 Thick

Natural resonances of a dipole

Thin center-fed dipole

20

sin 2

sin 2

Frequency bandwidth

21

Frequency bandwidth of antenna is connected to its input impedance function of frequency

Relative frequency bandwidth:

≅1

2

≅ 2 ≅ 2.34 1.29 ln

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13

4

5

6

7

8

9

10

11

12

13

100*a/

Q

QXselfQX (FEKO)

/2 dipole

The folded dipole


The folded dipole

23

For ≪ , the current distributions are identical

The two currents of closely spaced arms are equal to the one current of the ordinary dipole

2

Also the input power of the two dipoles are identical

12

12

4 ≅ 4 ⋅ 73 ≅ 300Ω

May be generalized for N arms

For /2 dipoles

≅

The folded dipole

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100 ≅ /2s 3

0.46

Symmetrization - balun

25

Balun properly connects a balanced transmission line to an unbalanced transm. line.

Equal and opposite currents – balanced mode. Closely spaced equal and opposite currents don’t radiate.


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“Balun transforms the balanced input impedance of the dipole to the unbalanced impedance of the coaxial line such that there is no net current on the outer conductor of the coax.”

Sleeve (bazooka) balun

/4 parallel line – very large impedance:• Suppression of the currents on the outer shield• No interference with the antenna input impedance


27

4 to 1 balun

75Ω300Ω

Monopole antennas – vertical current above PEC ground


• Method of images

Monopole antenna – infinite ground

29

12 36.5 21.25Ω

For infinite ground plane

This “ /4 “ antenna can be tuned by shortening the radiator.Using arms instead of real ground, could be made close to 50Ω and thus matched to coaxial cable.

It radiates only into the space above the ground plane (half the space of a dipole antenna), a monopole antenna will have a gain of twice (3 dBi over) the gain of a similar dipole antenna, and a radiation resistance half that of a dipole

Monopole antennas – low-gain base-station/mobile antennas

30

Discone antenna VSWR<3 for frequency 1 to 10.

Monopole above ground

31W. Weiner, Monopole Antennas, Marcel Dekker, 2003

Monopole above ground - resistance

32

.

W. Weiner, Monopole Antennas, Marcel Dekker, 2003

Monopole above ground - reactance

33

..

W. Weiner, Monopole Antennas, Marcel Dekker, 2003

Monopole top-loading, T-antenna


Monopole top-loading


Transmitting antennas


Vertical monopole


37

Horizontal dipole


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Horizontal dipole above ground plane

Transmitting antennas - Liblice

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• Highest construction in CR (355m)• Pin = 1.5 MW @ 639 kHz, 470


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41

Curtain antenna arrays – short wave

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Curtain antenna arrays


Literature

• C. A. Balanis, Antenna Theory and Design, Wiley, 2005• J. D. Kraus, Antennas, McGraw‐Hill, 1997• W. Weiner, Monopole Antennas, Marcel Dekker, 2003


Supplementary material

• Numerical solution of current on thin linear antennas

46


47

, /

/

4 1 2 3 /

/

Pocklington integral equation′

Thin‐wire approximation (reduced integral kernel)

voltagecurrent

Impedance operator EFIE

Method of Moments solution:

, R

≅

Basis (expansion) function: dirac pulses, rectangular/triangular/sin pulse,..

Unknown expansion coefficients

Result of the MoM is complex impedance matrix, which depends on frequency and topology only

Current on linear antenna (dipole)


Linear (wire) antennas 1

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